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• Book IV: Of Operations Subsidiary to Induction
• Chapter I: Of Observation and Description
• Chapter II: Of Abstraction, Or the Formation of Conceptions
• Chapter III: Of Naming, As Subsidiary to Induction
• Chapter IV: Of the Requisites of a Philosophical Language, and the Principles of Definition
• Chapter V: On the Natural History of the Variations In the Meaning of Terms
• Chapter VI: The Principles of a Philosophical Language Further Considered
• Chapter VII: Of Classification, As Subsidiary to Induction
• Chapter VIII: Of Classification By Series
• Book V: On Fallacies
• Chapter I: Of Fallacies In General
• Chapter II: Classification of Fallacies
• Chapter III: Fallacies of Simple Inspection; Or a Priori Fallacies
• Chapter IV: Fallacies of a Observation
• Chapter V: Fallacies of a Generalization
• Chapter VI: Fallacies of a Ratiocination
• Chapter VII: Fallacies of Confusion
• Book VI: On the Logic of the Moral Sciences
• Chapter I: Introductory Remarks
• Chapter II: Of Liberty and Necessity
• Chapter III: That There Is, Or May Be, a Science of Human Nature
• Chapter IV: Of the Laws of Mind
• Chapter V: Of Ethology, Or the Science of the Formation of Character
• Chapter VI: General Considerations On the Social Science
• Chapter VII: Of the Chemical, Or Experimental, Method In the Social Science
• Chapter VIII: Of the Geometrical, Or Abstract Method
• Chapter IX: Of the Physical, Or Concrete Deductive Method
• Chapter X: Of the Inverse Deductive, Or Historical Method
• Chapter XI: Additional Elucidations of the Science of History
• Chapter XII: Of the Logic of Practice, Or Art; Including Morality and Policy

^aCHAPTER XII^a

Of the Logic of Practice, or Art; Including Morality and Policy

§ 1. [Morality not a Science, but an Art] In the preceding chapters we have endeavoured to characterize the present state of those among the branches of knowledge called Moral, which are sciences in the only proper sense of the term, that is, inquiries into the course of nature. It is customary, however, to include under the term moral knowledge, and even (though improperly) under that of moral science, an inquiry the results of which do not express themselves in the indicative, but in the imperative mood, or in periphrases equivalent to it; what is called the knowledge of^b duties; practical ethics, or morality.

Now, the imperative mood is the characteristic of art, as distinguished from science. Whatever speaks in rules, or precepts, not in assertions respecting matters of fact, is art: and ethics, or morality, is properly a portion of the art corresponding to the sciences of human nature and society^c .^*

The Method, therefore, of Ethics, can be no other than that of Art, or Practice, in general: and the portion yet uncompleted, of the task which we proposed to ourselves in the concluding Book, is to characterize the general Method of Art, as distinguished from Science.

§ 2. [Relation between rules of art and the theorems of the corresponding science] In all branches of practical business, there are cases in which ^aindividuals are bound to conform their practice to a pre-established rule, while there are others in which it is part of their task to find or construct the rule by which they are to govern their^a conduct. The first, for example, is the case of a judge, under a definite written code. The judge is not called upon to determine what course would be intrinsically the most advisable in the particular case in hand, but only within what rule of law it falls; what the ^blegislature^b has ^cordained^c to be done in the kind of case, and must therefore be presumed to have intended in the individual case. The method must here be wholly and exclusively one of ratiocination, or syllogism; and the process is obviously, what in our analysis of the syllogism we showed that all ratiocination is, namely the interpretation of a formula.

In order that ^dour^d illustration of the opposite case may be taken from the same class of subjects as the former, we will suppose, in contrast with the situation of the judge, the position of ^ethe^e legislator. As the judge has laws for his guidance, so the legislator has rules, and maxims of policy; but it would be a manifest error to suppose that the legislator is bound by these maxims in the same manner as the judge is bound by the laws, and that all he has to do is to argue down from them to the particular case, as the judge does from the laws. The legislator is bound to take into consideration the ^freasons^f or grounds of the maxim; the judge has nothing to do with those of the law, except so far as a consideration of them may throw light upon the intention of the law-maker, where his words have left it doubtful. To the judge, the rule, once positively ascertained, is final; but the legislator, or other practitioner, who goes by rules rather than by their reasons, like the old-fashioned German tacticians who were vanquished by Napoleon, or the physician who preferred that his patients should die by rule rather than recover contrary to it, is rightly judged to be a mere pedant, and the slave of his formulas.

Now, the reasons of a maxim of policy, or of any other rule of art, can be no other than the theorems of the corresponding science.

The relation in which rules of art stand to doctrines of science may be thus characterized. The art proposes to itself an end to be attained, defines the end, and hands it over to the science. The science receives it, considers it as a phenomenon or effect to be studied, and having investigated its causes and conditions, sends it back to art with a theorem of the combinations of circumstances by which it could be produced. Art then examines these combinations of circumstances, and according as any of them are or are not in human power, pronounces the end attainable or not. The only one of the premises, therefore, which Art supplies, is the original major premise, which asserts that the attainment of the given end is desirable. Science then lends to Art the proposition (obtained by a series of inductions or of deductions) that the performance of certain actions will attain the end. From these premises Art concludes that the performance of these actions is desirable, and finding it also practicable, converts the theorem into a rule or precept.

§ 3. [What is the proper function of rules of art?] It deserves particular notice, that the theorem or speculative truth is not ripe for being turned into a precept, until ^athe whole, and not a part merely, of the operation which belongs to science, has been^a performed. Suppose that we have completed the scientific process only up to a certain point; have discovered that a particular cause will produce the desired effect, but ^bhave^b not ascertained all the negative conditions which are necessary, that is, all the circumstances which, if present, would prevent its production. If, in this imperfect state of the scientific theory, we attempt to frame a rule of art, we perform that operation prematurely. Whenever any counteracting cause, overlooked by the theorem, takes place, the rule will be at fault: we shall employ the means and the end will not follow. No arguing from or about the rule itself will then help us through the difficulty: there is nothing for it but to turn back and finish the scientific process which should have preceded the formation of the rule. We must re-open the investigation, to inquire into the remainder of the conditions on which the effect depends; and only after we have ascertained the whole of these, are we prepared to transform the completed law of the effect into a precept, in which those circumstances or combinations of circumstances which the science exhibits as conditions, are prescribed as means.

It is true that, for the sake of convenience, rules must be formed from something less than this ideally perfect theory; in the first place, because the theory can seldom be made ideally perfect; and next, because, if all the counteracting contingencies, whether of frequent or of rare occurrence, were included, the rules would be too cumbrous to be apprehended and remembered by ordinary capacities, on the common occasions of life. The rules of art do not attempt to comprise more conditions than require to be attended to in ordinary cases; and are therefore always imperfect. In the manual arts, where the requisite conditions are not numerous, and where those which the rules do not specify are generally either plain to common observation or speedily learnt from practice, rules may ^coften^c be safely acted on by persons who know nothing more than the rule. But in the complicated affairs of life, and still more in those of states and societies, rules cannot be relied on, without constantly referring back to the scientific laws on which they are founded. To know what are the practical contingencies which require a modification of the rule, or which are altogether exceptions to it, is to know what combinations of circumstances would interfere with, or entirely counteract, the consequences of those laws: and this can only be learnt by a reference to the ^dtheoretic^d grounds of the rule.

By a wise practitioner, therefore, rules of conduct will only be considered as provisional. Being made for the most numerous cases, or for those of most ordinary occurrence, they point out the manner in which it will be least perilous to act, where time or means do not exist for analysing the actual circumstances of the case, or where^e we cannot trust our judgment in estimating them. But they do not at all supersede the propriety of going through (when circumstances permit) the scientific process requisite for framing a rule from the data of the particular case before us. At the same time, the common rule may very properly serve as an admonition that a certain mode of action has been found by ourselves and others to ^fbe well adapted to^f the cases of most common occurrence; so that if it be unsuitable ^gto^g the case in hand, the reason of its being so will be likely to arise from some unusual circumstance.

§ 4. [Art cannot be deductive] The error ^ais therefore^a apparent, of those who would deduce the line of conduct proper to particular cases, from supposed universal practical maxims; overlooking the necessity of constantly referring back to the principles of the speculative science, in order to be sure of attaining even the specific end which the rules have in view. How much greater still, then, must the error be, of setting up such unbending principles, not merely as universal rules for attaining a given end, but as rules of conduct generally; without regard to the possibility, not only that some modifying cause may prevent the attainment of the given end by the means which the rule prescribes, but that success itself may conflict with some other end, which may possibly chance to be more desirable.

This is the habitual error of many of the political speculators whom I have characterized as the geometrical school; especially in France, where ratiocination from rules of practice forms the staple commodity of journalism and political oratory; a misapprehension of the functions of Deduction which has brought much discredit, in the estimation of ^bother countries^b , upon the spirit of generalization so honourably characteristic of the French mind. The common-places of politics, in France, are large and sweeping practical maxims, from which, as ultimate premises, men reason downwards to particular applications, and this they call being logical and consistent. For instance, they are perpetually arguing that such and such a measure ought to be adopted, because it is a consequence of the principle on which the form of government is founded; of the principle of legitimacy, or the principle of the sovereignty of the people. To which it may be answered, that if these be really practical principles, they must rest on speculative grounds; the sovereignty of the people (for example) must be a right foundation for government, because a government thus constituted tends to produce certain beneficial effects. Inasmuch, however, as no government produces all possible beneficial effects, but all are attended with more or fewer inconveniences; and since these cannot ^cusually^c be combated by means drawn from the very causes which produce them; it would be often a much stronger recommendation of some practical arrangement, that it does not follow from what is called the general principle of the government, than that it does. Under a government of legitimacy, the presumption is far rather in favour of institutions of popular origin; and in a democracy, in favour of arrangements tending to check the impetus of popular will. The line of argumentation so commonly mistaken in France for political philosophy, tends to the practical conclusion that we should exert our utmost efforts to aggravate, instead of alleviating, whatever are the characteristic imperfections of the system of institutions which we prefer, or under which we happen to live.

§ 5. [^aEvery Art consists of^atruths of Science, arranged in the order suitable for^bsome^bpractical use] ^cThe grounds, then, of every rule of art, are to be found in the theorems of science.^c An art, or a body of art, consists of the rules, together with as much of the speculative propositions as comprises the justification of those rules. The complete art of any matter, includes a selection of such a portion from the science, as is necessary to show on what conditions the effects, which the art aims at producing, depend. And Art in general, consists of the truths of Science, arranged in the most convenient order for practice, instead of the order which is the most convenient for thought. Science groups and arranges its truths, so as to enable us to take in at one view as much as possible of the general order of the universe. Art, though it must assume the same general laws, follows them only into such of their detailed consequences as have led to the formation of rules of conduct; and brings together from parts of the field of science most remote from one another, the truths relating to the production of the different and heterogeneous conditions necessary to each effect which the exigencies of practical life require to be produced.^*

^dScience, therefore, following one cause to its various effects, while art traces one effect to its multiplied and diversified causes and conditions; there is need of^d a set of intermediate scientific truths, derived from the higher generalities of science, and destined to serve as the generalia or first principles of the various arts. The scientific operation of framing these intermediate principles, M. Comte ^echaracterizes^e as one of those results of philosophy which are reserved for futurity.^[*] The only complete example which he ^fpoints^f out as actually realized, and which can be held up as a type to be imitated in more important matters, is the general theory of the art of Descriptive Geometry, as conceived by M. Monge.^[†] It is not, however, difficult to understand what the nature of these intermediate ^gprinciples must generally^g be. After framing the most comprehensive ^hpossible conception^h of the end to be aimed at, that is, of the effect to be produced, and determining in the same comprehensive manner the set of conditions on which that effect depends; there remains to be taken, a general survey of the resources which can be commanded for realizing this set of conditions; and when the result of this survey has been embodied in the fewest and most extensive propositions possible, those propositions will express the general relation between the available means and the end, and ⁱwill constitute the general scientific theory of the art; from which its practical methods will follow as corollaries.ⁱ

§ 6.^a[Teleology, or the Doctrine of Ends] But though the reasonings which connect the end or purpose of every art with its means, belong to the domain of Science, the definition of the end itself belongs exclusively to Art, and forms its peculiar province. Every art has one first principle, or general major premise, not borrowed from science; that which enunciates the object aimed at, and affirms it to be a desirable object. The builder’s art assumes that it is desirable to have buildings; architecture (as one of the fine arts), that it is desirable to have them beautiful or imposing. The hygienic and medical arts assume, the one that the preservation of health, the other that the cure of disease, are fitting and desirable ends. These are not propositions of science. Propositions of science assert a matter of fact: an existence, a coexistence, a succession, or a resemblance. The propositions now spoken of do not assert that anything is, but enjoin or recommend that something should be. They are a class by themselves. A proposition of which the predicate is expressed by the words ought or should be, is generically different from one which is expressed by is, or will be. It is true, that in the largest sense of the words, even these propositions assert something as a matter of fact. The fact affirmed in them is, that the conduct recommended excites in the speaker’s mind the feeling of approbation. This, however, does not go to the bottom of the matter; for the speaker’s approbation is no sufficient reason why other people should approve; nor ought it to be a conclusive reason even with himself. For the purposes of practice, every one must be required to justify his approbation: and for this there is need of general premises, determining what are the proper objects of approbation, and what the proper order of precedence among those objects.

These general premises, together with the principal conclusions which may be deduced from them, form (or rather might form) a body of doctrine, which is properly the Art of Life, in its three departments, Morality, Prudence or Policy, and Æsthetics; the Right, the Expedient, and the Beautiful or Noble, in human conduct and works. To this art, (which, in the main, is unfortunately still to be created,) all other arts are subordinate; since its principles are those which must determine whether the special aim of any particular art is worthy and desirable, and what is its place in the scale of desirable things. Every art is thus a joint result of laws of nature disclosed by science, and of the general principles of what has been called Teleology, or the Doctrine of Ends;^* which, borrowing the language of the German metaphysicians, may also be termed, not improperly, the principles of Practical Reason.

A scientific observer or reasoner, merely as such, is not an adviser for practice. His part is only to show that certain consequences follow from certain causes, and that to obtain certain ends, certain means are the most effectual. Whether the ends themselves are such as ought to be pursued, and if so, in what cases and to how great a length, it is no part of his business as a cultivator of science to decide, and science alone will never qualify him for the decision. In purely physical science, there is not much temptation to assume this ulterior office; but those who treat of human nature and society invariably claim it; they always undertake to say, not merely what is, but what ought to be. To entitle them to do this, a complete doctrine of Teleology is indispensable. A scientific theory, however perfect, of the subject matter, considered merely as part of the order of nature, can in no degree serve as a substitute. ^bIn this respect the various subordinate arts afford a misleading analogy. In them there is seldom any visible necessity for justifying the end, since in general its desirableness is denied by nobody, and it is only when the question of precedence is to be decided between that end and some other, that the general principles of Teleology have to be called in: but a writer on Morals and Politics requires those principles at every step.^b The most elaborate and well-digested exposition of the laws of succession and coexistence among mental or social phenomena, and of their relation to one another as causes and effects, will be of no avail towards the art of Life or of Society, if the ends to be aimed at by that art are left to the vague suggestions of the intellectus sibi permissus, or are taken for granted without analysis or questioning.^c

§ 7. [Necessity of an ultimate standard, or first principle of Teleology] There is, then, a Philosophia Prima peculiar to Art, as there is one which belongs to Science. There are not only first principles of Knowledge, but first principles of Conduct. There must be some standard by which to determine the goodness or badness, absolute and comparative, of ends, or objects of desire. And whatever that standard is, there can be but one: for if there were several ultimate principles of conduct, the same conduct might be approved by one of those principles and condemned by another; and there would be needed some more general principle, as umpire between them.

Accordingly, writers on moral philosophy have mostly felt the necessity not only of referring all rules of conduct, and all judgments of praise and blame, to principles, but of referring them to some one principle; some rule, or standard, with which all other rules of conduct were required to be consistent, and from which by ultimate consequence they could all be deduced. Those who have dispensed with the assumption of such an universal standard, have only been enabled to do so by supposing that a moral sense, or instinct, inherent in our constitution, informs us, both what principles of conduct we are bound to observe, and also in what order these should be subordinated to one another.

The theory of the foundations of morality is a subject which it would be out of place, in a work like this, to discuss at large, and which could not to any useful purpose be treated incidentally. I shall content myself therefore with saying, that the doctrine of intuitive moral principles, even if^a true, would provide only for that portion of the field of conduct which is properly called moral. For the remainder of the practice of life some general principle, or standard, must still be sought; and if that principle be rightly chosen, it will be found, I apprehend, to serve quite as well for the ultimate principle of Morality, as for that of Prudence, Policy, or Taste.

Without attempting in this place to justify my opinion, or even to define the kind of justification which it admits of, I merely declare my conviction, that the general principle to which all rules of practice ought to conform, and the test by which they should be tried, is that of conduciveness to the happiness of mankind, or rather, of all sentient beings: in other words, that the promotion of happiness is the ultimate principle of Teleology.^*

I do not mean to assert that the promotion of happiness should be itself the end of all actions, or even of all rules of action. It is the justification, and ought to be the controller, of all ends, but is not itself the sole end. There are many virtuous actions, and even virtuous modes of action (though the cases are, I think, less frequent than is often supposed) by which happiness in the particular instance is sacrificed, more pain being produced than pleasure. But conduct of which this can be truly asserted, admits of justification only because it can be shown that on the whole more happiness will exist in the world, if feelings are cultivated which will make people, in certain cases, regardless of happiness. I fully admit that this is true: that the cultivation of an ideal nobleness of will and conduct, should be to individual human beings an end, to which the specific pursuit either of their own happiness or of that of others (except so far as included in that idea) should, in any case of conflict, give way. But I hold that the very question, what constitutes this elevation of character, is itself to be decided by a reference to happiness as the standard. The character itself should be, to the individual, a paramount end, simply because the existence of this ideal nobleness of character, or of a near approach to it, in any abundance, would go further than all things else towards making human life happy; both in the comparatively humble sense, of pleasure and freedom from pain, and in the higher meaning, of rendering life, not what it now is almost universally, puerile and insignificant—but such as human beings with highly developed faculties can care to have.^a

^a§ 8.^a [Conclusion] With these remarks we must close this summary view of the application of the general logic of scientific inquiry to the moral and social departments of science. Notwithstanding the extreme generality of the principles of method which I have laid down, (a generality which, I trust, is not, in this instance, synonymous with vagueness) I have indulged the hope that to some of those on whom the task will devolve of bringing those most important of all sciences into a more satisfactory state, these observations may be useful; both in removing erroneous, and in clearing up the true, conceptions of the means by which, on subjects of so high a degree of complication, truth can be attained. Should this ^bhope be realized,^b what is probably destined to be the great intellectual achievement of the next two or three generations of European thinkers ^cwill have been in some degree forwarded^c .

APPENDICES

Appendix A

THE EARLY DRAFT OF THE LOGIC

Editor’s Note

The manuscript, bound in brown morocco, is in the Pierpoint Morgan Library, New York (catalogued V/11/A), having been obtained in Britain sometime before 1909. As folioed by the library, it consists of 344 folios, c. 23.9 cm. × 19 cm. At the head of the first folio (above the title, “Introductory Matter”) is written “ “Mill’s Logic” 2 Vols divide where marked cloth b^ds”, and on the first folio of the equivalent of Book II is written “Vol 2”. On an attached initial sheet the following note appears: “This copy of Mr. Mill’s Logic being an early manuscript draft was sent by the author to my Father the late Professor J. P. Nichol.”

The manuscript is in three scribal hands (henceforth referred to as A, B, and C), with corrections, additions, and some footnotes in Mill’s hand. The text is written on recto throughout, with the versos reserved for footnotes, except for the final five ff., which are covered recto and verso with text. Following one of his common practices, Mill used a sequence of letters, A to P, with a second N, placed in the upper right-hand corner of rectos, to indicate “gatherings,” usually of 20 folios. Three of these letters, the K, L, and M, are inscribed over partly erased letters G, H, and I. The paper is of various makes, and three dates, 1833, 1834, and 1836.

This evidence, plus short pages and gatherings, one long cancelled passage (ff. 114-20), the content, and some external evidence, establishes that the scribes copied parts of the manuscript at different times. The table on the following two pages sets out the relevant internal evidence. Inferences drawn from this evidence will be found in the section of the Textual Introduction dealing with the history of the text of the Logic (see lvii ff.).

In that section a summary comparison is made of the texts of the Early Draft and the Press-copy Manuscript. To facilitate comparison of the early and final versions, parallel passages are indicated in the text of the Early Draft. The book and chapter titles of the final version are given in square brackets as, for example, at 969 below, where it will be seen that the chapter of the Early Draft entitled “Statement of the Problem” corresponds to Bk. I, Chap. i of the final version. Because the wording is in many cases very close in the two versions, it is possible to indicate section and paragraph parallels, which are also placed in

square brackets. These indicators are normally in roman type; when they are in italic type they indicate that, while the wording is different in the two versions, the relevant section or paragraph in the final version replaced that in the Early Draft.

The final version being much fuller, there are gaps in the sequence of the inserted indicators, but an attempt has been made to show what happened to each paragraph of the Early Draft: when the material was deleted or greatly rewritten, footnotes are added; when the sequence was altered, the normal indicators appear non-sequentially (see, for example, 966, where in the Introductory Matter—equivalent to the Introduction—after the first paragraph of §7, the Early Draft has the equivalent of the second paragraph of §1, and then returns to the second paragraph of §7). When there is neither a footnote nor an indicator at the beginning of a paragraph, the preceding footnote or indicator gives the disposition; that is, in most cases, the paragraph was incorporated with the previous one. Sometimes Mill divided paragraphs in rewriting; in such cases indicators appear within the paragraphs of the Early Draft. It should be noted that the indicated parallels are between the Early Draft and the 8th edition, so that comparisons can be made by using the texts here printed. The Early Draft is, of course, closer to the Press-copy Manuscript, and therefore the variants between the 8th edition and the Press-copy Manuscript must be consulted.

Editorial alterations in the text have been kept to the minimum compatible with fluent reading. Footnotes describe those changes in Mill’s hand that indicate later rethinking of a point, but no indication is given of the places where Mill had to supply or correct a word that the scribe could not read, or of the places where the scribe made a current correction. The editorial footnotes are, with their indicators, given in square brackets; the manuscript’s footnote indicators have been regularized. Superscript abbreviations have been lowered.

The spelling of the original has been accepted (except in the few cases listed in the note below), as a record of the scribes’ habits. Only where there are syntactic oddities does “[sic]” appear. The corrections that have been made may be categorized as follows: 1. scribal repetitions deleted, 2. missing words supplied in square brackets, 3. words corrected, 4. italics regularized, 5. quotation marks regularized, 6. punctuation and capitalization regularized.^*

As a further aid to the study of the development of Mill’s thoughts on logic, the Bibliographic Appendix and the Index list references to the Early Draft, italicized and in parentheses, immediately after the parallel references to the text of the 8th edition. References that appear only in the Early Draft are given in italics at the end of the list of references to the 8th edition.

INTRODUCTORY MATTER^[*]

[Introduction]

[§1]

[¶1] There is as great a diversity in the modes which different authors have adopted of defining Logic, as in their modes of treating of it. This is no more than we might expect, on all those subjects on which different authors have availed themselves of the same language, as a means of delivering ideas in any respect different. Morals and Jurisprudence are liable to this remark in common with Logic. Almost every philosopher having taken a different view of some of the particulars which these branches of knowledge are usually understood to include, each has so framed his definition of the subjects themselves as to indicate beforehand his own peculiar tenets, and perhaps to beg the question in their favour.

[§2]

[¶1] Logic has been often said to be the Art of Reasoning. This definition has been adopted, and improved, by a recent writer of great eminence, who defines Logic to be the Science, as well as the Art, of Reasoning: the analysis of the mental process which takes place whenever we reason, as well as the practical rules, which have been grounded upon that analysis, for conducting the process correctly. The propriety of this emendation is obvious. A right understanding of the mental operation itself, is the only basis on which a connected or comprehensive system of rules fitted for the direction of it, can possibly be founded. Art necessarily presupposes Science: and every Art should bear the name of the Science on which it rests, were it not that several Sciences are often necessary to form the groundwork of one single Art. Such is the complication of human affairs that to enable one thing to be done, it is often requisite to know the natures and properties of many.

[¶2] Logic, then, comprises a Science as well as an Art. But it admits of question whether even when thus amended, the above definition of Logic is coextensive with the received employment of the term.

The word Reasoning, like almost all scientific terms which are in common use, abounds in ambiguities. With some persons, Reasoning means Syllogizing; or, in other words, that mode of inference which may be called with sufficient accuracy for the present purpose, concluding from generals to particulars. With others again, to reason is simply to infer any truth from truths already known. Induction, therefore, according to this nomenclature, is as much entitled to be called Reasoning, as the demonstrations in Euclid.

[¶3] Writers on Logic have generally preferred the former acceptation of the term; the latter, and more extensive signification is that in which I shall use it. The reasons for this departure from the custom of professed Logicians will appear as we advance. To the general usage of the English language, I believe mine to be the nearer approximation.

[§3]

[¶1] But even this, the widest sense in which the term Reasoning is ever employed, is not so wide as to be coextensive with the ordinary acceptation of the word Logic. The practice of using the denomination Logic to denote peculiarly the Science which treats of Argumentation, originated with the Schoolmen: yet even in their systematic treatises, Argumentation formed the subject only of the third Part: the two former treated of Terms, and of Propositions; under one or other of which heads were included, Definition, and Division. Professedly, indeed, all these subjects were attended to only on account of their connexion with Reasoning, and as a preparation for understanding the doctrine and rules of the Syllogism. Yet they were treated much more minutely, and dwelt on at much greater length than that purpose required. More recent writers on Logic have generally understood that term nearly in the sense in which it was employed by the Authors of the Port Royal Logic; viz: as synonymous with the Art of Thinking. Nor is this large acceptation of the word confined to philosophers. Even in common conversation, the ideas which seem to be connected with the word Logic, include at least precision of language and accuracy of classification: and we, perhaps, oftener hear ordinary persons speak of a logical arrangement, or of expressions logically defined, than of a conclusion logically deduced from premises. But to name, to affirm or deny, to define, to classify, are not acts of inference; they are not processes by which, from premises, we deduce a conclusion. Whether, therefore, we assume as a standard the practice of those, who have made the subject their particular study, or that of popular writers & common discourse, we shall find reason to include in the province of Logic several operations of the intellect which it is not customary to consider as falling within the meaning of the terms Reasoning or Argumentation.

[¶2] These operations might be brought within the compass of the Science, and the additional advantage be obtained, of a very simple definition, if an extension, sanctioned by very high authorities, were given to the meaning of the term; by defining Logic to be the Science which explains, and the rules which may be devised to assist, the operations of the human understanding in the pursuit of truth. For to this ultimate end, naming, classification, definition, and all the other operations over which Logic has ever claimed jurisdiction, are merely subsidiary. The object of all of them is that a person may enable himself to know at any given time, all those truths the knowledge of which is needful for him at that time. Naming has, indeed, in addition to this, an ulterior object; to enable him to communicate this knowledge to others. But when viewed with reference to this purpose, it has never been considered to fall within the province of Logic; the sole object of which is the guidance of one’s own thoughts. The fittest means of communicating them to others, fall under the consideration of Rhetoric, in the large extent in which that Art was conceived by the ancients; or of the still more extensive art of Education. Logic takes cognizance of any of our intellectual operations, only as they conduce to the perfection of our own knowledge, and of our command over that knowledge for the purposes of our own use. If there were but one rational being in the universe, that being might be a perfect Logician; & the Science & Art of Logic would be precisely the same for that one person, as for the whole human race.

[§4]

[¶1] The definition, however, which we have now suggested, although exempt from the fault which was chargeable upon the former one, that of including too little, labours under the opposite vice of including too much. It comprehends some things never yet considered as belonging to Logic; and some which are altogether unfit to be classed, in any scientific arrangement, under the same head with those which will be treated of in the present work.

[¶2] Truths are known to us in two ways: some are known directly, and of themselves; some through the medium of other truths. The former are the subject of intuition or consciousness; the latter, of inference. The truths which we know by intuition are the original premisses from which all others are deduced: for the truth of the conclusion being founded upon the assumption that the premisses are already known to be true, we never could arrive at any knowledge by reasoning, unless there were something which we knew antecedently to all reasoning.

[¶3] Examples of truths which are known to us by immediate consciousness, are our own sensations. Examples of truths which we know only by way of inference, are, events which took place while we were absent; the occurrences recorded in history; or the theorems of mathematics. The two former we infer from the testimony which is adduced, or from the traces which the events have left behind them; the latter, from the premisses which are laid down in books of geometry, under the title of definitions and axioms.

[¶5] Whatever is known to us by consciousness, is known beyond possibility of question. What one sees & feels, whether bodily or mentally, one cannot but be sure that one sees & feels. No Science is required for the purpose of arriving at such truths; no rules of art can render our knowledge of them more certain than it is in itself. There is no Logic, therefore, for this class of truths.

[¶6] But we may fancy that we see & feel, what in reality we infer. A truth, or supposed truth, which is really the result of a very rapid inference, may seem to be apprehended intuitively. It has long since been agreed by philosophers of all schools, that this mistake is actually made in so familiar an instance as that of the eye-sight. There is nothing which we appear to ourselves to be more directly conscious of, than the distance of an object from us. Yet it has been proved to absolute certainty, and is now admitted by all who have examined the subject, that when we fancy that we see distance, what we really see is only a certain diminution of apparent size, and a certain faintness of colour; and that our estimate of the object’s distance from us is the result of a comparison, (made with so much rapidity that we are unconscious of making it) between the size and colour of the object as they appear to us, and its size & colour as they appeared on former occasions, when we knew at what distance from us it was. The perception of distance by the eye, which seems so like intuition, is thus, in reality, an inference, grounded on experience: an inference, too, which we learn to make, and which we make more & more correctly as our experience encreases; though in familiar cases it takes place so rapidly as to appear exactly on a par with those perceptions of sight which are really intuitive, our perceptions of colour.

[¶7] Of the Science, therefore, which explains the operations of the human understanding in the pursuit of truth, nothing can form a more essential part than the inquiry, what are the truths which are the subject of intuition or consciousness, & what are those which we merely infer. But this inquiry has never been considered a portion of Logic. It is the subject of another, and a perfectly distinct branch of Science: the higher or transcendental metaphysics; as that department of Science may be termed which attempts the solution of the question, what part of the furniture of the mind belonged to it originally, and what part was constructed by itself out of materials furnished to it from without. To this Science belong the great and much agitated questions, of the existence of matter and of spirit; of the existence of any connexion between cause and effect, other than the constancy of their succession; of the reality of time & space as entities per se, distinguishable from the objects which are said to exist in them. For, in the present state of these various questions, it is universally allowed that the existence of matter, or of spirit, of space, or of time, cannot be proved; & if known at all, is known by immediate intuition. To the same Science belong the inquiries into the nature of conception, perception, memory, and belief; all of which are operations of the understanding in the pursuit of truth; but operations with which the Logician has no concern, further than to assume their existence as a fact. To this Science must also be referred the following, and all analogous questions: Whether our emotions are innate, or the result of association: Whether God, & duty, are realities the existence of which is manifest to us a priori by the constitution of our rational faculty; or whether our ideas of them are acquired notions, the origin and growth of which we can trace and explain, and the reality of the objects themselves a question not of consciousness or intuition, but of evidence and reasoning. To determine, in short, what are, and what are not, the truths known per se, the original premisses of all our knowledge; is the object of the higher, or remoter metaphysics.

[¶8] But as soon as it is known, or assumed, that a particular truth or a proposition into the truth of which we are inquiring, is not intuitively obvious, but requires proof; in other words, is not to be admitted but as an inference from some other truth; then, the operation of the understanding in judging of the sufficiency of the evidence, or in judging what sort of evidence ought to be required, is properly the subject of Logic.

Another distinction requires to be made. The province of Logic is not the evidence itself, but the operation of the understanding in judging of the evidence. Logic does not teach us by what evidence a given fact becomes known to us; but how we are to judge of the evidence which shall be sufficient to prove that fact. It does not itself solve the problem, but determines whether it has been solved satisfactorily, and if not, what is still wanting to render the solution complete.

[§5]

[¶1] If it did more, it would embrace all human knowledge.

All human life is taken up in deducing conclusions from premisses. Every one has daily, hourly, and momentary occasion for ascertaining numerous particular facts; not from any general purpose of adding to his stock of knowledge, but because the individual facts themselves are of moment to him, or to those whose interests are under his charge. The business of the judge, of the commander, of the navigator, of the physician, of the husbandman, is merely to judge of evidence, and to act accordingly: and as they do this well or ill, so they discharge well or ill the duties of their several callings. It is the only occupation in which the intellect never ceases to be engaged; and is the subject not of Logic, but of knowledge in general. [¶2] Logic does not instruct the surgeon from what symptoms he is warranted in inferring a violent death. This he can only learn from his own experience and observation, or that of others, recorded in the books of his peculiar Science. But though Logic will not tell him what the symptoms are, it will tell him how, where he already knows them, he may determine whether they are or are not conclusive. Though it will not supply the place of experience, it will guide his understanding in judging whether his experience is sufficient to establish any given proposition, and if not, what kind of additional experience he has still to seek, in order to obtain a solution of the problem.

[¶3] It is in this sense that Logic is, what Lord Bacon most expressively called it, Ars artium; the Science of Science itself. All Science consists of premisses and conclusions, of the Proof, and That which is proved: now Logic analyses the process or processes by which, in all the Sciences, the mind proceeds from the premisses to the conclusion, from the proof to that which is to be proved. ^[*] Each particular department of Science furnishes the evidence necessary to establish its own particular conclusions, but Logic decides whether that evidence is sufficient; and if not, sends back the question to the Science to which it belongs, for such further evidence as observation and experiment can be made to yield; having first indicated the exact nature of the deficiency to be supplied.^*

[§6]

[¶2] A Science may certainly be brought to a very advanced stage of improvement without the application of any other logic to it than what all persons who are said to have a sound understanding acquire, acquire empirically in the course of their studies. But this is only saying what every one knows; that a thing may be very well done by particular individuals, before there has been any accurate thinking respecting the mode of doing it. This does not, however, prove that accurate thinking is of no use. Men judged of evidence, and often very correctly, before Logic was studied, as men talked and made themselves understood before they thought of inventing rules of grammar. But they talk and write far more intelligibly by means of grammar, and they judge of evidence far more correctly after having studied Logic. No Science is completely a Science, until Logic is superadded to it. Whatever may be the case with the collection of the evidence, the appreciation of it is mere empiricism, until the process of drawing conclusions from evidence has been subjected to the same accurate analysis, which it is already allowed must be supplied to the evidence itself, in order to constitute a Science. In whatever degree, therefore, Science is superior to empiricism; in whatever degree accurate and careful analysis affords a surer ground to proceed upon, than extemporaneous and gross apprehension; in that same degree a Science which has been brought into subordination to the Science of Logic, is more certain and more valuable than one which has not.

[§7]

[¶1] Logic, therefore, may be defined, the Science which treats of all operations of the human understanding, subservient to the estimation of evidence; both the actual operation of proceeding from premisses to a conclusion, and all the other intellectual operations which are auxiliary to this. It includes, therefore, naming, and predication; that is to say, the operation of giving names, and that of applying them to their principal use; and it also includes Definition, & Classification. For the use of every one of these operations (putting all other minds than one’s own out of consideration) consists in their being means, not only of keeping our conclusions themselves, and the evidence of them, permanent, and readily accessible, in the memory; but also of so marshalling the evidence, as to enable the mind to judge more easily, and with fewer chances of error, whether the evidence is sufficient or not. Language has been called an instrument of thought; and systematic arrangement is equally entitled to be so characterized: now the word thought, if it means anything, means proceeding from truths which are self-evident, to establish other truths. Language and Classification being instruments for accomplishing this end, the analysis of the instruments is an indispensable part of the analysis of the operation itself. The art is not complete, unless another art, that of constructing the tools and fitting them for the purposes of the art, is embodied in it.

[§1, ¶2] If any of my readers has been accustomed to use the word Logic in any other sense than that which I have attached to it; and finding old habits the most convenient, should be disinclined to alter them at my bidding; it is not probable that I could state in this place the advantages of my own definition, in such a manner as to convince him. But, if he peruse this work to the end, he will probably be enabled, from the view which I take of the particulars comprehended in the Science, to collect the reasons which induce me to define it as I have done. It is useless to dispute about the definition of a Science until we are agreed about the Science itself. Each man builds his wall according to the shape and dimensions of his own piece of ground. If my definition is not the right definition of Logic, it is the right definition of the subject of this book. As much as is to be expected from a definition placed at the commencement of a subject, is that it should define the scope of our inquiries.

The definition we set out with, is seldom that which a thorough knowledge of the subject shews to be the most appropriate. The particulars, which it is the object of the definition to segregate from all others, are not yet known to us, and till then we cannot know what is the most natural or the most convenient mode of grouping them. The definition with which we begin, is merely the statement of a problem: the definition with which we end is the solution of that same problem, or as much of the solution as can be conveniently and usefully compressed into the compass of a single proposition. So long, therefore, as the Science is imperfect, the definition must partake of its imperfections: and, if the former is progressive, the latter ought to be so too. The reader who shall have accompanied me through the details of the subject, may turn back and question my definition, but as against any one else I claim full liberty of stating the problem in my own way.

[§7, ¶2] My object, then, will be to attempt the correct analysis of the intellectual process called reasoning or inference, and of such other mental operations as are intended to facilitate this. [¶3] I do not undertake to analyse these operations into their ultimate elements. I shall only endeavour that the analysis as far as it goes may be correct, and that it may go far enough for the practical purposes of Logic, considered as an Art. The analysis of a phenomenon is not like a connected chain of proof. If one link of an argument breaks, the whole drops to the ground; but one step towards an analysis holds good of itself, and has a substantial value of its own, though we should never be able to make a second. The analytical processes of chymistry are not the less valuable, though it may hereafter be discovered that all which we have called simple substances are in reality compounds. All things have at any rate been decomposed into those elements. Whether they admit of still further decomposition by the decomposition of the elements themselves, is an important inquiry, but one which does not affect the certainty of the Science up to that point.

[¶4] I shall attempt to analyse the process of inference, and the processes subordinate to inference, so far only as may be requisite for determining with precision what is necessary for the correct performance of those processes, & framing rules to assist it accordingly. Any further & minuter analysis I leave to transcendental metaphysics; which in this, as in other parts, of our mental nature, decides what are ultimate facts, and what are resolvable into other facts. And I believe it will be found that the conclusions at which I arrive have no necessary connexion with any particular views respecting the ulterior analysis. The partizans of Hartley and those of Reid, those of Locke and those of Kant, might concur in nearly everything that I shall have to say, consistently with the fundamental principles of their several systems. Particular and detached opinions of all of them will no doubt occasionally be contested, since all of them are Logicians as well as Metaphysicians; but the field in which their great battles have been fought, lies beyond the boundaries of our Science.

Being thus unconnected with those questions which have divided philosophers in the higher regions of Metaphysics, the present work if it be unobjectionable in other respects will be adapted both to a larger number of students, and to an earlier period of their philosophical studies, than an analytical treatise on Mental Philosophy in general.

[Book I:

Of Names and Propositions]

STATEMENT OF THE PROBLEM^[*]

[Chapter i: Of the Necessity of Commencing with an Analysis of Language]

[§1^† ]

The object of the present enquiry being in the first place to analyse the process by which the understanding proceeds from truths which are known, to establish others which are unknown; the purport of the question which is to be enquired into cannot be understood, unless we understand distinctly what is meant by a truth; what is that property of an assertion, which determines us to say that it is a true assertion; what is the peculiarity which distinguishes the true from the false. When this shall be cleared up, (if such fate should attend the present attempt), the great problem of the Science may be clearly stated, which is always a great way, and, in this case, almost half way, towards its solution. For as logical studies in no way contribute more to give soundness to the understanding, than by accustoming it to enunciate both what it knows, and what it seeks to know, in definite and unambiguous expressions; so the difficulties of Logic itself will in a great measure vanish, when the few fundamental notions with which the Science is principally conversant are distinctly and accurately conceived.

In receiving anything as a Truth, there are two different matters which demand attention. One is, the act or operation of the mind when it is said to believe; the other is, that which it believes. We must distinguish, in short, the thing believed, & the state of the believing mind.

With respect to the nature of the phenomenon of Belief, the Logician, as such, has no concern with it. Every one knows what kind of feeling it is; and for the purposes of Logic, it is not necessary to know anything more of it than what every one knows. To analyse the act of Belief, or to determine whether it is susceptible of analysis, must be left to the higher metaphysics. To ascertain the nature of the immediate Object of Belief, is all that will here be aimed at.

[§2]

[¶1] What is the immediate object of Belief, or, in other words, what every Truth, or everything which is received as Truth, is found, when correctly analysed, to consist in, is a question which we shall best solve a posteriori; by examining the import of all the various Kinds of Propositions. For our belief, when put into words, always expresses itself in a Proposition. We believe that the thing, which we conceive in our minds, exists or exists not; is, or is not, so and so. What, by a convenient misapplication of an abstract term, we call a Truth, is more properly called a True Proposition. In proceeding to enquire what constitutes a True Proposition, it is necessary to begin by defining, that is, analysing, the notion of a Proposition itself.

[¶2] For the present purpose, the ordinary and simple definition will be sufficient. By a Proposition, is meant discourse, in which something is affirmed or denied of something. Thus, in the proposition, Gold is yellow, the quality yellow is affirmed of the substance Gold. In the proposition, Franklin was not born in England, the fact expressed by the words born in England is denied of the man, Franklin.

^[*] An affirmative proposition is also called a predication. To predicate one thing of another, is to affirm one thing of another.

[¶3] Every proposition consists of three parts, which are called, the subject, the predicate, and the copula. The predicate is the name denoting that which is affirmed or denied. The subject is the name denoting the person or thing, which something is affirmed or denied of. The copula, is the sign denoting that there is an affirmation or denial; and thereby enabling the hearer or reader to distinguish a Proposition, from any other kind of discourse. Thus, in the proposition, The Earth is round, the predicate is the word round, which denotes the quality affirmed: the earth, words denoting the object of which that quality is affirmed, are the subject of the proposition. The word is, which serves as the connecting mark between the subject and predicate, to shew that one of them is affirmed of the other, is called the copula.^*[Bk. I, Chap. iv, §1, ¶3] It may perhaps be thought that this is not all which is signified by the copula; that it also denotes existence; as, for instance, in the proposition, Socrates is just, it may be supposed to be implied, not merely that the quality just may be affirmed of Socrates, but moreover that Socrates is, i.e. exists. Undoubtedly this shews that there is an ambiguity in the word is; a word, which not only performs the functions of the copula in affirmations, but has also a meaning of its own, in virtue of which it may itself be made the predicate of a proposition. That the employment of it as a copula, however, does not necessarily include any affirmation of existence, appears from such a proposition as this, A centaur is a fiction of the poets: where it cannot possibly be implied that a centaur exists, since the proposition itself expressly asserts that it has no real existence.

[Ibid., ¶4] If the Greek philosophers, and their followers, the Schoolmen, had adverted to this double meaning of the verb to be (for the ambiguity exists equally in all languages) they would have been saved much quibbling, many paradoxes, and the creation of several needless abstractions, which they mistook for objective realities. Yet it becomes us not to triumph over the gigantic intellects of Plato and Aristotle, because we are now able to preserve ourselves from errors into which they, perhaps inevitably, fell. The fire-teazer of a modern steam-engine produces by his exertions far greater effects than Milo of Crotona could, but he is not therefore a stronger man. The Greeks seldom knew any language but their own. This rendered it far more difficult for them than it is for us, to acquire the habit of detecting ambiguities. Among the many inestimable advantages derived from the systematic study of more languages than one, this is among the greatest. By finding that a single word in the foreign language often corresponds, on different occasions, to different words in our own, we learn practically that the same word does not always mean the same thing. Even the strongest understandings, when not thus exercised, find it difficult to believe of things which have a common name, that they have not also, in some respect or other, a common nature; and often take infinite quantity of fruitless trouble to find it out; as the writings of the two great philosophers whom we recently named, abundantly exemplify.

The ambiguity of the word which has been selected to perform the office of the copula, has misled the moderns scarcely less than the ancients; though their mistakes do not appear equally ridiculous, precisely because our understandings are not yet so completely emancipated from the influence of them. The quantity of futile speculation which has been caused by a misapprehension of the nature of the copula was first hinted at by Hobbes; but Mr. Mill was, I believe, the first who pointed out, how many errors in the received systems of philosophy (errors which this is not the place for particularizing) it has partly to answer for.

A Proposition, then, being defined to be, a portion of discourse, by which something denoted by a name called the predicate, is affirmed, or denied, of something denoted by a name called the subject; we are next to enquire what is meant by a True Proposition.

^[*] The ordinary explanation of the nature of a true proposition, which, though superficial, is sufficient for the common purposes of human intercourse, is also the point from which, in any attempt towards a deeper analysis of the truth of propositions, it is necessary to start. This explanation cannot be more appropriately given than in the words of the Schoolmen: Propositio vera est, quæ est conformis rei significatæ: A true proposition is that, the assertion contained in which is in accordance with the fact. This, however, only staves [sic] the difficulty further back, without removing it; for what does the definition amount to? merely to this: that a proposition is true, if the fact asserted in it is true. The question, of course, still remains, What is meant by a fact? Or what constitutes the truth of facts? The answer to this question is very obvious in some cases. When, for instance, the proposition is, that on such a day, I fell off a horse and hurt my shoulder, every one understands what is the matter of fact asserted; and it is not possible to give any more recondite theory of its truth, than that if I did fall off my horse and hurt my shoulder on the day mentioned, it is true, & false if I did not. But when the proposition stated is such, for instance, as the following, The three angles of any rectilineal triangle are together equal to two right angles, The doctrine of unlimited obedience to all persons in authority is mischievous and immoral, It is the duty of every one to practise beneficence, temperance, and fortitude;—it is by no means so easy, as in the simple case before supposed, to perceive clearly and precisely at first sight, what we mean by calling this a Truth; what matter of fact is really asserted; what is the immediate object of belief in this proposition. Propositions, however, of this Kind, compose some of the most important classes of truths which are the subject of human thought. In an enquiry having for its object to ascertain in what manner the mind proceeds in arriving at these truths, or in satisfying itself that they are truths, it is indispensable to know what distinct matter of fact the propositions assert, and of what kind of truth such facts are susceptible. It is therefore necessary to inquire what is required to constitute a matter of fact, capable of being the subject of affirmation or denial; how many kinds of matters of fact there are, and what each is found to resolve itself into, when analysed into its simple elements; and how far the nature of the matter of fact asserted, can be collected from the form of the proposition. These are the first great problems of Logic, in its speculative branch; of Logic considered as a Science, contradistinguished from Logic considered as an Art. And I believe it will be found that when these problems are solved, all the remaining difficulties of the Science are singularly smoothed down.

There is a proposition, wherever there are a predicate & a subject: anything which is affirmed or denied, and anything which it is affirmed or denied of. But there may be a subject and a predicate wherever there are two names. The field of affirmation and denial, or, to speak technically, the field of Predication, is coextensive, therefore, with that of naming. Any two names, are capable of being affirmed or ^[*] denied of each other; and either the affirmation or the negation will be the expression of an actual Truth. The converse moreover holds: for every Truth, and whatever is believed as Truth, can be expressed in words, by coupling together two names so as to form an affirmative or a negative Proposition. It would therefore be a great step towards ascertaining what constitutes a Truth, if we could ascertain the signification of all Names.

There are consequently two modes of enquiring into the nature and varieties of Matters-of-fact. We may commence our enquiry with Things, or we may commence it with Names. We may take a survey of the field of Thought, observe what things, or entities, it includes, and attempt an analysis and classification of those entities; or we may examine all the different kinds of names, and by ascertaining what they respectively signify, ascertain what are all the Things which mankind have hitherto found inducements to name.

Neither of these modes of proceeding has been neglected by logicians. The classification of names is the subject of the introductory chapters in most of their elementary works, & of the doctrine of the Predicables. The classification of things is attempted in their doctrine of the Predicaments. On both subjects they [have] done something, and have left much undone. Profiting by what they have done, and doing what we can to supply their omissions, we shall endeavour, like them, to unite both the above methods.

In the order of nature, things, of course, exist before their names: and as those who first imposed names had no names to guide them in the investigation of things, some may think that we ought to do as they did; and without regarding names, go at once to the things themselves. It may not be obvious to every one in what manner an analysis and classification of names, can be necessary for distinguishing the different Kinds of matters of fact.

The use, however, of enquiring into the signification of names, is, that we may be the less liable to overlook any of the things. It is from the different kinds of names which mankind have agreed in imposing, that we learn what Kinds or varieties of things they recognized. If we analyse the signification of all kinds of names; if by examining the cases in which they are employed, we can discover what they respectively serve as marks of; an enumeration and classification of nameable objects, grounded upon this analysis, will have for its basis the whole experience of mankind. There is another advantage which will be gained by proceeding in this order. It will appear hereafter that there are many more kinds of names than there are things capable of being named: and many distinctions among names, which do not answer to any distinctions among things, but only to distinctions in the manner of naming them. Now unless these anomalies of language are carefully noted and distinctly understood beforehand, they are sure to confuse and vitiate our speculations on Things. For howsoever, in looking at Things, we may endeavour to forget names, we cannot help letting ourselves be led by established language, and making words, in a manner, the index which directs us to Things. And those persons who most pique themselves upon disregarding “mere words,” are often in greatest danger of being misled by them, if not protected by an accurate analysis of their meaning. Such persons, at the very moment when they most imagine themselves to be intent exclusively upon things, are often viewing those things solely through the fallacious medium of some familiar phraseology.

OF NAMES

[Chapter ii: Of Names]

[§2]

[¶1] Before we attempt to discriminate between the different kinds of names, we must distinguish from names of all descriptions those words which are not names, but only parts of names. Such are all particles, as of, to, truly, often; the inflected cases of nouns substantive, as me, him, John’s; and even adjectives, as large, heavy. These words do not express anything of which something can be affirmed or denied. We cannot say, Heavy fell, or A heavy fell, Truly, or A truly, was asserted, Of, or an Of, was in the room;—unless, indeed, we are speaking of the mere words themselves, as when we say, Truly is an English word, or Heavy is an adjective: in which case, they are certainly complete names, viz: names of those particular sounds, or of those particular collections of written characters. This employment of a word, to denote the mere letters and syllables of which it is composed, was called by the Schoolmen the suppositio materialis of the word. In any other sense, we cannot make one of these words the subject of a proposition, unless by combining it with other words: as, a heavy weight fell, A truly important fact was asserted, a person of merit was in the room.

[¶2] Among the words which we have characterised as not names, but parts of names, we have included adjectives. An adjective, however, is capable of standing by itself as the predicate of a proposition. We may say, Snow is white. But white, in this case, is a mere abbreviation of the compound expression white-thing. The Greeks and Romans were permitted, by the rules of their language, to employ this ellipsis in the subject as well as in the predicate of a proposition. In English, this cannot, generally speaking, be done. We may say, The Earth is round; but we cannot say, A round is easily moved; we must say, A round object.

Whenever, in this work, we may appear to class an adjective among names, we must be understood to speak of its equivalent substantive; to use round, as a synonym of round object.

[¶3] Words which were not capable of being used as names, but only as parts of names, were sometimes called by the Schoolmen Syncategorematic words: from συν with, and κατηγορεω, to predicate, because it was only with some other word that they could be predicated. A word which could be used either as the subject or predicate of a proposition without being accompanied by any other word, the Schoolmen termed a Categorematic word. A combination of a Categorematic & a Syncategorematic word, as, “A heavy weight,” they sometimes called a mixt word; but this seems a needless multiplication of technical expressions. A mixt term is, in the only useful sense of the word, strictly Categorematic. It belongs to the class of what have been called many-worded names.

[¶4] For, as one word is frequently not a name, but only part of a name, so a number of words taken together often compose one single name, & no more. Thus, in the opening of the Paradise Lost, these words—

• the fruit
• Of that forbidden tree, whose mortal taste
• Brought death into the world, & all our woe,
• With loss of Eden, till one greater Man
• Restore us, & regain the blissful seat

form in the estimation of the logician only one name: one Categorematic word. A method of knowing whether any set of words makes only one name, or more than one, is by predicating something of it, and observing whether, by this predication, we make only one assertion or several. Thus, when we say, John, who is the father of Thomas, came to us; we make but one assertion; whence it appears that “John, who is the father of Thomas” is no more than one name. It is true, that in this proposition besides asserting that John came to us, we also assert that John is the father of Thomas. But this last assertion was already made; we did not make it by adding the predicate “came to us.” Suppose, however, that the words had been “John, and the father of Thomas,” they would have formed two names instead of one: for when we say, John and the father of Thomas came to us, we make two assertions; one, that John came to us; the other, that the father of Thomas came to us.

[¶5] This is as much as it seems necessary to say at present in illustration of many-worded names. We now proceed to state the distinctions which have been established among names, not according to the number of words they are composed of, but according to their signification.

[§3]

[¶3] The first grand division of names is into general, and individual or singular. A general name is familiarly defined, a name which is capable of being truly affirmed, in the same sense, of each of an indefinite number of things. An individual or singular name is a name which is only capable of being truly affirmed, in the same sense, of one thing.

[¶4] Thus, man is capable of being truly affirmed of John, Peter, Thomas, and other persons without any assignable limit: and it is affirmed of all of them in the same sense: for the word man expresses certain qualities, and when we predicate it of those persons, we make known that they all possess those qualities. But John, is only capable of being truly affirmed of one single person, at least in the same sense. For although there may be many persons who bear that name, it is not conferred upon them to indicate any qualities, or anything else which belongs to them in common; and cannot be said to be affirmed of them in any sense at all, consequently not in the same sense.

“The present King of England,” is also an individual name. For, that there never can be more than one person of whom it can be truly affirmed, is implied in the meaning of the words.

[¶5] It is not uncommon, by way of explaining what is meant by a general name, to say that it is the name of a class. But this, though a convenient mode of expression for some purposes, is objectionable as a definition, since it explains the clearer by the more obscure. It would be more proper to give as the definition of “a class,” that it means the indefinite multitude of individuals, denoted by a general name.

[¶6] It is necessary to distinguish general from collective names. A general name is one which can be predicated of each individual of a multitude; a collective name cannot be predicated of each separately, but only of all taken together. Thus, “the 76th Regiment of Foot,” which is a collective name, is not a general, but an individual name; for although it can be predicated of a multitude of individual soldiers, taken jointly, it cannot be predicated of them taken severally. We may say, Peter is a soldier, and John is a soldier, and Thomas is a soldier, but we cannot say, Peter is the 76th Regiment, and John is the 76th Regiment, and Thomas is the 76th Regiment. We can only say, Peter, and John, and Thomas, and James, and so forth, (enumerating all the soldiers) are the 76th Regiment.

[¶7] “The 76th Regiment” is a collective name, but not a general one: “A regiment” is both a collective & general one: general, as respects all individual regiments, of each of which separately it can be affirmed; collective, as respects the individual soldiers, of whom each regiment is composed.

[§4]

[¶1] The next general division of names is into concrete & abstract. A concrete name is a name which stands for a thing, an abstract name is a name which stands for an attribute of a thing. Thus, John, man, white are names of things; whiteness, is the name of an attribute of a thing. We have already observed that white, though otherwise a mere Syncategorematic word, is properly a name when used by way of ellipsis for the compound expression white-thing.

[¶2] I have used the words concrete and abstract in the sense attached to them by the Schoolmen, who, notwithstanding the imperfection of their metaphysics were unrivalled in the construction of technical language, and whose definitions, I conceive, have seldom been altered but to be spoiled. A practice, however, has grown up in more modern times, which, if not introduced by Locke, has gained currency chiefly by his example, of applying the expression “abstract name” to all names which are the result of abstraction or generalization, consequently to all general names, instead of confining it to the names of attributes. The philosophers of the Condillac School, whose admiration of Locke, passing over the profoundest speculations of that truly original genius, usually fastened with peculiar eagerness upon his weakest points, have gone on imitating him in this abuse of language until there is now some difficulty in restoring the word to its original signification. A more wanton alteration in the meaning of a word is rarely to be met with; for the expression general name, the exact equivalent to which exists in all languages with which I am acquainted, was already available for the purpose to which abstract has been misappropriated, while the misappropriation has left that important class of words, the names of attributes, without any compact distinctive appellation. The old acceptation however, has not gone so completely out of use, as to deprive those who now adopt it of all chance of being understood. By abstract, then, I shall always mean, the opposite of concrete; by an abstract name, the name of an attribute; by a concrete name, the name of an object.

[¶3]^[*] Do abstract names belong to the class of general, or to that of singular, names? Those which are names of single attributes, belong properly to neither one nor the other: for instance, visibleness; tangibleness; equality; squareness; milkwhiteness. These cannot in strictness be called general names, for none of them is the name of a class, comprising individuals in it: we cannot call the squareness of the square ABCD, the squareness of the square EFGH, & so forth, individuals. Yet neither can any abstract name be called singular; for if it be not a name of many individuals, as little is it the name of one individual. They must be placed in a class apart. There is, however, a kind of abstract names which are indisputably general; they are those which are names not of one attribute but of a class of attributes. Such is the word colour, which is a name of whiteness, redness, &c. Such is the word whiteness, in virtue of the various shades of whiteness to which it is applied in common; the words magnitude, weight, & the like, in virtue of the various degrees of magnitude & weight. Such also is the word attribute itself, the common name of all particular attributes.

^[*] We must be careful not to confound names of attributes with one important class of concrete names, names of sensations. Our sensations seldom receive separate names. We have a name for the object which gives us a certain sensation: the name white. We have also a name for the quality in the object, to which we ascribe that sensation; the name whiteness. But when we wish to speak of the sensation itself, we must use a circumlocution, & say, the sensation of white, or the sensation of whiteness. We have no name which expresses the sensation itself, simply; existing, as it might easily be conceived to exist, without any object to excite it. In the case of our sensations of hearing, we are more fortunate: we have the word sound, & a whole vocabulary of words to denote the various kinds of sound. For, as we oftener have these sensations in the absence of any perceptible object, we can more easily conceive having them in the absence of any object whatever. But in most instances, we have no name peculiarly appropriated to the sensation: and in that case the same name denotes indiscriminately the attribute, & the sensation. Thus colour stands for sensations of sight, as well as for the quality in the coloured object. Virtue denotes not only the quality of being a virtuous person, but also the virtuous acts themselves: as when we speak of living in the practice of virtue. We must bear in mind therefore, that whenever the word commonly denoting an attribute, is taken to express the sensation or sensible phenomenon which is called the effect or manifestation of the attribute, it then ceases to be an abstract name, & becomes concrete. Attention to this remark will save much confusion.

[¶4] It may be objected, that not only abstract names, but adjectives, which I have placed in the concrete class, are names of attributes: that white, for example, is as much the name of the colour, as whiteness is. To this the answer is, that white is not the name of the colour, but of the thing having the colour. The word white may be predicated of snow, or milk or linen; we may say, Snow is white, Milk is white, Linen is white: but we cannot say, Whiteness is white. White, therefore, is not a name of the quality whiteness, but of every white object. It is true this name was given to the objects on account of that colour; and we may therefore say, without impropriety, that the quality forms part of its signification; but not, that white is the name of the quality. A name can only be correctly said to stand for, or to be a name of, those things of which it can be predicated. All names, except those which are mere unmeaning marks, put upon individuals for the purpose of distinguishing them when they occur in discourse; all names which can be said to have any signification; all names by applying which to an individual we communicate any information respecting that individual,—may be said to imply an attribute of some sort; but they are not names of the attribute; and the attribute has its own proper name besides. This leads us to the consideration of

[§5]

[¶1] The third great division of names, that into connotative and non-connotative, sometimes, but improperly, called absolute.[¶2^* ] A non-connotative term is one which signifies a subject only, or an attribute only. A connotative term is one which denotes a subject, and implies an attribute. By a subject is here meant anything which possesses attributes; in contradistinction to attributes themselves. Thus John, or London, or England, are names which signify a subject only. Whiteness, Length, Virtue, are names which signify an attribute only. None of these names, therefore, are connotative. But white, long, virtuous, are connotative. The word white, denotes the subjects, snow, paper, &c. and implies, or as it was termed by the Schoolmen, connotes, the attribute whiteness. It is of the snow or the paper, (and not of the colour) that the word white is predicated: but when we predicate it of them, we imply, or connote, that the attribute whiteness belongs to them. The same may be said of all the other words above cited. Virtuous, for example, is strictly the name of a class, which includes Socrates, Howard, the Man of Ross, and an undefined number of other individuals, past, present, and to come: and it is these individuals, collectively and severally, who can alone be said with propriety to be denoted by it; of whom, alone, it can be properly said to be the name. But it is a name imposed upon them all in consequence of a certain attribute which they possess in common, namely, that of virtue. It is imposed upon all beings that are believed to possess this attribute; and it is not imposed on any which are not believed to possess it.

[¶3] All concrete general names which are names of substances, are connotative. The word man, for example, denotes John, Thomas, and an indefinite number of other individuals, of whom, taken as a class, it is the name. But it is applied to them because they possess, & to signify that they possess, certain attributes. These seem to be, corporeity, animal life, rationality, and a certain external form, which, for distinction, we call the human. Every existing thing, which possessed all these attributes, would be called a man; and anything which possessed none of them, or only one, or two, or even three of them without the fourth, would not be so called. For example, if in the interior of Africa were to be discovered a race of animals, possessing reason equal to that of man, but with the form of an elephant, they would not be called men. Swift’s Houyhnhms [sic] were not so called. Or if such newly discovered beings possessed the form of man without his reason, it is probable that some other name than that of man would be found for them. The word man, therefore, signifies all these attributes, and all subjects which possess those attributes. But it can be predicated only of the subjects. It is said, therefore, to signify the subjects directly, and the attributes indirectly; it denotes the subjects, and implies, or involves, or indicates, or connotes (as the Schoolmen most aptly termed it) the attributes. It is a connotative name.^*

>Folio from the Early Draft in Scribe A’s hand, with Mill’s emendations Pierpont Morgan Library

[¶6] Those names of substances which are names of individuals, require separate consideration.

[¶7]Proper names are not connotative. They denote the individuals who bear them; but they do not indicate or imply any attributes belonging to these individuals. When a man Christens his child by the name Thomas, or names his dog by the name Cæsar, those names are simply marks used to enable those individuals to be made subjects of discourse. It may be said that he had some reason for giving them those names rather than any others. It may be so; but the name gives no intimation of that reason. A man may be called ^[*] John, because that was the name of his father; a town may be called Dartmouth, because it is situated at the mouth of the Dart. But it is no part of the signification of the word John, that the father of the person in question bore the same name; nor even of the word Dartmouth, to be situated at the mouth of the Dart. For if sand should choke up the mouth of that river, or an earth quake change its course, so that the town should no longer be situate upon it, there is no reason to suppose that the name of the town should be changed. That fact, therefore, can form no part of the signification of the word; for, otherwise, when the fact ceased to be true, the name would cease to be applied. Proper names are attached to the objects themselves, and not to the continuence of any attribute of the object.

[¶8] But there is another class of names, which, although they are individual names, that is, predicable only of one object, are really connotative. Such is the name which we have already once used as an example, “The present King of England.”

For, although we may give to an individual a name utterly unmeaning, which we call a proper name; a word which answers the purpose of shewing what thing it is we are talking about, but not of telling anything about it; yet a name peculiar to an individual is not necessarily of this description. It may be significant of some attribute, or some union of attributes, which, not being possessed by any but one object, determines the name exclusively to that individual. “The sun” is a name of this description. “God” is another. These, however, are scarcely examples of what it is our present object to illustrate, being, in strictness of language, general and not individual names: for although they are, in fact, predicable only of one object, there is nothing in the meaning of the words themselves which implies this: and accordingly when we are imagining and not affirming, we may speak of many suns, and the majority of mankind have believed and still believe that there are many gods. But it is easy to produce words which are real instances of connotative individual names. It may be part of the signification of the connotative name itself, that there exists but one individual possessing the attribute which it connotes: as for instance, “the only son of John Stiles:” “the first Emperor of Rome.” Or the attribute connoted may be a connexion with some individual event, (by which I mean not an event of a particular kind, but one actual determinate event, which is past and over): and the connexion with that event may be of such a kind as only one individual could have; or without being this, it may be such as only one individual actually had, and this may be implied in the form of the expression. “The father of Socrates” is an example of the one kind, (since Socrates could not have had two fathers); “The author of the Iliad;” “The murderer of Henri Quatre,” of the second. For although it is conceivable that more persons than one might have participated in the authorship of the Iliad or in the murder of Henri Quatre, the employment of the article the implies that this was not the case. What is here done by the word the, is done in other cases by the context: thus, “Cæsar’s army” is an individual name, if it appears from the context that the army meant is that which Cæsar commanded in a particular battle. The name, being a many-worded name, may consist, in the first place, of a general name, capable, therefore, in itself, of being affirmed of more than one thing, but so limited by other words joined with it, that the entire expression can only be predicated of one object, consistently with the meaning of the general term. This is exemplified in the instance so often cited, “The present King of England.” King of England is a general term: the attributes which it connotes may be possessed by an indefinite number of persons: in succession, however, not simultaneously, since the meaning of the word imports (among other things) that there can be only one King of England at a time. This being the case, and the application of the name being afterwards limited by the word present, to such individuals as possess the attributes at one indivisible point of time, it becomes applicable only to one individual. And this appearing from the meaning of the word, without any extrinsic proof, it is strictly an individual name.

[¶9] From the above particulars it will be easily perceived, that whenever names of substances have properly any meaning, the meaning resides not in what they denote but in what they connote. The only names of substances which connote nothing are proper names; and these have in reality no signification.

[¶10] If, like the robber in the Arabian Nights, we make a mark with chalk upon a house to enable us to know it again, the mark has a purpose, but it has not properly any meaning. The chalk does not say, This is my house, or This is the house which I mean to rob. The object of making the mark is merely distinction. I say to myself, All these houses are so exactly alike, that if I once lose sight of them I shall not again be able to distinguish that which I am now looking at, from any of the others. I must therefore contrive to make the appearance of this one house unlike that of the others, that I may hereafter know, when I see the mark,—not, indeed, any attribute of the house—but simply that it is the same house which I am now looking at, and wish to be able to recognize again. Morgiana chalked all the other houses in a similar manner, & defeated the scheme: how? Simply by obliterating the difference of appearance between that house & the others. The chalk was then no longer of any use for the purpose of distinction, & not serving that purpose, it served no other.

[¶11] When we impose a proper name, we perform an operation in some degree analogous to what the robber intended in chalking the house. A proper name, so far as respects ourselves (for of its uses in communicating with others we have not here to speak), is merely an unmeaning mark, which we do not, indeed, inscribe upon the object itself, but which we endeavour to connect with the idea of the object in our minds, in order that whenever the mark meets our eyes or occurs to our thoughts, we may think of that individual object. Not being attached to the thing itself, it does not enable us as the chalk does, to distinguish the object when we see it; but it enables us to distinguish it when it is spoken of, either in the records of our own experience or in the discourse of others: to know that what we find asserted in any proposition of which it is the subject, is asserted of that individual object with which we are already acquainted.

[¶12] Objects thus ticketed with proper names, resemble, until we know something else about them, men & women in masks. We can distinguish them from one another, but can conjecture nothing with respect to their real features. It is otherwise with objects which are spoken of by connotative names. Such names are not signs of the mere objects, invented because we have occasion to think and speak of these objects individually; but signs which accompany an attribute, a kind of livery in which the attribute clothes all objects which are discovered to be endowed with it. They are not mere marks, but more, that is to say, significant marks: and it is the connotation which constitutes their signification.

[¶13] A proper name, which connotes nothing, but which denotes an individual, is called the name of that individual. The importance of adhering to analogy in the employment of words, requires us in like manner to say that a connotative word is the name of what it denotes, not of what it connotes. But by knowing what thing it is the name of, we do not know the meaning of the name: for to the same thing we may often with propriety apply many names; which are not on that occasion equivalent in meaning. Thus, I call a certain man by the name Sophroniscus: I call him by another name, “the father of Socrates.” Both these names are names of the same object, the same individual human being; but their meaning is altogether different, because they are applied to that individual for two different purposes; the one, merely to distinguish him from other persons who are spoken of; the other to indicate a particular fact relating to him, viz: the fact that Socrates was his son. I also apply to him these other expressions: a man, a Greek, an Athenian, a stone-cutter, an old man, an honest man, a brave man. All these are names of Sophroniscus, not indeed of him alone, but of him and each of an indefinite number of other human beings. Each of these names is applied to Sophroniscus for a different reason, and each, if I understand its meaning, informs me of a distinct fact or number of facts concerning him. I might be informed that each of these names was applicable to Sophroniscus, and might yet not know what they respectively signified with regard to him. It is even conceivable that I might know every single individual of whom the name could be with truth affirmed, and yet could not be said to know the meaning of the name. A child knows who are its brothers & sisters, long before it has any definite conception of the nature of the fact which is involved in the signification of those terms.

[¶14^* ] In some cases it is not easy to decide with certainty, how much a particular word does or does not connote; that is, we do not exactly know (the case not having arisen) what degree of difference in the object would occasion a difference in the name. Thus, it is clear that the word man, besides animal life and rationality, connotes also a certain form; but it would be impossible to say precisely what form; that is, to decide how great a deviation from the form ordinarily found in the beings whom we are accustomed to call men, would suffice in a newly discovered race to make us refuse them the name of man. In all such cases, the meaning of the general name is so far unsettled and vague. In the particular case in question, the vagueness is of no practical moment, because it does not occasion any variableness or doubt as to the applicability of the name to any objects which actually exist, nor any material uncertainty as to what we mean to predicate when we apply it to such. But there are innumerable cases in which a vague connotation is a most serious evil.

[¶15] One of the chief sources indeed, of lax habits of thought, is the custom of resting satisfied without any more precise notion of the meaning of connotative terms, than can be loosely collected from observing what objects they are used to denote. It is in this manner that all of us acquire and inevitably so, our first knowledge of our vernacular language. A child learns the meaning of the words man or white, by hearing them applied to a variety of individual objects, and finding out by a process of generalization and analysis of which he is but imperfectly conscious, what these different objects have in common. In the case of these two words the process is so easy as to require no assistance from culture; the objects called men, and the objects called white, differing from all others by qualities of a peculiarly definite and obvious character. But in many other cases, objects bear a general resemblance to one another, which leads to their being familiarly classed together under a common name, while, without more analytic habits than the generality of mankind possess, it is not immediately apparent what are the particular attributes, upon the possession of which in common by them all, this general resemblance depends. When this is the case men use the name without any recognized connotation, that is, without any precise meaning: they talk, and consequently think, vaguely: and remain contented to attach only the same degree of significance to their own words, which a child of three years old attaches to the words, brother and sister. The child at least is seldom puzzled by the starting up of new individuals having pretensions to be his brothers and sisters, and whom he knows not whether so to denominate; because there is usually an authority at hand to solve all doubts, whose infallibility on such points is unquestionable. But a similar resource does not exist in other cases, and new objects are constantly presenting themselves to men, women, and children, which they are called upon to class proprio motu. They accordingly do this on no other principle than that of superficial similarity, giving to each new object the name of that familiar object the idea of which it most readily recals, or which, on a cursory inspection, it appears to them most to resemble. In this manner, a name which was originally appropriated to A, becomes communicated to B, then extended to C, then to D, each time, by reason of a gross and general resemblance to some only of the things which it previously denoted, until all traces of a common meaning sometimes disappear, and the word comes to denote a number of things not only independently of any common attribute, but which have actually no attribute in common, or none but what is shared by other things to which the name is capriciously refused. Even philosophers have frequently aided in this perversion of general language from its purpose, sometimes because, like the vulgar, they knew no better; and sometimes in deference to that aversion to admit new words, which induces mankind, on certain subjects, to attempt to make the original small stock of names serve with but few additions to express a constantly encreasing number of objects and distinctions, and consequently to express them in a manner progressively more and more imperfect.

[¶16] The manifold evils consequent upon this loose mode of classing and denominating objects will be further particularized and illustrated in that portion of the present work which will treat of Classification. To what a degree it has rendered almost the whole vocabulary of the mental and moral sciences, unfit for the purposes of accurate thinking is best known to him who has most reflected on the present condition of those Sciences. In the meanwhile it may here be observed that since the introduction of a new technical language as the vehicle of speculations on moral subjects would not be tolerated, and if tolerated would deprive those subjects of the benefit of the habitual feelings which have grown round the established terms and the established groups, and which would not for a long time take an equally strong hold of new ones; the problem for the philosopher, & one of the most difficult ones which he has to resolve, is, in retaining the existing nomenclature, how best to alleviate its vices. This can only be accomplished by giving to every general concrete name a definite and fixed connotation; in order that it may be known what attributes, when we call an object by that name, we really mean to predicate of the object. And the question of most nicety is, how to give this fixed connotation to a name, with the least possible change in the objects which the name is habitually employed to denote; with the least possible disarrangement (either by addition or subtraction) of that group of objects which it names, in however imperfect a manner, the circumscribe and hold together [sic]: and with the least possible vitiation of the truth of any propositions, which are commonly received as true.

[¶17] This desirable purpose of giving a fixed connotation where it is wanting, is the end aimed at whenever any person attempts to give a definition of a general name already in use. And the fact that no questions which have arisen in the moral sciences, have been subjects of keener controversy than the definitions of almost all the leading expressions, is a proof to how great a length the evil above adverted to has proceeded: every definition of a connotative name being an attempt either merely to declare, or to declare & analyse, the connotation of that name. What are the conditions which such an attempt ought to conform to, in order to be most useful, is a question that has not yet received from logicians all the attention which it seems to merit, and which will be bestowed on it in a subsequent part of the present work.

[¶18] When it is found in attempting to define any word, that no definition can be framed which will be true of all the objects which the word is used to denote; that therefore no one connotation which can be given to it, will allow of its continuing to denote all those objects; it may perhaps be found that the word is ambiguous, or, in other words, that by giving it two, or more than two separate and distinct connotations, the objects may all be brought within it. The word will then have several meanings, but all of them fixed and recognized ones; and the paucity of existing names, in comparison with the demand for them, may often render it advisable to retain the name in this multiplicity of acceptations, distinguishing these so clearly as to prevent their being confounded in future. But it will be found almost as frequently, that neither in one nor in any moderate number of fixed meanings, can the word be made truly predicable of all the objects of which it is customarily predicated. In such a case there remains no alternative, except either to do without the word altogether, or to define it in such a manner as to leave out some of the things of which it is commonly used as a name: under the disadvantage that in forbidding it to be henceforth predicated of those objects, and asserting such predications to be false, you appear to persons of illogical habits as if you asserted a paradox, when you are only mending a tool.

^[*] Thus far, in considering connotative terms, we have confined our attention to names of substances. There are two classes of names which still remain to be considered, the names of sensations, and other feelings; & the names of attributes.

All names of feelings are connotative. If, indeed, we ever gave a distinguishing name to one single feeling, to the passing sensation of an instant, the name would, like a proper name, connote nothing: there would be nothing for it to connote. But all names of sensations are names of classes of sensations; mostly indeed of classes very heterogeneous in their composition; as sound; taste; sweet taste; bitter taste; hope; fear; pleasure; pain. Even if all the sensations which enter into the class were exactly alike; if for instance we had a name to denote the exact colour of newfallen snow, & no other colour at all; still being a name common to all the sensations we have during our whole life, of that exact kind, it would be connotative; it would denote the particular sensations, & connote the kind; that is, would connote their resemblance to each other: When predicated of a present sensation, it would denote that sensation, & connote its resemblance to all the sensations we had ever had before, which were called by that name.

We have arrived, therefore, at the conclusion, that all concrete general names are connotative: whether they be names of classes of substances, or names of classes of feelings.

Abstract names for the most part are not connotative. It may be said, indeed, that they are connotative in the same manner in which names of classes of feelings are so: that whiteness, for instance, denotes the whiteness of the snow of today, the whiteness of the snow of yesterday, &c. and connotes their resemblance. I answer, no: The two whitenesses may indeed without impropriety be said to resemble: but when we use the word whiteness, we are not thinking of the resemblance of the attributes, but of the resemblance of the sensations. When I say, “Whiteness is a quality of this snow,” I am not thinking of former snow & its quality of whiteness, but of former sensations of white: The whiteness which I affirm to be an attribute of this snow, may be defined, the quality of giving me sensations similar to those former ones. What is involved, then, in the signification of the word whiteness, is not the resemblance of one whiteness to another whiteness, but of one sensation of white to another sensation of white: & it is involved not as a connotation, but as part of the denotation. The abstract name whiteness does not denote the attribute & connote the resemblance, as the concrete word white denotes the object & connotes the quality. The quality is something distinct from the object; but the resemblance is not something distinct from the attribute; it is the very meaning of the attribute; & when we have said that the abstract name signifies the attribute, we have said all that it signifies.

[¶5] Nevertheless, there are abstract names which are strictly connotative; names which denote attributes, & connote an attribute of those attributes. Such, for instance, is the word fault; equivalent to bad or hurtful quality. This word is a name common to many attributes, & connotes hurtfulness, which is an attribute not of the mere fact or phenomenon, but strictly of the attributes themselves. When for example we say that slowness, in a horse, is a fault, we do not mean that the slow movement is in itself hurtful; we mean that the property or peculiarity in a horse, of being a slow mover, is so.

[¶18,n] We may now quit the subject of connotative names. Before doing so, however, it is proper to observe, that the only modern writer, who, to my knowledge, has adopted from the Schoolmen the word to connote, has employed it in a signification different from that which is here given to it. The writer to whom I allude is Mr. Mill, in his Analysis of the Phenomena of the Human Mind. He seems to use the word in a sense coextensive with its etymology, applying it to any case in which a name, while it seems to point most directly to one thing, which is consequently termed its signification, includes at the same time a tacit reference to some other thing. In the case which we have had under consideration, that of the signification of concrete general names, Mr. Mill’s language is the direct converse of mine. Agreeing with me in considering the signification of the word to lie in the attribute, he speaks of the word as connoting not the attribute, but the thing possessing the attribute. And he describes abstract names as being properly concrete names with their connotation dropt; whereas in my view it is the denotation which should be said to be dropped, that which was previously connoted becoming now the whole signification.

My reason for preferring my own phraseology was the urgent necessity of a term to be appropriated exclusively to express the peculiar manner in which a concrete general name serves to mark the attributes which are involved in its signification. This necessity can scarcely be felt in its full force by any one, who has not gone through the whole labour of thought which has been necessary for writing this work. I think it is scarcely an exaggeration to say that some of the most prevalent of the errors which have been committed in the Philosophy of Logic, would in all probability have been avoided if a term had been in common use to express exactly what I have signified by the word to connote. And the Schoolmen, to whom we are indebted for all the rest of our logical language, gave us this also, and in this very sense. For although some of their general expressions afford a colour for using this word in the more extensive and vaguer acceptation in which it is taken by Mr. Mill, yet when they came to define it specifically, and to fix its meaning with that admirable precision which always characterised their definitions, they clearly explained, that nothing was said to be connoted except forms, which word may generally, in their writings, be understood as synonymous with attributes.

Now, if the word to connote, so well suited to the purpose to which they applied it, be diverted from that purpose by being taken to fulfil another for which it does not seem to me to be at all required; I am unable to find any expression to replace it but such as are commonly employed in a sense so much more general, that it would be useless attempting to associate them peculiarly with this precise idea. Such are the words, to involve, to imply, &c. By employing these I should fail of attaining the object, for which alone there is occasion for the name at all, namely to distinguish this particular kind of involving or implying from all other kinds, & to assure to it the degree of habitual attention which its importance demands.

[§6]

[¶1] The fourth great division of names is into positive and negative. Positive, as man, stone, good; negative, as not-man, not-stone, not-good. For every positive concrete name, a corresponding negative one might be framed. After giving a name to any one thing or to any plurality of things, we might create a second name which should be a name of all other things except that particular thing or things. These negative names might be usefully employed whenever we had occasion to speak collectively of all things other than some thing or class of things. When the positive name is connotative, the corresponding negative name is connotative likewise, but in a peculiar way, connoting not the presence but the absence of an attribute. Thus, not-white, denotes all things whatever except white things; and it connotes that they do not possess the attribute whiteness.

The non-possession of any given attribute, may itself without impropriety be called an attribute: that attribute may receive a name; and thus negative concrete names will obtain negative abstract names to correspond to them.

[¶2] Names which are positive in form, are often negative in reality, and others are really positive though their form is negative. The word inconvenient, for example, does not express the mere absence of convenience; it expresses a positive attribute, which consists in being the cause of actual pain or mischief. The same may be said of the word unpleasant, which, notwithstanding its negative form, does not connote the mere absence of pleasantness, but a less degree of what is signified by the word painful, which will be admitted to be as positive in its signification as any other. The word idle, on the other hand, though positive in its form, expresses nothing but what would be signified either by the word not-working, or by the word not disposed to work; and sober, either not-drunk or not-drunken.

[¶3] There is a class of names called privative. A privative name is equivalent in its signification to a positive and a negative name taken together; being the name of something which has once had a particular attribute, or for some other reason might have been expected to have it, but which has it not. Such is the word blind, which is not equivalent to not-seeing; for it would not, except by a poetical or rhetorical figure, be applied to a stone or to a tree. A thing is not said to be blind, unless the class to which it is most familiarly referred, be chiefly composed of things which can see; as in the case of a blind man, or a blind horse; or unless it is supposed for any reason that it ought to see; as when we say of a man, that he rushed blindly into an abyss, or of philosophers or the clergy that the greater part of them are blind guides. The names called privative, therefore, connote two things: the presence of certain attributes, and the absence of others.

[§7]

[¶1] The fifth great division of names is into relative and absolute, or, to speak more precisely, relative and non-relative.[¶2] Relative names are such as father, son; like; unlike; longer, shorter; cause, effect. Their characteristic property is that they are always given in pairs. Every relative name which is predicated of an object, supposes another object of which we may predicate either that same name or another relative name which is said to be the correlative of the former. Thus, when we call any man, a son, we suppose another man who must be called a father. When we call any event a cause, we suppose another event, which is an effect. When we say of any distance that it is longer, we suppose another distance which is shorter. When we say of any object that it is like, we mean that it is like another object, and this other may also be said to be like the first. In this last case the relative name is its own correlative. The pair of objects both receive the same name.

[¶3] It is evident that relative names, when concrete are, like other concrete names, connotative. They all denote a subject, and connote an attribute. It is to be observed, moreover, that although the objects denoted by two correlative names are different; both names connote the same attribute; or, to express the truth more accurately, what both names connote is some fact or circumstance in which both objects are alike concerned, & which, according as it is considered an attribute of the one object or of the other, gives rise to the one or to the other name.

[¶5] Thus, when we predicate of A that he is the father of B, and of B that he is the son of A, we assert the very same fact in different words. The two propositions are precisely equivalent. Neither of them asserts one tittle more or one tittle less than the other. The paternity of A and the filiation of B are not two facts, but two names for the same fact. What that fact is, every one who understands the meaning of the words, is aware. The only difference is, that the abstract term paternity is a name of the fact, considered as an attribute of A: the abstract term filiation is a name of the same fact, considered as an attribute of B.

[¶6] I said at first that both the correlative names connoted the same attribute: but, in saying this, I permitted myself a verbal inaccuracy for the advantage of a compact expression. We cannot with propriety say that paternity and filiation are one and the same attribute, otherwise to call a man father and to call him son would mean the same thing. The fact which both words, when predicated not of the same person but of two different persons, express, is, however, one and the same. And all that appears necessary, to account for the existence of relative names, is merely this, that a fact, in which two individuals are equally concerned, may be viewed & spoken of as an attribute either of one or the other, as we think fit.

[¶4] This kind of attribute is commonly called a relation; and has usually been regarded as something unusually recondite and mysterious. Why it should be more so than any other attribute, I am unable to conceive, seeing no greater difficulty to be encountered in a fact which respects two objects, than in a fact which respects only one. But this question, of the nature of Relation, will partly fall under our consideration in a subsequent chapter, & partly belongs to the higher metaphysics.

[¶7] For the present, and without prejudice to whatever conclusion may be come to hereafter on the subject of Relation, Relative names may be provisionally defined as follows. A name is called relative, when, in addition to the object which it denotes, it implies in its signification the existence also of another object, also deriving a denomination from the same fact which is connoted by the first name. Or, (to express the same thing in other words), a name is said to be relative, when, being the name of one thing, its signification cannot be explained but by mentioning another. Or we may state it thus: when the name cannot be employed in discourse so as to express a meaning, unless the name of some other thing than what it is itself the name of, be either expressed or understood. We may take our choice among these definitions. They are all, at bottom, equivalent; being modes of variously expressing this one distinctive circumstance, that all the other attributes of an object might be conceived, without a contradiction, still to exist, if all objects besides itself (or at any rate all except itself and the percipient mind), were at once annihilated: But those of its attributes which are expressed by relative names, would, on that supposition, be swept away.

[§8]

[¶1] Names have been further distinguished into univocal and æquivocal: these, however, are not two kinds of names, but two different modes of employing names. A name is univocal, or applied univocally, with respect to all those things of which it can be predicated in the same sense: but it is æquivocal, or applied æquivocally, as respects those things of which it is predicated in different senses. It is scarcely necessary to give instances of a fact so familiar as the double meaning of a word. In reality, an æquivocal or ambiguous word, is not one name, but two names, accidentally coinciding in sound. File standing for an iron instrument, and file standing for a row of soldiers, have no more title to be considered one word, than grease and Greece have, merely because they are pronounced alike. They are one sound, appropriated to form two different words.

[¶2] An intermediate case is that of a name used analogically or metaphorically; that is, a name which is predicated of two things, not univocally or in exactly the same signification, but in significations somewhat similar, and derived one from the other; as when we speak of a brilliant jewel, and a brilliant achievement. The word is not applied in the same sense to the jewel and to the achievement; but, having been applied to the jewel in its original sense, that of brightness to the eye, it is transferred to the achievement in a derivative signification supposed to be somewhat like the primitive one. The word, however, is just as properly two names instead of one, in this case, as in that of the most complete ambiguity.

The different kinds of ambiguity or æquivocalness in names, the various disguises under which those ambiguities escape from detection, and the incorrect reasoning, incorrect generalization, and incorrect classification, of which they are the fruitful source, will be considered and illustrated in that part of the present work which treats of Fallacies.

CLASSIFICATION OF THINGS

[Chapter iii: Of the Things denoted by Names]

[§1]

[¶1^* ] We have now made sufficient progress in the analysis of the meaning of names for the purpose of that portion of our enquiry in which we are at present engaged. Much more indeed is required to complete such a theory of names as may suffice to form the Scientific basis of an Art of Nomenclature. This, however, will belong to a subsequent part of the work. Our object at present is merely to analyse the import of Propositions. In the pursuit of that object, since everything which is capable of receiving a name may be made the subject or the predicate of a Proposition, we found it necessary to enter into the question, What things are there, capable of receiving names? To facilitate the enquiry, we examined what are the things signified by the existing names. And we have carried this examination sufficiently far, to enable us to turn to the contemplation of the things themselves, without incurring the danger of overlooking any class of entities, recognized by the existing nomenclature and thence making such an enumeration of things as shall leave any class of Names destitute of an appropriate meaning.

[¶2] The necessity of an enumeration of Entities as the Basis of Logic did not escape the attention of the schoolmen, nor of their master, Aristotle, the most comprehensive, though not the most penetrating, of the ancient philosophers. The categories, or predicaments, the former a Greek word, the latter its literal translation in the Latin language, were intended by him & his followers as an enumeration of all things capable of being named; an enumeration by the Summa genera, i.e. the most extensive classes into which Things could be distributed, there being no other mode of enumerating individuals of indefinite number. The following are the classes into which, according to these philosophers, all things nameable might be reduced:

[¶3] The imperfections of this classification are too obvious to require, and its merits are not sufficient to reward, a minute examination. It is a mere catalogue of the distinctions rudely marked out by common language, with little or no attempt to penetrate, by philosophic analysis, to the rationale even of those distinctions. Such an analysis, even though imperfect, would have shewn that the enumeration is both redundant & defective, some objects being omitted, & others repeated over and over under different heads. It is not unlike a division of animals into men, beasts, horses, asses, and ponies. That, for instance, could not be a very comprehensive view of the nature of Relation, which could exclude Action, Passion, & Local Situation, from that category. The same observation will apply to the categories Ubi and Quando; though not so obviously. On the other hand, Sensations, & Feelings in general, are excluded from the enumeration. The impropriety of erecting into a Summum genus the class which forms the tenth category, is manifest.

In so far as the ten categories of Aristotle contain any distinctions which appear worthy to be preserved in the present more advanced state of analytical psychology, they will be included, by implication at least, in the attempt which we are about to make towards a better enumeration of summa genera, or classed Catalogue of Nameable Things.

[§2]

[¶1] It is indispensable, before we commence, to take notice of a very unfortunate ambiguity in all concrete names which correspond to the most general of all the abstract names, the word Existence. When we have occasion for a name which shall be capable of denoting whatever exists,—or in other words, (for the expressions are convertible) whatever is capable of being made a separate object of thought, and of receiving a separate name—there is hardly a word applicable to this purpose, which is not also, and even more familiarly, taken in a sense in which it denotes only substances. But substances are not all that exists; sensations also exist; and according to all systems of philosophy, however opposite, attributes may be asserted to have a real existence, with as much propriety as substances. Yet when we speak of an object, of a thing, we are almost always supposed to mean a substance. There would seem to be a kind of absurdity in using such an expression as this, that a thing may be merely an attribute of another thing: and at first sight of the heading of this chapter, “Classification of Things,” there are, I believe, few persons who would not be led to expect a classification like that of naturalists, starting with the three great divisions of Animal, Vegetable, and Mineral, and subdividing these into classes and orders. If, rejecting the word Thing, we endeavour to find another of a more general signification, or at least more exclusively appropriated to that general signification; a word, denoting all that exists, and connoting nothing but simple Existence, no word might be presumed fitter for our purpose than Being; originally the present participle of a verb which in one of its meanings is exactly equivalent to the word exist; and therefore suited, even by its grammatical construction, to be the concrete of the abstract Existence. But this word, strange as it may appear, is even more completely spoiled for the purpose which it seems expressly made for, than the word Thing. Being is, by custom, exactly synonymous with Substance; except that it is free from a slight taint of ambiguity, being applied impartially to Matter & to Mind; while Substance, though originally in strictness applicable equally to both, is apt to suggest preferably the idea of matter. A Sensation is never called a Being; nor is an attribute ever called a Being. A Being is that which causes Sensations, that which possesses attributes. The soul may be called a Being; God, and Angels may be called Beings; but if we were to say, Extension, Colour, Wisdom, Virtue are Beings, we should perhaps be suspected of thinking with some of the ancients, that the cardinal virtues are animals; or at least, of holding, with the Platonic School, the doctrine of self-existent ideas, or with the followers of Epicurus, that of Sensible Forms, which detach themselves in all directions from bodies, and, coming casually in contact with the human organs, are the causes of our sensations. We should be supposed, in short, to believe, that Attributes are Substances.

[¶2] In consequence of this perversion of the word Being, philosophers, looking about for something to supply its place, laid their hands upon the word Entity, a piece of barbarous Latin, invented by the Schoolmen to be used as an abstract name, in which class, by its form, it would seem to place itself, but being seized by logicians in distress, to stop a leak in their terminology, has ever since been used as a concrete name. The Kindred word Essence, born at the same time ^[*] and of the same parents, scarcely underwent a more complete transformation, when, from being the abstract of the verb to be, it came to denote something sufficiently concrete to be contained in a glass bottle. The word Entity, since it settled down into a concrete name, has retained its universality of signification somewhat less unimpaired than any of the names before mentioned. Yet the same gradual decay, which seems to affect all the language of psychology after a certain age, has been at work even here. If you call virtue an entity, you are indeed somewhat less strongly suspected of believing it to be a substance, than if you called it a being; but even then you are not quite sure that no more meaning will be taken than you intended to give. Every word which originally was intended to connote mere existence, seems after a time to enlarge its connotation to separate existence, or existence freed from the condition of belonging to a substance; which condition being precisely what constitutes an attribute, attributes in this manner are gradually shut out. Strange that when the greatest embarrassment of all who have many thoughts to express, is to find a sufficient number of words wherewith to express them, there should be no practice which philosophers are more addicted to, than that of taking valuable words to express ideas which are sufficiently expressed by other words already appropriated to them.

[¶3] When it is impossible to get good tools, the next best thing is to know accurately the defects of those we have. I have therefore warned the reader of the ambiguity of the very names which, for want of better, I am necessitated to employ. It must now be the writer’s endeavour so to employ them, as in no case to leave his meaning doubtful or obscure. No one of the above words being altogether unambiguous, I shall not confine myself to any one, but shall employ on each occasion that word, the associations connected with which will least conflict with those which must be excited in order that what I have to say may be understood. The word Thing, being the least spoilt of any which are equally familiar, is that which I shall most frequently make use of. [¶4] The difficulty under which, in spite of all I can do, I must expect that both myself and my reader will labour in the attempt to use vague words with a precise meaning, is not wholly a matter of regret to me. Philosophical language will for a long time, and popular language, perhaps, forever, retain so much vagueness and ambiguity, that Logic would be of little use, if it did not, among its other advantages, exercise the understanding in performing its work neatly and correctly with imperfect tools.

[§6]

[¶1] All Things, then, are either Feelings, substances or attributes: or, to state the same proposition in other words, every name except the names of feelings, is either the name of a Substance or the name of an Attribute. These words, Substance and Attribute, are of so much importance in the Philosophy of Logic, that it is highly desirable to fix their meaning with precision. But it is scarcely possible to define strictly the distinction between them, without trespassing into the higher metaphysics. Nor is this absolutely indispensable for most of the purposes of this work; it would perhaps be sufficient to take the distinction for granted, & to suppose that the reader can tell a substance from an attribute, whether he be capable of metaphysically analysing the two notions or not. Nevertheless not to omit an enquiry so intimately connected with my subject, I shall attempt as much of the analysis of each as seems necessary for an accurate conception of the difference between them.

[¶2] Logicians have endeavoured to define Substance and Attribute: but their definitions are not so much attempts to point out the distinction between the two ideas, as instructions what difference it is customary to make in the grammatical construction, according as you are speaking of substances or of attributes. Such definitions are rather lessons of English, or of Latin or Greek, than of mental philosophy. An attribute, say the Schoolmen, must be the attribute of something: whiteness, for example, must be the whiteness of something; goodness must be the goodness of something. And if this something should cease to exist, or should cease to be connected with the attribute, the existence of the attribute would be at an end. A substance, on the contrary, is self-existent; when we are speaking about it, we need not put of after its name: a stone is not the stone of anything; the moon is not the moon of anything, but simply the moon. Unless, indeed, the name which we choose to give to the substance be a relative name: if so, it must be followed either by of, or by some other particle, implying, like that preposition, a reference to something else: but then the other characteristic peculiarity of an attribute would fail: the something might be destroyed, and our substance might still subsist. Thus, a father must be the father of a child, and so far resembles an attribute, in being referred to something besides himself: if there be no child, there can be no father: but this, when we look into the matter, only means that we should not call him father, as he would no longer come within the meaning of that term. The man called father might still exist, though not only the child, but all the universe, himself excepted, were destroyed; that is, the supposition would involve no contradiction. But destroy all white substances, and where would be the attribute whiteness? To suppose that it still continued to exist, would be a contradiction in terms.

[¶3] This is as near an approach towards a solution of the difficulty as will be found in the treatises on Logic; metaphysicians, however, have probed the question deeper. And in truth the above explanation was anything but satisfactory. If an attribute is distinguished from a substance by being the attribute of something, it seems highly necessary to explain what is meant by of: that pregnant particle, which, on this shewing, carries the whole of Intellectual Philosophy in its womb. And as for the self-existence of Substances, it is very true that a Substance may be conceived to exist without any other substance, but so also may an attribute without any other attribute; and we can as little imagine a substance without attributes as we can an attribute without a substance.

[¶4] Since, however, every attribute is an attribute of a substance, let us consider, in the first place, Substances. These are commonly divided into Bodies & Minds.

[§7]

[¶¶1,2] It would be remote from our purpose to embark in the controversy on which so much ink has been expended, that of the Existence of Matter as a Being in itself, distinguishable from the sensations or states of consciousness which it generates in sentient beings. This question belongs to the higher metaphysics; and I may add, that I am aware of no inquiry more utterly fruitless and barren, saving always the advantage of learning to think justly on any subject on which we are compelled to think. For the tyro, at least, in logic, nothing is more to be desired than that he should never even hear that such a question had been raised. In an Enquiry into the Philosophy of Logic, it is, however, indispensable to state the question, though but for the purpose of putting it aside.

[¶3] It is certain, then, that part of our notion of a body consists of the notion of a number of sensations of our own, or of other sentient beings, habitually occurring simultaneously. Our conception of a block of granite, for instance, is compounded of its visible form and size, which are complex sensations of sight; its tangible form and size, which are complex sensations of our organ of touch and of our muscles, its weight which is a sensation of touch and of the muscles, its colour which is a sensation of sight, its hardness which is a sensation of the muscles, its chemical properties which are said to be perceived by our various senses, and which are in reality nothing but sensations received through those senses. All these various sensations frequently are, and, as we learn by experience, always might be, experienced simultaneously: whence the thought of any one of them comes to excite the ideas of the others, and the whole become mentally amalgamated into one mixed state of consciousness, which, in the Language of Locke & Hartley, is called a complex idea, and which, though a compound of so many heterogeneous elements, has the appearance of being instantaneous and indivisible. With these feelings called sensations, other states of feeling frequently intermix themselves, of the kinds called thoughts, and emotions; for many objects, besides the impression they produce on our senses, excite in our minds other states of consciousness to which we give these other names.

[¶4] Now, there are philosophers who have argued thus: If we take an orange, and conceive it to be divested of its natural colour, without acquiring any new one; to lose its softness without becoming hard, its roundness without becoming square or polygonal or of any other figure whatever; to be deprived of its size, of its weight, of its taste, of its smell, to lose all its mechanical and all its chemical properties and acquire no new ones; to become, in short, invisible, intangible, inaudible, & without taste or odour; nothing would remain. Of what nature, in fact, could be the residuum? and by what tokens could it manifest its existence? And if there do really exist such a residuum, let us imagine it to be this instant annihilated by the fiat of omnipotence, by what signs should we be able to discover that it had ceased to exist? Should we not have as much reason to believe [in] its existence, after its annihilation had been accomplished, as we have now? But if its removal would make no change in our consciousness, we are not now conscious of its existence. Hence these metaphysicians were led to conclude, that what we call a Body is nothing distinguishable from the sensations which it is said to produce in us. They characterised an object as merely a bundle, group, or cluster of sensations. The philosophers who took this view of the nature of bodies, were said to deny the existence of Matter.

[¶5] Other philosophers, on the contrary (and this is the prevalent opinion) contend that an object is not a group of sensations only, but the sensations & something else; or rather, that the object is not the sensations, but something which we regard as the immediate cause of the sensations. The schoolmen used to call it a substratum, and supposed that its attributes inhered in it, as they expressed themselves; literally stuck in it. This language is now exploded; but the idea which it was intended to express still remains. To this substratum, the name Matter is usually given in philosophical discussions. It was soon, however, acknowledged by all who reflected on the subject, that it was impossible to prove, by extrinsic evidence, the existence of Matter. Being asked, therefore, how they knew it, they answered, by direct intuition. And here, according to the definition formerly given, the inquiry enters into the field of Transcendental Metaphysics; where we intend to leave it.

[¶6] While, however, philosophers have been thus divided on the question whether objects are anything besides our sensations, the only point which is of much real importance, is one on which there has at length been brought about a very general agreement: viz: that all we know of objects is merely the sensations which they give us. Kant himself, on this point, is as explicit as Berkeley or Locke. There are few Ontologists among modern metaphysicians. However strongly they may be convinced that there exists a universe of “things in themselves,” totally distinct from the universe of Phenomena, or things as they appear to our senses; and even though they may invent, like Kant, a technical expression as Noumenon, to denote what the thing is in itself, as contrasted with the representation of it in our minds; they nevertheless allow that this representation, which is a mere compound of our own sensations, is all we know of the object, and that the real nature of the thing itself, is, and by the constitution of our faculties must ever remain, an impenetrable mystery to us. [¶7] There is not the slightest reason for believing that what we call the sensible qualities of an object bear any affinity to the nature of the object itself. The object is merely the cause of them: and a cause does not always resemble its effects; a north wind is not at all like the feeling of cold, nor a coal fire like the steam of boiling water: why then should matter, the cause of our sensations, resemble the sensations themselves? [¶6,n] An attempt has indeed been made by Dr. Reid to establish that although some of the properties which we ascribe to objects exist only in our sensations, others really exist in the things themselves, being such as cannot possibly be copies of any impression on the senses; and he asked, with a triumphant air, from what sensation our notions of extension and figure can have been arrived [sic]? These, according to him, must be qualities of things in themselves, known to us like the existence of those things, intuitively. The gauntlet thrown down by Dr. Reid was taken up by Dr. Brown: who, applying greater powers of analysis than any of his predecessors had done to the notions of extension & figure, shewed clearly what were the sensations from which those notions were derived, and of the ideas of which, they were compounded: viz: sensations of touch, combined with sensations of a class previously too little adverted to by metaphysicians, those which have their seat in our muscular frame. Whoever wishes to be more particularly acquainted with this admirable specimen of metaphysical analysis, may consult the first volume of Brown’s Lectures, or Mill’s Analysis of the Phenomena of the Human Mind. To introduce the discussion here, would swell an inquiry essentially subordinate and parenthetical, into such a bulk as to detain the mind longer than is desirable on its passage from what precedes to what follows.

[§9]

[¶¶1,2] Since, then, we know nothing of bodies, except the sensations and other states of feeling or consciousness which we are said to derive from them; and these being either permanent or changeable; it evidently follows, that the sensations or states of consciousness excited by an object, and the changes in those sensations or states of consciousness, constitute its attributes.

Sensations, or rather states of feeling, excited by objects taken one by one, form that kind of attributes commonly called the qualities of objects. Sensations or other states of feeling excited by two or more objects jointly, and which could not be produced by the same objects taken separately, form that kind of attribute called a relation: a relation among these objects; a relation between each one of them and all the rest.

Those propositions require some elucidation.

[¶3] Let us take, for the purpose of illustration, any one of what are termed the sensible qualities of objects. Say, for example, whiteness. When we ascribe whiteness to any substance, as for instance, to snow; when we say that snow has the quality of whiteness, what is it we really assert? Simply, that when snow is present to my organs, I have a particular sensation, which I am accustomed to term the sensation of white. But how do I know that Snow is present? Obviously by the sensations which I derive from it, and not otherwise. According to one theory my consciousness of these sensations is all I really mean by the presence of the object; according to another theory it only proves the presence of the object. We shall not inquire into this. The object, however, is neither more nor less than a cluster of sensations, or an unknown something which gives me a cluster of sensations. And when I ascribe to the object the attribute whiteness, my meaning is only that of this group, or series of sensations, whether simultaneous of successive, that which I call the sensation of white forms a part.

[¶4] An objection may here be made. It may be admitted that we know nothing of sensible objects, except the sensations which they excite in us: that the fact of our receiving from Snow that particular sensation, which we call the sensation of white, is the only ground we have for ascribing to that substance the quality whiteness; the only proof that Snow possesses that quality. But because one thing may be the sole evidence of the existence of another thing, it does not follow that the two things are one and the same. The attribute whiteness, it may be said, is not the sensation, nor the fact of our receiving the sensation, but something in the object itself; a power inherent in it; something which produces the sensation; which is the real cause of its being excited when the object is presented to our organs. And when we affirm that Snow possesses the attribute of whiteness, we assert not merely that the presence of snow produces in us that sensation; but that it does so by virtue of this mystical entity, called a quality.

[¶5] For this doctrine of the existence of a distinct and peculiar species of entities termed qualities, I can see no foundation except in a tendency of the human mind, which is the cause of many delusions. I mean the disposition, wherever we meet with any two names which are not precisely synonymous, to suppose that they must be the names of two different things,—whereas in reality, both are often names of the same thing, viewed (to use a popular expression) in different lights. Thus, in the present case, because quality and sensation cannot be put indiscriminately one for the other, it is supposed that they cannot both of them signify the same thing, viz: the impression or feeling with which we are affected when we see any white object: although there is at least no absurdity in supposing that this identical impression or feeling may be called a sensation when considered merely in itself, & a quality when regarded as accompanying or as emanating from any one of the numerous objects, the presence of which to our organs, excites in our minds that among various other sensations or feelings.

If this be not a sufficient account of the meaning of the word quality, it rests with the believers in an entity per se bearing that name, to produce some proof of its existence. Until they do so, their opinion can only be held to be a lingering remnant of the Scholastic doctrine of occult causes; the very absurdity, in fact, which is so happily ridiculed by Moliere, when he makes one of his pedantic physicians account for the fact that “l’opium endormit” by the maxim “parcequ’il a une vertu soporifique.”

[¶6] It is evident that when the physician stated that opium had “une vertu soporifique,” he did not account for, but merely asserted over again, the fact that it “endormit.” In like manner, when we assert that snow has the quality of whiteness, we are only affirming over again in more technical language, that it excites in us the sensation of white. The other expression conveys no explanation, because it informs us of no new fact, or, if of any, of one which is not conceivable by our faculties, and cannot be proved to be true. If it be said that the sensation must have some cause, I answer, undoubtedly; the presence of the object is that cause. When I have asserted, that whenever the object is present and my organs in their natural state, the sensation takes place, I have stated all that I know or can know about the matter. I have stated the effect, and assigned its cause. I have no occasion, in addition to this certain and intelligible cause, to suppose an occult cause besides. If I am asked, why does the presence of the object cause this sensation in me, I cannot tell; I can but say, because such is the law of my nature, & of the nature of the object: the Author of the universe, or the constitution of things, will have it so. And this, after all, is what we must come to at last, even when we have interpolated the imaginary entity. Whatever number of links the chain of causes and effects may consist of, how any one link produces that which is next to it remains still equally inexplicable to us. It is as easy to comprehend that the object should produce the sensation directly and at once, as that it should produce the same sensation by the aid of a third entity called the power of producing it.

[¶7] If, however, any reader considers these arguments insufficient, and still holds to the belief that a sensible quality is something different both from the sensation in our minds, and from the object which produces that sensation, I shall not argue further with him in this place, but refer him to the higher metaphysics, to which Science this, as part of the great question of Causation or Power, properly appertains. It rests with that Science to determine whether we have an intuitive perception of Qualities or Attributes in the sense which persons of these views attach to the words. For, all persons having any pretension to the character of philosophers, who believe that such entities exist, have been reduced to the necessity of admitting that we cannot prove their existence, so that they are either known to us intuitively or not at all. Should the conclusion be that they really exist, it will not vitiate the subsequent part of this work, the deductions of which do not in any material degree depend upon the view which I have taken of the nature of Attributes. For my purpose it is sufficient that some names are names of objects, and some of attributes, and some are names of objects, connoting attributes. All this is true, in whatever way we may analyse Attributes, or though we should not analyse them at all.

[§10]

[¶1] We have thus far attended only to those attributes which are commonly called qualities: being those which respect only the object itself, and us, the sentient mind; & which would remain, if we were to suppose all other objects annihilated. These attributes we have found to consist of the various sensations, or groups or trains of sensations, which the object causes us; or of the other feelings of all sorts, the purely mental, as they are called, which the contemplation of it excites in our minds.

But there is another class of attributes, the conception of which necessarily includes the ideas of other substances besides the object itself to which the attribute is ascribed. These attributes of an object are called its relations to other objects. The observations in the preceeding chapter on relative names, united with what has just been said on the nature of the first class of attributes, render it easy for the reader to anticipate the view which will be taken of the nature of the attributes to be now adverted to.

[¶2] It is certain that there may, with propriety, be said to be a relation between any two things, to which two correlative names are or may be given. This is only inverting the tritest and least disputable (though least significant) definition of a relative name: viz: that it is a name which signifies a relation. By enumerating, therefore, the principal cases in which mankind have imposed correlative names, & observing what all those cases have in common, we may expect to discover, if it be discoverable, what is that which constitutes a relation.

[¶3] What then is the character, which is possessed in common by states of circumstances so heterogeneous & discordant as these:—one thing like another, one thing unlike another; one thing near another, one thing far from another; one thing before another, one thing after another, one thing along with another; one thing greater, equal, less than another; one thing the cause of another, one thing the effect of another; one person the father, child, master, servant, husband, wife, sovereign, subject, attorney, client, of another; & so on?

[¶4] There seems to be nothing whatever that is common to all these cases, except only this; that in each of them there exists or occurs, or has existed or occurred, some fact or phenomenon, into which both the things which are said to be related to each other, enter as parties concerned. This fact or phenomenon, the Aristotelian philosophers called the fundamentum relationis. Thus, in the relation of greater and less between two lines or surfaces, the fundamentum relationis is the fact that when one of the two magnitudes is applied to the other, it does not entirely cover it. In the relation of husband and wife, the fundamentum relationis is, that the parties are a man and a woman, that they have promised certain things with certain formalities, and are in consequence invested by the law with certain rights and subjected to certain duties. It would be easy to multiply examples. It is obvious that when we examine the signification of a relative name, and find out correctly and completely what it connotes, that forms the fundamentum of the relation which that relative name is said to express.

[¶5] Now, examination will shew that this kind of attributes, like that which we previously enquired into, consists of nothing whatever but states of human consciousness. In the highly complicated case last cited, for example, the relation of husband & wife, the fact or phenomenon which is the fundamentum relationis, and which is of an extremely complex nature, is wholly composed of the following elements, viz: 1. Sensations, thoughts, emotions, and volitions of the parties themselves. 2. Sensations, thoughts, emotions, and volitions of other people, excited by acts of the parties themselves, or which would be excited were they to act in a particular way: the intentions, for instance, which would be formed by a Judge, in case a complaint of the violation of the conjugal engagement were brought before his tribunal; and the acts which the Judge would perform in consequence. If it be asked what an act is, it is nothing whatever but one of the states of consciousness called volitions, causing in the mind either of the individual himself, or of some other individual, one of the states of consciousness called sensations. The whole, therefore, resolves itself into states of consciousness; human feelings, either bodily (as they are called) or mental: feelings, however, which are not excited by one of the two related objects, but by both of them taken together. In the case of the complicated matter of fact, connoted by the words husband & wife, all the simpler matters of fact which make it up are states of things which concern one of the two persons in precisely the same degree as the other; and no other object except those two, is concerned in all of them.

[¶6^* ] All cases of relation are not so complicated as that to which we last alluded. In the case of nearness for instance, or remoteness in place, the fundamentum relationis is the two objects themselves, with the space intervening between them. In the case of likeness, it is 1. the two objects in juxtaposition, or the ideas of the two objects succeeding one another in our minds, and 2. that state of consciousness called the feeling of resemblance (in whatever way we may analyse this feeling) immediately succeeding the contemplation of them. In the case of antecedent & consequent, as between two events, the fundamentum of the relation is the events themselves, succeeding one another in order of time. But an event is merely a change; one thing ending or another beginning; an object ceasing to exist, or ceasing to cause certain sensations; or another object beginning to exist, or beginning to cause certain sensations. Whatever relation we examine, we still find nothing except the related objects, and the sensations or other states of consciousness which they excite. And we may consequently consider it as proved, that the attributes commonly called relations as well as those commonly called qualities, are but names for states of the consciousness of sentient beings, considered as excited by objects.

[§14]

[¶1^† ] We have hitherto spoken only of the attributes of bodies. Minds also have attributes: but the analysis of these, after what has preceded, presents little difficulty. The attributes of minds, like those of bodies, are merely states of feeling or consciousness. But in the case of a mind we have to consider its own states of feeling or consciousness, as well as those which it excites in other minds. Every attribute of a mind consists either in being affected in a certain way, or affecting other minds in a certain way. In the former case, nothing is implied, external to the mind itself, not even the existence of another percipient mind.

The only attributes which can with truth be ascribed to a mind, without reference to any other substance, either mental or corporeal, are its own various states; that is to say, the actually being in one of those states, or the liability to be in one of them. Now, all in the mind which even the mind itself is aware of, is a certain thread of consciousness; a certain series of feelings, that is, thoughts, volitions, sensations, & emotions, more or less numerous and complicated. Respecting mind as respecting body, there are two systems of philosophy. The one holds that the mind itself is this thread of consciousness, & nothing more; the other, that there is the thread of consciousness, and likewise a something which is conscious, a thinking principle, as it has been called, a peculiar kind of being, called a mind. To decide between these two theories belongs not to Logic, but to the more abstruse Science so often alluded to. But whichever of these two theories may be true; whether what I call myself, be only the series of feelings which I experience, and which constitute my sentient existence, or whether there be these feelings and something besides these feelings called myself; it must in either case be admitted that of any self, other than the series of my feelings, I do not & cannot know anything except its bare existence. As bodies only manifest themselves to me through the sensations which I feel when they are present, so the thinking principle, or mind, in myself, makes itself known to me only by the feelings of which it is conscious. We can predicate no quality of it, considered in itself, but the series of its own feelings. When we say of any mind that it is devout, or superstitious, or meditative, or cheerful, we mean that the ideas, emotions, and volitions implied in those words, form a frequently recurring part of the series of feelings or states of consciousness, which fill up the existence of that mind.

[¶2] Besides those attributes of a mind which consist of its own states of feeling, we may also ascribe attributes to a mind as well as to a body, considered as an object of contemplation to other minds. The most important instance of this is, the employment of terms expressing approbation or blame. When, for example, we say of any mind, that it is admirable, we mean, that the idea of it excites the sentiment of admiration in us, together with the feeling of moral approbation, for the word implies that we not only feel admiration, but approve that feeling in ourselves. Just as when we say of snow that it is white, we mean that the perception of it excites in us the sensation of white.

In some cases, under the semblance of one single attribute, two are really attributed, one of them a state of the mind itself, the other a state with which other minds are affected by the contemplation of it. As when we say of any man that he is generous. The word generosity expresses a certain state of mind; but it also expresses that this state of mind excites in us another mental state called approbation. The assertion, therefore, really made is double; and of the following purport: Certain feelings form a frequent part of this person’s thread of consciousness, and moreover the idea of those feelings of his, excites in us the sentiment of approbation.

^[*] Minds as well as bodies may be related in a variety of ways, to other minds, & to bodies. A mind may be like, or unlike, another mind; it may be prior or posterior in order of time, to another mind, or to a body: a mind may perceive, & a body may be perceived; a body may act upon a mind, that is, may cause it to be conscious of certain feelings: a body may be acted upon by the mind which animates it, that is, the mind may cause the body to act in a particular way on its own or other minds. These relations between minds, and between body & mind, require no other explanation from us, than that already given of the relations between bodies.

[§3, ¶3^* ] So much for the attributes of bodies and of minds. It is now necessary to recal the reader’s attention to a remark already made; that the division of all things into substances & attributes, and of substances into bodies & minds, and consequently of all things whatever into bodies, minds, and attributes, is not exhaustive^[†] . A sound, for example, cannot be said to be either a body or a mind; yet it is not an attribute. Sonorousness is the name of an attribute, but sound is a concrete name. It is a name for a certain sensation considered in itself, not implying that it emanates from any object. We know in point of fact that sounds always are produced by objects; but we can conceive that the case might be otherwise. We may conceive everything annihilated in the universe, except sounds, and ourselves hearing them. If we shut our eyes and listen to music, we may form to ourselves a conception of such a universe.

In like manner, hope, joy, fear, are names of other states of consciousness, considered independently of the mind which is conscious of them. If we considered them as states of any particular mind, or even thought of them as modifications of a substance called a mind at all, the words we should use would be hopingness, or hopefulness, or a state of hope, but not hope simply. Hope is a concrete name. Hopingness and hopefulness are abstract ones.

In this class of nameable objects, we must rank names themselves, and other portions of discourse; these being either sounds, or written characters. Thus, noun, verb, &c. are names of names.

We have thus three classes of names. Names of substances; i.e. of the bodies which excite and the minds which experience feelings; Names of attributes, i.e. of feelings, considered as excited or experienced by substances; and names of the feelings considered in themselves.

Substances may have attributes; feelings or states of consciousness may have attributes; and attributes themselves may have attributes.

Of the attributes of substances enough has been said. The attributes of feelings and the attributes of attributes themselves, present scarcely any additional difficulties.

The qualities of which a feeling, or a combination of feelings or a series of feelings, is susceptible, seem to consist only in being composed of certain parts, and in exciting certain ideas and emotions in our own mind when it thinks of them. All the other attributes of a feeling are relations. Such is, for instance, the attribute of belonging to a certain mind: for this supposes something other than the feeling itself and its parts and our mind contemplating the feeling: it supposes a mind to which the feeling belongs.

It is not necessary to enumerate all the possible relations of a feeling, or series of feelings. A feeling may be like, or unlike, another feeling, and so related to the feeling: it may be like or unlike a feeling of another mind; and so related to that mind. A feeling may be excited or caused by a body, or by a mind, or by a feeling; and in its turn it may cause another feeling. All these relations of feelings, correspond to relations of precisely the same nature between bodies; and whatever explanation suffices for the latter, will serve equally for the former.

Remains only the attributes of attributes. But neither in the analysis of these is there any peculiar difficulty.

An attribute is never said to be composed of parts. The sensation or other state of consciousness which constitutes the attribute, may be composed of parts; but however complex the matter of fact may be, the attribute itself is considered to be one and indivisible.

An attribute, however, as well as a subject, may be an object of thought or contemplation to a percipient mind; and being contemplated, may excite in that mind any thought or emotion. To excite any state of consciousness is itself an attribute; one of those which we have named qualities. An attribute, therefore, may have qualities, when considered as an object of contemplation to a mind.

An attribute may also have relations. We may say that one attribute resembles another; that one attribute is the cause, or effect, of another. The meaning of this is obvious. What constitutes an attribute being always some phenomenon, that is, some state of consciousness,—some feeling, or combination or series of feelings; when we say that one attribute resembles another, the resemblance which really exists is between the feelings, or combinations of feelings, which constitute those attributes respectively: and when we say that an attribute is the cause, or the effect of anything, the real cause or effect is either the feeling constituting the attribute, or the object to which the attribute belongs.

^[*] A relation may exist even between relations. One relation may resemble another; one relation may coexist with another; one relation may succeed to another; one relation may cause another. In all these cases, what really resemble, or coexist with, or succeed, or cause each other are the facts or phenomena, the complicated states of consciousness, which, when considered as proceeding from the conjunction of two or more objects, are called relations. [§11, ¶3] The case of resemblance between relations is one of the commonest of all the cases in which an attribute is ascribed to attributes. Thus, the relation in which Priam stood to Hector, namely that of father and son, resembles the relation in which Philip stood to Alexander: resembles it so closely that they are called the same relation. This means that in the complicated set of phenomena which constitutes the fundamentum of the relation between Priam and Hector, and that other set of phenomena equally complicated which constitutes the fundamentum of the relation between Philip & Alexander; as much of each of these two histories (for they are nothing less) as is signified by the words father and son, is exactly the same, or (to speak with stricter propriety), undistinguishably alike, in the two cases.

When two attributes are united, or coexist, there is a resemblance of relations. The two attributes stand in the same relation to the same substance; they both of them are attributes of it: the same substance excites both sets of sensations or feelings.

[§11, ¶4] There are other cases in which relations resemble, yet not so closely as to be called the same relation. Thus, we may say, that a thought suggested to the mind of a person of genius is like a seed cast into the ground, because the former produces a multitude of other thoughts, and the latter a multitude of other seeds. This is saying that between the relation of an inventive mind to a thought contained in it, and the relation of a fertile soil to a seed contained in it, there exists a resemblance: but no one would think of saying that there existed an identity. It is indeed evident that when two pairs of objects are concerned respectively, in two sets of phenomena, the slightest resemblance between these sets of phenomena will admit of its being said that the relation between the first pair and the relation between the second resemble one another.

[§11, ¶5] Whether we say that two objects resemble, or two qualities of objects, or two relations of objects, we always mean the same thing: that the sensations which we receive from the two objects,—or such part only of those sensations as constitute the two qualities,—or such complicated sets of sensations, (including those excited by the two objects) as constitute the two relations,—that these two sets of sensations in short, whether they are experienced together or only thought of together, are followed in our minds by a certain feeling, which, for want of any more appropriate name to express it by, we call the perception of resemblance. This feeling, the task of analysing which does not belong to Logic, may exist, like almost all other feelings, in different degrees. When it exists in the highest degree of all, i.e. when the two things, if perceived separately, could not be distinguished from one another, the resemblance is often called identity, and the two things are said to be the same: as when we say that the sight of any object, gives me the same sensation or emotion to-day that it did yesterday. This is an evident though often an inevitable, misapplication of the words “the same:” for the feeling which I had yesterday is gone, and never can return; that which I have to-day is another feeling, different from the preceeding, though so exactly like it, that no trace of any dissimilarity can be perceived. I think it will be found that great confusion of ideas is often produced, and many fallacies engendered in otherwise enlightened understandings, by the habit of always confounding under one name ideas so different as those of perfect likeness & identity. The Schoolmen had appropriate names to express this as well as many other distinctions, which philosophers have lost the habit of attending to since they began to look with disdain upon the Aristotelian Logic. Two things which were so perfectly alike as to be undistinguishable, were said to differ numero tantum; i.e. to differ only in being two instead of one, in being different numbers in a catalogue. But things which are in any the slightest degree unlike, may be said to differ not only numero but specie. This expression, as well as the former, is borrowed from the Schoolmen, but with a slight extension of its meaning.

[§15]

[¶¶1, 10] The analytical view which has been taken in the preceeding pages of the nature of Attributes, has brought under our notice all those leading distinctions which seem most suitable to be taken in the basis of a Classification of Entities, or enumeration of Summa genera, such as was attempted in the categories of Aristotle.

Attributes have been found to differ from one another in the following particulars, which may be taken as principles of so many mutually intersecting divisions:

1. Attributes are either Attributes of Substances, attributes of feelings or attributes of other attributes.

Substances are either Bodies or Minds; and accordingly Attributes of Substances are either Attributes of Bodies or Attributes of Minds.

^[*] 2. The fact or phenomenon constituting an Attribute, may either be a fact which concerns only the subject itself, with or without a percipient mind; or it may be a fact which concerns jointly that subject and other subjects. A fact of the first kind can only be considered as an attribute of that one subject; but in the second case, the same individual fact may constitute an attribute of every one of the subjects concerned in it. In the former case, the attribute is called a Quality; in the latter, a Relation.

To render the classification complete, a further consideration remains to be introduced. A thing may be considered either as it exists in any one given instant of time, or as it exists in successive instants. In other words, we may consider its mere state, or its changes of state: its attributes at any given moment, or the changes which it undergoes in its attributes, losing some and acquiring others. Hence attributes may be divided into states of the subject, and changes of state: into properties and changes of properties: into properties & events.

Such are the different kinds of attributes which may be possessed by one object. When we suppose two or more objects, we introduce an additional kind of attribute which cannot be possessed by one object only, viz: the attribute of number.

[¶5] The following, then, appears to be a complete enumeration of all nameable things:—

• 1. Substances.
• 2. Feelings.
• 3. Qualities.
• 4. Relations.
• 5. Events; or changes of feelings, qualities, and relations.
• 6. Numbers.

^[†] But if the analysis which we have attempted of quality & relation be correct, the distinction between these and feelings is not a distinction between things, but only a difference in the light in which they are viewed for the purpose of naming them.

The above classification of nameable objects could not be dispensed with in attempting an exposition of the Philosophy of Logic. As the nature of the subject renders it somewhat more abstruse than any other portion of the work, I would willingly have placed it at a greater distance from the commencement, had there been any other place suitable to it; but I could find none so suitable as this. I have aimed at including in the chapter itself, everything that is necessary to render it intelligible; but if I should have failed in making my arguments understood, or if, being understood, they should fail to convince, the reader will not, I believe, find this any considerable hindrance to the intelligibleness of the succeeding chapters.

>LINEA PRÆDICAMENTALIS.^[*]

OF PREDICATION

[Chapter iv: Of Propositions]

[§1]

[¶¶1, 2^* ] All enquiries into the nature of Predication must have one of two objects: To analyse the state of the human mind, called Belief; or to analyse that which is believed. The former problem belongs to the higher metaphysics, the latter to Logic. All language recognises a difference between a doctrine or an opinion, and the act of a man’s mind in entertaining the opinion; between assent, and that which we assent to. Logic, as I conceive the limits of that Science, has no concern with the nature of the act of judging, but only with the nature of the judgment which is the fruit of that mental operation. To use the language which the German metaphysicians have borrowed from the schoolmen, the Logician considers the phenomenon [of] Belief objectively only, and not subjectively.

^[†] Into the analysis of Predication, so far as it belongs to our subject, we are now prepared to enter. For inasmuch as whatever we believe, if we express it at all, expresses itself in the form of a proposition; & might, in all cases, be so expressed, if we thought fit; an enquiry into the nature of the immediate object of belief, is an enquiry into the meaning of propositions. But every proposition consists of two names connected by a copula. An enquiry therefore into the meaning of names, such as that which we have now concluded, is the proper foundation for an inquiry into the meaning of propositions, or into the nature of what is termed a judgment, an opinion, a doctrine, or (when we ourselves assent to it) a truth.

^[‡] By examining on the one hand names, on the other hand, nameable things, we have arrived at the following results. That names are either concrete or abstract. That concrete names are either proper or connotative. That proper names are merely unmeaning marks attached to single objects in order that we may be able to talk or write about them: but that all other words, whether connotative or abstract, express attributes: and that the meaning of all words whatever which have a meaning, consists in attributes. We have next analysed the notion of an attribute, & of each of the principal kinds of attributes. And we have found that they are all of them states of human consciousness; either excited by objects, or originating in the mind itself:—including in the idea of a state of consciousness, any series or succession of such states.

^[§] If the above be a correct analysis of the meaning of names, & if propositions consist of names, it cannot now be a very long process to analyse the meaning of Propositions.

[Chap. iv, §1, ¶5] But before we attempt this analysis we must premise an explanation of the technical terms commonly in use to express the principal distinctions which exist among propositions.

[§2]

[¶1] A Proposition is a form of discourse in which something is affirmed or denied of something.

The first division, therefore, of Propositions, is into Affirmative & Negative. An affirmative Proposition is that in which the predicate is affirmed of the subject; as, Cæsar is dead. A negative proposition is that in which the predicate is denied of the subject; as Cæsar is not dead.

[§3]

[¶1] The second division of Propositions is into simple and complex. A simple proposition is a proposition in which one predicate is affirmed of one subject. A complex proposition is a proposition in which there is more than one predicate, or more than one subject, or both.

[¶2] At first sight, this division has very much the air of an absurdity: a grand distinction of things into one and more than one: as if we were to divide horses into simple horses and complex horses, meaning by a complex horse, a horse which is several horses at once. And in truth, what is called a complex proposition is often not a proposition at all, but a plurality of propositions, held together by a copulative conjunction. Such, for example, as this: Cæsar is dead, & Brutus is alive: or even this; Cæsar is dead, but Brutus is alive. There are here two distinct propositions; and we might as well call a street a complex house, because all the houses in it are joined to one another, as call these two propositions a complex proposition because they are joined together by a particle. It is true that the Syncategorematic words and and but have a meaning; but that meaning is so far from making the two propositions one, that it adds a third proposition to the former two. All particles are abbreviations, generally abbreviations of propositions; a kind of short-hand, whereby that, which to express it fully would have required a proposition or a series of propositions, is suggested to the mind at once. Thus the words, Cæsar is dead and Brutus is alive, are equivalent to these:—Cæsar is dead; Brutus is alive; it is my wish that the two preceeding propositions should be thought of together. If the words were, Cæsar is dead, but Brutus is alive, the sense would be equivalent to the same three propositions, together with a fourth; viz: the following:—“Between the two preceeding propositions there exists a contrast:” i.e. either between the two facts themselves, or between their probable consequences.

[¶3] In the instances which we have given, the two propositions are kept visibly distinct: each subject having its separate predicate, and each predicate its separate subject. But it frequently happens, that for brevity, & to avoid repetition, the different propositions are jumbled together. Thus, John & William are good men, signifies John is a good man; and William is a good man. John is a good and a brave man, signifies, John is a good man, and John is a brave man. John & William are good and brave men, signifies, John is a good man, and John is a brave man, and William is a good man, and William is a brave man.

[¶4] We have seen that when the two or more simple propositions which compose what is called a complex proposition, are stated categorically, and not under any condition or proviso, the pretended complex proposition is not a proposition at all, but a plurality of propositions; since what it expresses is not a single assertion, but several assertions, which, if true when joined, are true also when separated.

But there is a kind of proposition, which, although it contains a plurality of subjects and of predicates, and may be said, in one sense of the word, to consist of several propositions, contains nevertheless only one assertion; and its truth does not at all imply that of the simple propositions which compose it. An example of this is, when the simple propositions are connected by the particle or; as, Either A is B, or C is D: or by the particle if; as, If A is B, then C is D. In the former case, the proposition is called disjunctive; in the latter, conditional: the name hypothetical is common to both. As Dr. Whately has well observed, the disjunctive form is resolvable into the conditional: every disjunctive proposition being equivalent to two or more conditional ones. Either A is B, or C is D means, If A is not B, C is D, & if C is not D, A is B. All hypothetical propositions, therefore, are conditional ones, and the two words are synonymous. Propositions which are not hypothetical, are said, in the language of logicians, to be categorical.

[¶5] A hypothetical proposition is not, like the pretended complex propositions which we previously considered, a mere aggregation of simple propositions. Though simple propositions form part of the words in which it is couched, they form no part of the assertion which it is intended to convey. When we say, If the Koran comes from God, Mahomet is the prophet of God, we do not mean to affirm either that the Koran really comes from God, or that Mahomet is really his prophet. Neither of these simple propositions may be true, and yet the truth of the complex proposition may be indisputable. What is asserted is not the truth of either of the two propositions, but the dependence of the one upon the other.

What, then, is the subject, and what the predicate, of the hypothetical proposition? for a subject and a predicate it must have, like every other proposition. “The Koran” is not the subject of it, nor is “Mahomet:” for nothing is affirmed, either of the Koran or of Mahomet. The real subject of the hypothetical predication is the entire proposition, “Mahomet is the prophet of God;” for it is of this that the affirmation is made: & the affirmation is that this proposition is a legitimate inference from the proposition “The Koran comes from God.” The subject and predicate, therefore, of a hypothetical proposition, are two many-worded names, both of them names of propositions. One of them, the subject, is the name of an individual proposition. The other, the predicate, is a general name, of this form, “an inference from so and so:” denoting a proposition, and connoting that its truth is apparent to any person, who, being capable of reasoning, believes a certain other proposition.

I have already observed that all particles are abbreviations; this observation is now exemplified in the particle if. If A is B, C is D, is an abbreviation of the following, The proposition C is D, is correctly inferrible from the proposition A is B.

[¶6] There is, therefore, no fundamental difference between hypothetical propositions and categorical ones. In a conditional as truly as in a categorical proposition, one predicate is affirmed of one subject, & no more. We may call it a complex proposition, but its real characteristic is, that it is a proposition concerning a proposition: that the subject of the assertion is itself an assertion. This, however, is not peculiar to hypothetical propositions. There are many other propositions relating to propositions; or, in other words, having propositions for their subjects. A proposition, like anything else, may have attributes; and those attributes may be predicated of it. One attribute which may be affirmed of a proposition, is that of being an inference from another proposition. But this is only one among many attributes of propositions: a conditional proposition, therefore, is only one of many kinds of propositions, having a proposition for their subject.

We may say, That the whole is greater than its part, is an axiom in mathematics: That the Holy Ghost proceeds from the Father alone, is a tenet of the Greek church: The doctrine of the divine right of Kings was renounced by the British Parliament at the Revolution: The infallibility of the Pope has no countenance from Scripture. Not one of these can possibly be mistaken for a conditional proposition. In all these, however, the subject is an entire proposition. That which these different predicates are affirmed of, is the proposition “The whole is greater than its part;” the proposition “The Holy Ghost proceeds from the Father alone;” the proposition “Kings have a divine right;” the proposition “The Pope is infallible.”

[¶7] There is nothing about this class of propositions which seems particularly difficult of comprehension. There is no difficulty in understanding that as we may make an assertion respecting anything else, so we may make an assertion respecting an assertion. A hypothetical proposition is one particular kind of assertion respecting an assertion; and there does not seem to be so generic a difference between it and any other kind, as to account for its having been selected to fill so conspicuous a place in Treatises on Logic, while the others have remained blended in the general mass of Categorical Propositions. Hypothetical propositions, indeed, have so far a peculiar claim to the attention of the Logician, that what they assert of an assertion, is its being a logical inference from another assertion.

[§4]

[¶1] The third division of Propositions is into universal, particular, indefinite and singular. This distinction is founded on the degree of generality of the subject of the proposition. The following are examples of the four classes:—

[¶2] The proposition is singular, when the subject is an individual name. It is not necessary that the individual name should be a proper name: “The founder of Christianity was crucified,” is as much entitled to the name of a singular proposition as “Christ was crucified.”

[¶3] When the subject of the proposition is a general name, it may either stand for all that it denotes or only for a part. Thus, man may either stand for all men, or only for some men. When the predicate is affirmed or denied of all and each of the things denoted by the subject, the proposition is universal. When of some non-assignable number of them only, the proposition is particular. Thus, All men are mortal, Every man is mortal, are universal propositions, because the predicate mortal is affirmed of each and every individual denoted by the term man. No man is immortal, is also a universal proposition, since the predicate immortal is denied of each and every individual denoted by the term man: the negative proposition, being exactly equivalent to the following, “Every man is not-mortal.” But “Some men are wise,” “Some men are not wise,” are particular propositions: the predicate wise being in the one case affirmed and in the other denied, not of each and every individual denoted by the term man, but only of each and every one of an unspecified portion of those individuals.

[¶4] When it is not clear from the form of the expression whether the general name which is the subject of the proposition stands for all the individuals denoted by it, or only for some of them, the proposition is called indefinite: but this, as Dr. Whately has observed, is an absurdity of the same kind as that committed by some grammarians, when, in their list of genders, they enumerate the doubtful gender. The whole truth in respect to an indefinite proposition is, that the form of the expression does not shew whether its author means to assert a universal proposition or a particular one: but we know that he must mean to assert either the one or the other. And very often, though the words themselves do not shew which he intends, the context or the usage of the language supplies the deficiency. Thus, when it is affirmed that “Man is mortal:” nobody ever doubts that the assertion is intended of all men, and the word indicative of universality is commonly omitted, only because the meaning is evident without it.

[¶5] When a general name thus stands for each & every individual which it is a name of, or in other words denotes, it is said by Logicians to be distributed, or employed distributively.[¶6] These terms enable us to express very concisely the definitions already given of a universal and of a particular proposition. A universal proposition is that of which the subject is distributed; a particular proposition is that of which the subject is undistributed. The words distributed and undistributed are of great service in stating and demonstrating the rules of the Syllogism, as those rules have been commonly conceived. The view which will be taken in this work of the nature of the Syllogism renders these technical expressions less indispensable; but they are still very convenient for a variety of purposes.

[¶7] There are many other distinctions among propositions; but for explaining and illustrating these, in so far as their importance may render it desirable, more suitable opportunities will occur.

[Chapter v: Of the Import of Propositions^* ]

[§1]

[¶6] We are now prepared to analyse the meaning of Propositions: to inquire into the nature of the immediate object of belief; into the nature of an assertion or judgment; or of the matter of fact signified by a proposition. In other words, we are about to inquire, What is that which is expressed by the form of discourse called a proposition, and the conformity of which to fact, constitutes the truth of the proposition.

[§2]

[¶1] One of the closest and most consecutive thinkers whom this country, or the world itself, has produced, I mean Hobbes, has given the following answer to this question. In every proposition, he says, what is really asserted is, that the predicate is the name of the same thing of which the subject is the name; and if it really be so, the proposition is true. Thus, the proposition, All men are living beings, is true (he would say) because living being is a name of everything of which man is a name. All men are six feet high, is not true, because six feet high is not a name of everything (though it is of some things) of which man is a name.

[¶2] That what is here given as the definition of a true proposition, is a property really belonging to all true propositions, must be admitted: but not that it is any explanation of what we mean when we call a proposition true.

That all true propositions have the property ascribed to them by Hobbes is evident, since the subject and predicate being both names of things, if these things were wholly different, the one name could not, consistently with its signification, be predicated of the other. It could not be true, that Some men are black, unless among the individuals denoted by the name man, there were some who are also included among the individuals denoted by the name black. It would not be true that All oxen ruminate, unless all the individuals denoted by the name ox, were included among the individuals denoted by the name ruminating.

[¶3] Hobbes’s definition, therefore, of a true proposition, contains nothing erroneous. But it fails in this; that it gives altogether an inadequate notion of what the truth of the proposition depends upon—of what the proposition really asserts.

[¶4] The only propositions of which Hobbes’s definition can be admitted as a sufficient explanation, are that very limited and unimportant class, in which both the subject and the predicate are proper names. For, as has already been remarked, proper names have strictly no meaning; they are merely marks for individual objects: and when a proper name is predicated of another proper name, all the meaning conveyed is that both the names are marks for the same object. But this is precisely what Hobbes produces as a theory of predication in general. This doctrine is a full and satisfactory explanation of such predications as these, Hyde was Clarendon, or Tully is Cicero. It exhausts the whole meaning of these propositions. But it is a sadly inadequate theory of any others. That it should ever have been thought of as such, can be accounted for only by the fact, that Hobbes, in common with the other Nominalists, entirely overlooked the connotation of words; and sought for their meaning exclusively in what they denote: fancying that all names were (what none but proper names really are), marks put upon individuals; and seeing no difference between a proper name and a general name, except that the first denotes only one individual, and the last a greater number. It was the natural consequence of such views that a theory of predication which only suits the case in which both terms of the proposition are proper names, should be brought forward to explain predication in all cases whatever.

[¶5] We, however, have shewn, that the meaning of all names, except proper and abstract names, resides in the connotation. When, therefore, we are analysing the meaning of any proposition, of which the predicate and subject are neither proper nor abstract names, it is to the connotation of those terms that we must exclusively look, and not to what they denote, or, in Hobbes’s language, to what they are names of.

[¶7] A man, or a bird, or a stone, means simply an object having such and such attributes. The real meaning of the word man, is those attributes, and not John, Peter, Thomas, &c. The word mortal, in like manner, connotes certain attributes: and when we say, All men are mortal, the meaning of the proposition is, that all beings which possess the one set of attributes, possess also the other. If, in our experience, the attributes connoted by man are found to be always accompanied by the attributes connoted by mortal, it will follow, as a necessary consequence, that the class man will be wholly included in the class mortal, or that mortal will be a name of all things of which man is a name: for why? those objects are brought under the name, by our having discovered that they possess the attributes connoted by it: but their possession of the attributes is the fundamental fact on which the truth of the proposition depends; not their being called by the name. Connotative names always follow the attributes which they connote. If any two attributes happen to be conjoined, whether it be in one instance only or in all instances, the concrete names answering to those attributes will of course be predicable of the same subject, and may be said in Hobbes’s language (in the propriety of which I fully concur) to be two names for the same thing. But the coincidence in the application of the two names is a mere consequence of the conjunction between the attributes; and was, very likely, never thought of, when the names were invented, and their signification fixed. That the diamond is combustible was a proposition certainly not dreamt of when the words diamond and combustible received their present meaning; and could not have been discovered by the most ingenious and refined analysis of those words. It was found out by a very different process, viz: by exerting the five senses, and learning from them, that the attribute of combustibility existed in all those diamonds upon which the experiment was tried; these being so numerous, and the circumstances of the experiment being such, that what was true of those individuals might be concluded to be true of all substances coming within the name, that is, of all substances possessing the attributes which it connotes. The assertion, therefore, when analysed, is, that wheresoever we find certain attributes, we shall find a certain other attribute. And this is not a question of the signification of names, but of the laws of nature; the order which exists among phenomena.

[§3]

[¶1] Although Hobbes’s theory of Predication has not, in the words in which he stated it, met with a very favourable reception from philosophers; a theory precisely identical with it, and not by any means so perspicaciously expressed, may almost be said to have taken its place among established opinions. The most generally received notion of what Predication is, among those who have attempted to consider it metaphysically, is decidedly this—that it consists in placing something in a class; i.e. either placing one class under another class, or placing an individual under a class. Thus, the proposition Man is mortal, asserts according to this view of it, that the class man is included in the class mortal. “Plato was a philosopher,” asserts that the individual Plato was one of those who compose the class philosopher. If the proposition is negative, then, instead of placing something in a class, it excludes something from a class. Thus, if the following be the proposition, The Elephant is not carnivorous; what this proposition asserts is, that the elephant is excluded from the class carnivorous, or is not numbered among the things which compose that class.

When we consider that a class is absolutely nothing but an indefinite number of individuals denoted by a general name, the identity of this theory with that of Hobbes is too manifest to require elucidation. [¶2] How widely these views have prevailed, is evident from the fact, that they are the basis of the celebrated dictum de omni et nullo. When the syllogism is resolved by all those who treat of it, into an inference that what is true of a whole class, is true of all things whatever belonging to that class; and when this is almost universally laid down by logicians as the principle upon which all reasoning ultimately rests; it is clear that in the general estimation of logicians, the propositions, of which reasonings are composed, can be the expression of nothing but the process of dividing things into classes, and referring every object to its proper class.

[¶3] I cannot but consider this theory to be both unsatisfactory and illogical. Unsatisfactory, because we have already seen that by digging deeper for a solution, a more complete one may be found. Illogical, because instead of explaining the effect by the cause, it explains the cause by the effect. It is I conceive founded upon a latent misconception of the nature of classification.

[¶4] It seems to be supposed that classification is an arrangement and grouping of definite and known individuals: That when names were imposed, an inventory was made of all the objects in the universe, and these being divided into parcels or lists, a name was given to each list to be common to all the objects in it; in the same manner, (allowance being made for the difference between a name of one individual & a name of more than one) in which a man gives a name to each of his children, to distinguish them from one another: That the objects were then brought again into a common stock, & rearranged on some other principle, each of the new lists having also a name given to it; and so on; until all the general names in our language had been arrived at. This having been done; if a question subsequently arises whether a certain general name can be truly predicated of any particular object, we have only to consult our former proceedings, and see whether that object is to be found in the list corresponding to that name. It has been predetermined by the inventors of language what individual objects each class shall consist of; and all we have to do is to refer to the record of an antecedent decision.

[¶5] When broadly stated, this seems ridiculous enough. But it is curious to observe how closely the received explanations of classification and naming are related to this absurd theory: and how well calculated they are to introduce into the mind, though indistinctly yet so much the more effectually, this very idea.

[¶6] General names are not marks put upon definite objects. Classes are not made by drawing a line round a certain number of given individuals. The objects which compose any given class are perpetually fluctuating. We may frame a class, without knowing even one of the individuals composing it; we may do so, believing that no such individuals exist. If by the meaning of a general name are to be understood the things which it is the name of, or which it denotes, no general name, except by accident, has any fixed meaning at all. The meaning of a general name resides exclusively in what it connotes. The only mode in which any general name has a definite meaning, is in being a name of all things, known and unknown, past, present, or future, which possess certain definite attributes. When, by studying not the meaning of words, but the phenomena of nature, we discover that the attributes in question are possessed by some objects not previously known to possess them,—as was the case when chemists found out that the diamond was combustible,—we then include the object in the class: but it did not already belong to the class. We place the individual in the class, because the proposition is true: the proposition is not true because the object falls within the class.

[¶7] It is of some importance to enter thus fully into the analysis of these theories of Predication, as the logical habit in which they originate is very widely diffused; and it is to the influence of this habit I must ascribe the fact that notwithstanding the great advances which have been made in the analytical study of the mind since the days of the Schoolmen, the theory of logic has, in my opinion, actually retrograded since that time. The habit which I allude to, is that of assimilating all the operations of the human understanding which have Truth for their object, namely, the assent to it, & the demonstration of it, ^[*] to processes of mere classification and naming.

When we come to treat of Reasoning, we shall, I think, be convinced how much the theory of that intellectual process has been vitiated by the influence of the views which I have just been combating. [¶8] I have only further to remark in this place, that, although Hobbes’s theory of predication, as Leibnitz pointed out, renders truth and falsity perfectly arbitrary, without any standard but the will of man, it must not be concluded that either Hobbes, or any of the other philosophers who have in the main agreed with him, did in fact consider the distinction between truth and error as less real, or attached one jot less importance to it, than other people. To suppose that they did so, would argue total unacquaintance with their other speculations. But this shews how little hold their doctrine possessed even over their own minds. No person, at bottom, ever imagined that there was nothing more in truth than mere propriety of expression; than using language in conformity to a previous convention. With whatever illusions even profound thinkers may have contrived to satisfy themselves when endeavouring to find a general solution for a great metaphysical problem,—when they came to the practical application of their doctrines, they were always prepared with some means of explaining the solution away. When the inquiry was brought down from generals to a particular case, every one has always acknowledged a distinction between verbal questions & real questions; has freely admitted that some false propositions are uttered from ignorance of the meaning of words, but in others the source of the error is in things: that in the former case, there is no impropriety in saying, that the assertion intended is true, and the falsity lies in the words only: That a person who has not the use of language may form true propositions mentally, that is, he may believe matters of fact. ^[*] No doubt, indeed, when the matter of fact is correctly conceived in my mind, and my opinion or judgment is strictly true, if I attempt to put that opinion into words, I may, from ignorance of their conventional meaning, convey a false proposition instead of a true one. The question whether I have correctly expressed a given matter of fact, or what are the words I must use for the correct expression of it, is a question of naming, entirely. But this is no philosophical discovery. Every child knows that the mode of putting a truth into words depends upon the meaning of words; and Hobbes’s definition must shrink into the dimensions of this barren truism, in order to be true at all.

The ease with which what would satisfy nobody if brought to explain what constitutes the truth of any one fact, is accepted as a perfectly satisfactory solution of the nature of Truth in general, merits particular attention; & adds one more to the numerous examples which shew that the chances of error in our speculations are nearly in direct proportion to their generality.

The countenance which this particular error derives from an imperfect conception of the distinction between essential and accidental propositions, & from a misapprehension of the nature of mathematical reasoning, and in particular of the algebraic calculus, will fall under our notice, in another place. Hereafter, also, in treating of classification and naming, it will still more clearly appear that these operations are completely arbitrary; that their sole object is convenience; and that instead of determining the truth of propositions, they bend to it, and, in all cases, shape and mould themselves according to those judgments, of which propositions are the expression. That, in short, we name & classify things according to their attributes; & do not ascribe attributes to them in obedience to a previous meaning and classification.

In combating the superficial views of some philosophers on the nature of Predication, we have already done nearly everything which is necessary for shewing what Predication really is.

The Predicate of a Proposition must be either a proper name, or a connotative name, or an abstract name.

A proper name being merely an unmeaning mark used to speak of an object by; in predicating of any object a proper name, we convey no meaning, we express belief in nothing, except only that this is the object which it is a mark of. If the proposition is negative instead of being affirmative, the assertion conveyed is, that this is not the object which the proper name is a mark for. It is of no consequence what kind of name forms the subject of the proposition. It must, indeed, be an individual name, otherwise the proposition would be neither true nor false, but simply unmeaning. “The father of Socrates was Sophroniscus,” is a true proposition: “Pericles was Sophroniscus,” is a false proposition; but “All men were Sophroniscus,” can hardly be called a false proposition, nor “Some men were not Sophroniscus” a true one; both are simple nonsense: they are a kind of solecisms in language. For nothing of which the human mind can frame a conception, is affirmed in the one case, or denied in the other. The propositions are equivalent to these: “many men are one man:” “many men are not one man:” now what image do these sentences raise in the mind, more than if the words were read backwards? No more than Abracadabra. We cannot predicate a proper name of a general name, either truely or falsely; such a predication is mere gibberish. But the subject of the proposition, so long as it is only the name of one individual, may be either proper or connotative. In both cases, equally, the subject of the proposition is simply this, that the individual, in whatever manner designated, who is denoted by the subject, bears or does not bear the name which is the predicate.

The case is very different when the predicate is a connotative name. When that is predicated of any object individually designated, there is always asserted a matter of fact, distinct from the mere meaning of a name. This matter of fact is, that the object thus individually pointed out, possesses the particular attributes connoted by the connotative names.

[§4, ¶1] When, therefore, the subject is a proper name, and the predicate a connotative one, the proposition, if affirmative, asserts that an individual, to be known by a particular mark which has been put upon it, possesses the attributes connoted by the predicate. From the analysis of attributes, it will be remembered that this means that the said individual excites in our minds & those of others, certain sensations or other states of consciousness; or, if itself a sentient being, experiences certain sensations or other states of consciousness.

The subject as well as the predicate may be a connotative name. And this is the most important of all the cases; as it comprehends all general propositions, except those in which the subject is an abstract name.

[§4, ¶2] In this case, as in the last, what the proposition asserts or expresses a belief in, is, of course, that the objects denoted by the subject possess the attributes connoted by the predicate. But the characteristic of this case is that the objects are not individually designated. They are pointed out only by some of their attributes: and the only thing known of them may be those attributes: in the case of a general proposition, the objects denoted by the subject being indefinite in number, some of them are not known individually at all. The assertion, therefore, is not that the attributes connoted by the predicate are possessed by any individual or any number of individuals known previously as John, Thomas, Richard, &c. but that those attributes are possessed by each & every individual possessing certain other attributes; in other words, that one set of attributes is constantly conjoined with another set.

It is easy to accommodate this explanation to the diversities of universal, particular, and singular, of affirmative and negative propositions: thus:

All men are mortal, signifies that the attribute connoted by mortal, constantly accompanies the attributes connoted by man. In other words, that all objects which have the attributes connoted by man have likewise the attributes connoted by mortal. Or, again changing the expression; that all objects which excite and experience the sensations connoted by man, excite and experience the sensations connoted by mortal. (I use the word sensations merely for shortness; the entire phrase would be, sensations, thoughts, emotions, and volitions.)

Some men have black hair, means, that the attribute connoted by “having black hair,” sometimes accompanies the attributes connoted by man. Or that some objects which have the attributes connoted by man, have also the attribute connoted by having black hair. Or that some objects which excite and experience the sensations connoted by man, excite also the sensations connoted by having black hair.

The Archbishop of Canterbury has black hair, means, that the attribute connoted by having black hair, accompanies the attributes connoted by Archbishop of Canterbury, in the single instance of the individual at present possessing those attributes, to whom the assertion is limited, by the particle the, which also marks that there is but one such individual.

The same analysis will hold, with the necessary variations, in the case of negative propositions.

No birds are four-footed, signifies that the attribute connoted by four-footed, never accompanies the attributes connoted by bird. In other words, that none of the objects which have the attribute connoted by bird, have the attributes connoted by four-footed. Or finally, that of the objects that excite and experience the sensations which the name bird connotes as being experienced & excited, there is not one which excites, in addition, the sensations connoted by the name four-footed.

Some men are not mathematicians, signifies, that the attribute connoted by mathematician, does not always accompany the attributes connoted by man. Or that some of the objects which have the attributes connoted by man, have not that which is connoted by mathematician: Or that some of the objects which excite and experience the sensations connoted by man, do not excite and experience the sensations connoted by mathematician.

The first navigator was not a mathematician, means that the attribute connoted by mathematician, did not accompany the attributes connoted by navigator, in the first instance in which those attributes ever existed; or, to put the same meaning into another form, do not accompany the attributes connoted by first navigator, one of which attributes is that of being the only individual of its class.

In all these cases I repeat that the word sensation is used as the representative of all states of consciousness whatever; though it is a name properly belonging only to what are commonly but incorrectly called bodily feelings, meaning such as can be proved to be organic. The exact import of this word, it is not necessary to discuss, except in a work, treating either of physiology, or of metaphysics. The word sensation has been adopted in the above analysis merely to avoid complicating the sentence with four words instead of one.

The truth, then, of a general proposition of which the subject and predicate are connotative names, depends upon a fact ascertainable by experience, viz: whether certain phenomena, of the external senses or of external consciousness, do or do not constantly accompany certain other phenomena, either in all or in some of their combinations. The word attribute, when so understood as not to suggest the notion of an occult cause, affords the most compact and concise phraseology for expressing the conclusion at which we have arrived. We may, therefore, state as the final result of this portion of our inquiry into the nature of predication, the following maxims:

Every general proposition of which the subject and predicate are connotative names, either affirms or denies, that either all or some of the objects possessing the attributes connoted by the subject, possess also the attributes connoted by the predicate.

If the two sets of attributes are thus conjoined in all or some of those objects, the affirmative proposition is true and the negative false; if they are not so conjoined, the negative proposition is true and the affirmative false.

[Chapter vi: Of Propositions Merely Verbal^* ]

[§1]

[¶3] This leads us to a distinction of very great practical importance; the distinction between essential and accidental propositions, and between essential and accidental properties or attributes.

[§2]

[¶1] The Schoolmen, and most other philosophers prior to Locke, as well as many since his time, have made a great mystery of what they called essential predication, being that in which the predicate was of the essence of the subject: meaning, as they said, by its essence, that without which it could neither be, nor be conceived to be. Thus, rationality, they said, was of the essence of man, because, without rationality, man could not be conceived to exist. It is not necessary here to state particularly the connexion which this distinction had with the doctrines of substantiæ secundæ, or universal substances, and substantial forms, doctrines which under varieties of phraseology, pervaded alike the Aristotelian and the Platonic Schools. I allude to these dogmas of the Realists, which were the technical expression of the erroneous notion that genera and species are made by nature, and cannot be altered for man’s convenience, merely because these false views of the nature of classification & generalization, satisfactorily account for what would otherwise be inexplicable, viz: that the Schoolmen should not have seen what is so extremely obvious, as the real nature of those essences which held so conspicuous a place in their philosophy. They said truly, that man cannot be conceived without rationality. But we can conceive an animal exactly like a man, in all except that one quality, and those others which are the consequences of it. All, therefore, which is really true in the assertion, that man could not be conceived without rationality, is only, that if he had not rationality, he would not be reputed a man. There is no impossibility in conceiving the thing: nor, for aught we know, is there any impossibility in its existing: the impossibility is only in the conventions of language, which will not allow the thing, even if it exist, to be called by the name which is reserved for rational beings. Rationality, in short, is involved in the meaning of the word man: it is one of the attributes connoted by that name. The essence, therefore, of man, simply meant the whole of the attributes connoted by the word. And any one of these attributes, taken singly, may be called an essential property of man.^*

[¶3] Now, as the most familiar of the general names predicable of an object, in most cases connote not one only, but several of the attributes of object [sic]; each of which attributes may also be taken separately to form the bond of union of some class, and the meaning of some general name; it is obvious that we may predicate of a name connoting a variety of attributes, another name which connotes only one of those attributes, or some smaller number of them than all. In such cases, the universal affirmative proposition will be true; it being self-evident, that every object which possesses the whole of any set of attributes, must possess a part of that same set. In such cases, however, the proposition conveys no information, to any person who previously understood the whole meaning of the terms. The propositions, Every man is a corporeal being, Every man is an animal, Every man is rational, convey no knowledge to any one, who was already perfectly aware of the entire meaning of the word man; for the meaning of the word man includes all this: and, that every man has the attributes connoted by these different predicates, is already asserted when he is called a man. Now, of this nature are all the propositions which have been called essential propositions. They are accordingly, in fact, identical propositions.

[¶4] Every proposition, indeed, which ascribes any attribute to the thing denoted by a name, involves, it is true, a tacit assertion that there really exists a thing corresponding to the name, and possessing the attributes which it connotes; and this, no doubt, may convey information, even to those who perfectly understood the meaning of the name. But all the information of this sort which is conveyed by all the essential propositions of which man can be made the subject, are included in the single assertion, Men exist. And this assumption of real existence is only the result of an imperfection of language. It arises from the ambiguity of the copula, which in addition to its proper function of a mark to shew that there is a predication, is also, as we have already remarked, a concrete word, connoting existence. The actual existence of the subject of the proposition is only apparently, not really, implied in the predication, if an essential one; for we may say, A ghost is a disembodied spirit, without believing in ghosts. But every proposition not essential does imply the real existence of the subject, or else the proposition is mere non-sense. Thus, the proposition, The ghost of a murdered person haunts the couch of the murderer, can only have a meaning, if understood as signifying a belief in ghosts; since the attribute predicated is clearly not implied in the signification of the word ghost: unless, therefore, the speaker intends to express a fact or phenomenon, which really takes place, he expresses nothing more than if he uttered inarticulate sounds.

[¶5] It will be shewn, in a subsequent place, that whenever any important consequences appear to flow, as in mathematics, from an essential proposition, or a proposition deduceable from the meaning of a name, it is from this tacit assumption of the real existence of the object so named, that these consequences really flow. Apart from this assumption of real existence, propositions in which the predicate is of the essence of the subject, that is, in which the predicate connotes the whole or part of what the subject connotes, but nothing besides, answer no purpose except that of unfolding the whole or some part of the meaning of the name which is the subject, to those who did not previously know it. Accordingly, the most useful class of essential propositions are Definitions, which, to be complete, should unfold the whole of what is involved in the meaning of the word defined, i.e. the whole of what it connotes. But it is usual, in defining a name, not to indicate all the attributes which it connoted, but only so many of them as are sufficient to segregate all the known objects denoted by it, from all other known objects. And sometimes some merely accidental property, not involved in the meaning of the name at all, answers this purpose equally well. The various kinds of Definition which these distinctions give rise to, and the purposes to which they are respectively subservient, will be minutely considered in the proper place.

[§3]

[¶1] According to the above view of essential propositions, no proposition is essential which relates to an individual by name, i.e. to a proper name. This is a deviation from the language of the Schoolmen. They regarded everything as of the essence of an individual, which was of the essence of the species to which they were accustomed to refer that individual; that is of the class to which it was most familiarly referred, & to which, therefore, they conceived, that it by nature belonged. Thus, because the proposition Man is a rational being, was an essential proposition, they held this to be the case likewise with the proposition, Julius Cæsar is a rational being. This naturally followed if genera and species were to be considered as entities distinct from the individuals composing them. If man was a substance inhering in every individual man, it was natural to conclude that the essence of man was something inherent in man, and by necessary consequence inherent in all individual men and forming their common essence. It might then be said that rationality was not only of the essence of man, but of the essence of Julius Cæsar. But this expression has no meaning when severed from the metaphysical theory out of which it grew.

[¶2] A fundamental error, however, is seldom expelled from philosophy by a single victory. It retreats slowly, defends obstinately every inch of ground, and often retains a firm footing in some difficult fastness, after the whole of the open country has been wrested from it. The essences of individuals were an absurd figment arising entirely out of a misapprehension of the essences of classes, yet so profound a philosopher as Locke, when he discarded the parent error, still held fast to that which was its offspring. He divided essences into two classes, real and nominal essences. Real essences were the essences of individual objects: these, he says, are the causes of the sensible properties of objects. What they are we do not know, but if we did, from them alone, we could demonstrate the sensible properties of the object, just as we demonstrate the properties of the triangle from the definition of the triangle. The nominal essences of Locke were the essences of classes, explained nearly as we have explained them; in short, the connotation of general names. Nor is anything wanting to render the third book of Locke’s Essay a nearly perfect treatise on the connotation of names, except to disengage it from the assumption of abstract ideas, which unfortunately is inextricably mixed up in all his language, but not in the thoughts of which that language is in every other respect the appropriate expression. Because a name may be given to an object to signify some only of the properties of the object; Locke concluded that we may have an idea of those properties by themselves, independently of any others: and he always spoke of the name as expressing that idea of the properties, & not the properties themselves. This extremely vicious phraseology has had a most unfortunate influence upon the fate of his speculations; for when Berkeley afterwards pointed out that these pretended abstract ideas do not exist; and that all our ideas are “clothed in circumstances” and are in fact ideas of individuals more or less completely conceived, philosophers ceased to attend to those observations of Locke on the meaning of words, which appeared to involve a theory subsequently recognized as erroneous, and went off into pure Nominalism, from which the speculations of Locke, if properly understood, would have preserved them. And what is still more remarkable, the blindest admirers of Locke, whose doctrines on many subjects are a mere caricature of his, the school of Condillac and Helvetius,^[*] although they retained the exploded part of Locke’s system, the doctrine of abstract ideas, benefitted no more than other people by any of the other doctrines of that immortal third Book, in which the only flaw of importance, unless I am mistaken, is that erroneous theory.

[§4]

[¶1] Propositions not essential are called accidental. An accidental attribute of a class, is any attribute not involved in the signification of the general name appropriated to that class,—or in the precise and convenient language to which we have hitherto adhered, any attribute not connoted by the name. All general propositions, in which the predicate connotes any attribute not connoted by the subject, are accidental propositions. All such propositions, if true, add to our knowledge; they convey other information than that which is involved in the names employed. When I am told that all objects (or even some objects) which have certain qualities, or which stand in certain relations, have also certain other qualities or stand in certain other relations, not the same with any of those first mentioned, I learn from this proposition a new fact; a fact not included in, nor deducible from, my knowledge of the meaning of the words, nor even of the existence of things answering to the signification of those words. It is this class of propositions only, which are in themselves instructive, or from which any instructive propositions can be inferred.

[¶2] There is nothing which seems likely so greatly to have contributed to the general opinion so commonly prevalent, of the futility of the school logic, as the circumstance that almost all the examples used in the common school books to illustrate the doctrines of Predication & of the Syllogism, consist of essential propositions. They are usually taken either from the branches or from the main trunk of the Predicamental tree, which included nothing but what was of the essence of the species. Such were, Omne corpus est substantia, Omne animal estcorpus, Omnis homo est corpus, Omnis homo est animal, Omnis homo est rationalis, & so forth. It is scarcely to be wondered at, that the rules of the syllogistic process should have been thought to be of no use in assisting correct reasoning, when the only propositions, which, in the hands of its professed teachers, it seemed to be employed to prove, were such as every one assented to without proof the moment he comprehended the meaning of the words. I have therefore throughout this work, studiously avoided the employment of essential propositions as examples, except where the nature of the principle to be illustrated particularly required them.

^[*] We have now concluded our analysis of those kinds of Predication, in which the subject and predicate are concrete names. The only remaining kind of names are abstract names, or those which instead of denoting an object and connoting an attribute, denote the attribute itself directly: in other words, denote a certain combination or succession of states of consciousness, implying at the same time that these are excited by some object which is not specified.^[†]

^[*] These are of two kinds; those in which both the subject & predicate are abstract names; and those in which the subject is an abstract and the predicate a concrete name. There is no class of propositions in which the subject is a concrete & the predicate an abstract name. An abstract name cannot be predicated of a concrete. A concrete name is the name of an object; a body or mind; or else, the name of a feeling, considered merely in itself, & without being referred to any object, as its source. It would be absurd to predicate of any of these things, the name of an attribute. It would be absurd to say that an object is a quality, or that an object is a relation; that a sensation is a quality, or that a sensation is a relation. It would not conduce to the ends of language to couple words together in such a mode. A predication of this sort would not be true, nor even false. For when we say that a proposition is false, we mean that it contains some assertion; that it expresses a belief in something, although that something does not appear to be conformable to fact: as, that three angles of a triangle are equal to ten right angles. But a predication such as those we have supposed, would not convey the notion of anything intelligible; not even an intelligible error or falsehood.

Though an abstract name cannot be predicated of a concrete one, a concrete name may in certain cases be predicated of an abstract one. It would be as absurd, certainly, to say of an attribute, that it is an object, as to say of an object that it is an attribute. But when we predicate of any thing a concrete connotative name, we do not thereby affirm that the thing of which the name is predicated is an object; we merely affirm, that it is something which possesses attributes, (namely, those attributes which the predicate connotes). Now an attribute as well as an object may possess attributes. Every name, therefore, which connotes attributes capable of being possessed by attributes, may be predicated of an abstract name. Thus we may predicate of an attribute, the relation in which it stands to any object of which it is an attribute, as when we say, whiteness is the colour of snow; Dissimulation is the quality of a coward. We may predicate of it names connotative of various other relations. An attribute, for instance, may be the cause of an object, of an attribute, of an event,^* or of a feeling; as is expressed in the proposition, Philosophical instruction strengthens the intellect; wherein it is affirmed, that the attribute of being instructed in philosophy, causes or produces the attribute of intellectual strength. In like manner an attribute may be an effect; as in the last example, intellectual strength is asserted to be an effect of philosophical insruction.

^[*] An attribute may precede, follow, or accompany, an object, an attribute, an event or a feeling. But the largest class of relations of attributes, are their mutual resemblances, or unlikenesses. As attributes are merely states of human feeling or consciousness, considered with reference to the objects which cause them, or to the minds which experience them; whenever two sensations or states of feeling are alike, the corresponding attributes may be said to be alike: and when unlike, unlike.^*

Besides the class of the attributes of attributes, which we have now examined, namely, their relations; Attributes may also have qualities. The contemplation of an attribute may, like the contemplation of an object, excite certain feelings in the mind. But to excite in the mind a certain feeling, is that sort of attribute which we have termed a quality. We may, therefore, predicate of the abstract name which expresses an attribute, the concrete name which connotes a quality. Thus we may say with acknowledged propriety—Her beauty is delightful, just as we may say, Her person is delightful. In this case the predicate connotes a quality.^[*] In the following proposition, His thoughtlessness is dangerous, the predicate connotes a relation; for dangerous means that which is a probable cause of evil or inconvenience to some sentient being.

In all these cases any one who has followed carefully the preceding part of this exposition, will easily perceive what is the matter of fact asserted.

^[†] For the ordinary purposes of the elementary parts of Logic it is sufficient to say, that in these propositions, as in all others in which the predicate is a connotative term, the assertion is that the subject (which in this case is an attribute) possesses the attributes connoted by the predicate. If we wish to probe the matter deeper, we shall find that in these, as in the propositions, which we have previously examined, the import of the proposition always is, that some phenominon or state of consciousness, does or does not resemble, is or is not accompanied by, some other phenomonon or state of consciousness. The fact affirmed is therefore exactly the same kind of fact which we assert, when one concrete name is predicated of another. In many cases, it is not the same kind of fact only, but the very same fact. Thus, when we say that one sensible quality is like another, what is it but to say, that one sensation is like another? When we say of any attribute, that it is an attribute of some particular object, what is it but merely inverting the proposition that the object in question possesses that particular attribute? When we say of an attribute (as of thoughtlessness) that it is a cause of something (as of danger) what is [it] but to affirm, that the actions done by a thoughtless person (that is, states of his volition followed by visible outward phenomena) are causes of probable evil or inconvenience?

^[‡] There are various modes in which a proposition, of which the subject is an abstract name, may be translated into a proposition composed of concrete names. There is one mode in particular, of very extensive application, by which a proposition relating to an attribute, is changed into a proposition relating to the objects possessing the attribute. The latter proposition is, in this case, of a peculiar form, which is best displayed by means of examples. Thus, Courage is deserving of honor, is a proposition equivalent to this “All courageous persons are deserving of honour, so far forth as they are courageous,” which is manifestly equivalent to this: “All persons who are courageous deserve an addition to the honor, or a diminution of the disgrace, which may attach to them from other causes.” Again, Virtue is beneficial to society, is equivalent to “All virtuous persons are beneficial to society, so far forth as they are virtuous:” i.e. to this, All virtuous persons produce more beneficial effects to society, than persons similarly situated & similar in their other qualities, who are not virtuous.

There still remains for our consideration, the case in which both the subject and the predicate are abstract names. And we have now to enquire what is the nature of the matter of fact asserted in such a proposition.

It is here necessary to call to mind a distinction which we early made between two kinds of abstract names. We found that some were connotative and others not. There are names given to attributes which connote nothing, involve nothing in their signification except those attributes; there are other names given to attributes, which connote attributes of those attributes. Many of these last, indeed, are, as we have seen concrete names; for they connote an attribute which, though it may belong to an attribute, may also belong to a substance or a feeling. Such are all the connotative names which we used as predicates in our last set of examples. These denote either objects, or feelings, or attributes, as it may happen. But there are names which denote only attributes, & connote attributes of those attributes; or as we may express it, there are names, part of whose connotation is, that the thing they denote is an attribute, & nothing but an attribute. Thus there is on the one hand, the word hurtful, which denotes either objects or attributes, & connotes, what may be an attribute of either, namely, the production of evil or inconvenience; & on the other hand, we have the word fault, which connotes the very same thing, but denotes only attributes; & may be said without impropriety to connote, (in addition to the connotation already mentioned) that the thing it is predicated of, is an attribute. There might be an unlimited number of such words; there are a considerable number. In these cases the import of the proposition is clear. It is a proposition exactly similar to those which we last examined; the matter of fact affirmed is, that the attribute which is the subject of the proposition, possesses, or does not possess, the attribute which the predicate connotes; or (if we analize it further) that the phenomenon, or state of consciousness, which constitutes the former attribute is or is not accompanied by, does or does not resemble, some other phenomenon or state of consciousness.

Remains the case in which (the subject being still an abstract name) the predicate is one of those abstract names which are not connotative.

If an abstract name be not connotative, that is, do not involve in its signification any attribute of an attribute, & yet can be truly predicated of some other abstract name, that is, of some other name denoting an attribute; it must either be another name of the very same attribute, or it must be a name of a class of attributes, in which that particular one is included. The proposition “Cohesion is a tendency in objects to adhere together” is a specimen of the first kind. The subject & predicate are both names of the same attribute. The proposition “whiteness is a colour” is a specimen of the same class. Colour is the name of a class of attributes, and whiteness is the name of one of the attributes falling under that class.

As in names of objects, so in names of attributes, when the subject & predicate denote each the very same thing or things, neither more nor less, the proposition is either merely frivolous, or it expresses the meaning of a word. It either asserts that two words are synonymous, or it defines a word. We have already remarked, that the definition of a connotative name consists in the enumeration of the attributes which it connotes. The definition of one of those abstract names, which are not connotative, is necessarily somewhat different: & is of two kinds.

If the attribute to be defined, be itself a union of several attributes; we have only to join together the names of those attributes taken separately, & we have the definition of the name which belongs to them all taken together. This definition of the attribute will correspond exactly to the definition of the concrete name connoting the attribute. For as we define a concrete name by enumerating the attributes which it connotes, & as the attributes connoted by a concrete name constitute the entire signification of the corresponding abstract one, the same enumeration will serve for the definition of both. Thus, if the definition of a human being, be thus “a being, corporeal, animated, rational & of such and such a form”; the definition of humanity will be, corporeity & animal life combined with rationality & with the same form.

When the abstract name does not express a complication of attributes but one single attribute, the phenomenon constituting that attribute may yet be of a complex nature, consisting of several parts either coexistent or in succession. We may then join together the names of the separate parts, & predicate them of the name of the whole. And this also will be a definition. Thus, eloquence might be defined, the power of influencing the affections of human beings by means of speech or writing.

In all these propositions the import is clear. They belong to the class of essential propositions; & the information which they communicate is simply the meaning of a term; with or without an implied assumption, that there exists an attribute corresponding to the definition, & by consequence objects possessing that attribute.

When the abstract name, which is the predicate of a proposition, is not convertible with the subject, it must be the name of a class of attributes, which includes the attribute denoted by the subject. The proposition therefore affirms that an attribute belongs to a certain class. But why does it belong to that class? why was it placed there? what does its belonging to that class import? In other words, why do we arrange attributes in classes, when the classification is not founded on any attribute of those attributes? The answer is clear. When we arrange attributes in classes, not according to the impression made on our minds by the contemplation of the attributes, nor according to the relation in which they stand to some other things; not, in short according to any attribute of those attributes; we can have but one other principle of classification, the resemblance of the sensations or other states of consciousness which constitute the attributes. Thus, paper-colour, milk-colour, snow-colour, & many others, are ranged in the class whiteness, on account of the resemblance of the sensations. To assert, therefore, that any of these attributes belongs to that class, is merely to assert, that the sensations resemble. To say, paper-colour is a whiteness, or is a white colour, is merely to say, The sensation we receive from the sight of paper, resembles to a certain degree, the sensations we receive from the sight of milk, of silver, of snow &c.

“Whiteness is a colour,” is a proposition of the same class. If we conceive our sensations of colour to be classed together on account of their resemblance to each other, the proposition, Whiteness is a colour, will evidently express that resemblance only, & will therefore belong to the class we are now examining. Perhaps, however, in the very meaning of the word colour, is involved the notion of being received. Still, however, it is the sensation, not the attribute which is received through the eye; what the word expresses is an attribute of the sensation; & this attribute of the sensation, is not an attribute of the attribute. Colour, therefore, is one of the abstract names which are not connotative; & the proposition Whiteness is a colour, merely asserts that the sensations we receive from the things we call white, resemble the sensations we receive from other coloured things: the resemblance being in this case partly a resemblance of relations, viz. both bearing an exactly similar relation to the object called the eye.

The same may be said of the propositions, Colour is a quality, & A quality is an attribute. Neither the word colour nor the word attribute are connotative. Denoting attributes, they do not imply an attribute of those attributes. Quality implies, not that the attribute (as Colour) but that the sensation, is received from the coloured object itself, without the aid of any other object. Attribute implies, not that the particular attributes denoted, but that the sensations, which constitute them, emanate from a subject. In predicating these names therefore, we are, as in the preceding instance, affirming a resemblance between sensations; & that resemblance is in these as in the preceding instance, a resemblance of relations.

But resemblance, as we have before remarked, between two simple feelings, means simply this, that when the two feelings are experienced together, or in immediate succession, a peculiar feeling, called the feeling of resemblance, succeeds. Resemblance between things more complex than simple feelings, means that into those complex wholes, particular parts enter, which resemble each other; that is, which excite the feeling of resemblance, perhaps of exact similarity. All propositions, therefore, which assert resemblance, merely assert, that certain human feelings are followed by certain others.

We have now examined all the possible cases of Predication. What may be deficient or obscure in our analysis of them, will be rendered more intelligible by the sequel of this work. We have, however, unless I am mistaken, established clearly, what, in all propositions whatever, is the assertion made; the matter of fact which is the object of belief.

Propositions, we have found, do not, agreeably to the doctrine of Hobbes, assert in all cases whatever, only one kind of fact, namely an agreement between the significations of two names. Propositions may, on the contrary, be divided into two species; of which one only answers to Hobbes’s definition:

1st. Propositions containing assertions respecting the meaning of names: these are, propositions of which the predicate is a proper name; definitions, & other essential, or in other words identical, propositions.

And 2dly. Propositions which either affirm or deny a fact of the following description. That two phenomina, cognizable by the external senses or by internal consciousness, occur in conjunction; i.e. that when a certain phenomenon takes place, a certain other phenomenon takes place likewise; either simultaneously or in succession; with or without an interval of time.

If it be now asked, what constitutes a true proposition; we can give no other answer, than the apparently superficial one with which we commenced. The proposition is true, if the assertion contained in it, be conformable to the fact; or in other words, if there exist any real fact, of which the assertion contained in the proposition, is an exact representation.

Having now, however, analysed the assertion contained in every proposition, and found that the fact asserted is either the identity of the meaning of two names, or the coexistence of the phenomina; we may, in consequence, add to the general definition of a true proposition, a more particular description of what constitutes the truth of each of the two species into which propositions have just been divided.

^[*] A proposition, then, which asserts that one name denotes or connotes all that is denoted or connoted by another, is true, if, according to the signification which usage or express appointment has attached to the two names, this identity in their connotation or denotation really exists. The standard of truth, therefore, in respect to this class of propositions, is usage or convention.

A proposition which asserts that in whatever subjects one attribute or set of attributes are found, in those same, or in a part of those same subjects another attribute or set of attributes also exist:

Or that a particular attribute or set of attributes exist in a given subject, individually designated;

Or that two objects or attributes resemble, either in themselves or in their relations;

All these propositions affirm in other words, that one phenominon or state of our consciousness, is always or sometimes accompanied (simultaneously or successively) by another phenominon or state of consciousness. The proposition, therefore, is true, if these two phenomina really are conjoined in the manner asserted & false if they are not. And the standard of truth, in respect to this class of propositions is human consciousness or experience.

OF THE PREDICABLES OR UNIVERSALS

[Chapter vii: Of the Nature of Classification, and the Five Predicables]

[§2]

[¶1] Having considered the nature of Predication in general, & its various sorts, we may, not without advantage, touch upon the doctrine of the Predicables; a set of distinctions handed down to us by Aristotle and his follower Porphyry, & some of which are well worthy of a place in modern philosophy, in which indeed several of them have taken firm root.

The Predicables are a classification of general names, arising out of Predication; and founded, not (like the numerous divisions & distinctions among general names of which we have hitherto treated) upon diversities in the meanings & functions of the words themselves, but upon diversities in the relation which they bear to some particular subject of which they happen to be predicated. Logicians reckon five different Predicables. We may predicate of the name of any thing, five different kinds of general names.

[¶2] But, as we have already intimated, general names are not parcelled out among these five classes, in such a manner that each inherently & for ever belongs to only one of the classes. The same name is in one class or another, according to the subject of which we conceive it to be, on the particular occasion, predicated. Animal is a genus with respect to man, or John; a species with respect to substance, or creature. Rectangular is one of the differentiæ of a geometrical square; it is merely one of the accidentia of the table on which I am writing.

We proceed briefly to characterize, & distinguish from one another, the five Predicables; in other words, the five different relations in which a general name, predicated of a given subject, may stand to that subject.

[§3]

[¶1]Genus, species, & differentia, are used in two different acceptations; their popular acceptation, in so far as such a term is applicable to any of the technical expressions of Logic; & the narrower sense in which they are used by the Aristotelian Logicians.

In their more popular acceptation, the mutual relations of these three terms are easily stated. As the power of framing classes is unlimited, we may frame two, one of which shall include the whole of the other and more. Such, for instance, are animal and man: man & mathematician. The larger of the two classes, which includes the smaller, is called the Genus. The smaller of the two, which is included in the larger, is called the Species. The distinction holds, whether the classes be classes of substances, of feelings, or of attributes. Animal, for instance, is a Genus; man & brute, its two Species; or we may divide it into a greater number of species, as man, horse, dog, &c. Biped or two-footed animal may also be considered a genus of which man & bird are two species. Taste is a genus, of which, sweet taste, sour taste, salt taste, &c. are species. Virtue is a genus; justice, generosity, courage, fortitude, prudence &c. are its species.

[¶2] The same class, which is a genus with reference to the subclasses or species included in it, may be itself a species with reference to a superior genus. Thus, man is a species with reference to animal, but a genus with reference to the species mathematician. Animal is a genus divided into two species, man & brute; but animal, also, is a species, which with another species vegetable, makes up the genus “Organized Being.” Biped is a genus with reference to man & bird, but a species with reference to the superior genus animal. Taste is a genus divided into species, but it is also a species under the genus Sensation. Virtue, a genus with reference to justice, temperance &c. is one of the species of the genus Mental Quality.

[¶3] In this popular sense the words Genus & Species have passed into common discourse. The word Differentia, or Specific Difference, is hardly used except by professed metaphysicians; by them, however, it is generally employed in a sense sufficiently extended, to correspond with the popular extension of the words Genus & Species. In this sense, the Differentia of a Species is any attribute, common to every individual of that species, & serving to distinguish it from all other species of the same genus. Thus, rationality may be considered the Differentia of the species man, with reference to the genus animal; being an attribute possessed by all the individuals of that species, & by them alone among all the individuals belonging to the genus; serving, therefore, to distinguish the species man from the coordinate species, brute. If instead of referring man to the genus animal, we placed him under the genus biped, his differentia according to the old jest, would be featherless; or featherlessness, for in this loose employment of language,^[*] it is not material whether the concrete, or the abstract name be employed.

[¶4] By the Aristotelian logicians, the terms are used in a more confined sense. Animal would by them be considered a genus & man & brute, coordinate species under that genus; but biped would not be admitted to be a genus, with reference to man, nor featherless one of the differentiæ of that species. It was necessary, according to their theory, that genus, species & differentia, should be of the essence of the subject. Whatever was not of its essence, belonged not to these three predicables, but to proprium & accidens. Biped was not of the essence of man, & therefore did not stand in the relation of genus to that species, but of proprium or accidens only.

[¶5] In the previous chapter, we entered at large into the distinction between essential & accidental predication, & between essential and accidental attributes or properties. We found that this distinction, which has been the occasion of so much abstruse speculation, & to which so mysterious a character was formerly, & by many writers is still, attached, amounts to nothing but the difference between those attributes of a class which are involved in the signification of the name of the class, & those attributes which are not so involved. We found that there are no essences of individuals; that, as applied to individuals, the word essence has no meaning, except as connected with the exploded tenets of the Realists: but that when we predicate of the name of a class, the name which connotes any one or more of the attributes constitutive of the class, we produce an Essential Predication.

[§4^* ] The schoolmen, however, did not recognize this doctrine. The class to which any individual was most familiarly referred, (as John, Peter, &c to the class man) they considered as properly & inherently the species to which that individual belonged. Any further subdivisions into which that same class might be capable of being broken down (as man into black, white, & red man, or into priest & layman) they did not admit to be species. Having thus made over every individual in the universe to the indefeasible paramountcy of some one particular species, they next held that whatever was of the essence of the species, (by which they meant, though they knew it not, whatever was involved in the signification of its name) was of the essence of the individual also. Animality, therefore, & rationality, being of the essence of the species man (i.e. connoted by the name) were, according to them, of the essence likewise of John & William: but bipedity having nothing to do with the essence of man (for the word man involves not that quality in its signification) is not of the essence of John either; & consequently two-footed is neither a genus of John nor one of his Differentiæ; but is merely predicable of him accidentally, & belongs not to one of the first three, but to one of the two latter, Predicables.

The Aristotelians being the original authors of these important terms & distinctions, it is reasonable that before we attach a meaning of our own to them, we should ascertain how far that which was given to them by their inventors is capable of being reconciled to the true theory of the subject. Dropping therefore, the essences of individuals, a figment of which nothing rational can be made, but adhering to the assumption that the Genus & the Differentia must be of the essence of the Species, let us enquire what mutual relations of the three terms are consequent upon that supposition. And first, when the classes in question are classes of substances or of feelings, & the names, consequently, connotative.

[§5]

[¶4] From the very fact that the Genus includes the Species, in other words, denotes more than the Species, or is predicable of a greater number of individuals, it follows that the Species must connote more than the Genus. It must connote all the attributes which the Genus connotes; otherwise there would be nothing to hinder it from denoting individuals not included in the Genus. And it must connote something besides, otherwise it would include the whole Genus. Man denotes all the individuals denoted by mathematician & many more: Mathematician, consequently, must connote all that man connotes, otherwise there might be mathematicians who were not men; & it must connote something more than man connotes; otherwise all men would be mathematicians. The Species, therefore, connotes all that the Genus connotes, & something more.

Take from the Species all that it connotes more than the Genus, & let there be another word which connotes this surplus taken by itself; that word is the Differentia, or Specific Difference. Or it may be stated thus: The Differentia is the word which connotes what must be added to the connotation of the Genus, to make up the connotation of the Species. [¶5] The Differentia is said properly enough to constitute the Species. The Differentia of the class mathematician considered as a species of the genus man, is, “knowing mathematics;” for that is the word which connotes what mathematician connotes more than man. The differentia of the class man, considered as a species of the genus animal, is two-fold, “rational & of a certain ^[*] particular form” (the form which we all know). Both these attributes are connoted by man, exclusively of what it connotes in common with animal: & there is no single word which connotes these attributes without connoting any others. The compound word, rational & of the human form is therefore the Differentia or Specific Difference of the species man, considered as referred to the genus Animal. This same Differentia, which is said to be the Specific Difference of man, is called a Generic Differentia with reference to any sub-class, with regard to which man is itself a Genus. With regard to man, it is the Specific Difference, or the Difference which constitutes the Species itself: with regard to mathematician, it is the Difference which constitutes a prior class, a class which, with reference to mathematician is but a Genus, not the Species.

^[†] Thus we have a very clear view of the relation between Genus, Species, & Differentia, when the things classified are either Substances, or Feelings. But how when they are neither Feelings nor Substances, but Attributes? for these also are classified; are formed into classes & subclasses, which are not only popularly called Genera & Species, but are reckoned such by the schoolmen themselves. Thus, quality is a genus, of which colour is one of the species; colour is a genus, whiteness one of its species. These genera, equally with any of the others, are said by the Aristotelians to be of the essence of their species. “Colour is a quality” they would call an Essential Predication; “whiteness is a colour” the like. In what sense? for the terms, as we have formerly shown, not being connotative, the explanation which we have already given of essences & essential predication, will not serve.

I apprehend that the word essence, in this case, has no meaning; no more than in the case of the pretended essences of individuals. In the case of connotative names, we found that essence, & essential predication had a meaning; though one which the inventors of those phrases did not see to the bottom of. They said, that is of the essence of any thing, without which it could neither be, nor be conceived to be; now that without which a man could not be nor be conceived to be, is that, in the absence of which we should not call him man; that is, the attributes which the name man connotes. Such attributes, therefore, are really of the essence of man, in the scholastic sense; & the propositions in which words which connote any of those attributes, are predicated of man, form a class apart, distinguished from other predications by the fact that they communicate no information to any one who previously knew the meaning of the word which is the subject of the proposition. Now, if, taking for the subject of our proposition an abstract name which is not connotative, we can frame any predications which shall possess this same property of affirming nothing but what is already implied in the meaning of that abstract non-connotative name, we may with great propriety call these predications, essential ones. But in our last chapter we found but one such predication; the definition of the abstract name, & not even that always; as we shall see hereafter. The proposition “Whiteness is a colour,” tried by this criterion, certainly is not an essential proposition. The idea of colour is certainly not implied in the meaning of the word whiteness. Any one knows the meaning of the word whiteness, who knows the sensation of white. But when we place whiteness in the class colour, we imply much more than the sensation of white; we place it there on account of a distant resemblance to the numerous other sensations which we call colours; or else, on account of a wholly extrinsic circumstance, that of being perceived through the eye. Colour, therefore, is not of the essence of whiteness, in the sense in which animality & rationality are of the essence of man, viz. as being implied in the meaning of the name. But we found that this was the only rational sense, in which the term essence could be understood. In no rational sense, therefore, is colour of the essence of whiteness,^[*] and the doctrine, that the genus must be of the essence of the species, will not, in this case, hold.

What then, did the Aristotelians mean, or what reason had they for maintaining that in the case of attributes as well as of substances, the genus must be of the essence of the species? Merely this: that the genus is, as they expressed it, predicated in quid: that is, in answer to the question, What the thing is. Thus if you ask, what is John? the first answer is, A man; if you ask, what is a man? the answer is, An animal, or A rational animal: If, What is whiteness? the answer is, A colour. But the reason of this is very simple. When we are asked, What a thing is? we naturally answer by naming the class to which the thing is most familiarly referred. If we are pressed still harder, then, besides naming the class to which the thing is most familiarly referred, we mention the circumstance which distinguishes it from the other things belonging to the class. This explains why the Genus & Differentia were held to be of the essence of the subject. But if this explanation be correct, then the distinction set up by the schoolmen between the Genus to which anything belonged, & any other class which could be formed including that thing was a mere difference of custom & convenience: & (as we have already seen in the case of what they called their lowest Species, which they did not allow to be divisible into other species) all they did was, to take the classification which had become most habitual, & ascribe to it a prerogative of supremacy, imposing on every individual an indefeasible allegiance to a particular series of classes (rising one above another like the middleman & the head landlord of an Irish estate) because the custom which had associated it with those particular groups was so strong that it was mistaken (as custom so often is) for a law of nature.

The definition which I shall endeavour to give of Genus & Differentia, will retain as much of the spirit of the Aristotelian employment of the terms as is compatible with the rejection of this notion of jure divino classifications. Those terms on the one hand, & proprium & accidens on the other, may, I conceive, with little variation from their original meaning, be employed to mark distinctions which really exist, & are well worth preserving, and dwelling upon.

In all classifications, that is, in all parcelling out of a mixed multitude of objects into classes & subclasses, we may distinguish one main division & a number of cross divisions. We may make as many divisions as we can conceive attributes; we in fact, do so whenever we give a name which connotes any attribute; for by the fact of giving the name, we establish a division of things in general, into those which possess the given attribute & those which do not. But notwithstanding this, there is in all cases some one particular system of divisions and subdivisions, which forms as it were the ground-work of all other divisions which are made of the same complex whole. There is some one particular way of grouping the objects, to which the general course of our ideas seems to adapt itself, & upon which all other arrangements of the same objects are as it were engrafted. Thus, for instance the division of substances into organized & inorganic; that of organized substances, into animal & vegetable; of animals into man, beasts, birds, fishes, insects, reptiles, &c. constitute a system of divisions, (or, as we commonly say, a classification) founded upon the most obvious resemblances & upon the most obvious differences, of the things which are thus classed: an arrangement, in which those which are manifestly & at the first view alike, are placed together; those which are manifestly & at the first view unlike, are placed separate: an arrangement, therefore, into which the mind so naturally falls (that is, falls so readily, & as it were of itself) that the schoolmen may be excused for having thought that this classification, was the work of nature, while all other arrangements of the same objects were arbitrary, & the work of men.

This, therefore, is an example of a main division; we shall come to the cross divisions presently. All the classes, which are constituted by a main division, are genera & species: each class being a genus with reference to its own subdivisions, & a species with regard to those superior classes of which it is itself a subdivision.

[§6]

[¶1] Besides the main divisions, which are such because they accord with the arrangement & grouping into which our ideas naturally fall without any express intention, we may also artificially make other main divisions, for reasons of special convenience. For example, a naturalist considers the various kinds of animals, & looks out for the classification of them which may most accord with the order in which, for the purposes of his science, it is desirable that his ideas should present themselves; with this view he finds it advisable that one of his fundamental divisions should be that into warm-blooded & cold-blooded animals; or into the animals which breathe with lungs, & those which breathe with gills; or into carnivorous, & frugivorous or graminivorous; or into those which walk on the flat part and those which walk on the extremity of the foot, a distinction on which some of Cuvier’s families are founded. These classes, not being those to which the individual animal is familiarly & spontaneously referred, or in which we should ever think of arranging the animal kingdom unless for a preconcerted purpose, or in pursuance of a previous convention; the schoolmen would not have allowed to them the character of genera or species. For, the schoolmen would allow no classification, as the fundamental one, except that which being most familiar they deemed to be the work of nature. But we, who know that classification is arbitrary, and exists for the sake of human convenience, must allow that the groups into which objects first class themselves, according to their obvious & superficial resemblances, may not be the most convenient ones for the purposes of a particular art or science. For that special purpose, the objects, which are most conveniently placed together, are those which agree in the properties which that art or science takes special cognizance of. And even for the general purposes of human knowledge, when pursued scientifically, objects should be classed not according to the resemblances & differences which are the most obvious, but according to those which are either in themselves the most interesting, or are an indication of others which are so. These considerations often suggest the expediency of adopting, as fundamental divisions, on which to ground an author’s main classification, distinctions very remote from the obvious ones which the mind forms as it were spontaneously. But the classes which are the result of these divisions, are as much entitled to be considered genera & species, as any other classes, so soon as the speaker or writer has adopted them into his main division.

^[*] But let us now take any attribute of objects, which has not been adopted as the basis of their classification; for instance, (in speaking of plants, or animals) their colour. On this attribute is actually founded as real a classification of plants or animals as on any other attribute which we have named.

The word white, of itself divides all objects, & plants or animals among the rest, into two classes; white objects, & objects which are not white. If we were to enumerate all the names which connote colours, they would provide us with a general arrangement & classification of all substances. We have white substances, black substances, red substances &c.: We have even classes & subclasses: red substances, for instance, are either scarlet, crimson, or of various other shades & varieties of red colour. Why are these classes not genera & species? Merely because nobody has ever thought of making the division of objects according to their colour, his main & fundamental classification of them, & presenting all other divisions as engrafted upon & growing out of that. It was open to any person to do so; this, like any other division, might have been made the fundamental division, if anyone had chosen. But nobody’s purposes were answered by it. The colours of objects are neither in themselves the most interesting, or important of their attributes; nor do they point to any considerable number of attributes besides themselves. Plants & animals which agree in colour, differ in almost every other attribute; & others, again differ in colour, which agree in almost every thing else. There would have been no convenience, therefore, in making the division of objects according to colours the main division; it accordingly continues in the state of a cross division; objects are grouped according to quite other attributes, & the divisions constituted by colour are as it were lines drawn across the other classification & cutting off a segment from each of the groups, founded on some other attribute; from the group flowers the segment white flowers; from the group animals the segment white animals, & so on. These segments are classes, but are not genera & species. They belong to the predicables proprium & accidens.

^[†] Having now settled, with as much precision as the case seems to admit, the notions of Genus & Species, we shall easily frame a correspondent notion of Differentia. Every Differentia is called such, in relation to a particular Genus & to a particular Species; & is the name (whether abstract or concrete) signifying the attribute which constitutes the Species; in other words, the attribute which we had in view when we cut that Species out of the Genus; & which we intended to constitute the distinction between that Species & all other Species of the same Genus.

[¶2] Now if we cut a species out of a genus, the species man, for instance, out of the genus animal with the intention on our part that the distinction between man & all other species of animal should be rationality, then rationality is involved in the signification of the word man; in other words connoted by it; for it is obvious that what we have expressly in view when we impose a name, forms part of the meaning of that name. If again, being naturalists, we for the purpose of our particular study, cut out of the genus animal the same species man, but with an intention on our part that the distinction between man & all other species of animal should be, not rationality, but the possession of thirty two teeth, so many cutting teeth & so many grinders; it is evident that the name man, when used by us as naturalists, no longer connotes rationality, but connotes the possession of thirty two teeth. We may therefore, lay it down as a maxim, that whereever there is a Genus, & a Species marked out from that Genus, by an assignable Differentia, the name of the Species must be connotative, & must connote the Differentia; but it may be a special connotation, not involved in the signification of the term as ordinarily used, but given to it when employed as a term of art or science. The word man, in common use, connotes rationality & a certain form, but does not connote the number of teeth; in the Linnean system it connotes the number of teeth, but does not connote rationality or any particular form. The word man, therefore has two different meanings; but it is not commonly considered ambiguous, because it happens in both senses, to denote the same individuals. But we may easily conceive a case in which the ambiguity would be obvious; we have only to imagine that some new species of animal were discovered, possessing thirty two teeth, but not rational nor of the human form. In ordinary parlance these animals would not be called men; but in natural history, they must be called so, if the Linnean classification were adhered to; which, however, in all probability it would not be.

[¶3] Words not otherwise connotative may in this manner acquire a special or technical connotation. Thus, the word whiteness, as we have so often remarked, connotes nothing; it merely denotes the attribute corresponding to a certain sensation; but if we are making a classification of colours, & desire to mark out, or to justify, the particular place which we have assigned to whiteness in an arrangement, we may define it, “the colour produced by the mixture of all the simple rays;” & this fact, though by no means implied in the meaning of the word whiteness as ordinarily used, becomes part of its meaning in the particular essay or treatise, & becomes the Differentia of the Species.

[¶4] The Differentia, therefore, of any Species, may be defined to be, that part of its connotation (whether ordinary, or special & technical) which distinguishes it from all other Species of the Genus to which on the particular occasion we are referring it.

[§7]

[¶1] Having now disposed of Genus, Species, and Differentia we shall find no difficulty in attaining a clear conception of the distinction between the other two Predicables.

[¶2] According to the schoolmen, Genus & Differentia are of the essence of the subject, (that is, form part of the ordinary connotation of the name of the Species): Proprium & Accidens on the other hand form no part of the Essence, but are predicated of the Species accidentally. Of these two, Proprium, they continue, is predicated accidentally, indeed, but necessarily; that is, signifies an attribute which is not, indeed, part of the essence, but flows from, or is a consequence of, the essence, & therefore is inseparably attached to the Species: as the properties of a triangle, though no part of its definition, yet must necessarily be possessed by whatever comes under the definition. Accidens, on the contrary, has no connection at all with the essence; & whether separable or inseparable from the Species in reality, its removal would not alter our conception of the Species.

^[*] As we have found it necessary to include under the head of Genus & Differentia, much which is not of the essence of the species, that is, which forms no part of its ordinary connotation, we must alter the other definitions accordingly. We shall then define the five Predicables as follows:

Species is any class.

Genus is any class which stands above & includes, that class, in our main or fundamental classification: whether that be the classification most familiarly used in ordinary life, or one made for the specific purpose of some Art or Science.

By placing a Species under a Genus, it acquires a special Connotation, even if it had not already an ordinary one. Differentia is that attribute, or (if there be several) any one of those attributes, which, being either ordinarily or specially connoted by the name of the Species, serve to distinguish it from the other species of the same Genus.

[¶3] A Proprium of the Species, is any attribute belonging to all the individuals included in it; not, however, connoted by its name, either ordinarily (if the classification be for ordinary purposes) or specially (if it be for a special purpose) but following from some attribute which is either ordinarily, or (as it may happen) specially, connoted by it.

[¶4] One attribute may follow from another in two ways, & there are consequently two kinds of Proprium. It may follow as a conclusion follows premisses, or it may follow as an effect follows a cause. Thus, the attribute of having the opposite sides equal, (which is not one of those connoted by the word parallelogram) nevertheless follows from those connoted by it, viz. from those of having the opposite sides straight lines & parallel. The attribute of having the opposite sides equal, is therefore, a Proprium of the species Parallelogram; & a Proprium of the first kind, which follows from the connoted attributes by way of demonstration. The attribute of being capable of understanding language is also a Proprium of the species man, since, while not connoted by the word, it follows from an attribute which the word does connote, viz. from the attribute of rationality. But this is a Proprium of the second kind, which follows by way of causation. Whether a Proprium follows by demonstration or causation, it follows necessarily; that is to say, it cannot but follow, consistently with the known laws of the universe.

[§8]

[¶1] Remains the fifth Predicable, Accidens. Under this name are comprehended all the attributes which are neither involved in the signification of the name, (whether ordinarily or as a term of art) nor have, as far as we know, any necessary connexion with attributes which are so involved. They are commonly divided into Separable & Inseparable Accidents. Inseparable Accidents are such as are universal, but not necessary. Thus blackness is an attribute of a crow: & as far as we know, a universal one. But, if we were to discover a race of brown birds, in other respects resembling crows, we should call them crows; crow, therefore does not connote blackness; nor, from any of the attributes which it does connote, whether as a word in vulgar use or as a term of art, could blackness be inferred. Not only, therefore, can we conceive a brown or red crow, but we know of no reason why such an animal should not exist.

[¶2] Separable Accidents are such as do not belong to every individual of the species, but only to some; or if to all not at all times. Thus, the colour of a European is one of the separable accidents of the species man, because it is not an attribute of all human beings: Being born is also a separable accident of the species man, because though it is an attribute of all human beings, it is so only at one particular time.

OF DEFINITION

[Chapter viii: Of Definition]

[§1]

[¶1] The object & nature of Definition will not require much elucidation, as the greater part of what is necessary to make them apparent, has been already stated, incidentally to other topics.

[¶2] The simplest and most correct idea of a Definition, is a proposition which declares the meaning of a word: namely, either the meaning it bears in common acceptation, or that which the speaker or writer, for the particular purposes of his discourse, intends to annex to it.

[¶3] The Definition of a word being the proposition which enunciates its meaning, it follows that words which have no meaning, are unsusceptible of definition. Proper names, therefore, cannot be defined. A proper name being a mere unmeaning mark put upon an individual, we cannot declare its meaning; though we may indicate by language, as we might indicate still more conveniently by pointing with the finger, what is the individual upon which that particular mark has been or is intended to be put. It is no definition of “John Thomson” to say, he is “the son of General Thomson,” for the name “John Thomson” does not express this. It is no definition of “John Thomson” to say he is “the man who is now crossing the street.” These propositions may serve to make known who is the particular man to whom the name belongs, but that may be done still more unambiguously by pointing to him, which however has never been esteemed one of the modes of Definition.

[¶4] In the case of Connotative names, the meaning, as we have so often observed, is the connotation: & the definition of a connotative name, is a proposition which declares its connotation. Now this may be done either directly or indirectly. The direct way would be by a proposition in this form: “Man” (or whatever the word may be) “is a name connoting such & such attributes” or “is a name which signifies the possession of such & such attributes, by all the things whereof it is predicated.” This would be the most precise form. The definition of Man, in this form, would be, man is a name connoting corporeity, organization, life, rationality & a certain well known external form.

[¶5] This, however, is not sufficiently brief, & is moreover too technical & apparently pedantic for common discourse. The more usual mode of declaring the connotation of a name, is to predicate of it another name or names, of known signification, which connote the same aggregation of attributes. This is done either by predicating, of the name intended to be defined, another connotative name, exactly synonymous; as, “Man is a human being;” this is not commonly reckoned a definition at all; or a plurality of connotative names, which among them, make up the whole of the connotation of the name which is to be defined. In this last case, again, we may either take the several attributes singly, & join together the whole of the names which connote those attributes separately; as, Man is a corporeal, organized, animated, rational being, of a certain form; or we may employ names which connote several of the attributes at once; as, Man is a rational animal of a certain form.

[¶6] The definition of a name, therefore, according to the notion of it which we have been endeavouring to inculcate, is the sum total of all the essential propositions which can be formed concerning the name. All the propositions, the truth of which is self-evident; all those which we are made aware of by merely hearing the name, are included in the Definition if complete, and are included indirectly & expressly, not by way of inference; whether the definition comprehends them in a few words, or in a larger number.

When Condillac & other writers have said that a definition is an analysis, what they have really meant seems to be merely what we have now stated. To resolve any complete whole into the elements of which it is compounded, may properly be called an operation of analysis: & this we in some measure do, when we replace one word which connotes a whole set of attributes by two or more words, which connote the same set of attributes singly, or in smaller groups.

[§2]

[¶1] From this however the question naturally arises, in what manner we are to define a name which connotes only a single attribute? for instance, the name white which connotes nothing but whiteness, rational, which connotes nothing but the possession of reason. It would seem that such names could only be defined in two ways; by a synonymous term, if any can be found; or in the direct way already alluded to, “White is a name connoting the attribute of whiteness.” Let us see, however, whether the analysis of the meaning of the name, that is, the breaking down of that meaning into separate parts, admits of being carried farther. In the case of the word white, it would seem not; but in the case of rational, it is obvious that some further explanation may be given of the meaning of that term, than is contained in the proposition “Rational is a name connoting the possession of reason,” since the attribute, reason, itself admits of being defined. And here we are obliged to turn our attention to the definitions of attributes, or rather of the names of attributes, that is, of abstract names, having hitherto confined ourselves to the first two classes of names, proper & connotative.

[¶2] What the definition of the name of an attribute consists in, has been very clearly shown in the preceeding chapter. Some names of attributes are connotative. These, like other connotative names, must be defined by declaring their connotation. In other cases, we found that the attribute denoted by the abstract name, is itself a union of several attributes; in this case the analysis must be carried on, by enumerating those attributes; as when we defined humanity to be, corporeity & animal life combined with rationality & a certain form. [¶3] We found still another class of cases, in which though the attribute denoted by the abstract name, is not a complication of attributes, still the phenominon constituting that attribute, is a complication of phenomina. We must then carry on the analysis, by defining those more simple and elementary phenomina. Under this class comes our former example, rationality, which in whatever way we may resolve to define it, expresses a series of very complicated phenomina. We have already employed an apter example, the word eloquence, which we defined “the power of influencing the affections of human beings by means of speech or writing.”

[¶4] Thus, then, we define a name, whether concrete or abstract, whenever we are able to analyse, that is, to distinguish into parts, the attribute or set of attributes, which constitute their meaning: if a set of attributes, by enumerating them; if a single attribute, by dissecting & exhibiting in its separate elements, the fact or phenominon, that is the cluster or series of human feelings, or states of consciousness, which constitute that attribute, or rather which when considered as excited or as experienced by any object, are that attribute. Even when the fact which constitutes the attribute, is unsusceptible of analysis, that is to say, is a simple sensation or other simple feeling, the name of the object & the name of the attribute, still admit of definition. Whiteness, we may say, is the property of giving the sensation of white; a white object is an object which gives the sensation of white. The only names which are wholly unsusceptible of definition are the names of the simple feelings themselves. These are in the same predicament as proper names. They are not indeed, like those names, unmeaning; for the words sensation of white signify that the individual sensation which we call by that name, resembles the sensations formerly experienced by us, to which the same name was given: but as we have no words by which ^[*] to recall those former sensations, except the very word which we want to define, or some other exactly synonymous with it, words cannot unfold the signification of this class of names; and we are obliged to make a direct appeal to the party’s own ocular experience.

[§3]

[¶1] Having stated what we conceive to be the philosophical idea of a Definition, we proceed to examine some popular conceptions of it, which conflict more or less with the above.

[¶2] The only Definition of a name, which will satisfy a philosopher, is one which declares the facts, and the whole of the facts, which are involved in the signification of the name. But in most cases, & with most persons, the object of a definition does not embrace so much. They look for nothing more in a Definition, than a guide to the proper use of the term; a protection to them against applying it in a manner inconsistent with custom & convention. Anything, therefore, is to them a sufficient definition of a term, which will serve as a correct index to what it denotes; although not embracing the whole, & sometimes perhaps not even a part, of what it connotes. This gives rise to two kinds of imperfect or unscientific definitions; namely, Essential but incomplete Definitions, & Accidental Definitions, or Descriptions. In the former, a connotative name is defined by a part only of its connotation; in the latter, by something which forms no part of its connotation at all.

[¶3] An example of the first kind of imperfect definitions, is the following: Man is a rational animal. It is impossible to consider this as a complete definition of the word man, since if we adhered to it we should be obliged to call the Houyhnhms men: but as there happen to be no Houyhnhms, this imperfect definition is sufficient to mark out, & distinguish from all other things, the objects at present denoted by man; all the beings actually in existence, of whom the word is predicable. Though the word is defined by an enumeration of some only among the attributes which it connotes, not of all, yet it so happens that all things which possess the attributes enumerated, possess also those which are omitted, so that the field of denotation which the word covers, & that employment of it in predication, which is conformable to usage, are quite as well indicated by the incomplete definition, as by a complete one. Such a definition, however, is always liable to be overset by the discovery of new objects in nature.

[¶4] Definitions of this kind are what philosophers have had in view when they laid it down as a rule that the definition of a species should be per genus et differentiam. A complete definition according to the philosophical idea of it should be per genus et differentias rather than differentiam: it should include, with the name of the superior genus, not merely some attribute which distinguishes the species intended to be defined, from all other species of the same genus, but all the attributes implied in the name of the species, which the name of the superior genus does not by connotation include.

The assertion, however, that a definition must of necessity consist of a genus & differentiæ at all, is not tenable: for, as was early remarked, the summum genus in any classification, having no superior genus, cannot be defined in this manner: yet we have seen that all names, (even summa genera) except the names of simple sensations or other elementary feelings, may be defined, and in the very strictest sense, by setting forth in words the sensations or other facts of consciousness, of which the connotation of all words is ultimately composed.

^[*] The notion that a Definition should consist of the superior Genus & some one specific Difference, a notion which we first find distinctly enunciated by Aristotle & his followers, seems to have arisen from a peculiar connection which existed in the minds of those philosophers between the idea of Definition and that of Division or Classification; & is closely allied to the erroneous notion which they entertained of the latter process. In laying down a Definition, they did not consider themselves as setting forth the meaning of a name, but as declaring a classification; drawing as it were a line round a particular class, to point out its limits, designate the objects which fall under it, & indicate its place in the network of genera & species, which they had spread over all nature. In my view of classification, the connection between that operation and nomenclature is as close as it was deemed to be by Aristotle; but I regard names as being oftener the instruments, the sources, or the occasions of classification, than its results: whenever we give a name to any thing, intending by that name to express any of its properties, we by that very fact accomplish a classification; we divide all things into two kinds, those which possess the properties in question, & those which do not. Classification therefore, is in general not the cause but the result of nomenclature; by every significant name which it suits our convenience to construct we create a new classification. The ancients however viewed classification in a totally different light. They thought that Nature herself had marked things out into classes; & they consequently regarded general names, & the Definitions which declared the import of those names, not as operations from which there resulted classifications of man’s making, but as the exponents of a classification already made. It naturally, therefore, appeared to them, that a definition had attained its purpose, if it was such as would enable them to discriminate, & segregate from all others, the individuals composing the class thus framed by the hand of nature.

[§4]

[¶1] These considerations explain why the ancients, and philosophers in general, have considered the first kind of incomplete definition (viz. that which defines a connotative name by a part only of its connotation, but a part sufficient to mark out correctly the boundaries of its denotation) as a complete definition. But, in order thus to satisfy them, it was necessary that all the attributes employed should really form part of the connotation of the term: because any attribute not connoted by the term would not in their estimation have been part of the essence of the class, & would not therefore have answered their purpose of discriminating the real nature of that particular class from that of other classes. Our second kind of incomplete definition, therefore, that which defines a connotative name by means of its accidents, i.e. those of its attributes which are not included in its connotation, has been rejected from the rank of genuine Definition by all philosophers, & has been termed Description.

[¶2] This kind of imperfect definition, however, takes its rise from the same cause as the other, namely, the disposition to be satisfied with a definition which whether it expounds the meaning of the name or not, enables us to discriminate the things denoted by it, from all other things, and consequently to employ the term in predication, without deviating from established usage. This purpose is duly answered by enumerating any whatever of the attributes which happen to be common to all the things composing a class, though perhaps having no connexion with the motives which led to their being formed into a class, & called by a common name. It is only necessary that the definition or description thus formed, should be convertible with the name it happens to define; that is, should be exactly coextensive with it, each being predicable of every thing of which the other is predicable. The following are correct definitions of ‘man’ according to this test: Man is an animal having (by nature) two hands (for all human beings answer to this description, & no other animal does): Man is an animal who cooks his food: Man is a featherless biped.

[¶3] What would otherwise be a mere Description, may be raised to the rank of a true Definition by the peculiar purpose, which the speaker or writer has in view. As has been seen in the preceding chapter, it may for the purposes of a particular branch of science, or for the statement of an author’s particular views on some branch of science, be convenient to give to some general name, a special connotation different from its ordinary one. When this is the case, a Definition of the name by means of the attributes which make up this special connotation, becomes on the particular occasion & for the particular purpose a genuine & complete Definition, although in general it would be a mere Accidental Definition, or Description. This actually happens in regard to one of our last examples, “Man is an animal having two hands;” which is a complete and scientific Definition of the word Man, considered as the name of one of the species in Cuvier’s classification of animated beings.

^[*] In cases of this description, the notion which the ancients had of Definition really applies, & the object of Definition is not to state the meaning of a word, but to expound a classification. The special meaning which Cuvier assigned to the word man (quite foreign to its ordinary meaning, though involving no change in the denotation of the word,) was incidental to a previously conceived plan of arranging all animals into classes on a certain principle, that is according to a certain kind of distinctions. And since the definition of Man according to its ordinary connotation, though it would have answered all the other purposes of a definition, would not have pointed out the place of the species Man in that particular classification, he gave the word a special connotation, that he might be able to define it by attributes of that kind on which he, for reasons of scientific convenience, had determined to found his division of the animal kingdom.

[§5]

[¶1] We have now said enough on the subject of the two incomplete or unscientific kinds of Definition, & the distinction between them & the complete or scientific kind. We shall now proceed to examine an ancient, & at one time generally prevalent doctrine, which we consider as entirely erroneous, & the source not only while it was universally entertained but even since it has been generally rejected, not only of important errors, but of a great part of the obscurity which still hangs over the real nature of some of the most important processes of the understanding in the pursuit of truth.

The notion to which I allude, is, that definitions of names are not the only, or the most important class of definitions; that Definitions may be divided into two classes, Definitions of Names, & Definitions of Things. The former, it is affirmed, are intended to explain the meaning of a term, the latter, the nature of a thing.

[¶2] This opinion was held by all the ancient philosophers & their followers, except the Nominalists; but as the most widespread schools of modern philosophy have generally been Nominalists, the notion of Definitions of Things has not been in modern times the received notion, & has contributed rather by its consequences than by itself to introduce confusion into the philosophy of logic. It has, however, (along with several other of the errors & misleading modes of expression of the schoolmen, which the author’s intellectual indolence prevented him from casting off) recently reappeared in a deservedly popular work, Dr. Whateley’s Logic. In a superficial & in some points, erroneous article on that work, published by me in the Westminster Review for January 1828, I made the following observations, which still appear to express sufficiently what I have to say on the question now in issue.

[¶3] “The distinction between nominal & real definitions, between definitions of words & what are called definitions of things, though conformable to the ideas of most of the Aristotelian Logicians, cannot, as it appears to us, be maintained. We apprehend that no definition is ever intended to ‘explain & unfold the nature of the thing.’ It is some confirmation of our opinion, that none of those writers who have thought that there were definitions of things, have ever succeeded in discovering any criterion by which the definition of a thing can be distinguished from any other proposition relating to the thing. The definition, they say, unfolds the nature of the thing: but no definition can unfold its whole nature; & every proposition in which any quality whatever is predicated of the thing, unfolds some part of its nature. The true state of the case we take to be this. All definitions are of names, and of names only: but, in some definitions, it is clearly apparent, that nothing is intended except to explain the meaning of the word; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word. Whether this be or be not implied in any given case, cannot be collected from the mere form of the expression. ‘A centaur is an animal with the upper parts of a man & the lower parts of a horse;’ & ‘A triangle is a rectilinear figure with three sides,’ are, in form, expressions precisely similar; although in the former it is not implied that any thing conformable to the term, really exists, while in the latter it is; as may be seen by substituting, in both definitions, the word means for is. In the first expression, ‘A centaur means an animal’ &c., the sense would remain unchanged; in the second, ‘a triangle means,’ &c. the meaning would be altered, since it would be obviously impossible to deduce any of the truths of geometry from a proposition expressive only of the manner in which we intend to employ a particular sign.

[¶4] “There are, therefore, expressions, commonly passing for definitions, which include in themselves more than the mere explanation of the meaning of a term. But it is not correct to call an expression of this sort a peculiar kind of definition. Its difference from the other kind consists in this, that it is not a definition, but a definition & something more. The definition above given of a triangle, obviously comprises, not one, but two propositions, perfectly distinguishable. The one is, ‘There may exist a figure bounded by three straight lines,’ the other, ‘& this figure may be termed a triangle.’ The former of these propositions is not a definition at all; the latter is a mere Nominal Definition, or explanation of the use & application of a term. The first is susceptible of truth or falsehood, & may therefore be made the foundation of a train of reasoning: the latter can neither be true nor false; the only character it is susceptible of is that of conformity or disconformity to the ordinary usage of language.”

[¶5] The distinction, then, between Definitions of Names, and what are erroneously called Definitions of Things, is that the latter, along with the definition of a name, covertly asserts a matter of fact. This covert assertion is not a definition, but a postulate. It is not an essential, but an accidental proposition. It is an assumption, which is not like a definition, a mere identical proposition, from which no conclusions on matters of fact can possibly be drawn; but, on the contrary, may be made the foundation on which to build a whole fabric of scientific truth.

[¶6] We have on a former occasion remarked, that those philosophers, who overthrew Realism, have very generally retained in their philosophy numerous propositions which could only have a rational meaning as part of a realistic system. It had been handed down from Aristotle & perhaps from still earlier times as an obvious truth, that the science of Geometry is deduced from definitions. This, so long as a Definition was supposed to be a proposition “unfolding the nature of the thing,” did well enough. But Hobbes came, and after scattering to the winds the notion that a Definition is any thing but an explanation of the meaning of a name, continued nevertheless to affirm as broadly as any of his predecessors, that the αρχαὶ, principia, or original premisses of mathematics, & not only of mathematics, but of science in general, are Definitions: Thus producing the monstrous paradox (which for years confused the intellect of him who is now expressing his sense of its absurdity) that a whole system of scientific truth, nay, all truth at which we arrive by reasoning, is deduced from the mere arbitrary conventions of mankind concerning the signification of words.

[¶7] I know it will be said that in order that any scientific truths may be deducible from our definitions, those definitions must be framed conformably to the phenomina of nature, that is, things must actually exist, conformable to the definition, i.e. possessing the collection of attributes which it enumerates. This correction being applied to the doctrine, it will stand thus: No truths can be deduced from a definition, unless it tacitly involves a proposition affirming the real existence of a thing answering to the definition, & unless this proposition thus tacitly assumed be true: But if this other proposition, covertly involved in the definition, be true, then we may deduce other truths—not from this tacit proposition, but from the definition. Surely we need not refute this. The other truths, if they follow at all, follow from the tacit assumption, not from the definition.

[¶8] Take, for instance, the definition of a circle, as laid down in Euclid’s Elements: & which, when analysed resolves itself into two propositions, one an assumption with respect to a matter of fact, the other a genuine definition. “A figure may exist, having all the points in the line which bounds it, equally distant from a single point within it.” “Any figure possessing this property is called a circle.” Now let us see which of these propositions it is, on which Euclid’s demonstrations depend. “About the centre A describe the circle BCD.” Is there not here a manifest assumption that a figure such as the definition expresses may be described? which is no other than the postulate, or covert assumption, involved in the so called definition. But whether that figure be called a circle or not, is quite immaterial to the conclusion. Again, the circle being described, “the radius BA is equal to the radius CA;” from what does this follow? from the arbitrary meaning of the word? or from the tacit assumption of the possibility of a figure of which all the radii are equal? We need not carry the analysis further.

[¶9] It seems hardly necessary to dwell at so much length upon what is so obvious; but when a distinction, however self-evident, has been long confounded, by persons of indisputable intellect, it must not be quitted until it is familiar. We will therefore point out one of the most glaring of the many absurdities which follow from the supposition that Definitions, as such, are ever premisses in any of our reasonings, except those which relate to words only. This is, that we may by an argumentation strictly correct according to logical rules, deduce from true premisses a false conclusion. Let us begin by laying down the following definition:

“A centaur is an animal having the fore parts of a man & the hinder parts of a horse.”

[¶10] No one can deny the correctness of this proposition, considered as a definition. The tacit assumption, indeed, (if there were any such assumption in this case) of the existence of an object with properties corresponding to the definition, would be false. Now then we frame the following syllogism:

• A centaur is an animal having the hinder parts of a horse:
• But a centaur is an animal having the fore parts of a man;
• Therefore
• Some animal or animals having the fore parts of a man,
• have the hinder parts of a horse.

[¶11] A syllogism strictly correct in the first mode of the third figure, & in which both the premisses are true, & yet the conclusion false. This is as every Logician knows, absurd. The conclusion being false & the syllogism correct, the premisses cannot be true. But the premisses considered as parts of a definition are perfectly uncontrovertible. It is clear, therefore, that the real premisses in this syllogism are not the definitions, but the tacit assumptions involved in them, of the existence of objects conformable to them; thus: A centaur is a really existing animal with the hinder parts of a horse; & so forth. Now these implied premisses being false, the falsity of the conclusion presents no absurdity. [¶12] If we would determine what conclusion follows from the same ostensible premisses when the tacit assumption is left out, let us, according to the recommendation in the Westminster Review, substitute means for is. We then have

• A centaur is a word meaning an animal with the hinder parts of a horse:
• A centaur is a word meaning an animal with the fore parts of a man:
• Therefore
• Some word or words which mean an animal with the fore parts of a man, also
• mean an animal with the hinder parts of a horse:

where the conclusion as well as the premisses is true & is the only kind of conclusion which can ever follow from a definition, namely a conclusion relating to the meaning of words.

[¶13] We need not illustrate any further the difference between a Definition, & the tacit assumption of a matter of fact, which is sometimes involved in it. We shall only further remark, to show in what cases that assumption is to be understood as being made, & in what cases not—that unless we declare the contrary, we always convey the impression that we intend to make the assumption, when we profess to define any name which is already known to be a name of really existing objects. This is the reason why it was doubtful whether such an assumption was included in the definition of a centaur, & not doubtful that it was included in the definition of a circle.

[§7]

[¶1] Although Definitions are of names only, & not of Things, it is nevertheless true, that how to define a name may be not only an enquiry of considerable difficulty & intricacy, but one which turns upon considerations going deep into the nature of the things which are denoted by the name. Such, for instance, are the great enquiries which form the subjects of the most important of Plato’s Dialogues, as, “What is rhetoric” the subject of the Gorgias, or “What is justice,” that of the Republic. Such also is the question scornfully asked by Pilate, “What is truth?” and the great question with speculative moralists in all ages, “What is virtue.”

[¶2] It would be a complete mistake to represent these difficult & noble enquiries as having nothing in view, but to ascertain the conventional meaning of a name. They are enquiries not so much to determine what is, as what shall be, the meaning of a name: which like all practical questions of nomenclature, requires for its solution that we should enter very deeply into the properties not only of names but of the things named.

^[*] The principles of philosophical nomenclature will form the subject of one of the last chapters of this work, as the whole field of Logic must be surveyed before all the considerations on which the goodness or badness of a nomenclature depends, can be properly estimated. In that chapter, the apparent paradox which we have just noticed, would naturally be cleared up; but it appears desirable to give an anticipated solution here, as without it the theory of Definition, considered as a mere theory, would remain both obscure & imperfect.

[¶3] Although the meaning of every concrete general name, resides as we have seen, in the attributes which it connotes; yet the objects received names before the attributes, as appears from the fact that almost all abstract names in all languages are compounds or derivatives of the corresponding concrete names. Connotative names, therefore, were after proper names, the first which were used. The meaning of a connotative term lies as we have so often observed, in the connotation; & in the simpler cases, no doubt, a distinct connotation was present to the minds of those who first used the name, & was distinctly intended by them to be conveyed by it. Thus, the first person who used the word white, in speaking of snow or any other object, had, no doubt, in his mind a perfectly distinct idea of whiteness, & knew that to be the quality, & the only quality, which he meant to predicate of snow in calling it white.

[¶4] But when the qualities by which objects are discriminated from one another, are not of so palpable & easily ascertainable a kind; & in particular where the resemblances & differences of objects arise not from any one quality but from a number of qualities, the effects of which are so mixed up together as not to be easily distinguished from one another; it often happens that names are applied to objects, with no distinct connotation present to the minds of those who apply them: In naming a new object by an old name, all that their minds are conscious of is a general resemblance between the new object & all or some of the old & familiar objects which they have been accustomed to call by that name. This, as we have seen, is the law which even the mind of the philosopher must follow, in giving names to the simple elementary feelings of our nature: but where the things to be named are complex wholes, which, if they resemble, resemble not in all points alike, but in some of their parts, qualities or features only, or in some more than others, a philosopher is not satisfied when he merely finds himself struck by a general resemblance; he examines & discovers what particulars the resemblance consists in; & he will only give the same name, to things which resemble one another in the same definite particulars. The philosopher, therefore, uses all his general names with a definite connotation. But language was not made, & can only in a small degree be mended, by philosophers.^[*] In the minds of those by whom language is made, general names (& especially the names of large & complex classes which embrace numerous individuals not at all, or not accurately known to mankind in general) connote nothing but a vague gross resemblance to the objects which they were earliest or have been most accustomed to call by those names. When, for instance, ordinary persons predicate the words just or unjust of any action, refined or vulgar of any expression, attitude or gesture, statesman or charlatan of any personage figuring in politics, they do not mean to affirm of those various subjects, any distinct attributes of whatever kind; they merely recognize, as they think, some general resemblance, more or less vague & loose, between them & some other things, which they have been accustomed to denominate or to hear denominated by those appelations.

[¶5] Language, as Sir James Mackintosh used to say of governments, “is not made, but grows:” a name is imposed not at once & by premeditation upon a class of objects, but is first applied to one object, & then passes by successive transitions to another & another. By this process (as has been remarked by several writers, among others by Dugald Stewart in his Philosophical Essays) a name sometimes passes from one object to another, & from that to a third & so on, each time by reason of a resemblance between the new object, & the last link in the previous chain, until at last it becomes extended to things which have nothing whatever in common with the first things to which the name was given: these, on the other hand, do not drop the name, which, consequently now denotes a confused huddle of objects having nothing whatever in common; & connotes nothing at all, not even a vague & general resemblance.

When a name has got into this state, in which by predicating it of any object we assert positively nothing at all about the object, it has become utterly unfit for the purposes of philosophy or thought, & can only be made serviceable by stripping it of some part of its multifarious denotation, & confining it to objects possessed of some attributes in common, which it may be made to connote. Such are the inconveniences of a language which “is not made but grows.” It requires, like the roads which are not made, but make themselves, to be continually remade in order to be passable. [¶7] At the same time it is necessary to remark, that the study of the spontaneous growth of languages is of the utmost importance to the philosopher who would logically remake them, & is indeed often his best guide to that classification of objects which is even philosophically the best. We do not allude merely to the inconveniences & difficulties of altering the established classifications, & disturbing the correctness of received propositions by altering the meaning of the names in which they are expressed. The classifications rudely made by established language, are very generally, when retouched as they almost always require to be, by the hands of the philosopher, in themselves the classifications best suited to many of his purposes. These classifications, when compared with those of a philosopher, are like the customary law of a country, which grows up as it were spontaneously, compared with laws methodized & digested into a code: the former are far inferior in practical utility to the latter, but being the result of a long though unscientific course of experience, they contain the greater part of the materials out of which the systematic body of written law may & ought to be formed. In like manner the established grouping of objects under a common name, though usually founded on a gross & general resemblance, is evidence, in the first place, that the resemblance is obvious, & therefore considerable, & in the next place that it is a resemblance which has struck great multitudes of persons during a long series of years or ages. Even when a name, by successive extensions of its application, comes to be applied to things among all of which there does not exist even a general resemblance, still at every step in its progress we shall find such a resemblance; & these transitions of the meaning of words are often an index to real connexions between the things denoted by them, which might otherwise escape the notice even of philosophers who, from using a different language, or from any other difference in their habitual associations, have had their attentions fixed in preference upon some other aspect of those things. The history of philosophy abounds in striking instances of oversights of this nature, which would not have been committed, if the philosopher had seen the hidden link which connected together the seemingly disparate meanings of some ambiguous word.^*

[¶8^* ] Words, then, being often used by the vulgar, without any distinct connotation, except that of a general & gross resemblance among the things which they denote; it becomes necessary for the philosopher, to take precautions against the deceptious consequences likely to be produced by thus classing objects together on account of a mere general likeness, without analysing it & ascertaining what it depends upon. For we usually find that as soon as two things become habitually classed together, & called by the same name, a disposition arises to believe that any thing which is true of the one, is true of the other also. It is hence of the utmost importance in philosophy, that whenever objects are to be classed together & named alike, it shall be distinctly known how far the resemblance which gives occasion to their being so classed, extends, & what it consists in; that it may be known how far the inferences which are sure to be drawn respecting ulterior resemblance, are well-founded; and for this among [other] reasons, it is also of importance, that objects should be classed together on account of those resemblances by preference, which lead to the greatest number of interesting consequences, (this as we shall see hereafter is the principal feature in the idea of what is called a Natural Classification) & which are an index, therefore, to the greatest number of other resemblances, & those of a kind most likely to excite attention. But, whatever the resemblances may be, it is of the first importance, that they should be distinctly ascertained & defined; & that the name, which is given to the resembling objects, may acquire a distinct instead of a vague connotation; & by acquiring a distinct connotation may become susceptible of Definition.

And thus it is that the Definitions of names become subjects of enquiry & controversy. But in so far as that enquiry or controversy relates to the properties of things, & not to the mere usage of language, it will be found to affect not the definition itself, but the suppressed proposition, which we have already stated to be tacitly included in every Definition of a name which is known to be the name of any real object.

When we enquire into the meaning of such a name, & our enquiry consists of any thing else than a mere comparison of verbal authorities, we tacitly assume that a meaning must be found for it, compatible with its continuing to denote all or the greater part of the things of which it is commonly predicated. The enquiry, therefore, must have for its object to ascertain, first whether there really exists among all the things usually denoted by the name, any general resemblance; & next, supposing that there does, what that resemblance consists in. In other words, to enquire into the Definition of a name, is to enquire what attributes may be predicated in common, of all the various things denoted by the name: &, among those common attributes, what are those, the possession of which gives to all those things the character of resemblance, which has led to their being classed together. Of these two enquiries, the first is a case of comparison among a variety of objects, to ascertain their resemblances, and differences; the latter is a question of causation.

[¶9] In giving, therefore, a distinct connotation to the general name, the philosopher will endeavour to fix upon such attributes as, while they are common to all the things usually denoted by the name, are at the same time those which are in themselves of most importance, either from the number, the obviousness, or the interesting character of the consequences to which they lead. He will endeavour to select such differentiæ as lead to the greatest number of interesting propria. For it is these rather than the more obscure and recondite qualities on which they usually depend, which give that general character & aspect to a set of objects, which determine the groups into which they naturally fall. But to mount up to the more hidden agreement on which these obvious & superficial agreements depend, is often one of the most difficult of scientific problems. As it is among the most difficult, so it seldom fails to be among the most important. And since upon the result of this enquiry respecting the causes of the properties of a class of things, there incidentally depends the question what shall be the connotation of a name; some of the most profound and most valuable investigations which philosophy presents to us, have been introduced by, & have offered themselves under the guise of, enquiries into the Definition of a Name.

[Book II:

Of Reasoning]

OF INFERENCE, OR REASONING^[*]

[Chapter i: Of Inference, or Reasoning, in General]

[§1]

[¶4] In the most extended acceptation of the term, we may be said to reason, whenever we draw a conclusion; whenever we infer one proposition from another. In the narrower sense, reasoning is confined to that particular kind of inference which is called ratiocination, and which admits of being put into the form of a syllogism.

To the particular character of that kind of inference which is termed reasoning in the limited sense, we shall presently advert. We shall first take a general view of the various cases in which inferences may be legitimately drawn.

[§2]

[¶1] The first class of cases which we shall mention, is a class in which the inference is rather apparent than real, and which requires notice chiefly in order that it may be distinguished from cases of inferences properly so called. This is where from one proposition we seem to infer another, which, however, when analysed appears to be merely a repetition of the same, or part of the same, assertion, put into other words. All the cases mentioned in books of Logic as examples of the Æquipollency, or equivalence, of propositions, are cases of this sort. [¶2] Another case is where, from a universal proposition, we affect to infer another which differs from it only in being particular: as All A is B, therefore some A is B: No A is B, therefore Some A is not B. This is plainly not to deduce one proposition from another, but to repeat the same proposition a second time; not, indeed the whole of it, but as great a portion of it as we have occasion for.

[¶4] The most complex case of this kind of inference or rather apparent inference, is what is called the Conversion of Propositions; that is, turning the predicate into a subject, and the subject into a predicate, and framing out of the same terms thus reversed, another proposition, which must be true if the former is true. Thus, from the proposition, Some A is B, we may infer that Some B is A. From this, No A is B, we may infer that No B is A. From the proposition All A is B, it cannot be inferred that All B is A; though all water is liquid, it does not follow that all liquids are water, but it follows that some are so. The proposition All A is B is therefore legitimately convertible into Some B is A. This is called convertion per accidens. From this, Some A is not B, we cannot even infer that Some B is not A: for though some men are not cobblers, it does not follow that some cobblers are not men. The only legitimate conversion, if such it can be called, of a particular negative proposition, is thus; Some A is not B, therefore some things which are not B are A; which is called conversion by contraposition. But here the predicate and subject are not merely reversed but changed; instead of [A] and [B] the terms of the new proposition are [things which are not B] and [A]. The proposition Some A is not B, is first changed into the æquipollent proposition, Some A is a thing which is not B; the proposition is now no longer a particular negative, but a particular affirmative, and therefore admits of being converted in the first mode, or that which is called simple conversion.

[¶5] In all these cases it is evident that there is not really any inference, that is to say, any new truth in the conclusion, not already asserted in the premises. The fact asserted in the conclusion is either the very same fact, or part of the same fact, which was asserted in the original proposition. This is plain from our analysis of Predication. Thus, when we say that Some A is B, we mean that the attributes connoted by A and those connoted by B, are sometimes found to coexist in the same subject: now this is also precisely what we mean, when we say that some B is A; which, therefore, is not another proposition inferred from the first, any more than the English translation of Euclid’s Elements can be considered as a set of ulterior truths deduced from those contained in the Greek original. Again, when we say that No A is B, we mean that the attributes connoted by A & those connoted by B never coexist in the same subject; which is also the meaning, & the whole meaning, of the proposition, No B is A. When we assert that, All A is B, we assert not only that the attributes connoted by A and those connoted by B sometimes coexist, but that the former never exist without having the latter joined with them. Now the proposition, Some B is A, merely expresses the first half of this truth, without the other half, and therefore has been asserted by implication when we affirmed both halfs together in the proposition, All A is B. But, That all B is A, in other words that the attributes connoted by B never exist but in conjunction with those connoted by A, has not been asserted, nor can it be inferred. In order to reassert, in an inverted form, the whole of what was involved in the proposition All A is B, we must convert it by contraposition, thus, Nothing which is not B is A. These two propositions are exactly equivalent, & may be mutually substituted for one another: for to say that when the attributes of A are present those of B are present, is to say that when the latter are absent the former are absent.

[¶6] In a manual of logic for young students, it would be proper to insist at greater length upon the conversion & æquipollency of propositions. For, although that cannot be called reasoning or inference which is merely a reassertion in other words of what has been asserted before, yet there is no more important habit, nor any one the cultivation of which falls more strictly under the province of the art of logic, than that of readily & at once discerning the identity of an assertion, when disguised in language that is dissimilar. That important chapter in logical treatises, which relates to the Opposition of Propositions, and the excellent technical language which logic provides for distinguishing the different kinds or modes of opposition, are chiefly of use for this purpose. Such considerations as these, that contrary propositions may be both false, but cannot both be true, that Sub-contrary propositions may both be true, but cannot both be false, that of two Contradictory propositions one must be true & the other false, that of two subalternate propositions the truth of the universal proves the truth of the particular, and the falsity of the particular proves the falsity of the universal, but not vice versâ; all this appears very technical and mysterious at first sight, but when the meaning of the words is explained, the whole is so obvious, that it is apt to be thought little more than solemn trifling to lay it down with the imposing air of Science: since the same degree of explanation which is necessary to make the principle itself intelligible, would enable the truth which it conveys to be apprehended, in any particular case which can occur, without the aid of the principle. To which I answer, that in this respect, these principles are precisely on the level of geometrical axioms. That things which are equal to the same are equal to one another, is fully as obvious in any particular case, as it is in the general maxim; and if it had never been laid down as a maxim, none of the demonstrations of Euclid would ever have halted for any difficulty in stepping across the gap, which this axiom serves at present to bridge over. Yet no one has ever censured Euclid for giving a list of these self-evident propositions at the head of his treatise: for the best introduction to a Science consists in beginning with those of its truths which can be comprehended with least effort. And the student of logic, in the manipulation even of such truths as those which we have cited above, acquires habits of circumspect interpretation of words; and of taking an exact measure of the length and breadth of every assertion which he utters or which is tendered for his assent, which habits, when raised by culture to adequate constancy & strength, are among the most valuable acquisitions for which the understanding is indebted to logical discipline.

[§3]

[¶1] Having noticed, for the purpose of excluding from the province of Reasoning or Inference properly so called, the cases in which there is only an apparent process from one truth to another, the logical consequent being a mere repetition in other words, of the logical antecedent, we are now prepared to consider the various cases of inference in the correct acceptation of the term, that is, the deducing of one distinct, independent truth, from another.

[¶2] Reasoning, in the widest sense of the term, is popularly said to be of two kinds; reasoning from particulars to generals, and reasoning from generals to particulars. The former is Induction, the latter Ratiocination, or Syllogism. Before interpreting these brief expressions, by others which are longer but more precise, I must observe, that to these two cases of inference a third must be added; reasoning from particulars to particulars. Some will deny that we can legitimately reason in this last mode; and if the word reasoning be understood in its most confined sense, in which it is synonymous with ratiocination or syllogism, the objection must be allowed; but if by reasoning be meant every kind of inference, or every case of concluding one proposition from another, it will presently be shewn that reasoning from particulars to particulars is the foundation of all other reasoning, & that no reasoning whatever is legitimate if this is not. The grounds of which assertion, although they cannot as yet be fully stated, may be indicated by observing that every general proposition ultimately rests upon, or rather resolves itself into, particulars, so that particulars are the original premises of every argumentation.

[¶3] To say nothing further at present on this topic, which will be amply discussed hereafter, it is necessary to observe that the expressions, to reason from particulars to generals, & to reason from generals to particulars, do not adequately mark out, without the aid of a commentary, the boundaries between Induction and Ratiocination. The correct expressions would be, to infer any proposition from propositions less general than itself, and to infer it from propositions equally or more general. When, from the observation of a number of individual instances, we infer a general proposition, or when, from a number of general propositions we conclude another more general still, this is Induction. When, from a general proposition, by combining it with other propositions (for else [sic] we cannot) we infer a proposition equally general, or less general, or not general but individual, this is Ratiocination. In short, when the conclusion is more general than any of the premises, the argument (if it be a legitimate argument at all) is Induction. When the conclusion is less general or equally general with the largest of the premises, but not more so; the argument is Ratiocination.

[¶4] As all experience begins with particulars, and proceeds from thence to generals, it would be more conformable to what seems the natural order to treat of Induction before touching upon Ratiocination. There are, however, advantages which will gradually manifest themselves as we proceed, in making the analysis of Ratiocination preceed that of Induction. And, in general, it will be found advantageous, in treating of a Science which has for its chief object to trace all our knowledge to its source, to commence with the later rather than with the earlier stages of the process of acquiring knowledge, and to trace derivative truths backward to those prior truths from which they are deduced and on which they depend for their evidence, before attempting to point out the original spring from which they all equally take their rise.

[¶5] With respect to Induction, then, we shall only for the present observe, that it is a process of real, genuine inference; that the conclusion embraces more than is contained in the premisses. The general principle or law which we are said to discover—the general proposition in which we embody the result of our experience,—covers a much larger extent of ground than the individual experiments which form its basis. A principle ascertained by experience is not the mere summing up of what we have observed in the cases we have examined; it is a conclusion, founded on those cases, and expressive of our belief, that what we there found to be true, is true in an indefinite number of other cases which we have not examined.—The nature and grounds of this inference, and the conditions required to render it legitimate, we shall attempt to analyse hereafter, in the chapter on Induction. We shall now merely remark by way of suggestion, that the inference is drawn in conformity to the received principle, that the course of nature is uniform, or (as it is sometimes very inadequately expressed) that the future will resemble the past.

In Induction, then, we proceed from truths which we know, to truths which we did not before know: from facts certified by observation, to facts which we have not observed, and perhaps could not have observed—future facts, for example; but which we believe, with the fullest conviction, upon the sole evidence of the Induction itself.

[¶6] Having noticed this, which is the only truth with respect to Induction to which it will be necessary to advert in the exposition of Syllogism, we proceed at once to that other branch of the subject.

OF RATIOCINATION, OR SYLLOGISM

[Chapter ii: Of Ratiocination, or Syllogism]

[§1]

[¶1] The analysis of the Syllogism has been so fully and admirably given in most of the common manuals of logic, that in the present work, which is not designed as a manual, it is sufficient to recapitulate the leading particulars of the analysis, memoria causâ, to serve as a foundation for the subsequent reflections.

[¶2] To a legitimate syllogism it is essential that there should be three & not more than three, propositions; namely, the proposition to be proved, called the conclusion, and the two propositions which prove it, called the premisses. It is essential that there shall be three, and no more than three terms, viz: the subject & predicate of the conclusion, and another term called the middle term which must be found in both premisses. The predicate of the conclusion is called the major term of the syllogism. As there can be but three terms, the major & minor terms must each be found in one, and only one, of the premisses, along with the middle term, which is in them both. That premiss which contains the middle term and major term, is called the major premiss; that which contains the middle term and the minor term is called the minor premiss.

[¶3] Syllogisms are divided by some logicians into three figures, by others into four, according to the position of the middle term; which may be the subject of both premises, the predicate of both, or the subject of one, and the predicate of the other. The commonest case is that in which the middle term is the subject of the major premiss and the predicate of the minor. This is called the first figure. When the middle term is the predicate of both premisses, the syllogism is said to be in the second figure; when the subject of both, in the third. In the fourth figure the middle term is the subject of the minor premiss and the predicate of the major: those who do not reckon more than three figures, include this in the first.

[¶4] These figures are again subdivided into modes, according to what are called the quantity and quality of the propositions, that is to say, according as the propositions are universal or particular, affirmative or negative. The following are examples of all the legitimate modes, that is, all those in which the conclusion legitimately follows from the premisses: C is the major term, A the minor, B the middle term.

[¶6] The reasons why these premises are legitimate, that is, why if the premisses be true, the conclusions must necessarily be so, and why this is not the case in any other possible Mode except these alone, any person taking interest in the present speculations, may be presumed to have either learned from the common books of logic, or to be capable of divining by himself. The reader may however be referred to Dr. Whately’s logic, where he will find stated with uncommon perspicuity, almost everything which it is necessary to know on this part of the subject.

[¶7] All valid ratiocination; all reasoning by which from general propositions we infer propositions equally or less general, may be transformed into a series of syllogisms according to some of the above formulæ. The whole of Euclid, for instance, might easily be thrown into a series of syllogisms regular in mode and figure.

[¶8] Although a syllogism according to any of the above formulæ is a valid argument, that is, conclusive from the mere form of the expression; it has been shewn by logicians that all valid ratiocinations may be stated in syllogisms of the first figure alone. The rules for throwing an argument in the other figures into the first figure are called the rules for the reduction of syllogisms. It is done by the conversion of one or other, or both, of the premisses. Thus an argument in the first mode of the second figure, as

No C is B

All A is B

ergo

No A is C

is reduced as follows: The proposition No C is B, being converted, stands thus, No B is C, which, as we have shewn in treating of conversion, is merely the same assertion put into other words—the same fact, differently expressed. The argument will then stand thus

No B is C

All A is B

ergo

No A is C,

which is a good syllogism, in the second mode of the first figure. Again, an argument in the first mode of the third figure would be

All B is C

All B is A

ergo

Some A is C.

Now the minor premiss, All B is A, being converted per accidens, gives this proposition, Some B is A [sic]: which, though it does not express the whole of the fact previously asserted, expresses part of it, and must therefore be true, if the former proposition be true: we have, therefore, the following syllogism in the third mode of the first figure:

All B is C

Some A is B

from which it obviously follows that

Some A is C.

[¶9] In the same manner, or in a manner which is easily suggested by the above exemplification, every mode of the second, third, and fourth figures may be reduced to some one mode of the first. Every valid ratiocination therefore may be stated in one of the following forms.

Or dropping the signs A, B & C, and replacing them by more significant expressions;

[¶10] To prove an affirmative, the argument must admit of being stated in this form:

[¶11] To prove a negative the argument must be capable of being thrown into this form

No persons capable of reflection are incapable of Moral excellence

[¶13] Not only does all ratiocination admit of being thrown into one or other of these two forms, but when stated in these forms its conclusiveness is more obvious at the very first glance than when it is stated in any other form though equally legitimate. These forms, moreover, strike every understanding as being those in which the ideas involved in a ratiocination would most naturally and spontaneously arrange themselves. We may therefore consider the two forms cited above as the universal types of all correct ratiocination: the first, when the conclusion arrived at is affirmative, the last, when it is negative.

[§2]

[¶1] On examining these formulæ, we find that in both of them, one of the premisses, that which is called the major, is a universal proposition; & according as this is affirmative or negative, the conclusion is so too. All ratiocination starts from a general proposition, principle, or assumption: a proposition in which a predicate is affirmed or denied of an entire class, that is, in which some attribute, or the absence of some attribute, is ascribed to an indefinite number of objects possessing a common name.

[¶2] The other premiss is always affirmative, and asserts that some other class of objects, or some part of some class, or only some individual, belongs to the class, of the whole of which something had been affirmed or denied in the major premiss. And the conclusion, of course, necessarily follows; to this effect, that the attribute which was asserted to be possessed by the entire class, must, if that be true, be possessed by the objects which have been affirmed to be included in the class; or that the attribute which was asserted not to be possessed by any part of the class, cannot, if that be true, be possessed by the objects which have been affirmed to belong to the class.

[¶3] This, which is a correct statement of what takes place in all cases of ratiocination, has been generalised and erected into a logical maxim. It is laid down in most treatises on Logic, that all Ratiocination rests upon one principle; or, in other words, that every argument consists in affirming in some particular case, a truth which expressed generally forms the following maxim: That whatever can be truly affirmed or denied of a class, can be truly affirmed or denied of everything belonging to that class. This fundamental axiom has been termed by the schoolmen, the dictum de omni et nullo.

[¶4] Now, of this maxim, considered as the principle of all reasoning, we may venture to affirm, that it naturally belongs to a system of metaphysics extremely remote from that which is at present received by any philosopher in this country, & perhaps even in the world. At the time when universals, as they were termed, were supposed to have a separate objective existence, distinct from the individual objects which were classed under them, the dictum de omni not only expressed a definite meaning, but contained something which, assuming the above theory, was very important to be known, namely this, that the attributes, which we somehow contrived to discover in the universal, the genus or species, the substantia secunda, as it was termed, are likewise attributes of all the individual objects, of which that universal can be truly predicated. The maxim, in short, asserted that particular substances, & the supposed universal substances, were mysteriously connected in such a manner, that the entire nature and properties of the universal substance formed part of the nature & properties of each of the particular substances called by its name. On the scholastic system, this, as I have just observed, was a substantive fact or truth; by the knowledge of which we were made wiser. But now, when it seems to be generally admitted, that a universal, a class, a genus or species, is not an entity per se, but neither more nor less than the particular substances themselves which are placed in the class, and that there is nothing real in the whole matter except the individual objects, a common name given to them, and common attributes indicated by the name; what, I should be glad to know, do we learn by being told, that whatever can be affirmed of a class, may be affirmed of every object contained in the class? The class is nothing but the objects contained in it; and the dictum de omni is nothing better than the identical proposition, that whatever is true of all of a certain number of objects, is true of each of these objects. If all ratiocination were merely the application of this general maxim to some particular case, the syllogism would indeed be, what it has so often been asserted to be, solemn trifling. The dictum de omni is an axiom precisely on a par with the celebrated truth, Whatever is, is; & decidedly less instructive than the equally renowned aphorism, It is impossible for the same thing to be and not to be. It can only be considered as having a meaning, by being complaisantly understood as a paraphrastic & circuitous definition of the word class.

[¶5] An error which seemed completely refuted and expelled from science, often has only to put on a new suit of phrases, in order to be cordially welcomed back to its old quarters, and there repose unquestioned for another cycle of ages. Thus it has been with the scholastic dogma that genera and species are a peculiar sort of substances, and that all knowledge is only the knowledge of these universal substances, and not of the infinite number of individual substances which are classed under them. Whether disguised under the abstract ideas of Locke, (whose speculations, however, have been, I conceive, less vitiated by it than those of any other writer who has been infected with it before or since) the ontology of Cousin & the later Kantesians [sic], or the ultra-nominalism of Hobbes, this same doctrine has ever continued to poison philosophy. Having been accustomed to consider philosophical investigation as essentially consisting in the study of universals, men did not drop this habit when they ceased to regard universals as possessing an independent existence; and even those who came to consider them as mere names, still could not free themselves from the notion that the investigation of truth consisted entirely or partly, in some kind of conjuration or juggle with those names. Few philosophical opinions have ever been more widely spread than this, that the process of arriving at new truths by reasoning, in all sciences, or at any rate in all those to which Algebra is applied, consists in the mere substitution of one set of arbitrary signs for another. If there is any process in sorcery or necromancy more preternatural than this, I shall be much surprised. The culminating point of this philosophy in modern times is the well known aphorism of Condillac, that a Science is nothing, or scarcely anything, but une langue bien faite. A paradox, which, if divested of its epigrammatic dress, amounts to this, that we know the whole nature and properties of objects, or as much of them as is within the reach of our faculties, if we know what names they are called by. Can it be necessary to do more than simply affirm that none, not even the smallest and most trifling knowledge with respect to things, ever was, or ever can be originally got by any conceivable manipulation of mere names; that whatever can be learnt from names, is only what somebody, who used the names, knew before us; that the function of names is exclusively confined to being a contrivance for remembering & for communicating our thoughts; and that their use in acquiring knowledge, immense as it is, amounts only to the advantage, in so difficult an operation, of any contrivance which aids the memory, and assists communication with others? Doubtless, it is necessary to do something more than simply affirm this: it is necessary to explain the real process by which those things are done, which so many have imagined to be done by a mere arrangement of words. But when this shall be effected, the proposition just stated will not be rendered at all more obvious, than it is in its own nakedness the first moment it is uttered.

[§3]

[¶1] If truths cannot be discovered or proved by a process of naming, neither can they by a process of classification. It has been observed in a preceeding chapter, that classification does not precede, but follows our knowledge; and that we do not affirm a predicate of a subject because we have placed that subject in a class, but, on the contrary, we place it in the class, because we find that the predicate in question may be truly affirmed of it.

What is the real nature of a process of ratiocination, and what the principle or maxim of which every syllogism is one of the applications, will best be understood by remembering what it was which we found to be the real nature and import of every proposition or predication.

We found that the matter-of-fact asserted in every proposition, not identical, and which constitutes the real and only immediate object of belief when we assent to the proposition, is always the conjunction or non-conjunction of two phenomena: or, to express the same idea in other words, the coexistence or non-coexistence of two attributes or sets of attributes, in one and the same subject. I have already observed, that every phenomenon, when analysed, resolves itself into a sensation, thought, emotion, or volition, or a series of such, with or without a substance or object which excites them: and that an attribute is nothing but a name for the sensation, thought, emotion, or volition, considered as excited by that substance or object. But to this more recondite analysis, we need not do more than advert, since it is not necessary to the proof of what we have to advance; and indeed, one of the objects which I propose to myself in this work is to shew, that Logic is common ground to the partisans of different metaphysical sects; and that all its most valuable truths may be apprehended and assented to by persons adopting the most opposite views of the higher or transcendental metaphysics. If therefore I continue to use the received language respecting the distinction between attribute and subject, I again repeat that I intend to prejudge nothing respecting the real nature or ultimate analysis of that distinction, but to assume its existence, as what must be allowed in all systems, either as a distinction in entities themselves or in our modes of viewing them.

[¶2] Since, then, every proposition, if affirmative, asserts, or if negative, denies, the coexistence of two attributes, or sets of attributes; this must be equally the case with propositions arranged in a syllogism. The major premiss, which, as I have already observed, is always universal, asserts that all things which have one particular attribute, have in addition to it a certain other attribute; or else, that they have not. The minor premiss asserts that a given object,^* or a given class of objects,^† or part of a given class of objects,^‡ has the first mentioned attribute; and the conclusion infers in the one case that it has, in the other that it has not, the second. Thus in the syllogism

All men are mortal

Socrates is a man

therefore

Socrates is mortal

the subject and predicate of the major premiss are concrete connotative terms, denoting objects and connoting attributes. What the major premiss asserts, is the constant union of those two sets of attributes. Its purport is, that all objects which have the attributes connoted by the word man, have also the attributes connoted by the word mortal. In other words, that the phenomenon which is composed of corporeity, animal life, rationality, and the form called human, never exists without being, at some time or other, terminated by the phenomenon called death.

Now, while the major premiss asserts this, with regard to all objects which have certain attributes, the minor premiss asserts that the individual object called Socrates possesses these attributes, or, in other words, is a phenomenon answering to this description. We therefore conclude that this individual object also possesses the attribute of mortality; in other words, that this phenomenon will also be, at some time or other, cut short by the phenomenon death.

In this example, the minor premiss is a singular proposition. Suppose now that both the premises are general propositions: thus

All B is C

All A is B

therefore

All A is C.

A, B, & C, being connotative terms. The minor premiss asserts that along with the attributes connoted by A are always found the attributes connoted by B. The major premiss asserts, that along with the attributes connoted by B are always found the attributes connoted by C. The conclusion, therefore, follows, that wherever we find the attributes connoted by A, there also will be found the attributes connoted by C.

[¶3] If the major premiss is negative, thus,

No B is C

All A is B

therefore

No A is C

the argumentation is, that the attributes connoted by C never coexist with the attributes connoted by B: but the attributes connoted by B always coexist with those connoted by A: therefore the attributes connoted by C never coexist with those connoted by A.^*

In the same manner, we might analyse all the other cases of the syllogism.

^[*] According to this view of ratiocination, the propositions which are concerned in it, whether as premisses or conclusion, are conversant not with the propriety of the application of names, nor with the arranging of objects in classes, both of which are matters of arbitrary convention; but with the conjunction or non-conjunction of attributes, in other words of phenomena, in other words of objects, and the feelings which those objects exite in us.^†

[¶4] We have thus arrived at a preliminary axiom, a first and fundamental principle of all reasoning, different from the unmeaning dictum de omni et nullo. This axiom is analogous to those of mathematics, and consists of two propositions. The first is, that things which are constantly conjoined with the same thing, are constantly conjoined with one another. The second is, that a thing which is constantly conjoined with something, from which another thing is constantly disjoined, is constantly disjoined from that other thing. Or thus; Two things, one of which is always, and the other never, conjoined with a third thing, are never conjoined with one another.

[Chapter iii: Of the Functions and Logical Value of the Syllogism^* ]

[§1]

[¶1] It has now been shewn what is the nature of the truths with which the syllogism is conversant, and what the principle on which its probative force or conclusiveness depends. But the question still remains whether the syllogistic process, or, in other words, reasoning from generals to particulars, is or is not a process of inference: a process from the known to the unknown, a means by which we come to a knowledge of something which we did not know before.

[¶2] Of this question, the solution is obvious; and no one has ever treated [?] upon the subject without hitting upon it. All logicians allow that a syllogism is vicious if there be anything more in the conclusion than is assumed in the premisses. But this is as much as to say that nothing ever was or can be proved by syllogism, which was not known before. Ratiocination, therefore, is not a process of inference. Syllogism, to which the word reasoning has so often been deemed to be exclusively appropriate, is not even a process of reasoning at all.

But although the principle that a syllogism never proves more than is involved in the premisses, has, as before observed, been admitted by all writers on the subject, the admission has, for the ^[†] most part, either remained barren of consequences, or has produced none but positively erroneous ones. The acknowledgment thus explicitly made has not prevented one set of writers from continuing to present the syllogism as the correct analysis of the actual process which the mind pursues in establishing that large class of truths which are currently said to be got at by reasoning, as distinguished from induction; while it has induced another set to make the petitio principii which they affirm is inherent in every syllogism, a ground for imputing uselessness, futility, and frivolity, to the syllogistic theory itself.

That both these opinions are equally remote from the truth, may I think be conclusively demonstrated: and the real character of the syllogistic process, and of the purposes which it fulfils in philosophy, more clearly shewn than has ever yet been done.

[§2]

[¶1] It must be conceded that in every syllogism, considered as an argument to prove the truth of the conclusion, there is a petitio principii. The proposition to be proved is assumed in the major premiss. When we say,

All men are mortal

But

Socrates is a man

Therefore

Socrates is mortal

it is unanswerably urged by the assailants of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general proposition, All men are mortal: that we cannot be assured of the mortality of all men, unless we are previously assured of the mortality of every individual man; that if the mortality of Socrates was doubtful before, the same degree of uncertainty must hang over the proposition that all men are mortal, and the general principle, instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any of the particular cases included in it previously, is dispelled by evidence aliundè: and then, what is left for the syllogism to prove? That, in short, no reasoning from generals to particulars can prove anything: since from a general principle you cannot infer any particulars, but those which the principle itself assumes as preknown.

^[*] The justness of these strictures is by no means obviated by the analysis which we have given of the ultimate meaning of import of the syllogism, and the propositions composing it. For, let the argumentation be as follows

• Wherever attribute a exists, attribute b is joined with it:
• But a is one of the attributes of the object X:
• therefore
• b is also an attribute of the object X.

The major premiss begs the conclusion, just as much in this mode of stating the argument as in the other. For what does the major premiss assert? That attribute b enters into all the combinations of attribute a. But X, by supposition, is one of those combinations. Unless, therefore, it was already certain beyond a doubt, that a enters into the combination X, the major premiss was prematurely assumed; there were still doubts of its universality; and it could not be legitimately called in to prove that, on the previous establishment of which its own evidence was dependent. The pretended conclusion is a mere reassertion, in other words, of part of the premisses. All A is B, therefore Some A is B, we observed in a former place, is no inferring of a new truth, but a mere reassertion of the old. But the truth is, every syllogism which it is possible to put into words, is precisely analogous, if considered as an argument, to such reasoning as All A is B therefore Some A is B.

[¶2] All this is sufficiently obvious: and if logicians have usually, though unable to dispute it, shewn a strong disposition to explain it away, and to forget it as much as they could, this seems to have arisen from a difficulty which they found in reconciling it with other parts of their knowledge. They knew that the syllogism is a petitio principii; but they also knew that truths previously unknown, facts which have not been directly observed, are continually got at by way of inference; that subsequent experiment, whenever an opportunity occurs, corroborates their truth; and that the process by which these inferences are drawn, seems, at least, to be a process of reasoning from generals to particulars. We believe that William the Fourth is mortal. We do not know this by direct observation, seeing that he is not yet dead. If we were asked how, when this is the case, we know William the Fourth to be mortal, we should probably answer, because all men are so. Here, therefore, it may be said, we arrive at the knowledge of an unobserved truth, by a reasoning which is correctly resolved into the following syllogism:

• All men are mortal
• But
• William the Fourth is a man
• Therefore
• William the Fourth is mortal,

which, consequently, is an instance of an argument from generals to particulars, proving a fact which we did not know before. [¶3] And on the evidence of such cases, which are infinitely numerous, logicians have persevered in affirming that the syllogism is a process of inference, or proof, although none of them has hitherto succeeded in giving any sufficient solution of the apparent inconsistency between that assertion, and the principle expressly laid down by all of them, that if there be anything in the conclusion which was not already included in the premisses, the argument is vicious. One cannot help fancying that if they had suffered themselves to follow out this last proposition to what would have appeared, even to themselves, its necessary consequence, they would have been led to the conclusion that no new truths could be come at by ratiocination; and that this would have seemed to them a priori to be evident, had not they been stopped by thinking that the contrary was equally evident à posteriori. If they had been perfectly candid in stating to themselves what really passed in their own minds, they would have confessed that they believed a mystery; giving credit to two propositions, each of which, separately taken, seemed to them to be perfectly certain, but which they were completely unable to reconcile with one another.

[§3]

[¶2] This difficulty, and apparent paradox, arises, I conceive, from not distinguishing with sufficient clearness between the two parts of the process of philosophizing, the inferring part and the registering part; and from attending too exclusively to the latter. The mistake committed is like referring a man back to his own notes, for the origin of his knowledge. If a person is asked a question, and is at the moment unable to answer it, he may naturally enough turn to a memorandum which he carries about with him, to refresh his memory. But if he were asked how the fact came to his knowledge, he would scarcely answer, because it was written in his pocket book. Good, if the memorandum was made for him by an angel, or an enchanter; but not if he made it himself.

[¶3] Assuming that the proposition, William the Fourth is mortal, is an inference from the general proposition, All men are mortal, whence do we derive the knowledge of this more comprehensive truth? If it came to us by experience, and not by revelation, the evidence which convinces us of it consists of particular cases. It is because John, and Thomas, and every other person we know of in whose case the experiment has been fully tried, has turned out to be mortal, that we conclude all other men to be so.

All which man can observe, are individual cases. From these all general truths must be deduced; and into these they may be again resolved; for every general truth is but an aggragate of particular truths; a comprehensive expression by which a large and commonly indefinite number of particular facts are denied or affirmed at once.

But a general proposition is not merely a compendious form for recording & preserving in the memory a number of particular facts, all of which have been previously observed. Generalization is not a process of naming merely; it is also a process of inference. From a certain number of instances which we have been able to observe, we conclude that what holds in those instances, holds in all similar instances, past, present, and future, however numerous they may be: and then, by employing one of the contrivances of language, which enables us to speak of many as if they were one, we record all that we have observed and all that we have inferred, in one concise expression. The immediate and obvious advantages of this process, consist in the greater facility of remembering one proposition instead of a great number, and the great saving of time and trouble in the communication of knowledge from one person to another, where the results of many observations and inferences, and instructions for making innumerable inferences in unforeseen cases, can be all compressed into one short sentence.

[¶4] When, therefore, we conclude from the deaths which we have heretofore observed, that William the Fourth, like so many of his fellow-men, is mortal; though we may, not improbably, pass through the intermediate generalization, All men are mortal; it is not in the latter half of the process, the descent from All men to William the Fourth, that the inference resides. All the inference that there is in the matter is already made, the moment we have asserted that All men are mortal. All that remains to be performed afterwards, is merely decyphering our own notes.

[¶5] Logicians, and in particular Dr. Whately, have with an uncommon degree of earnestness, set themselves about to establish, that syllogizing, or reasoning from generals to particulars, is not, agreably to the vulgar idea, a particular mode of reasoning, but the analysis of the mode in which all mankind reason, and must reason, otherwise they can conclude nothing. This doctrine appears to me to be metaphysically incorrect. If, from our experience that John, Thomas, and so many other human beings were mortal, we are intitled to conclude, that all men are so, surely we might, without any logical inconsequence, have concluded at once that William the Fourth is mortal. The mortality of John & Thomas, is, after all, the sole evidence we have for the mortality of William the Fourth. Not one iota is added to the proof by interpolating a general proposition. Seeing, therefore, that the particular cases are all the evidence we can procure, evidence which all the logical modes of dressing it up which were ever hit upon, cannot make greater than it is; since that evidence is sufficient, without generalization, or else is not sufficient, even with generalization; I cannot see why we should be forbidden to take the shortest cut from these sufficient premisses to the conclusion; and constrained to travel the “high priori road” because logicians tell us that it is the King’s highway. I cannot perceive why it should be impossible to journey from one place to another, unless we “march up a hill, and then march down again.” It may be the safest road, and the most convenient, and there may be a good resting place on the top of the hill from whence we can see far around us: but supposing we wish only to arrive at our journey’s end, our taking that particular road is perfectly optional. It is altogether a question of time, troubles, and danger. The syllogistic logic, in short, is, precisely what Dr. Whately says it is not. It is an art of reasoning, and, as we shall presently shew, very frequently the best. But it is not the art of reasoning.

[¶6] Not only may we reason at once, from particulars to particulars, without passing through generals, but we very frequently do so reason. All our earliest inferences are from particulars to particulars. From the very first dawn of intelligence we draw inferences; but we live long before we learn the use of signs, particularly those which compose general language.

The child, who, having once burnt his fingers, avoids to thrust them again into the fire, has reasoned or inferred, though he has not thought of the general maxim, that fire burns. He knows from memory that he has formerly been burnt, and on this evidence he fully believes, that if he put his finger into the flame of the candle on the table near him, he will be burnt again. He believes this in each particular case as it occurs; but he is never thinking of any other case than the one before him. He is not generalizing; he is inferring a particular from particulars.

It is in this way that brutes reason. There is little, if any, ground, for ascribing to any of the lower animals the use of conventional signs. But an animal profits by experience, and avoids what he has observed to cause him pain, in the same manner, though not always with the same skill, as a human creature. Not only the burnt child, but the burnt dog, dreads the fire.

[¶10] Even the philosopher, who is accustomed to state the result of his experience in the form of general propositions, needs not always revert to those generalizations in order to apply his experience to a new case. Dugald Stewart is the author of this remark, though he most unnecessarily restricted its application to the narrow case of mathematical axioms. He observes, that when in Euclid’s Elements it is inferred that AB is equal to CD because both of them are equal to EF, the most uncultivated understanding, would, without hesitation, assent to the inference as soon as the propositions were understood, without having ever heard of the axiom, “Things which are equal to the same thing are equal to one another.” But here, as in many other instances which might be pointed out, this thoughtful and elegant writer has perceived an important truth only by halves, and his speculations suggest far more than he himself saw. The use which he makes of the above observation is to establish that axioms are not the foundations or first principles of geometry; are not analogous to the laws of motion and of the composition of forces in mechanics, the equal mobility of fluids in hydrostatics, the laws of the reflection and refraction of light in optics, and similar propositions, from which all the other truths of those and other Sciences may be synthetically deduced; but are merely necessary assumptions, self-evident indeed, and the denial of which would annihilate all demonstration, but which are themselves barren, and bring forth no corollaries or derivative truths, either in the way of demonstration or in any other way whatever. That this attempt to distinguish axioms from any other general truths is ineffectual, & indeed, in its own nature self-contradictory I shall hereafter give my reasons for maintaining. I mention it here only as an indication how little guidance Stewart derived from a light, which, if he had continued to keep it in view, would have afforded him a clearer insight than had been possessed by any philosopher before him, into the theory of ratiocination. Finding, in the case of geometrical axioms, that general names had not in them any mysterious virtue, whereby a philosopher is enabled, with them as his talisman, to conjure new truths out of the abyss of darkness; and not seeing that this was equally true of any other generalization, he contended that axioms were in their nature barren of consequences, and that the really pregnant truths, the genuine first principles of geometry, were the definitions. That the definition of a circle, for instance, is to the properties of the circle, what the laws of equilibrium and of the pressure of the atmosphere are to the rise of the mercury in the Torricellian tube. Yet all that he had asserted respecting the function which the axioms perform in the demonstrations of geometry, holds equally true of the definitions. Every demonstration in Euclid might be carried on without them. That this is the case must be obvious to every one, who reflects on the process of proving a proposition by means of a diagram. What, in fact, is the assumption from which Euclid starts to demonstrate by the aid of a diagram any of the properties of the circle? Not, that in all circles the radii are equal; but only, that they are so in the circle ABC. From this, which is not a general but an individual or singular proposition, combining it with other propositions of a similar kind, some of which, when generalised, are called definitions, & others axioms, we prove, that a certain conclusion is true, not of all circles, but of the particular circle ABC; or at least would be so, if the facts precisely accorded with our assumption. The enunciation, as it is called, i.e. the general theorem which stands at the head of one of Euclid’s demonstrations, is not the proposition which he in fact demonstrates; nor does he demonstrate any general proposition whatever. He merely demonstrates one individual instance, by a process of reasoning, which, when we duly consider its nature, we perceive might be exactly copied in any other instance among an indefinite number: and we then, by the contrivance of general terms, assert all this indefinite number of truths at once. By dropping the use of diagrams, and substituting in the demonstrations, general phrases for the large letters of the alphabet, we might demonstrate all the cases by one operation. To do this, we must of course express our premises, be they called definitions or axioms, in language equally extensive. But this is merely saying, that if we can prove an individual conclusion by assuming an individual fact, in whatever case we are entitled to make an exactly similar assumption, we may draw an exactly similar conclusion. The definition is a sort of notice to ourselves and others, what assumptions we think we are entitled to make. The general propositions, (whether definitions, axioms, or laws of nature) which we lay down at the beginning of our reasonings, are merely abridged statements, in a species of short hand, of the particular facts, which as occasion arises, we either think we may proceed upon as proved, or intend to assume. In any one demonstration, it is enough if we make, for one particular case, the assumption which in the statement of the definition or law, we announce that we intend to make in all cases which may arise. The definition of the circle, therefore, is, to one of Euclid’s demonstrations, exactly what, according to Stewart, the axioms are: that is to say, the demonstration does not depend upon it, but yet, if we deny it, the demonstration fails. The reason of which is obvious. The demonstration rests, not upon the general assumption, but upon an assumption confined to the particular case. But, if once we deny the general proposition, we have no right to assume the particular one which is included in it, for it is not pretended that there is more ground for the assertion in that case than in any other: if there were, it could not have been without a logical impropriety selected as a specimen of the whole class of cases included in the enunciation of the theorem.

[¶11] Both the definitions and axioms, and the enunciations of the theorems, are stated in general terms, memoriæ causâ, because they can be more easily carried in our recollection than diagrams and demonstrations, and for other reasons which we shall hereafter state. But that an unpractised learner, even in making use of one theorem to demonstrate another, reasons rather from particular to particular, than from the general theorem, is manifest from the difficulty he finds in applying a theorem to a case in which the configuration of the diagram is extremely unlike that of the original one by which the theorem was demonstrated:—a difficulty which long practise can alone remove, and that chiefly by rendering him familiar with all possible configurations compatible with the conditions of the hypothesis.

[§4]

[¶1] From the considerations which we have now educed, it may be considered as fully made out that all inference is from particulars to particulars: that general propositions are merely registers of such inferences already made, or short formulæ for making more; and that Syllogism, which necessarily proceeds from general propositions, is not a process of inference; the inference being made in laying down the major premiss, and being, therefore, already completed before the syllogism begins. It remains to be shewn, since the syllogism is not a process of inference, or reasoning, what it really is.

[¶2] There is no difficulty in solving this question. I have mentioned that the syllogism, in the ordinary course of our reasoning, is only the latter half of the process of travelling from premisses to a conclusion. There are, however, two peculiar cases in which it is the whole process, and by examining what is its character in those cases, we shall discern that which really belongs to it in all others.

In the ordinary course of acquiring knowledge, it begins as already mentioned, in particulars, because particulars only are capable of being subjected to observation. But our knowledge may, in certain cases, be conceived to come to us from other sources than observation. It may be revealed to us by a superior being; and thus communicated, may as easily be conceived to come to us in the form of general propositions as of individual ones: indeed, much more easily. Or the generalization may not be, in the ordinary sense, an assertion, but a command: a law, not in the philosophical, but the moral and political sense of the term: an expression of the desire of a superior that we, or any number of other persons, shall conform our conduct to certain general instructions. So far as this asserts a fact, namely, a volition of the legislator, it is not a general proposition at all; the fact asserted in it is an individual fact. But the description contained in it, of the conduct which it is the will of the legislator that his subjects should observe, is general. The proposition asserts, not that all men are anything, but that all men shall do something.

[¶3] In both these cases, that of a truth revealed to us in general terms, and that of a command intimated to us in the like manner, we arrive at the generalities first, and the particulars have the appearance of being deduced from them; by a process which correctly resolves itself into a series of syllogisms. The real nature, however, of this process of deduction, is sufficiently evident. It is a search for truth, no doubt, but through the medium of an inquiry into the meaning of a form of words. The problem is, whether the Being, who revealed to us the general principle, intended to include this case in it; or whether the legislator intended his command to apply to the present case among others, or not. This is a question only of language and classification. It relates entirely to the meaning of a certain form of discourse. The whole operation is not a process of inference, but a process of interpretation.

[¶4] This last expression appears to me very aptly to characterise the functions of the syllogism. It is a process of interpretation, simply. When we argue thus

• All men are Mortal
• But
• William the Fourth is a man
• Therefore
• William the Fourth is mortal

there is no inference in the case, but merely a more explicit statement, of part of what was asserted in the major premiss. “All men are mortal” was equivalent to, William the Fourth, and Julius Cæsar, and George Washington, & Tom, Dick, & Harry, &c. &c. are mortal. Of this voluminous predication, or rather series of predications, we take as much as we want, and leave the rest; and that is called syllogizing. The major premiss is like an algebraical formula with a, b, c, m, and n; in the conclusion we substitute particular numbers, as 16, 20, 50, 2 and 3, for those letters: but this is not inferring a new truth, for we had the same truth before, wrapped up, along with a great number of others, in a set of hieroglyphics. We decypher these as we find occasion, & put such of the truths they contain, as we happen to want, into more familiar language, so as to be more readily available for our purposes. Syllogizing, therefore, is decyphering: it is, once more, a process, not of inference, but interpretation.

[§5]

[¶1] Having, as it seems to me, sufficiently convicted of error, those who imagine that the syllogism is a correct analysis of any process of reasoning or inference; and, having established that there is but one legitimate process of reasoning or inference, namely, reasoning from particulars to particulars, properly called induction; I yet must enter a protest, quite as strong as that of any logician, against the doctrine that the syllogistic art is of no use in reasoning. Syllogizing is not reasoning: induction only is reasoning; but the syllogism is useful in reasoning, as a test of induction itself.

^[*] Hereafter, in treating of induction, it will behove us to inquire, in what cases it is allowable to infer particulars from particulars, by what tokens we are able to judge whether an induction is legitimate. For the present, we are only prepared to say, that the problem is very difficult; that the sufficiency of the proof is matter of very nice and delicate discrimination; and that there is scarcely any person whose conclusions do not very frequently outstrip the evidence, or fall short of it. Here is situated the great stumbling-block of philosophy; and any contrivance which can contribute in any the slightest degree to help us over it, is proportionally precious. Now, the syllogism is a contrivance of this sort.

[¶2] Whenever, from an induction of particular cases, we can legitimately draw any inference, our inference may legitimately be a general one. If, from observation and experiment, we can conclude to one new case, we may to an indefinite number. If that which has held in our past experience must therefore hold in time to come, it will not hold in one individual case only, but in all cases of a given discription. Every induction, therefore, which suffices to prove one fact, proves a multitude of facts: the experience which justifies a single prediction, must be sufficient to bear out a general rule. Now this general rule it is extremely advantageous to state fully out, in its broadest generality, and so to place before our minds in its entire extent the whole of what our evidence must prove if it proves anything.

[¶3] The advantage of this as respects the correctness of the induction, is twofold. First, the general principle presents a larger object to the imagination. A process of thought which leads to a comprehensive truth, is felt as more important than one which terminates only in an insulated fact, and the mind is unconsciously led to bestow greater attention upon the process, & to weigh more carefully the sufficiency of the experience. The other advantage is still more important. In reasoning to a particular case, which by the very supposition we are imperfectly acquainted with (or else it would not be a subject of investigation)—and in which, very probably, either our imagination or our wishes may be biassed one way, there is the most serious danger of our admitting insufficient evidence as sufficient. But if we place before ourselves an entire class of facts—the whole contents of a general proposition,—the whole of which are legitimate deductions from our premises, if that one particular conclusion is so,—there is a probability that if the premises are insufficient, this general inference will comprise within it some fact or facts, the opposite of which we already know to be true. We thus multiply to the utmost the chances that if there is an error in our reasoning, we shall discover it by a reductio ad impossibile.

[¶4] Thus, if during the reign of Marcus Aurelius, a subject of the Roman Empire, under the bias naturally given to the imagination and expectations by the lives and characters of the Antonines, had been disposed to conclude that Commodus also would be a virtuous man; if he stopped there, it is possible that he might only have been undeceived by experience. But if he reflected that he could not be justified in drawing this inference, unless, from the same premisses, he was also warranted in reasoning upwards, to the general proposition that All despots are virtuous men; (or some other generalization more or less extensive); he would immediately have thought of Nero, Domitian, and many other instances, which, by proving the falsity of the proposition as a general maxim, proved that it could not legitimately follow from true premisses; and that consequently those premisses would no better support the particular conclusion in favour of the virtue of Commodus, since the conclusion rests on no better foundation in that case than in any other.

[¶5] The advantage, in judging of any controverted inference, of referring to a parallel case, is universally acknowledged. Now, by ascending to the general proposition, we call in to our assistance not one parallel case merely, but all possible parallel cases at once.

[¶6] Now, therefore, if we are arguing from a certain number of known cases, to another case supposed to be analogous; we may transmute our argument into the form of an induction from those known cases up to a general proposition, and a subsequent reasoning downwards from the general proposition to the known case. The latter part of the process will thus be resolved into a series of syllogisms, the majors of which are broad general propositions, every one of which must be true, if our argument is conclusive. If any one fact therefore, fairly coming within one of these general propositions, is known or suspected to be other than the proposition makes it, this mode of stating the argument causes us either to know or to suspect that our reasoning will not hold. And in proportion to the greater chance of our detecting its fallacy, will be the encreased reliance we are entitled to place in it if no fallacy appear.

[¶7] The principles and rules of the syllogism are therefore highly useful. Not because they are the principles and rules according to which our reasonings are necessarily, or even usually, made: but because they furnish us with a form into which those reasonings may always be thrown, and in which, if they are incorrect, their incorrectness will more readily appear. The syllogism is not a form in which we must reason, but it is one in which we may reason, and into which it is advantageous to throw our reasoning, when there is any doubt of its validity. Not indeed the whole of the process of reasoning (except in those cases already noticed, where the entire process resolves itself into interpretation); but the latter part of it. An induction from particulars to generals, followed by a syllogistic process from those generals to other particulars, is a form in which we may always state our reasoning, if we please; though when the case is familiar and little complicated, and where no doubt exists, we safely may, and do reason at once from the known particular cases to unknown ones.

[¶8] As respects one single argument, the above are the uses of the syllogism. As respects the general course of our intellectual operations, this mode of stating an argument has the further advantage, that the induction may be made once for all: one single careful examination of the particular cases may suffice, and the result may be registered in the form of a general proposition, which is committed to memory, and from which, afterwards, we have only to syllogize. The particulars of our experiments may then be dismissed from the memory, in which it would be impossible to retain so great a number of details; while all the knowledge which those details were capable of affording, and which would otherwise be lost as soon as the experiments themselves were forgotten, is retained in a commodious and immediately available shape by means of general language.

[¶9] Against this immense advantage is to be set the countervailing disadvantage, ^[*] that inferences originally made on insufficient evidence, became consecrated & as it were hardened into the form of general maxims, and the mind cleaves to them from habit, long after it has outgrown any liability to be misled by such fallacious appearances if they were now for the first time presented to it. This strengthening of its powers does not avail for correcting the original inductions, because the mind has no longer present to it the particulars of the experiments from which that induction was made.

[¶10^† ] Upon the above great advantage of general propositions, and this its inevitable alloy, many opportunities will present themselves for further discussion.^[‡] I have only now to remark that so far as the syllogism is concerned in this function of general language, it is as a process of interpretation, merely. The knowledge is already acquired, and recorded in a general expression, of which it only remains to decypher the sense.

We have now shown, that the distinction between Induction & Reasoning, as commonly understood, has no real foundation. There are not two modes of arriving at truth, one proceeding upwards from particulars to generals, another downwards from generals to particulars. All knowledge is knowledge of particulars; all inference is from particulars to particulars. General propositions are mere signs for registering indefinite multitudes of particulars; and what is called ratiocination, or reasoning from generals to particulars, is merely decyphering those signs.

But, although all argumentation is from particulars to particulars, all argumentation may be thrown into the circuitous form of a double process, from particulars to generals, & from those generals to other particulars. And it is highly advisable, it is even indispensable to correct reasoning, when the subject is obscure or complicated, thus to interpolate a general proposition between the real premises and the real conclusion. For all particulars which will prove any conclusion at all, will prove a general conclusion. Whatever we have ground to believe of any one individual, on mere inference, without specific experience, we have equal ground to believe of all individuals whatever, which agree with that individual in the circumstances upon which the inference is founded. We are enabled therefore to judge more correctly whether we can conclude to the individual case, by trying [?] whether in concluding to the entire class of cases, we are led into anything which is in contradiction to our previous knowledge.

Generalization, in short, is not a necessary part of reasoning, but it is a highly useful operation for verifying the correctness of reasoning.

[§6]

[¶1] As much has now been said as seems necessary, not only for proving but for duly illustrating the above propositions. The theory, however, of ratiocination is not yet complete. The syllogism consists of a conclusion and two premisses, the major & the minor. We have analysed the major, and have shewn that it is no part of the process of reasoning at all. We have also shewn what it really is, and what are its offices and uses in philosophy. But there is also the minor. What is its office? Is it as unnecessary a part of the process as the major? Should we be able to reason without it? And is it only useful in as much as it is a part of that syllogistic dress into which it is advantageous to put an argument, in order to be more certain of its validity?

[¶2] A philosopher, to whom mental science owes much, Dr. Thomas Brown, has answered this question in a manner which demands our notice. The minor premiss, according to him, is not merely a part of the process of argumentation, but the whole. A is B therefore A is C is a formula which he considers to represent the whole operation of the human intellect in reasoning. The major premiss he rejects as we do, because it assumes by implication the truth of the conclusion which it affects to prove: but the error of the Aristotelian logicians he conceives to lie in not resting satisfied with the minor premiss & the conclusion, as a full and satisfactory analysis of the reasoning process. “All men are animals, Socrates is a man, therefore Socrates is an animal,” is, according to him mere trifling. “Socrates is a man, therefore Socrates is an animal,” is all that really passes through the mind.

^[*] There is no doubt that in the particular case which we have selected as an example, Dr. Brown’s observation would be just. “Socrates is a man, therefore Socrates is an animal,” requires no third proposition to render the inference legitimate. If Socrates is a man, we may know without further inquiry that he is an animal: but why? Because we know it already. We have asserted it in the very words we used. The meaning of the word “animal” is involved in the meaning of the word “man.” Man connotes all that animal connotes, & more. There is, therefore, no inference in this case at all, but a mere reassertion of part of the antecedent. The proposition, which must be supplied if the argument is to be stated syllogistically, viz: “All men are animals,” is an essential proposition, and all essential propositions are, as we have long since shewn, merely identical. Dr. Brown’s theory of reasoning, though given by him as a substitute for the syllogistic doctrine, is liable to precisely the same objection which lies against that doctrine itself, considered as an analysis of reasoning; i.e. it is quite a correct analysis of the operation of the intellect in certain cases, but these unhappily are precisely the cases in which there is no reasoning. Such indeed are the cases usually selected by the scholastic logicians, as examples of reasoning. We have formerly commented on the injury which the reputation of the syllogistic art has suffered from this habit of exemplifying its rules by specimens which have only the form of reasoning without the substance; syllogisms in which the major premiss being an essential proposition conveys no information whatever. Were there not evidence to the contrary in his own choice of examples, we might almost have suspected that Dr. Brown, who, though a very penetrating, was a very hasty thinker, and seldom proceeded with due circumspection, had, when he turned his attention to the syllogism, unluckily fallen upon one of these ill-chosen specimens; in which the major premiss really is utterly futile, and the conclusion wholly involved in the minor premiss; and that, overlooking the very peculiar character of the example, he had inferred at once, that what was true of such a syllogism was true of all others. This would only have been one instance among many of that precipitation, which has rendered Dr. Brown fully as remarkable for what he did not see, as for what he saw. In reading his speculations, your wonder is alternately excited at the acuteness which discerns a truth not easily discoverable, and the oscitancy which misses another, lying close to the former, and far more obvious.

If, instead of a syllogism in which the main premiss is an essential proposition, we choose one in which that premiss conveys information of a matter of fact; if, for instance, instead of “All men are animal,” the major premiss is this, “All men are mortal,” and the remainder of the syllogism, “Socrates is a man, therefore Socrates is mortal” we arrive at far other notions of the reasoning process. For although we may dispense with the major premiss, “All men are mortal,” we can only do so by putting in its place, the particular truths from which that generalization was made. The arrangement, when stated fully will stand not thus:—

• Socrates is a man
• therefore
• Socrates is mortal;

but thus;

My father, and his father, and his father’s father, and Tom, and Dick and Harry, and so on (to the end of the series of all persons of whose deaths I have direct evidence) were mortal:

(We cannot add, But Socrates is a man, for there would be nothing to connect this with the other premiss, and the two together would not prove anything. The minor premiss must therefore undergo a transformation, and stand as follows:)

But Socrates resembles my father, and his father, and his father’s father, and Tom and Dick and Harry (to the end of the enumeration as before):

• Therefore
• Socrates is mortal.

Here, we have at length a correct statement of the nature of the argumentation, which the syllogistic doctrine rudely expresses thus: “All men are mortal, but Socrates is a man, therefore Socrates is mortal.”

The major premiss, “All men are mortal,” when divested of the petitio principii, and cut down to as much as is really known when the argumentation begins, is reduced to an assertion of the mortality of certain definite individuals.

The minor premiss, “Socrates is a man,” is equivalent to an assertion, that Socrates resembles those definite individuals; namely, in possessing certain attributes, which are involved in the signification of the word man. It is true, the proposition, “Socrates is a man,” in itself only asserts that Socrates possesses those attributes; his resemblance to those other individuals is only asserted by implication; and for anything that appears on the face of the proposition, they may never have existed. But from the mere possession of those attributes by Socrates, we cannot conclude anything as to his mortality. The ground on which we infer his mortality is his resemblance to other individuals, whose mortality is known to us by experience. This resemblance happens to consist in those particular attributes which we predicate of him when we call him a man. But the attributes themselves would not bear us out in any conclusion, if no other being possessed them, or possessed attributes in any way resembling them. All reasoning is from a parallel case, or from cases more or less analogous, never from the very case itself.^* We may learn any number of properties of a thing, by intuition or consciousness, but we never can infer one property from another, except so far as that other constitutes a resemblance to some other thing, which possesses both the properties united. All reasoning, all inference, is founded upon resemblance.

Dr. Brown must have know all which we have now stated: but it probably never presented itself to his mind in this precise shape; other wise he could not have committed the mistake of resolving an argument into nothing but the minor premiss and the conclusion. For he would have seen that what is directly asserted in the minor premiss, not only does not prove the conclusion, but does not go any part of the way towards proving it. What really contributes to the proof is a proposition, which is not the minor premiss itself, but which must be true if that premiss is true; viz: that the individual which is the subject of the minor premiss resembles certain other definite individuals, of whom that which we are attempting to prove, is already known to be true.

[§7^* ]

[¶1] Whether the resemblance is such, in kind & in degree, as is necessary to warrant us in concluding that an object which resembles the others thus far, must resemble them further, is a question the difficulties of which remain untouched by anything we have yet said. This is the great problem of Induction; and it is in the chapter on Induction, that we shall enquire what can be done to facilitate its solution. What is necessary at present is, that it should be distinctly seen, that all reasoning may be reduced to the following formula: Certain individuals have certain attributes, A particular individual resembles those individuals in some other attributes, Therefore it possesses these also. And these three propositions, which are necessarily found in every argument, whether it be called Induction or Demonstration, correspond, the first to the major, the second to the minor, and the third to the conclusion of the Syllogism.

If it be said, that in the Syllogism, the correctness or incorrectness of the process, appears from the form of the expression, and that the mode of stating it which we propose to substitute, affords no such test of its having been properly performed, I answer, it affords it just as much as the Syllogism. Neither affords any test of the sufficiency of the induction, because that is complete before the syllogism begins. To imagine that any form or expression can help us to that, would be like relying on magic. But when the induction has been performed, and the result recorded in general terms, the rules of the syllogism are of great use in the interpretation of the general proposition; for if they are strictly observed, they ensure that what is inferred in any particular case shall be the same thing which it has previously been concluded that there was ground for inferring in a whole class of cases of which that is one.

In decyphering, therefore, the records of a previous induction, the rules of the syllogism are of the greatest value. And it will be seen in a subsequent place, how many of our most insidious errors have their seat in this part of the intellectual process.^[*]

OF TRAINS OF REASONING^[*]

[Chapter iv: Of Trains of Reasoning, and Deductive Sciences]

[§1]

[¶1] From our analysis of the syllogism it has appeared that the minor premiss always affirms a resemblance between a new case and some cases previously known: while the major premiss states something which has been found to be true of those old cases, and which by induction we consider ourselves at liberty to infer to be true of any other case resembling them in certain given particulars.

[¶2] If all ratiocinations resembled, as to the minor premiss, the example which we chiefly employed in the last chapter; if the resemblance which the minor premiss asserts, were obvious to the sense, as in the proposition “Socrates is a man,” or were at once ascertainable by direct observation; there would be no necessity for trains of reasoning, and Deductive or Ratiocinative Sciences would not exist. Trains of reasoning exist only for the sake of applying an induction founded (as all inductions must be,) upon observed cases, to other cases which are not only unobserved but are not even directly observable.

[§2]

[¶1] Thus, suppose the syllogism to be, All cows ruminate, This which is before us is a cow, therefore This which is before us ruminates; the minor is obvious; the only one of the premisses which requires for its establishment any anterior process of enquiry is the major, and provided the induction of which that premiss is the expression, was correctly performed, the conclusion respecting the animal now present was already drawn before the animal appeared: we have only, as it were, to identify her—to ascertain by reference, that she was included in the inductive inference of which the general proposition “All cows ruminate,” is a record. But let the syllogism be the following, “All Arsenic is poisonous,” This which is before us is arsenic, therefore This which is before us is poisonous; the minor in this case, may not be obvious at first sight; may be itself known by inference, and not by direct intuition: it may be the conclusion of another syllogism, such as this: All things which produce a precipitate of a certain colour, with a certain chemical test, are arsenic; This which is before us produces such a precipitate, therefore it is arsenic. The ultimate conclusion, This which is before us is poisonous, requires therefore to establish it, a process which to be syllogistically expressed will require two syllogisms; and we have a Train of Reasoning.

[¶2] It is however obvious that in thus adding syllogism to syllogism, we are really adding Induction to Induction. Two inductions must have taken place to render this chain of inference possible: two inductions, founded probably on two distinct sets of individual instances, but which converge in their results so that the instance supposed to be the subject of speculation, comes within the scope of them both. The register of these two inductions is contained in the majors of the two syllogisms. We examined several substances yielding to the supposed test the supposed precipitate, & we found that they possessed the properties connoted by the word arsenic; they were metallic, volatile, their vapour had a smell of garlic &c. We have examined several (though probably not the same) substances of this metallic, and volatile nature, with vapour smelling of garlic, and we have found them poisonous. The first observation we think we may extend to all substances which yield the precipitate; the second, to all such metallic and volatile substances, and consequently not only to what are seen to be such, but to what are concluded to be such by the prior induction. The substance before us is brought within the one induction by being seen to come within the other: We are still concluding from particulars to particulars; but in this case we conclude from particulars observed to other particulars which are not seen to resemble them in the material points, but inferred to do so because resembling them in some other points, from which resemblance, it has been concluded from a quite different set of instances, that resemblance in the former points is inferrible.

[¶3] The process necessary for the establishment of the minor premiss is often far more complex than in the foregoing example. Take for a fresh example the following syllogism: The foolish do not prosper long, Napoleon is foolish, therefore he will not prosper long. The major premiss is the record of an induction which may be correct or erroneous, but which can only have been founded upon observation of persons concerning whose foolishness there was no doubt. It has been found or supposed to be found, that they did not prosper long, and it has been deemed that the induction which those instances warrant, is an extension of the same predicate to any and every person who resembles those persons in the one attribute of being foolish. But does Napoleon resemble them in that attribute? This may be debated pro and con by countless arguments; and must in any case, be proved by another induction; for we cannot observe his foolishness directly; we never saw him: and every argument to prove it must be in this form, Whoever does so and so is foolish, Napoleon has done so and so, therefore he is foolish. But has he done so and so? This minor may require proof: still another induction; as thus: What is asserted by many disinterested witnesses, must be believed to be true, That Napoleon committed this action is asserted by many disinterested witnesses, therefore it must be believed to be true. Here Napoleon being seen to resemble the particular instances which experience presents to us, of persons concerning whom something is asserted by many disinterested witnesses, we infer, first, that he is a person concerning whom that “something” is true. The “something” being in this case, his having done a particular act, he is thus brought into resemblance with those persons before observed, who were foolish, and thereupon by a second induction, we infer him to be foolish. This brings him into resemblance with the foolish persons, who were observed not to prosper, and thence by a third induction, we predict that his prosperity will not continue. In this way we are enabled to reason from the particular foolish people whom we had observed not to prosper, to people whom we did not even know to be foolish when we made the induction; yet if the induction was good, and therefore applicable to all persons whose fortunes we have not observed, but whom we see to be foolish, it must be no less applicable to all whom we do not see but infer to be such, provided the induction by which we so infer them be correct. It is still reasoning from particulars to particulars, but we now reason to the new instance from several distinct sets of former instances: to one only of these sets of instances do we directly see it to be similar; but from that similarity we inductively infer that it has the attribute, which constitutes its similarity to the next set, and renders the induction founded upon them, applicable to it likewise.

[§3]

[¶1] It may appear a forced use of language to say that the syllogistic, or ratiocinative process, when carried out to this length of applying an induction to cases which not only were not dreamed of when the induction was made, but if known of at the time, would not necessarily have been known to come within it, is still a process of interpretation merely. The induction that Napoleon will not prosper, from the general proposition No foolish persons prosper, when the fact of his being a foolish person itself needs proof, cannot, it may be said, be justly characterized as a mere decyphering of what is written in the general proposition. But a metaphorical expression ought not to be strained beyond its intended meaning. When we said that reasoning from generals to particulars is mere interpretation of the general propositions, what we meant to affirm was this: That the general proposition is not a step in the reasoning, an intermediate link in the chain of inference between the particulars observed, and the particulars to which we apply the observation: the reasoning (if we had sufficiently capacious memories) could go on without any general propositions; they are mere formulæ for inferring particulars from particulars. The essence of all reasoning is, that from observation of certain known particulars, we may draw a similar conclusion with respect to others which are unknown: but if we may with respect to any others, we may with respect to all others of a certain general description; and in order that we may never fail to draw this conclusion in a new case, whenever it can be drawn correctly, we determine with ourselves once for all, what are the distinguishing marks by which such cases may be recognized. The subsequent process of identifying an object, and seeing whether it has those marks, cannot be called an inference; even when we identify it not by those very marks, but by others which we have ascertained (by another and a similar process) to be marks of those marks. The only inference involved in the case, is an inference from the observed particular instances, to the new and unobserved one. In drawing this inference, we conform to a formula which we have prescribed to ourselves expressly for our guidance in drawing such inferences, and which formula is an exact record of the judgment we previously formed, as to how we were to know when the inference could be drawn or not. In this sense, what we do when we actually draw it, may be called an interpretation of the record. Often too the formula is all that is left to us of the evidence from which we infer; having forgotten the experiments or observations from which we originally generalized (when our first illustration, that of referring to our own notes, most obviously holds): or perhaps, they were the observations of other people and not ours at all. Still it is those observations that are the original premisses of our argumentation: we have them not before us, but we have before us evidence that we or others once thought them sufficient grounds for an induction, and we have marks to show whether any new case is one of those to which if then known the induction would have been deemed to extend. Those marks we either recognize at once, or by the aid of other marks, which by another former induction we collected to be marks of them. These marks of the marks, may, again, be known only through other marks; and thus we may have a train of reasoning of any length, bringing a new case within the scope of the induction warranted by particulars its resemblance to which is only known from its resemblance to other particulars that resemble them.

[¶2] Thus in the speculation concerning Napoleon, the inductive inference ultimately arrived at was, that he would not prosper: this inference was drawn according to a formula which made foolishness a mark of not prospering; a mark of this mark was, having done a particular action; & a mark of having done that action was, being asserted by many disinterested witnesses to have done it: this mark, Napoleon was seen to possess. Hence he fell within the last induction, and that brought him within all the others—His resemblance to one set of observed particular cases brought him into resemblance with another group, & that with another.

OF DEDUCTIVE SCIENCES^[*]

[§4]

[¶1] The considerations which have just been stated, furnish the means of reconciling our doctrine, that all reasoning is induction, with the fact that there are Deductive or Ratiocinative Sciences. It might at first seem that if all reasoning be induction, all the difficulties of reasoning, that is of science, must lie in making the inductions, and in determining whether they be duly made: and that therefore where all the inductions were easy and certain, there could be no science, or no difficulties in science. But it has been seen from the preceding chapter, that even when the inductions are of the simplest and most obvious nature, there may be much difficulty in finding whether the particular case, which forms the subject of enquiry, comes within them; and ample room for ingenuity in so combining various inductions, as by means of one, within which the case obviously falls, to bring it within others, its inclusion in which is not obvious.

[¶2] Suppose that all the inductions, which are possible in a given science, have been made, or rather formulized into general propositions, by the aid of which we judge to what new cases they are applicable: when a new case arises, which can be at once seen to come within the formula, the induction is applied to that new case, and the business is ended: But new cases are continually arising, which cannot be at once perceived to come within any formula, which would answer the questions we want answered in respect to them. Take an instance from Geometry, the fifth proposition of the first book of Euclid. The enquiry is “Are the angles at the base of an isosceles triangle, equal or unequal?” For inferring equality we have the following formulæ: Things which being applied to one another coincide, are equal. Things which are equal to the same thing, are equal. The sums of equal things are equal. The difference of equal things are equal. For inferring inequality we have the following formulæ: A whole and its part are unequal. The sums of equal things and unequal things are unequal. The differences of unequal things and unequal things are unequal. These are the only formulæ we have. The angles at the base of an isosceles triangle do not obviously come within any of these formulæ. They cannot be seen to have any of the marks either of equality or inequality which the formulæ specify. We are to consider whether they have any properties which in any other formulæ are set down as being marks of these marks. We examine, and find that they have. The formula within which we ultimately succeed in bringing them, is this, “The remainders of equal things are equal.” We find that they are remainders of equal things. The difficulty in finding this, arises from the circumstance, that out of the innumerable pairs of angles of which they may be the remainders, we have to imagine and select two, which can either be seen to be equal, or possess some of the marks of equality, specified by the various formulæ. By an exercise of ingenuity, which on the part of the first inventor, deserves to be regarded as considerable, two pairs of angles were hit upon, which, while it could be seen that their differences were the two angles at the base, possessed one of the marks of equality, namely, coincidence when applied to one another. Even this coincidence was only proved by a fresh induction: it appeared that unless they coincided, two straight lines would enclose a space: thus though they were not seen to coincide, they were brought under a formula for coincidence. This again is done by two steps, and requires two formulæ: Angles coincide when the straight lines which form them coincide: Straight lines coincide whose extreme points coincide. (See the demonstration of the fourth proposition on which the demonstration of the fifth is founded.)

[¶10^* ] The ingenuity which is here exercised is that of figuring in our imagination the two angles at the base of the triangle, as remainders made by cutting out of one pair of angles, another pair of angles, which pairs are severally the corresponding angles of triangles having two sides and the intervening angle equal. It is by this happy contrivance that so many different inductions are brought to bear upon the same particular case. For, this being done, and the figure constructed, the induction, Two straight lines cannot enclose a space (aliis verbis Two straight lines of which the extremes can be applied to each other, will coincide) is seen to be applicable to the bases of the two pairs of triangles; this brings the angles at those bases within a second induction, Angles whose sides coincide, coincide; and consequently within a third induction, Things which coincide, are equal; and the equality of these angles, brings their remainders within a fourth induction, The remainders of equals are equal. Another induction is involved, The sums of equals are equals: it is by this we prove the equality of the sides of the triangles: There are in all six formulæ.

[¶3] We may state it thus. AB, AC, the sides of the triangle, being prolonged to equal distances and the extremities joined, we have

Half the proof is therefore accomplished.

It is easy by similar means to accomplish the other half; that is, to bring the angles EBC, DCB also within the fourth formula: we have then

[¶10] There is ample scope for scientific dexterity and ingenuity in so combining a few simple inductions, as to bring within each of them, great numbers of cases, which are not obviously included in it: and the processes necessary for bringing the inductions together, may be very long, numerous and complicated, when the inductions themselves are very easy and simple. This is the case in mathematics. All the inductions involved in all Geometry are those simple ones the formulæ of which are the Axioms and a few of the so-called Definitions. All the rest of Geometry is made up of the processes employed for bringing unforeseen cases within the inductions—or (in syllogistic language) for proving the minors necessary to complete the syllogisms. But all these processes are Inductions; at each step, the case under examination is taken into the formula of some one or other of the Inductions which the Axioms and Definitions are the record of. The Inductions being of the most familiar kind and so few in number, and the connecting of several of them together which constitutes Deductions, or Trains of Reasoning, forming the bulk of the science, and its only difficult or intricate part; Geometry is a Deductive Science.

[§5]

[¶1] When we treat of Induction, it will be seen that there are strong reasons for giving to every science as much of the character of a Deductive Science as possible; that is, for endeavouring to construct the science from as few and as simple Inductions as possible, and (by even the most complex combinations) to make these suffice for proving even those truths with respect to complex cases, which could have been ascertained by specific observation of, and Induction from, cases obviously similar. This, for instance, is done when an experimental science is rendered mathematical. It was done when astronomy was brought by Newton within the laws of mechanics. To do this is the great triumph of the Investigation of Nature: as will be fully shewn and illustrated hereafter. In proportion as this is done, Sciences tend to become more and more Deductive. But they are not the less Inductive; every step in the Deduction is an Induction and nothing else. The opposition is not between Deductive and Inductive, but between Deductive and Experimental. A science is experimental in proportion as every new case, presenting any peculiar features, requires a new set of observations, or experiments, a fresh Induction: it is Deductive, in proportion as it is able to draw conclusions as to cases of a new kind, by processes for bringing those cases under old Inductions: by finding that cases not having the requisite marks, have, however, marks of those marks.

[¶2] We can now, therefore, see what is the generic difference between sciences which can be made Deductive, and sciences which must as yet remain Experimental. The difference consists in our having been able, or not yet able, to discover marks of marks. If, by our various Inductions, we have found that a quality which we will term a, is a mark which indicates and from which we may infer, a quality b, but have not found that b is a mark of anything, except, perhaps reciprocally of a; and our next induction is perfectly distinct, and gives us c as a mark of d, but we have no induction which establishes that c or d accompany and may be inferred from a or b; we have two scientific generalizations, perfectly distinct and independent of one another, as for instance that acids redden vegetable blues, and that alkalies turn them green: from neither of which propositions could we infer the other, and a science so far as it is composed of such propositions is purely experimental. Chemistry in the present state of our knowledge is principally of this character: its propositions are of this sort, a is a mark of b, c is a mark of d, e is a mark of f and so on.^* There are other sciences again of which the propositions are of this kind, a is a mark of b, b is a mark of c, c is a mark of d, d is a mark of e, &c. In these sciences we can mount the ladder from a to e by a process of ratiocination, and conclude that a is a mark of e, although apparently quite unlike anything which was visible in the instances upon which the first of the inductions in which e figures in the predicate was founded: those being instances in which d was perceptible, while it is not perceptible but only inferrible in the case to which that induction is now extended. Or varying the metaphor, we may say that we get from a to e underground; the marks b, c, d which indicate the route must all of them be possessed somewhere by the object concerning which we are enquiring, but they are all of them below the surface: a is the only mark that is visible.

^[*] Such as now described has always been the character of the processes of science in Mathematics: it has now become so in Mechanics and Astronomy, and is becoming more and more so in politics and the philosophy of the mind. Even in chemistry the great generalization of Dalton, called the atomic theory, (or the doctrine of chemical equivalents), is a commencement of a similar transformation.^[†]

[§6]

[¶1] We can now understand how an experimental science may transform itself into a Deductive by the mere progress of experiment. In an experimental science the inductions lie detached; a a mark of b, c a mark of d, e a mark of f, and so on: a new set of instances and a consequent new induction, may at any time bridge over the gap between two of these unconnected arches: b may be discovered to be a mark of c, or of e. Or what is more frequently the case, some grand comprehensive induction raises an arch high in the air which bridges over hosts of them at once: b, d, f and the rest are all discovered to be marks of some one thing, or of things between which a connexion has already been traced. As when Newton discovered that all the motions, regular or seemingly irregular, of the bodies of the solar system (each of which motions had been discovered by a separate act of generalization and from its own separate marks) were all of them marks of moving round a common centre, with a centripetal force varying inversely as the square of the distance from that centre. This is the greatest instance which has yet happened of the transformation, at one stroke, of a science which was still to a great degree experimental, into a deductive science.

[¶2] A transformation of the same sort, on a small scale, would be operated in chemistry so far as regards the two propositions cited above, viz. Acids redden vegetable blues, Alkalies make them green; if we should conceive it to be discovered (which may easily be imagined possible) that the blue colour in vegetable substances, is a mark of some hitherto undetected elementary substance; and that this substance makes with all acids a red compound, with all alkalies a green one. Here we require a great number of new sets of instances, and consequent new sets of inductions, and when we have got them, instead of connecting all the truths of a science, we only connect the two solitary generalizations mentioned above. This however is so much gain; but has little tendency to convert an experimental into a deductive science, because the new courses of observation and experiment which thus enable us to connect a few general truths together, generally call into existence a still greater number of unconnected new ones. Hence chemistry, although such extensions and simplications of its generalizations are continually taking place, still remains essentially an experimental science; and is likely so to remain, unless some comprehensive Induction shall be hereafter arrived at, which like Newton’s shall connect a vast number of the smaller known Inductions together, and change at once the whole method of the Science.

OF DEMONSTRATION; AND NECESSARY TRUTHS^[*]

[Chapter v: Of Demonstration, and Necessary Truths]

[§1]

[¶1] If, as has been laid down in the preceding chapters, the foundation of all Sciences, even Deductive or Demonstrative Sciences, is Induction; if every step in the ratiocinations of Geometry is a process of Induction, and a train of reasoning is but bringing many Inductions to bear on the same subject of enquiry, and drawing the case within one Induction by means of another; wherein lies the peculiar certainty always ascribed to the Sciences which are entirely or almost entirely Deductive? Why are they called the Exact Sciences? Why are mathematical certainty, and the evidence of demonstration, common phrases to express the very highest degree of assurance attainable by reason? Why is mathematics, by most philosophers, set down as independent of experience and observation, and characterized as a System of Necessary Truth?

[¶2] The answer is, that this superior certainty in the truths of mathematics, this character of necessity which is ascribed to them, is an illusion; in order to sustain which it is necessary to suppose, that those truths relate to and express the properties of purely imaginary objects. It is acknowledged that the conclusions of Geometry are deduced from the so-called Definitions. In our chapter on Definition we showed (what seems obvious as soon as stated) that from a Definition as such, no proposition, unless it be a proposition concerning the meaning of a word, can ever follow: and that what apparently follows from a Definition, really follows from an implied assumption, that there exists a real thing, conformable to the Definition. This assumption, in the case of the definitions of Geometry, is false: there exist no real things, exactly conformable to the Definitions. There exist no points without magnitude, no lines without breadth, or perfectly straight, no circles with all their radii exactly equal, nor squares with all their angles perfectly right. This being obvious, and acknowledged, it is customary to say, by way of saving the credit of the supposed Systems of Necessary Truth, that the points, lines, circles, and squares which are the subject of Geometry, exist in our conceptions merely, and are a part of our minds: which minds by working on their own materials, construct an a priori science, having nothing whatever to do with outward experience. But this is just as far from the truth. The points, lines, circles, and squares, which anyone has in his mind, are simply copies of the points, lines, circles and squares which he has known in his experience; and it is astonishing that this should be questioned after Bishop Berkeley’s triumphant refutation of the theory of abstract ideas. All our ideas of objects, are of individual objects: We can reason about a line as if it had no breadth, but we cannot conceive a line without breadth; we can form no picture in our imagination of such a line: all the lines which we have in our minds are lines possessing breadth. If any one doubts this we may safely refer him to his own experience. No one, probably, who ever fancied that he could conceive what is called a mathematical line, fancied it from the evidence of his own consciousness, but solely because he could not reconcile the contrary supposition with the reality of mathematics as a science. How it may be reconciled therewith, I think the sequel will shew.

[¶3] Since then neither in nature nor in the human mind do there exist any objects exactly corresponding to the definitions of Geometry; while yet, Geometry cannot be supposed to be conversant about objects purely imaginary; nothing remains but to consider geometry as conversant with such lines, angles, and figures as really exist; and the definitions as they are called, must be regarded as our first and most obvious generalizations concerning those natural objects. These generalizations are correct, as generalizations; that is, each of the general propositions is true of the whole class referred to in it, as far as it is true of any one individual in the class; but it is not exactly true of any individual; it is only nearly true: so nearly that no error of any importance in practice will be incurred by feigning it to be exactly true. When we have occasion to extend these inductions or their consequences to objects varying in any appreciable degree from those which furnished the materials of our generalization—to lines of appreciable breadth or thickness, parallels which are not exactly parallel, and the like, we correct our conclusions by combining with them a fresh set of propositions relating to the property which was overlooked. [¶4] The difference however, in exactness between these elementary generalizations in geometry, and the elementary generalizations of any other physical science, is fictitious. The assertions on which the reasonings of the science are founded, do not, any more than in other sciences, exactly correspond with the fact; but we suppose that they do, for the sake of seeing what consequences will follow from the supposition. The science is built upon, its conclusions are deduced from, hypotheses.

[¶5] When, therefore, it is affirmed that the conclusions of geometry are necessary truths; it appears, that all the necessity which can be ascribed to them, is only that they necessarily follow from the suppositions from which they are deduced. These suppositions not being necessary, nor even true, the conclusions deduced from them are only necessary in the sense of necessarily following from the suppositions; which is only saying that for the suppositions to be true and the conclusions false would involve a contradiction. I conceive that this is the only correct use of the word necessity in science; that nothing ought to be called necessary, the denial of which would not be a contradiction in terms. To say that the conclusions of a deductive science are not true, although the inductions, or assumptions, are, involves a contradiction; & therefore the conclusions of all deductive sciences were called, by the ancients, necessary propositions. Whatever property of a thing could be deduced from its essence, that is, from the properties included in its definition, was a proprium, and was said to be predicated necessarily.

[§3]

[¶2] There is another set of the elementary generalizations of mathematics, the axioms, which are not hypotheses; in which there is no fiction, but which really are exactly and literally true. That things which are equal to the same thing are equal to one another, is as true of the lines and figures in nature as it would be of the imaginary ones assumed in the definitions. In this respect however, Mathematics are only on a par with most other sciences. In almost all sciences there are some general propositions which are exactly true, while the greater part are but very close approximations to the truth. Thus in mechanics, the first law of motion, that of the inertia of matter, is true without qualification and without the slightest particle of error; it is not affected by the frictions and rigidities, and miscellaneous resistances which qualify, for example, the theories of the lever and the pulley. In optics, the rectilineal propagation of light through the same medium, the equality of the angles of incidence and of reflection, are inductions of the same sort; nay, even in chemistry many of the propositions which express the properties of simple bodies are true without qualification; not being at all affected by those slight impurities which may be supposed to remain in the most carefully made chemical preparations. The rotation of the earth in twenty four hours of the same length as in our time, has gone on since the first recorded observations without the increase or diminution of one second in all that period. These are inductions which require no fiction to make them be received as accurately true: but along with them there are others, as for instance the propositions respecting the figure of the earth, which are but approximations to the truth, and to make the science deductive we must feign that these are exactly true although they really want something of being so.

^[*] It will doubtless be said, that the axioms of mathematics differ from our inductions respecting the rotation of the earth, the laws of motion, &c. in this, that although the latter are universally true, it is possible to conceive that they might not be so: the earth might stand still, and matter might have spontaneous motion: but the axioms of mathematics cannot be conceived not to be true; that things which are equal to the same thing should be unequal to one another, is unconceivable by the human mind: these, therefore, are entitled to be called necessary truths; for though the denial of them is not a contradiction in terms—it is a supposition which is inconceivable.

To this there is, as it appears to me, a completely satisfactory answer, but as it belongs to the region of transcendental metaphysics, I will merely indicate it and pass on. That the falsity of any proposition is inconceivable to us, is no proof that our belief in the proposition was not originally the result of experience. It is a consequence of the general laws of the human mind that when anything whatever is true of all objects of which we have ever had experience—when we have never had perception of any object which had not, or even which seemed not to have, the property in question, we are unable to conceive any object without it.

The acknowledged laws of association obviously account for this. We can for example, conceive the sun or moon falling, because though we never saw them fall, we have seen other things fall: but we never saw any object without something beyond it, nor had any sensation without something following it; therefore, we cannot conceive an object without having the idea irresistibly raised of some other object beyond it; nor a sensation, without having the idea irresistibly raised of some other sensation following it; we cannot conceive any end to space or time; the one irresistibly appears to us infinite and the other eternal. In like manner, the proposition, The sums of equal things are equal, being true (and seen to be true at the first glance) of all objects whatsoever, it is no more than natural that so strong an association should be formed, between the conception of equal objects, and that of equal sums, that we are utterly incapable of imagining the former without the latter.

For these reasons, which are to my mind conclusive, I cannot admit that what is not conceivable by the human understanding, cannot be; nor that propositions, the contradictories of which are unconceivable, stand upon at all higher or stronger grounds of evidence than any other propositions which sufficient experience has shewn to be universally true. The propositions whose contradictories are inconceivable are not truer, or more necessarily true than the others, but are only wider generalizations; inductions coextensive with the whole universe; propositions which are true of all things known to our experience.

If, however, the reader, adopting a different view of the origin of our knowledge, connected with a different system of transcendental metaphysics, should reject the opinion, that the axioms of mathematics rest upon the evidence of experience; he will still admit all that is necessary for the purposes of this work, if he acknowledges that these truths, whatever be their evidence, first became known to us in particular cases. That this is the fact, was pointed out to us by Mr. Dugald Stewart, who was most adverse to the doctrine that they are truths resting on experience. But though he held that the proposition, Things equal to the same thing are equal to one another, is intuitively and not experimentally evident, he held, that it is intuitively evident in each particular case, and that the axiom is but a statement in general terms of what we perceive to be true when we examine any particular case. Even if we admit the axioms to be necessary truths, it does not affect the account we have given of the reasoning process. Inference is still only from particulars to particulars; but at every step at which the major of a syllogism is an axiom, then according to our theory there is an inference from particulars to particulars, but on the theory of necessary truths there is (instead of any inference) a direct perception of a fresh set of particulars.^*

Whichever theory we adopt on the subject of axioms, whether we consider them as very comprehensive inductions, or as necessary truths; Geometry is not deduced from the axioms alone, but from the axioms together with those assumptions which are called the Definitions; and those assumptions not being exactly true, the conclusions of Geometry are so far from being necessary truths, that they are not so much as truths at all; but only very close approximations to truths; and necessary, only in the sense of necessarily following from the assumptions; being propositions which we are obliged to assume if we make those first assumptions; and to deny which, affirming the assumptions, would be a contradiction in terms.

If there be any Deductive Science which has the appearance of being a system of necessary truth, it must be one which is deduced wholly from propositions exactly true, and not at all from hypotheses or assumptions which are only approximations to truth. If any Science has this character, it must be the science of Numbers; the theory of the Calculus; Arithmetic and Algebra. This, therefore, is a case which seems to merit examination apart.

[Chapter vi: The Same Subject Continued^* ]

[§2]

[¶1] There are many philosophers who would solve the difficulty apparently inherent in this case, by representing the propositions of the science of Numbers as merely verbal, and its processes as mere transformations of language, substitutions of one expression for another. The proposition, Two and One are equal to Three, is not, according to these philosophers, a truth, is not the statement of any fact in nature, but a mere Definition of the word Three; a statement that mankind have agreed to give the name of Three to the same thing which they already called by the name Two and One. According to this doctrine, the longest process in algebra is but a repetition of such operations as the foregoing, a series of translations of the same fact out of one language into another: though how, after such a series of translations, it comes out a very different fact, (as when we demonstrate a new geometrical theorem by Algebra) they have not explained; and it is a difficulty which is fatal to their theory.

[¶3] It must be acknowledged, that there are two peculiarities in the processes of arithmetic and algebra which render the above theory very plausible, and have not unnaturally rendered those sciences the stronghold of Nominalism. The doctrine that we can ascertain facts, detect the hidden processes of nature, by an artful manipulation of language, is so contrary to common sense that a person must have made some advances in philosophy to believe it; for to believe any thing so difficult of belief, a person must see far enough to come within sight of some great apparent difficulties on the other side. Now the difficulty which has made many persons Nominalists is the difficulty of believing the reasonings of Arithmetic and Algebra to be anything but verbal processes. For we do not carry any ideas along with us when we use the symbols of those sciences. In a geometrical demonstration we have a diagram in our head, and AB, AC are always present to our imagination as lines, intersecting other lines, forming an angle with one another and the like: but not so a and b. These may represent lines or anything else, but the lines or anything else are never thought of; nothing is realized in our imagination but a and b. The ideas which they represent are banished from the mind during every intermediate part of the process between the beginning when the premisses are translated from things into signs, and the end when the conclusion is translated back from signs into things. Nothing, then, being in the reasoner’s mind but the symbols, what can seem more absurd than to pretend that the reasoning process has to do with anything but the symbols? It seems one of Bacon’s Prerogative Instances, an experimentum crucis on the nature of reasoning itself.

[¶4] Nevertheless it will appear on consideration, that this apparently decisive instance is no instance at all; that there is in every step of an arithmetical or algebraical calculation a real induction, a real inference of facts from facts; and that what disguises the induction is merely the extremely comprehensive nature of the induction itself, and the consequent extreme generality of the language. All numbers must be numbers of something: Ten, must mean ten bodies, or ten smells, or ten sounds, &c. There are no such things as numbers in the abstract. But though they must be numbers of something, they may be numbers of anything. The propositions therefore concerning numbers, have the remarkable peculiarity that they are true of all things; of all objects, all entities whatever, known to our experience. All things whatever possess quantity; consist of parts which may be numbered; and therefore all the properties of numbers are true of them. That half of four is two, must be true whatever object the word four represents, whether four miles, or four quarters of a mile, four ounces, four shillings, four minutes, or four bars of a piece of music. The properties of the number four are properties of all Things possessing the attribute which that word connotes; that is of all things whatever as soon as they are divided into four equal parts. But algebra extends the generalization much farther: every number represents that number of all Things, but every algebraical symbol represents all Numbers; every algebraical equation is a proposition affirmed of all numerable things into whatever parts divided or by whatever number designated: the proposition 2(a+b) = 2a + 2b, is a truth coextensive with the whole Creation. Since, then, in algebraical reasonings, the truths we have to deal with are true of all Things whatever, and not, like those of Geometry, true of lines only, or angles only; it is no wonder that the symbols should not excite in our minds ideas of any Things in particular: the mere letters, a, b, x, y, z, do as well for the representatives of Things in general, as any more complex conception. But, that we are conscious of their being signs of Things, is evident from the fact, that our whole process of reasoning is carried on by predicating of them the properties of Things. At each step in solving an algebraical equation, what do we do? We apply to a, b, and x, the propositions that equals added to equals make equals; that equals taken from equals leave equals; and other propositions deducible from these: which are not properties of letters, or of signs of any kind, but of all magnitudes, that is, of all things, and are quite without meaning unless so understood. At each step, therefore, there is an induction (or call it, if you adopt the other theory, an intuition) but in any case, the perception or the inference is concerning Things, not symbols: although as any Things whatever will serve the turn, there is no necessity for keeping the idea of the Thing at all distinct, and consequently the process of thought may in this case be allowed without danger to do what all processes of thought when they have been performed often will do if permitted, namely to become entirely mechanical. Hence the general language of algebra comes to be used familiarly without exciting ideas, just as all other general language is prone to do from mere habit: but when we look back, to see from whence the probative force of the process is derived, we find that at every single step, unless we consider ourselves to be thinking and talking of the Things, and not of the mere symbols, the evidence fails.

[¶5] In addition to the circumstance which we have now mentioned, there is another circumstance which gives great plausibility to the notion that the propositions of arithmetic and algebra are merely verbal. This is, that when they are considered as propositions respecting Things, they have the appearance of being all of them identical propositions. The proposition, Two and One are equal to Three, considered as an assertion respecting objects,—for instance, “Two pebbles and one pebble are equal to three pebbles,”—does not assert equality between two collections of pebbles, but actual identity. It affirms that if we put one pebble to two pebbles, those very pebbles are three. The objects, therefore, being absolutely identical, and the mere assertion that objects are themselves, being insignificant, it seems but natural to consider the proposition, Two and one are equal to three, as asserting merely identity of signification between the two names.

[¶6] The answer to this is short and conclusive. The expressions, “Two pebbles and one pebble,” and the expression “Three pebbles,” do indeed stand for the same aggregations of objects, but they do not stand for the same sensations; they are names of the same objects, but of those objects in two different states: although they denote the same thing, their connotation is different. Three pebbles in two separate parcels, and three pebbles in one parcel, do not make the same impression on our senses; and the assertion that the very same pebbles may by an alteration of place be made to produce either the one set of sensations or the other, is not an identical proposition though it is a very familiar one. It is a truth known to us by early and constant experience; an inductive Truth; and such truths are the foundation of the Science of Number. The fundamental truths of that science, all rest on the evidence of sense; they are proved by shewing to our eyes and our fingers, that any given number of objects, ten balls for example, may by separation and rearrangement exhibit to our senses all the different sets of numbers the sum of which is equal to ten. And all the improved methods of teaching Arithmetic to young children, proceed upon a knowledge of this fact. All who wish to carry the child’s mind with them in learning Arithmetic—all who (as Dr. Biber in his remarkable Lectures on Education expresses it) wish to teach numbers and not mere cyphers—now teach it through the evidence of the senses in the manner we have now described.^*

[¶7] Arithmetic is indeed founded upon Definitions in the same sense as Geometry is; the proposition, “Three is two and one,” may be called a definition of Three, as the proposition, “A circle is a figure bounded by a line which has all its points equally distant from a point within it,” is called a definition of a circle. But the proposition which is one of the fundamental principles of Geometry is, that figures exist answering to this description; and the fundamental truth in arithmetic is, that parcels of objects exist which may be separated into two and one. These propositions being granted, we call the figures circles and the parcels Three’s and thus superadd two definitions of words to two assertions respecting matters of fact.

[¶8] It being shewn by the considerations now adduced, that the science of Number is not any exception to the conclusion we had previously arrived at, viz. that the processes even of Deductive Sciences are wholly Inductive; it remains to examine whether this science resembles Geometry in the further circumstance that some of its Inductions are not exactly true; and that the peculiar certainty ascribed to it, on account of which its propositions are called Necessary Truths, is fictitious, and the result of a Hypothesis.

[§3]

[¶1] The inductions of Arithmetic are, first, those which we have just expounded, One and one are two, Two and one are three, &c. which may be called the Definitions of the various numbers, in the geometrical sense of the word Definition, though not in the logical; and secondly two Axioms, “The sums of equals are equal,” and “The differences of equals are equals;” two only are needed, for the corresponding propositions respecting unequals may be demonstrated from these by way of reductio ad absurdum.[¶2] Both the definitions and these axioms, as already remarked, are inductive truths, true of all objects whatever, and when true at all, exactly true: there is no fiction involved, no assumption of unqualified truth where there is a mere approximation to it; the conclusions also, therefore, when true at all are exactly true, and the Science of Numbers, when its conditions are complied with, is an exact science.

[¶3] What I mean by “when true at all” and “when its conditions are complied with,” is this. In propositions concerning numbers there is a condition implied, without which none of them would be true; and that condition is an assumption, which may be false. The condition to which I allude is, that 1 = 1; that all the numbers are numbers of the same unit, or of equal units. Let this be doubtful, and not one of the propositions of arithmetic will hold true. How can we know that two pounds and two pounds make four pounds, if some of the pounds may be troy and others avoirdupois? They may not make four pounds of either or of any weight. How can we know that a forty-horse power is equal to itself, unless we suppose that all horses are of equal strength? It is certain that 1 is always equal in number to 1, and in that sense there is no impropriety in saying that one hour is equal to one mile, or one mile equal to one inch. Therefore, in the cases (and they are very few) where the mere number of objects, or of the parts of an object, is all that is material, the conclusions of arithmetic so far as they go to that alone, are true without any mixture of hypothesis. There are a ^[*] few such enquiries; as for instance, an enquiry into the number of inhabitants in any country. It is indifferent whether they are grown people or children, strong or weak, tall or short, all we want to ascertain is their number. The science of arithmetic as applicable to such enquiries is an exact science. But whenever from equality or inequality of number, equality or inequality in any other respect is to be inferred, arithmetic carried into such enquiries becomes a hypothetical science like geometry; it must always be assumed that all units are exactly equal in that other respect as well as in number; and this is never precisely true, for one pound weight is never exactly equal to another, nor one mile’s length to another: a nicer balance, or more accurate measuring instruments, could always detect some difference. [¶4] We may, therefore, correctly say that the science of number is itself an exact science, but it is not true, as is sometimes supposed, that other sciences become exact sciences by being rendered Arithmetical; by being subjected to the laws of number, that is, brought within the inductions relating to Numbers.

The science of pure Number, that is, the science which takes cognizance of the properties of objects only as being numbered, must be called an Exact Science. But as it appears from what has been said, to be a science founded on Inductions, although universal and obvious ones, its truths cannot be called Necessary Truths; unless we call everything necessary, which results from the general laws of the universe. And the other sciences of quantity, that is, of Things considered as divisible into a number of equal parts—whether they be sciences of Extension, of Weight, of Force, of Motion, of Sound, or of whatever other measurable things—are not exact sciences, and the necessity ascribed to their conclusions is only the necessity of inferring them, if we grant a certain hypothesis; a necessity which only means, that we should otherwise incur a self-contradiction.

[§4]

[¶1] To complete the present subject, one observation still remains to be made. This is, that the Method of all Deductive Sciences is hypothetical. They all proceed by tracing the consequences of certain assumptions, leaving it for separate consideration whether the assumptions are true or not, and if not exactly true, whether they are a sufficiently near approximation to the truth. There are obvious reasons for this. To ascertain how far the assumptions are true, is generally a matter of observation which has to be repeated in every fresh case: or if it is to be settled by argument instead of observation, may require different evidence in each different case. But the other part of the process, to determine what else may be concluded when we have found the assumptions to be true—may be performed once for all, and the results held ready to be employed as the occasions turn up for their use. We thus do all beforehand that can be so done, and leave the least possible task to be performed when the case arises, and presses for a decision. [¶2] It is obviously as easy to arrive at new conclusions from facts assumed as from facts observed; from imaginary as from real inductions. Deduction, as we have seen, is inference in this form, a is a mark of b, b of c, c of d, therefore a is a mark of d, which last may be a fact neither observed nor observable. In like manner it is equally allowable to say, Suppose that a were a mark of b, b of c, & c of d, then a would be a mark of d, which is a proposition we did not think of when we laid down the premises. A system of propositions as complicated as Geometry might be deduced from assumptions which were false; as was done by Ptolemy, Descartes, and many others, in attempting to explain synthetically the phenomena of the universe. Sometimes the same thing is knowingly done for the purpose of shewing the falsity of the assumption; which is called a reductio ad absurdum. The reasoning then is as follows: a is a mark of b, and b of c; now if c were also a mark of d, a would be a mark of d; but d is known to be a mark of the absence of a; consequently a would be a mark of its own absence, which is a self-contradiction: therefore c is not a mark of d.

[§5]

[¶2] In addition to the reason now stated, other reasons why the Method of a deductive science must be hypothetical, will evolve themselves in the progress of that deeper investigation of the nature of Induction, which the time has now come for attempting.

[Book III:

Of Induction]

OF INDUCTION IN GENERAL^[*]

From the investigations in the preceeding chapter, we have been led to the conclusion, that all Inference, or Reasoning, when it is from facts, i.e., not from something hypothetically assumed, but from something actually believed, is inference from particulars to particulars: except in the solitary case of reasoning from premises supposed not to be arrived at by derivation, but to be directly revealed from heaven; which may as well be general as particular. But even in this case, as in all cases in which we are commonly said to reason from generals to particulars, the process which is called reasoning, and of which the syllogism presents the correct analysis, is in very truth a process of interpretation only; a decyphering of signs.

Deferring for the present all consideration of the case of reasoning from a hypothesis, a process which as we shall see hereafter, holds a most conspicuous place and performs most important functions in philosophy; we proceed to take a closer view of the process to which we are indebted for all our knowledge of the course of nature; reasoning from particulars to particulars: an operation to which the usage of philosophers has attached the name, Induction.

When the inference from facts observed, to facts unobserved is certain, it is nearly indifferent, for most purposes, whether we figure to ourselves that operation as a process of reasoning from particulars to particulars, or from particulars to generals. We must bear in mind that generals are merely classes of particulars; in other words collections of particulars, definite in kind, but indefinite in number. And we observed in the last chapter, that whenever our evidences, that is, the various particular cases which we have examined, justify us in drawing an inference respecting even one other particular case, we must be justified in drawing that same inference with respect to a whole class of cases. If from our experience of the finite duration of human life, in all the instances which have reached our knowledge, we can infer that ourselves or that any particular person is mortal, we may with exactly the same strength of evidence infer the general proposition, “All human beings are mortal;” and if there were doubt whether the general conclusion were sufficiently borne out, a rateable [sic] proportion of the same doubt would attach to the particular one. The inference either does not hold in any case, or it holds in all cases of a certain kind; in all cases which, in certain definable respects, resemble those we have observed.

But although there can be no certain inference, and therefore in the strict sense, no inference at all, from one particular case to another, until the evidence is sufficient to establish a general proposition, yet before the enquiry is ripe for a generalization, we may often with considerable confidence anticipate some one or more of the particular cases which will be included in the generalization when made. This affords ground for a distinction very generally made by philosophers, but more familiarly used than accurately understood: the distinction between Induction and Analogy. The term Induction, in accordance with its original acceptation, is commonly appropriated to inferences of which a completed and definite Generalization is the result. Reasoning by Analogy or Analogical Reasoning, are the phrases employed when we conclude from one or more particular cases, to some fresh particular case directly and at once—without framing any general proposition.

As has been already so often remarked, no conclusion from particulars known to particulars unknown, can be certain unless the inference admits of being generalized, and becoming a perfect Induction. But it may easily happen, that before our knowledge and examination of particular instances, has reached the point at which we are enabled distinctly to define the extent of the general conclusion which those instances if more accurately known would enable us to establish, we may yet from the closeness of the general resemblance of some new instance to the instances we have observed, be able to conclude, though not with certainty yet with a high degree of probability, that the generalization, whatever instances it does not cover, will at least be found to cover that one instance. Here, therefore, if we are obliged to form an immediate conclusion, we conjecturally infer at once from particulars to particulars; without testing the sufficiency of our evidence by passing to the particular conclusion through the medium of a general one. A striking instance of this mode of drawing a conclusion, (though, as we shall see hereafter, it belongs to a species which has some peculiarities, rendering it not in all respects an apt representative of the genus) is the inference we so confidently draw from past experience that the sun will rise tomorrow. We cannot in the present state of our knowledge, generalize this inference. Who will presume to affirm, as a certain truth, that the sun will always rise? or has always risen from eternity? No one. Nor do we understand the sun’s nature, and the causes of his continued existence and of the permanency of the laws of the solar system, sufficiently to know upon what his rising or not tomorrow will ultimately depend. If we did, we might at least ascend to the general principle, that he will continue to rise while certain causes endure. But we cannot do even this. We cannot venture to generalize at all. Yet tomorrow looking so like today, and being of all days yet to come, that which looks most like it, we have no hesitation in drawing the inference with the utmost assurance as to that one, the proximate instance; though we should hesitate to affirm confidently that the sun would rise this day twenty thousand years.

In the above instance we do not generalize at all: there are other cases in which we do generalize, but are conscious that our general conclusion does not deserve implicit reliance. For instance if after much intercourse with Hindoos we have usually or always found them accessible to bribes, we might with a high degree of probability presume that a particular Hindoo, of whom personally we knew nothing, would be found to be so. Yet the universal proposition “All Hindoos are accessible to bribes”—could not be inferred from any one person’s individual experience, nor would it, in all likelihood be true. Our experience, or the degree of analysis to which we had subjected that experience, has not, we may suppose, enabled us to give to the proposition that exact limitation which would render it a true proposition and yet leave it a general one. We cannot make any generalization on the subject which we can know to be absolutely correct. Not only we cannot [sic] say “All Hindoos are accessible to bribes,” we cannot even say, “All Hindoos of such and such a description are so.” We must therefore qualify our generalization, by limiting not its extent, but the degree of assurance with which we assert its universality: we must consider it as a proposition not proved to be literally true, but to be nearly so: and in concluding to fresh particular instances we must consider our proof as a presumption only, though a strong one; evidence amounting to probability only, not to certainty.

There are thus three cases of inference from particulars to particulars, characterized by three different degrees of strength in the evidence.

1st. The evidence may be sufficient to warrant the unqualified assertion of some universal proposition: every A is B. Or, in other words, we may conclude with absolute certainty that any particular A is B. This may be called, Perfect Induction.

2nd. The evidence may be sufficient to warrant the assertion of some proposition general in form and language, but with the express qualification, that it is only known to be true in most of the cases which its terms comprehend, not in all: Most A are B. Or in other words, we may conclude with preponderant probability, but not with absolute certainty, that any particular A is B. This may be termed Imperfect Induction, and is one kind of Analogical Reasoning.

In this class of cases, though we have not certainty, we can measure with considerable assurance, the degree of our approach to it.

3d. The third case is that in which we have not, from the evidence before us, been able to set up any general Proposition, as proved to be true either universally or for the most part; but since a certain case appears to us strikingly to resemble the cases which we are acquainted with, we dare say that what we have found to be true in those cases, will be true in that case too, whether true or not in any others. This mode of inference has never, so far as I know, received any other name than that of Analogical Reasoning. The inference can never be more than probable, & although as we have seen, the probability may reach the highest degree of strength; it is commonly much less strong in this than in the preceding class of cases; can very seldom be measured with any approach to exactness & is often entirely indefinite and inappreciable. Most reasonings from history are of this kind; and almost all the reasonings of persons of uncultivated minds, in the ordinary affairs of life.

Analogical Reasoning, therefore, when contradistinguished from Induction, means inference of the same kind exactly, but of an inferior degree of strength. Analogical Reasoning is an imperfect Induction; or a conjectural foretaste of an Induction yet to come. Induction, again, is merely Reasoning from perfectly conclusive Analogies, or resemblances. Dugald Stewart, therefore, appears to have made a distinction without a difference, or at least to have expressed the distinction which we have now considered, in a very misleading phraseology, when he distinguishes the evidence of Analogy from the evidence of Experience. The evidence of Experience is nothing, can be nothing, but the evidence of Analogy: when the analogies are conclusive, we call the process Induction; but it is Analogy still. In our analysis of the Syllogism we saw that all inference from experience, is inference from particulars to particulars, and that all inference from particulars to particulars, is from the resemblance of the one set of particulars to the other. Resemblance may be incomplete or complete, but it is resemblance still. The proposition, “Food nourishes”—rests Dugald Stewart could say, not upon analogy, but upon experience; the analogy no doubt amounts in this case to a perfect Induction, but the experience which the conclusion rests upon, is experience of today’s food, and yesterday’s, not tomorrow’s; how then do I know that tomorrow’s food will nourish? From its analogy to the food of today.

Induction, then, and Analogical Reasoning, are both of them names for inferences of the same kind, from particulars to particulars; but when the process of inference is certain, we call it Induction: when only probable or conjectural, Analogical Reasoning.

We have next to enquire into the nature and grounds of Induction; the conditions necessary to constitute a perfect, or conclusive Induction; and the means of measuring the degree of probability of the less certain inferences from Analogy.

OF THE VARIOUS GROUNDS OF INDUCTION

[Chapter ii: Of Inductions Improperly So Called]

[§1]

[¶1] Induction is the name given to the operation of the mind, by which we infer that what we know in a particular case or cases, will be true in any other case or cases of a similar kind; or in stricter language, Induction is the process by which a predicate which can be truly affirmed or denied of one or more individuals, is thence inferred to be truly affirmable or deniable of any or all individuals which resemble those individuals in certain particulars.

More briefly, Induction is the process by which we conclude that what is true of certain individuals of a class, is true of the whole class; that is, of every other individual in it.

[¶2] But why do we conclude that what can be truly predicated of certain individuals which we know, can be predicated of other individuals which we know not? What is our warrant for so concluding?

In order to answer this question it is necessary to advert to some further distinctions.

[¶3] Induction according to the definition we have given of it, is a process of inference, a process from the known to the unknown; and any process involving no inference, any process by which the conclusion we seem to arrive at, is no wider than the premises from which it is drawn, does not fall within our meaning of the word Induction. Yet in most books of logic, we find this laid down as the most perfect, indeed the only quite perfect case of Induction. For in most books of Logic, every process which starts from the less general & terminates in the more general, is called Induction, whether anything be really concluded or not: it is enough that the process admits of being stated in the form, This and that individual A is B, ergo every A is B. And when we affirm to be true of a class, what we have previously ascertained to be true of every individual in the class, this, which is no conclusion at all, but a mere reassertion of our premises, is sagely affirmed to be the most certain conclusion which Induction ever enables us to arrive at. Thus if we were to say “All the planets shine by reflected light”—because we have examined each of them separately and found this to be true; or “All the Apostles were Jews,” because Peter, Paul, John, and each of the other nine were so, this would be called, in the phraseology to which we are adverting, a perfect Induction. There is no harm certainly in calling this Induction, so long as we take care to understand what is meant; but it is Induction in a quite different sense from what we have designated by that name; since it is no inference from facts known to facts unknown, but a mere short hand registration of facts known. In truth, the two simulated argumentations cited above are not generalizations, nor are the propositions which stand as conclusions from them, general propositions. General propositions are those in which the predicate is affirmed or denied of an indefinite, an unlimited number of individuals, viz, of all individuals, few or many, existing or which can exist, possessing the properties connoted by the subject of the proposition. “All men are mortal” does not mean, all men now living, but all men past, present, and to come, actual or possible. When the signification of the subject is limited in such a manner as to denote, not any and every individual falling within a certain general description, but only each of a number (known, or if unknown, yet knowable) of individuals, marked off and designated as individuals; the proposition, however general in its form, is no universal proposition, but is only that very number of singular propositions written in an abridged character. This process, like all other forms of abridged notation, is of great use in philosophy, but it is not a process by which truth can be arrived at. The consideration of it however throws some light upon the case next to be examined.

[§2^* ] Where the Induction is real, that is, where it consists of a generalization, or extension to an entire class, of a predicate previously known to be true of certain individuals of the class; the grounds which warrant the generalization, will be found to be different, according to the manner in which our knowledge of the premisses is acquired. Those premisses, it is almost unnecessary to repeat, are the singular propositions from which we infer the general one—Now, our knowledge of the truth of these singular propositions can only be derived (unless revealed from heaven) from one of two sources; observation, that is, experience; or demonstration.

An instance of induction from premisses proved by observation, is the one so often cited: All human beings are mortal, for all the human beings of whom there is any record, have, after a certain period, died.

An instance of induction from premisses proved by demonstration, is any geometrical theorem proved by a diagram.^*

When we demonstrate a theorem by means of a diagram, either visible or only imaginary, the demonstration does not bring out a universal proposition, but only a singular one. In the demonstration of the fifth proposition of Euclid, what is proved? Not that the angles at the base of every isosceles triangle are equal, but only that the angles at the base of the triangle ABC are so. The enunciation of the proposition is not proved by the demonstration, but by a subsequent induction; an induction however of a peculiar kind; more resembling the simulated induction which produced the proposition “All the Apostles were Jews”—than the real induction by which we prove that “All men are mortal;” and yet a real induction, because containing a real inference. We do not indeed infer that all isosceles triangles have their angles at the base equal, because ABC has so. But having proved that ABC has that property, we infer that any other isosceles triangle has it, because we perceive that in the same way by which we have proved it of ABC, we could prove it of any other isosceles triangle. We perceive that if we had chosen to demonstrate it of any other isosceles triangle instead of ABC, we might have put that other triangle in the place of ABC throughout the demonstration, and neither would any of our premisses have ceased to be true, nor would the inference at each of the steps, have less followed from the premisses. The result then being that we have demonstrated our predicate to be true of one individual in the class, and perceived that we might similarly demonstrate it of any other individual in the class whether actual or even conceivable, we embody all these inferred and inferrible singular propositions, in one universal proposition, and affirm the predicate of the entire class.

This process of generalization, we may term Induction or not as we find most convenient. It differs from the Induction which is founded on experience, in this, that the general proposition is not inferred from any of the individual cases contained in it, but from ulterior premisses on which even those individual cases themselves rest. This illation cannot be thrown into the form “This and that individual A is B, therefore every A is B.” We may rather consider ourselves as demonstrating each individual case seperately, and then gathering them all up into a general proposition; and thus far the process resembles that Induction improperly so called, of which “All the planets shine by borrowed light,” was an example.

But on the other hand, the process which we are now considering is a real generalization; it enables us to conclude with the utmost certainty to particular cases which we have not actually examined, which have never even been specifically in our thoughts, and which we only know to be susceptible of the very same demonstration as the cases we examined, because we know that demonstration to be independant of all properties in the examined cases, except those common to them with the unexamined ones. Thus we conclude that all triangles have the sum of their three angles equal to two right angles, not because ABC has so, but because the process which proves ABC to possess that property, took no account of any attribute of ABC, except that of being a triangle.

This process therefore really concludes from the known to the unknown; from the examination of one case only, it proves something to be true of an indefinite multitude of unexamined cases. It agrees therefore with Induction from experience, in the characteristics most important in Philosophy; and may without any inconvenience or confusion be called Induction. The better to distinguish it from the Induction of which Experience is the basis, we shall give it the name of Induction from parity of reasoning.

We may now return to the question which we asked ourselves at the commencement of the chapter: Why do we conclude that what can be truly predicated of certain individuals which we know, can be predicated of other individuals which we know not? What is our warrant for so concluding?

To this question different answers must be given, according as the Induction is from parity of reasoning, or from Experience.

In the case of Induction from parity of reasoning, our warrant for affirming the general proposition, is, that we have a warrant for affirming every singular proposition contained in it. That warrant is demonstration; and the nature of demonstrative evidence cannot yet be explained.

^[*] We must, therefore, at present confine ourselves to the case of Induction from Experience. In this case, our warrant for the generalization, is the uniformity of the course of nature. The universe, we find, is so constituted, that whatever is found to be true in any one case, is true in all cases which exactly resemble it.

The explanation and illustration of this principle requires a chapter to itself.

OF THE UNIFORMITY IN THE COURSE OF NATURE

[Chapter iii: Of the Ground of Induction]

[§1]

[¶3] The fact which is our warrant for all inference from experience, is that which has been expressed by philosophers in such forms of language as these; That the course of nature is uniform; That the universe is governed by general laws; & the like. Our belief in this general truth, has been classed by a well-known school of philosophers, as one of the instincts of our nature, and termed our intuitive conviction that the future will resemble the past. Whatever be the origin of the belief, this is a very unphilosophical mode of describing it. Time, in its modifications of past, present, and future, has no relation direct or indirect either with the belief itself or with the grounds of it. We believe that fire will burn tomorrow because it burns today, but we believe on precisely the same grounds, that it burnt before we were born, and that it burns this very day in Cochin China. It is not from the past to the future, as past and future, that we infer, but from the known to the unknown; from what we have perceived and been directly conscious of, to what has never come within our personal experience. In this last predicament is the whole region of the future; but also the vastly greater part of the present & of the past.

[¶4] The principle of Induction, then, is that the course of nature is ^[*] uniform. I am far, however, from giving this large generalization as an explanation of Induction. On the contrary it is itself a case of Induction, and one of a very complicated kind. Far from being the first Induction we make, it is one of the very last; and the general proposition in which it is couched has scarcely entered into the conceptions of any but metaphysicians, nor even by them (as we shall see presently) have its extent and limits been always very accurately conceived. Yet, the principle in question, must be considered as the warrant for all our inductions from experience, in this sense, that unless it were true, those inductions would all be fallacious; and this as we have already seen, is the sole mode in which the general propositions, which stand as premisses in our reasonings when thrown into syllogism, ever really contribute to the establishment of the conclusions which stand apparently deduced from them.

Archbishop Whately remarks, that every Induction is an imperfect Syllogism, with the major premiss omitted. The remark is just; though I would rather express it thus, that every Induction may be thrown into the form of a Syllogism by supplying a major premiss. When this is done, the principle which we are now considering, that of the uniformity of the course of nature, will come forth as the invariable major premiss, immediately or remotely of all inductive argumentations; to which accordingly it will stand in the same relation as the major premiss always does; not contributing at all to prove the conclusion, but only assisting somewhat to verify the process by which it is proved.

[¶2, n] From the above remark, that every Induction may be thrown into the form of a Syllogism, Archbishop Whately concludes, that Induction itself is only a peculiar case of ratiocination; & that the universal type of all Inference, or Reasoning, is the Syllogism. This conclusion is directly the opposite of that to which our enquiries have led us. Instead of resolving induction into ratiocination, we have shown that ratiocination, on the contrary, is resolvable into induction. Dr. Whately’s conclusion may I think be refuted by merely following up his own argument. He justly observes that the induction, John, Peter, Thomas &c. &c. are mortal, therefore All mankind are mortal, is reduced into the form of a Syllogism, by prefixing as a major premiss the implied assumption, Whatever is true of John, Peter, Thomas &c. &c. is true of all mankind. Thus far all goes smoothly; and Dr. Whately (who, endowed with a penetrating and active, but not persevering intellect, seldom fails to send his sounding line to a greater depth below the surface than his predecessors, & who when he has done this, scarcely seems to care whether he reaches the bottom or not) omitted to ask himself the further question, How we come by this major premiss? It is not self-evident; nay, in all cases of precipitate generalization, it is false. How then is it arrived at? Necessarily either by induction or by ratiocination, and if by induction, then on Dr. Whately’s own principles it is by ratiocination still, that is, by a previous syllogism. Proceeding, therefore, to construct this previous syllogism, he will arrive by more or fewer steps at a final or original syllogism, starting from the principle which we are not yet prepared to express in precise terms, but which we have provisionally and popularly expressed in such phraseology as this, The course of nature is uniform. Having reached this ultimate major premiss, we have now the whole field of Induction spread before us, marked out in logical compartments, syllogized through and through; and every instance of Induction is now syllogistically accounted for, except one; but that one unhappily comprehends all the others. All inferences from experience are now resolved into conclusions syllogistically deduced from one general principle; but how did we get at the principle itself? Whence came the universal major? What proves to us that nature is governed by general laws? Point out to us the major of the syllogism of which that is the conclusion,—you cannot. Well, then, here at least is a case of Induction which cannot be resolved into Syllogism. And do not take shelter under the metaphysical doctrine, that the belief in the uniformity of the course of nature is an instinct. Let it be by instinct, if you will, that the child expects fire to burn him today, because it burnt him yesterday; let the inference from particulars to particulars be the result of instinct, as much as you please, but who ever dreamed of arriving by instinct at a broad metaphysical generalization? It may be instinct which makes a dog eat when he is hungry, but there is no instinct which tells him that “Every animal who is hungry has need to eat.” The comprehensive principle that the universe is governed by general laws, is itself the result of Induction; it is a generalization from the individual instances which have fallen within our personal observation; & moreover it is a generalization founded on prior generalizations: we never should have thought of making it, if we had not previously arrived at a knowledge of some of the laws themselves, which could have been no otherwise than by Induction, although Dr. Whately’s theory supposes that we never could have made any Induction without first assuming that general maxim.

^[*] There is no impropriety however, in speaking of this general truth, that the course of nature is uniform, as the warrant for all Induction. If the course of nature were not uniform, inference from experience would be impossible; Induction would convey no assurance of the truth of its results; and no conclusion got at by Induction, is to be relied upon any farther than as it can be shewn that the falsity of the conclusion would be inconsistent with that principle; that if the conclusion were not true, the course of nature would not be uniform.

It is therefore of the utmost importance to conceive clearly how far and in what sense it is true that the course of nature is uniform; in order that we may know, what are the Inductions to which the warrant of the principle extends.

In ascertaining this, it will be unnecessary to enter into the origin and psychological analysis of our belief in the uniformity of nature; i.e. in the evidence of Experience. Some philosophers have professed to resolve this mental phenomenon into a case of the Law of Association, others regard it as an original and ultimate element of our nature. To determine which of them is right, is a problem in the higher or transcendental metaphysics, into which it is not our business to enter. Either theory equally supposes that the process of concluding from Experience, is one in which we are liable to err, and that experience itself is the rule which ought to guide us in determining how far we can safely infer from experience. Whichever theory we adopt, experience itself can alone determine how far and in what sense experience is uniform; and the tendency to generalize from observation, whether innate or not, must be indulged within limits which it is the province of observation itself to find out. This is sufficient for our purpose, and we, therefore, proceed to enquire what is the real nature and what the limits of the uniformity in the course of nature.

We have already remarked that such a proposition as this “The course of nature is uniform,” possesses rather the brevity suitable for popular than the precision required in philosophical language. Indeed, its terms require to be explained, & a stricter than their ordinary meaning given to them, before the proposition can be admitted as true. [§2, ¶1] Every person’s consciousness assures him that he does not always expect uniformity in the course of events; he does not always believe that the future will resemble the past. Nobody believes that it will rain tomorrow, because it rained today. Nobody expects to meet the same man at the same spot every time he walks out, merely because he has once met him. On the contrary everybody is surprised; and mentions it as something extraordinary if the course of nature is constant, and resembles itself, in these cases.

[¶2] The course of nature is in truth not only uniform, it is also infinitely various. Some phenomena seem always to recur in the very same combinations in which we met them at first; others, which we have been accustomed to regard as equally bound down to a particular set of combinations, we unexpectedly find detached from some of the elements with which we had always found them conjoined, and united to others of quite a contrary description. To an inhabitant of central Africa half a century ago, no fact probably appeared to rest upon more uniform experience than this, that All human beings are black. To Europeans not many years ago, the proposition, All swans are white, appeared an equally decided instance of uniformity in the course of nature. Further experience has proved to both that both were wrong; but very many centuries elapsed before this additional experience came. During all these centuries mankind believed in a uniformity of the course of nature, where no such uniformity existed.

[¶3] According to the notion which the ancients seem to have entertained of Induction, these two were cases of as legitimate Induction as any other. In these two instances, in which the ground of inference must have been insufficient since the conclusion was false, there was yet in their conception of Induction, as much ground for drawing the inference as there is in any case whatever. This sort of Induction was that which Bacon describes as Inductio per enumerationem simplicem, ubi non reperitur instantia contradictoria; recording merely such instances as offered, and if all those instances agreed, generalizing upon them. [¶5] It is chiefly by pointing out the insufficiency of this kind of Induction, that Bacon merited the title of Founder of the Inductive Philosophy. The notions which he introduced, of a better kind of Induction than this, though still deficient in definiteness and precision, have had, if not all the influence which has occasionally been ascribed to them, yet a very large share of influence in causing the great and rapid progress of physical science since his time. Even to physical science however the application of just views of induction is yet far from perfect; and the chief reason why the moral and political sciences are so far behind the physical, is that to them there is yet scarcely a trace of the application of the improved notion of Induction which Bacon originated. The current and approved modes of reasoning on those subjects are still of the very kind which Bacon exploded: the Induction employed is the very Inductio per enumerationem simplicem which he condemns; and the experience, which we hear so confidently appealed to, is still in his own forcible words, “mera palpatio.”

^[*] This, in fact, is the kind of Induction, if such it can be called, which is natural to the human mind when unenlightened by philosophy. That tendency, which some call an instinct and others an association, to infer ‘the future from the past,’ the known from the unknown, is simply a tendency to expect that what has been found true once or several times will be found true again. It matters little whether the instances are few or many, conclusive or inconclusive. Those are considerations which occur only on reflection; the expectation follows the past experience, provided that be uniform,—provided no experience of a conflicting character comes unsought: the notion of seeking it, of experimenting for it, of interrogating nature as Lord Bacon has it, is of quite subsequent growth. The experience of uninstructed human minds is purely passive experience: they take such facts as present themselves, they do not ask themselves what facts they want, to enable them to come to a sure conclusion, and then search for these.

We are not, however, now to consider how evidence is to be sought, which is a question for the Art of Logic; we are to look out for a test of the sufficiency of evidence, the only question which belongs to the Science.

[§3]

[¶1] It is manifest that there are correct and incorrect Inductions; and that some which have for centuries been thought to be correct, were incorrect. That all swans are white, must have been an incorrect Induction, since it terminated in a false conclusion. The evidence, therefore, was insufficient. The experience, however, from which the inference was drawn, was genuine. From the earliest records, the observation of all the inhabitants of the known world, was unanimous on the point. The uniform experience, therefore, of the inhabitants of the known world, all agreeing in one common result, without a single known instance of variation from that result, is not always sufficient to establish a general conclusion.

[¶2] But let us now turn to an instance apparently very similar to this. Mankind were wrong, it seems, in concluding that all swans are white: are we also wrong, when we conclude that all men’s heads grow above their shoulders, and never beneath, in spite of the conflicting testimony of the naturalist Pliny? As there were black swans, although civilized man had existed on the earth nearly three thousand years without meeting with them, may there not also be “men whose heads do grow beneath their shoulders,” notwithstanding an almost equal unanimity of testimony to the contrary from all observers? Most persons will answer No: it was more credible that a bird should vary in its colour, than that man should vary in the relative position of his principal organs. And why more credible? Apparently because there is less constancy in the colours of animals, than in the general structure of their internal anatomy. But how do we know this? From experience doubtless. Then it is experience (as we have once before said), which must tell us, in what cases or what classes of cases experience is uniform. We must consult experience in order to learn from her, under what circumstances arguments from her will be valid. The course of nature is uniform in certain cases; in certain others, it is not uniform: & the Theory of Induction must begin by settling what these cases are.

[¶3] It is obvious that there are cases in which we reckon with the utmost confidence upon uniformity, & others in which we do not reckon upon it at all. In some we feel complete assurance that the future will resemble the past, that the unknown will be precisely similar to the known. In others, however uniform the result obtained from all the cases which we have observed, we draw from thence no more than a feeble presumption that the same result will hold in other cases. That a straight line is the shortest distance between any two points we feel convinced is true even in the region of the fixed stars. When a chemist announces the existence & properties of a newly discovered substance, if we have confidence in his accuracy of observation, we feel no doubt that the conclusions he has arrived at will hold universally, although the induction is founded but on a single instance. We do not withhold our assent, waiting for a repetition of the experiment; or if we do, it is from a doubt whether the one experiment was properly made, not whether if properly made it would be conclusive. Here then is a general law of nature inferred without hesitation from a single instance; a universal proposition from a singular one. Now mark another case, and contrast it with this: Not all the instances which have been observed since the beginning of the world, in support of the general proposition that all crows are black, would be considered a sufficient presumption in favour of the truth of the proposition, to outweigh the testimony of one unexceptionable witness who should affirm that in some region not yet explored, he had caught and examined a crow and had found it brown.

[¶4] Why is a single instance in one case sufficient for a complete Induction, while in another myriads of concurring instances without a single exception known or presumed, goes [sic] so slight a way towards establishing a general proposition? Whoever can solve this question, knows more of the Philosophy of Logic, than the wisest of the ancients, and has solved the great problem of Induction.

Appendix B

Supplementary Note to Book II, Chapter iii (“Of the Functions, and Logical Value of the Syllogism”), in the 3rd (1851) and 4th (1856) editions

[This note, added in the 3rd edition (1851), was replaced in the 5th edition (1862) by the note to p. 205, which in part retains the earlier wording. The text below is that of the 4th edition (1856), with variant notes giving the 51 readings, and those of the later editions as found at pp. 205 ff.]

Note Supplementary to the Preceding Chapter

This theory of the syllogism, (which has received the important adhesion of Dr. Whewell,^* ) has been controverted by a writer in the British Quarterly Review.^† The doctrine being new, discussion respecting it is extremely desirable, to ensure that nothing essential to the question escapes observation; and I shall, therefore, reply to this writer’s ^aarguments^a with somewhat more minuteness than their strength may seem to require.

The reviewer denies that there is a petitio principii in the syllogism, or ^bthat the proposition, All men are mortal, asserts or assumes that Socrates is mortal. In support of this denial, he argues that we may, and in fact do, admit the general proposition that all men are mortal, without having particularly examined the case of Socrates, and even without knowing whether the individual so named is a man or^csomething else^c . But this of course was never denied. That we can and do draw conclusions concerning cases specifically unknown to us, is the datum from which all who discuss this subject must set out. The question is, in what terms the evidence, or ground, on which we draw these conclusions, may best be designated—whether it is most correct to say, that the unknown case is proved by known cases, or that it is proved by a general proposition including both sets of cases, the unknown and the known? I contend for the former mode of expression. I hold it an abuse of language to say, that the proof that Socrates is mortal, is that all men are mortal. Turn it in what way we will, this seems to me to be asserting that a thing is the proof of itself. Whoever pronounces the words, All men are mortal, has affirmed that Socrates is mortal, though he may never have heard of Socrates; for since Socrates, whether known to be so or not, really is a man, he is included in the words, All men, and in every assertion of which they are the subject. If the reviewer does not see that there is a difficulty here, I can only advise him to reconsider the subject until he does: after which he will be a ^dbetter^d judge of the success or failure of an attempt to remove the difficulty.^* That he had reflected very little on the point when he wrote his remarks, is shown by his oversight respecting the dictum de omni et nullo. He acknowledges [p. 27] that this maxim as commonly expressed,—“Whatever is true of a class, is true of everything included in the class,” is a mere identical proposition, since the class is nothing but the things included in it. But he thinks this defect would be cured by wording the maxim thus,—“Whatever is true of a class, is true of everything which can be shown to be a member of the class:” as if a thing could “be shown” to be a member of the class without being one. If a class means the sum of all the things included in the class, the things which can “be shown” to be included in it are ^ea part of the sum^e , and the dictum is as much an identical proposition with respect to them as to the rest. One would almost imagine that, in the reviewer’s opinion, things are not members of a class until they are called up publicly to take their place in it—that so long, in fact, as Socrates is not known to be a man, he is not a man, and any assertion which can be made concerning men does not at all regard him, nor is affected as to its truth or falsity by anything in which he is concerned.

^fThe difference between the reviewer’s theory and mine may be thus stated. Both admit that when we say, All^f men are mortal, we make an assertion reaching beyond the sphere of our knowledge of individual cases; and ^gthat^g when a new individual, Socrates, is brought within the field of our knowledge by means of the minor premise, we learn that we have already made an assertion respecting Socrates without knowing it: our own general formula ^hbeing^h , to that extent, for the first time interpreted to us. But according to the reviewer’s theory, ⁱthe smaller assertion is proved by the larger: while I contend, that both assertions are proved together, by the same evidence, namely, the grounds of experience on which the generalⁱ assertion was made, and by which it must be justified.

^jThe reviewer says [p. 22], that if the major premise included the conclusion, “we should be able to affirm the conclusion without the intervention of the minor premise; but every one sees that that is impossible.” A similar argument is urged by Mr. De Morgan (Formal Logic, p. 259): “The whole objection tacitly assumes the superfluity of the minor: that is, tacitly assumes we know Socrates^* to be a man as soon as we know him to be Socrates.” The objection would be well grounded if the assertion that the major premise includes the conclusion, meant that it individually specifies all it includes. As however the only indication it gives is a description by marks, we have still to compare any new individual with the marks; and to show that this comparison has been made, is the office of the minor. But since, by supposition, the new individual has the marks, whether we have ascertained him to have them or not; if we have affirmed the major premise, we have asserted him to be mortal. Now my position is that this assertion cannot be a necessary part of the argument. It cannot be a necessary condition of reasoning that we should begin by making an assertion, ^ka part of which that assertion is to be employed in proving^k . I can conceive only one way out of this difficulty, viz. that what really forms the proof is the other part of the assertion; the portion of it, the truth of which has been ascertained previously: and that the unproved part is bound up in one formula with the proved part in mere anticipation, and as a memorandum of the nature of the conclusions which we are prepared to prove.

With respect to the minor premise in its formal shape, the minor as it stands in the syllogism, predicating of Socrates a definite class name, I readily admit that it is no more a necessary part of reasoning than the major. When there is a major, doing its work by means of a class name, minors are needed to interpret it: but reasoning can be carried on without either the one or the other. They are not the conditions of reasoning, but a precaution against erroneous reasoning. The only minor premise necessary to reasoning in the example under consideration, is, Socrates is like A, B, C, and the other individuals who are known to have died. And this is the only universal type of that step in the reasoning process which is represented by the minor. Experience, however, of the uncertainty of this loose mode of inference, teaches the expediency of determining beforehand what kind of likeness to the cases observed, is necessary to bring an unobserved case within the same predicate: and the answer to this question is the major.^l Thus the syllogistic major and the syllogistic minor start into existence together, and are called forth by the same exigency. When we conclude from personal experience without referring to any record—to any general theorems, either written, or traditional, or mentally registered by ourselves as conclusions of our own drawing, we do not use, in our thoughts, either a major or a minor, such as the syllogism puts into words. When, however, we revise this rough inference from particulars to particulars, and substitute a careful one, the revision consists in selecting two syllogistic premises. But this neither alters nor adds to the evidence we had before; it only puts us in a better position for judging whether our inference from particulars to particulars is well grounded.^jb

^mnThis brings me to the reviewer’s next objection;ⁿ that the formula in which the major is left out—“A, B, C, &c. were mortal, therefore the Duke of Wellington is mortal,” does not express all the steps of the mental process, but omits one of the most essential, that which consists in recognising the cases A, B, C, as sufficient evidence of what is true of the Duke of Wellington. This recognition of the sufficiency of the induction he calls an “inference,” and says, that its result must be interpolated between the cases A, B, C, and the case of the Duke of Wellington; and that “our final conclusion is from what is thus interpolated, and not directly from the individual facts that A, B, C, &c. were mortal.” [P. 25.] ^oIt is true, as the reviewer says, that the major is an affirmation of the sufficiency of the evidence on which the conclusion will be grounded. But to my thinking it would seem that the conclusion is inferred from the evidence itself, and not from a recognition of the sufficiency of the evidence. I infer the presence of my friend because I see him, and not because I recognise that my eyes are open, and that eyesight is a means of knowledge. In all operations which require care, it is good to assure ourselves that the process has been performed accurately: but the testing of the process is not the process itself; and besides, may have been omitted altogether, and the process be correct. Now it is precisely because that operation is omitted in ordinary unscientific reasoning, that there is anything gained in certainty by throwing reasoning into the syllogistic form. To make sure, as far as possible, that it shall not be omitted, we make the testing operation a part of the reasoning process itself. We insist that the inference from particulars to particulars shall pass through a general proposition. But this is a security for good reasoning, not a condition of all reasoning; and in some cases not even a security. Our most familiar inferences are all made before we learn the use of general propositions; and a person of untutored sagacity will skilfully apply his acquired experience to adjacent cases, though he would bungle grievously in fixing the limits of the appropriate general theorem. But though he may conclude rightly, he never, properly speaking, knows whether he has done so or not: he has not tested his reasoning. Now this is precisely what forms of reasoning do for us. We do not need them to enable us to reason, but to enable us to know whether we reason correctly.

It may be added, in further answer to the reviewer, that,—even when the test has been applied, and the sufficiency of the evidence recognised,—if it is sufficient to support the general proposition, it is sufficient also to support the inference from particulars to particulars without passing through the general proposition. The inquirer who has logically satisfied himself that the conditions of legitimate induction were realized in the cases A, B, C, would be as much justified in concluding directly to the Duke of Wellington as in concluding to all men.^o The general conclusion is ^pnever^p legitimate, unless the particular one would be so too; and in no sense, intelligible to me, can the particular conclusion be said to be drawn from the general one.^q That the process of testing the sufficiency of an inductive inference is an operation of a general character, I readily concede to the reviewer; I had myself said as much, by laying down as a fundamental law, that whenever there is ground for drawing any conclusion at all from particular instances, there is ground for a general conclusion. But that this general conclusion should be actually drawn, however useful, cannot be an indispensable condition of the validity of the inference in the particular case. A man gives away sixpence by the same power by which he disposes of his whole fortune; but it is not necessary to the lawfulness of his doing the one, that he should formally assert, even to himself, his right to do the other.

The reviewer has recourse for an example, to syllogisms in the second figure (though all are, by a mere verbal transformation, reducible to the first), and asks, where is the petitio principii in this syllogism, “Every poet is a man of genius, A B is not a man of genius, therefore A B is not a poet?” It is true that in a syllogism of this particular type, the petitio principii is disguised. A B is not included in the terms, every poet. But the proposition, “Every poet is a man of genius,” ^rsupposing it to be provable^r , cannot have been inductively proved, unless the negative branch of the inquiry has been attended to as well as the positive; unless it has been fully considered whether among persons who are not “men of genius,” there are not some who ought to be termed poets, and unless this has been determined in the negative. Therefore the case of A B has been decided by implication, as much as the case of Socrates in the first example. The proposition, Every poet is a man of genius, is confessedly æquipollent with “No one who is not a man of genius is a poet,” and in this the petitio principii, as regards A B, is no longer implied, but express, as in an ordinary syllogism of the first figure.

^sThe language of ratiocination would, I think, be brought into closer agreement with the real nature of the process, if the general propositions employed in reasoning, instead of being in the form All men are mortal, or Every man is mortal, were expressed in the form Any man is mortal. This mode of expression, exhibiting as the type of all reasoning from experience “The men A, B, C, &c. are so and so, therefore any man is so and so,” would much better manifest the true idea—that inductive reasoning is always, at bottom, inference from particulars to particulars, and that the whole function of general propositions in reasoning, is to vouch for the legitimacy of such inferences.^sm

Appendix C

Book III, Chapter v (“Of the Law of Universal Causation”), §9, in MS, 1st (1843), and 2nd (1846) editions

[This section was replaced in the 3rd edition (1851) by the present §11 (§§5 and 10 being added in the 8th edition). The 1846 version is printed below, with variant notes giving the readings of the 1st edition and the MS.]

§9. [^aDoctrine that volition is an efficient cause, examined^a ] Before concluding this chapter, it seems desirable to take notice of an apparent^b opposition between the doctrines which I have laid down respecting causation, and those maintained in a work which I hold to be far the greatest yet produced on the Philosophy of the Sciences, M. Comte’s Cours de Philosophie Positive. M. Comte asserts as his first principle, that the causes of phenomena are beyond the reach of the human faculties, and that all which is accessible to us is their laws, or, as he explains the term, their constant relations of succession or of similarity. Accordingly ^che^c sedulously abstains, ^din the subsequent part of^d his work, from the use of the word Cause: an example which I have not followed, for reasons which I will proceed to state. I most fully ^esubscribe to the doctrine^e that ultimate, or, in the phraseology of metaphysicians, efficient causes, which are conceived as not being phenomena, ^fnor^f perceptible by the senses at all, are radically inaccessible to the human faculties: and that the “constant relations of succession or of similarity” which exist among phenomena themselves, (not forgetting, so far as any constancy can be traced, their relations of coexistence,) are the only ^gsubjects^g of rational investigation. When I speak of causation, I have nothing in view, other than those constant relations: but I think the terms causation, and cause and effect, important to be preserved, for the purpose of distinctively designating one class of those relations, namely the relations of succession which so far as we know are unconditional; as contrasted with those which, like the succession of day and night, depend upon the existence or upon the coexistence of other antecedent facts. This distinction corresponds to the great division which Mr. Whewell and other writers have made of the field of science, into the investigation of what they term the Laws of Phenomena, and the investigation of causes;^[*] a phraseology, as I conceive, ^hnot philosophically sustainable^h , inasmuch as the ascertainment of causes, such causes as the human faculties can ascertain, namely causes which are themselves phenomena, is, therefore, merely the ascertainment of other and more universal Laws of Phenomena. And I cannot but look upon the revival, on English soil, of the doctrine (not only refuted by the school of Locke and Hume, but given up by their great rivals Reid and Stewart) that efficient causes are within the reach of human knowledge, as a remarkable instance of what has been aptly called “the peculiar zest which the spirit of reaction against modern tendencies gives to ancient absurdities.”

Yet the distinction between those constant relations of succession or coexistence which Mr. Whewell terms Laws of Phenomena, and those which he terms, as I do, Laws of Causation, is grounded (however incorrectly expressed) upon a real difference. It is ⁱonly the extreme slightness of his acquaintance with M. Comte’s speculations, which could have led Mr. Whewell to assume that he has overlooked this fundamental difference; and,ⁱ that by excluding the investigation of causes, he excludes that of all the most general truths^j, is a still more complete misapprehension.^j But it does appear to me that his disinclination to employ the word Cause has occasionally led him to attach less importance than it deserves to ^ka^k distinction, upon which alone, I am convinced, the possibility rests of framing a rigorous Canon of Induction. Nor do I see what is gained by avoiding this particular word, when M. Comte is forced, like other people, to speak continually of the properties of things, of agents and their action, of forces and the like; terms equally liable to perversion, and which are partial and inadequate expressions for what no word that we possess, except Cause, expresses in its full generality. I believe, too, that when the ideas which a word is commonly used to convey are overclouded with mysticism, the obscurity is not likely to be so effectually dispelled by abstaining from its employment, as by bringing out into full clearness the portion of real meaning which exists in the various cases where the term is most familiarly employed, and thereby giving a legitimate satisfaction to that demand of the intellect which has caused the term to remain in use.

Appendix D

Portion of Book III, Chapter x (“Of Plurality of Causes; and of the Intermixture of Effects”), §4, in the 4th (1856) through 7th (1868) editions; with two papers on the Conservation of Force by Mill and Alexander Bain and supporting correspondence

[This passage first appeared in the 4th (1856) edition, and after considerable revisions, was deleted for the 8th edition (see 442ⁱ) and replaced by Book III, Chapter v (“Of the Law of Universal Causation”), §10, which should be read in conjunction with this Appendix (see also Mill’s Preface to the 8th edition, cxvii above). The 1868 version is printed below, with variant notes giving the readings of the 4th, 5th, and 6th editions.

Given here as explicatory background are portions of the correspondence between Mill and Bain bearing on the matter in issue, the Conservation of Force, with two culminating papers that they exchanged. (Bain’s letters and the two papers are in the Milton S. Eisenhower Library, Johns Hopkins University; the papers were printed, with some errors, in Hugh S. R. Elliot, ed., The Letters of John Stuart Mill, 2 vols. [London: Longmans, Green, 1910], II, 321-8. One letter in the sequence, Mill to Bain, 29 May, 1870, has not been located.) On the MS Mill dates his paper as “end of 1871,” and Bain’s as “February, 1872.”]

^aThe very promising generalization now commonly known as the Conservation or Persistence of Force, bears a close resemblance to what the conception of chemical composition would become, if divested of the one circumstance which now distinguishes it from simple transformation. It has long been known that heat is capable of producing electricity, and electricity heat; that mechanical motion in numerous cases produces and is produced by them both; and so of all other physical forces. It has of late become the general belief of scientific inquirers^a that mechanical force, electricity, magnetism, heat, light, and chemical action (to which ^bhas subsequently been added^b vital ^caction^c ) are not so much causes of one another as convertible into one another; and ^dthey are now generally spoken of as^d forms of one and the same force, varying only in its^e manifestations. ^fThis doctrine may be admitted, without by any means implying that Force is a real entity, a Thing in itself, distinct from all its phenomenal manifestations to our organs. Supposing the doctrine true, the several kinds of phenomena which it identifies in respect of their origin would nevertheless remain different facts; facts which would be causes of one another—^f reciprocally causes and effects, which is the first ^gelement^g in the form of causation properly called transformation. ^hWhat the doctrine contains more than this, is, that in each of these cases of reciprocal causation, the causes are reproduced without alteration in quantity. This is what takes place in the transformations of matter: when water has been converted into hydrogen and oxygen, these^h can be reconverted into ⁱpreciselyⁱ the same quantity of water from which they were produced. To ^jestablish a corresponding law in regard to Force, it has to be proved that heat is^j capable of being converted into electricity, electricity into chemical action, chemical action into mechanical force, and mechanical force back again into the ^kexact^k quantity of heat which was ^loriginally expended; and so through all the interchanges. Were this proved^l , it would establish what^m constitutes transformation, as distinguished from the simple ⁿfactⁿ of reciprocal causation. ^oThe fact in issue is simply the quantitative equivalence of all these natural agencies; whereby a given quantity of any one is convertible into, and interchangeable with, a given, and always the same, quantity of any other: this, no less, but also no more. It cannot yet be said that the law has been fully proved of any case, except that of interchange between heat and mechanical motion. It does seem to be ascertained, not only that these two are^o convertible into ^peach^p other, but that after any number of conversions the original quantities reappear without^q addition or diminution^r, like the original quantities of hydrogen and oxygen after passing through the condition of water. If the same thing comes to be proved true of all the other forces, in relation to these two and to one another, the law of Conservation will be established; and it will be a legitimate mode of expressing the fact, to speak of Force, as we already speak of Matter, as indestructible. But Force will not the less remain, to the philosopher, a mere abstraction of the mind. All that will have been proved is, that in the phenomena of Nature, nothing actually ceases without generating a calculable, and always the same, quantity of some other natural phenomenon, which again, when it ceases, will in its turn either generate a calculable, and always the same, quantity of some third phenomenon, or reproduce the original quantity of the first.^r

Mill—Bain Correspondence

1.

Mill to Bain

Avignon, May 17, 1870

. . . Respecting the Conservation theory itself, you have given [in your Logic] by many degrees the clearest explanation of it that I have ever met with, & I now seem to myself to understand the facts of the case pretty completely. But about the mode of expression of the facts I still boggle, & have a stronger impression after reading your exposition than I had before that the men of science have not yet hit upon the correct generalization though they may be at no great distance from it. I am so anxious to understand this matter thoroughly that I write down my difficulties in hopes that you will help me to resolve them.

In the first place, you exclude from the theory two of the principal forces, Gravitation & Molecular Adhesion, expressly distinguishing these from the “correlated forces.” Of course you do so because there is at present no proof of the convertibility of the other forces into these; & you do not take any notice of the hypothetical explanation of gravitation by molecular motions, given by Tait (I believe) & others, which so strikingly resemble the argument of Descartes to shew that his vortices might generate a tendency to a centre. But though gravity does not take its place in the theorem of conservation, motion generated by gravity does. Suppose, then, a weight suspended by a string over the shaft of a mine—suppose that the string breaks, & the weight falls, with rapidly increasing velocity, to the bottom. Here is a positive addition to the active force at work in the universe, which, when it ceases its mechanical motion, remains in the form of heat or in some other of the correlated forms. Now, at the expense of what pre-existing energy has this force been generated? The conservationists are obliged to say, out of potential energy. A given quantity of potential energy has become actual; & if the weight is hoisted up again the power expended in raising it is so much taken back from the sum of actual energy & restored to the sum of potential.

Now I want to analyse the meaning of this phrase, “potential energy.” It seems to signify some force actually residing in the suspended weight. But it is nothing of the kind. There is a force actually residing in the weight; a force exactly measurable: viz. the downward pressure with which it pulls at the string, & by which it is able to neutralise an equal weight at the other end of a lever. But this force is limited to that with which the body would commence falling if the string broke, & is far short of the vastly accelerated force with which it would reach the bottom of the mine. When we are bid to say that this augmented force existed previously as potential energy in the weight, this potential energy is not to common sense & logic anything which really existed, but is a mere name for our knowledge that a force would be created if the body began to fall.

I am discussing the expressions, not denying any of the facts. I admit that when force is expended in placing a weight in a “more advantageous position,” as you express it (i.e. in a place from which it has further to fall in order to reach its centre of attraction) when it does fall to the depth from which it has been raised it will reproduce the exact amount of force expended in raising it (making allowance for any part which may have been transformed into heat). The expression “potential energy” is no doubt adopted to enable us to say that the total amount of force in all Nature can neither be increased nor diminished, the sum of the actual force plus the sum of the potential being a constant quantity. But this only means that there is a vast reserve of force not existing in any shape now, but which gravity could call into existence, & that this not actual but possible quantity of force has an extreme limit, viz. the whole of the motion that would be generated by the rushing together of all the gravitating bodies in the universe until they could not possibly get any closer together. From time to time a little of this possible force gets itself created & in that case it requires that an equal force sh^d be expended if the effects produced are to be counterbalanced or undone.

It seems to me a bad & misleading form of expression to ascribe the motion which would be gradually acquired by gravitating bodies if the obstacles which keep them apart were removed, to an energy of equivalent amount residing in the body before it begins to move.

But if this objection could be overruled a greater remains behind. You say (& this is a point quite new to me) that force may be, & is, expended in merely altering the collocation of bodies, without generating even potential energy. This I suppose is the case when force is expended in destroying molecular adhesion. But if this be so, how can the indestructibility of force be maintained? The sum of actual force plus the sum of potential is, in that case diminished.

When you have time, perhaps you will kindly explain to me how the theory of Conservation as at present expressed, can stand with this fact. . . .

2.

Bain to Mill

Inverurie, by Aberdeen, 19 July, 1870

. . . You have conceived the position of gravity, in the correlated forces, so exactly, that I can hardly add anything to your statement of the facts. And having the facts so clearly before you, you are as well able as any one else is, to say how the state of the case may be best expressed in language. If we were to exclude gravity (and cohesion) from the Universe, force would exist purely as actual motion, mechanical and molecular. There would be so much momentum of moving masses, and so much of moving molecules, as Heat, &c. The law of transference would hold strictly; and the mode of transference would always be from one moving mass to another. This would be Correlation in its purity and simplicity. But now the existence of gravity, and other attractive (as well as repulsive) forces, introduces a new aspect, whereby we may have the reality of force, without the fact of the actual movement of masses or molecules. The principle of equivalence still holds; and the existence of these attractions and repulsions neither create nor destroy the total of available force. They alter its direction, and they embody it in a form, that we should a priori have supposed impossible,—the form of absolute quiescence. These influences are not a primal source of moving power; although to appearances, and on the prevailing cosmical hypothesis, gravity is de facto the source of all the energies of our solar system. But gravity, in this sense, must be conceived as disgorging energy, namely, all that energy that was expended in separating the masses to the distance at which they begin to gravitate towards each other. Hence the force of gravity is termed potential, and also energy of position, because it may be without actual motion, and is inoperative until such time as the masses are separated by the consumption of other force.

These are merely a few varieties of expression of the broad facts. What is true of gravity applies to molecular adhesion, as in a spring, which is an equally familiar instance of an agency that can neither create nor destroy power, but may store up, and divert it; having the same peculiarity of embodying the power without actual movement, of either mass or molecule.

Your other difficulty can be resolved thus. Notwithstanding the absolute indestructibility of force, there is one situation where it is transmuted with remarkable facility into a form wherein it is practically useless; that is to say, the radiation of heat into (so-called) empty space. By a circumstance, which has often struck me as the most frightful act of prodigal waste within the whole compass of human knowledge, and sufficient of itself to damn any one pretending to be the Creator, nearly the whole of the accumulated energy of the sun, is passing off into the realms of boundless space, merely raising the temperature of space by an infinitesimal amount, such as to be of no value to any interest that we can conceive. Now what happens in the great scale of the sun’s unintercepted radiation, happens in the small scale, on many petty occasions. Suppose a block of granite dragged over a level space. The force expended upon the act would of course, in free space, impart a persisting momentum to the block. But all this momentum is destroyed by the friction of the ground; that is, an equivalent amount of heat, as rise of temperature, is generated in the surface passed over. In certain circumstances, the heat would continue, and would represent in all future time the momentum expended. But in actual fact, the heat soon radiates off into free space, there to join the waste radiation of all suns and stars, by which ultimately all the force in the universe must be dissipated beyond recall, without being in strict language annihilated.

It is true that my use of the word “Eliminate” passes beyond the mathematical signification. We need a word to express the act of separating the casual from the causal antecedents of a phenomenon. Now the word “eliminate” has already made one step in chemical physiology, where it signifies the extrication or separation of various products as carbonic acid, urea, &c by means of the lungs, kidney, and so forth. And, although it may be a farther stretch, to use it for the inductive problem, no better word occurred to me. The operation being a technical one seems to want a technical word. . . .

3.

Mill to Bain

Blackheath Park, Aug. 4, 1870

. . . I am much obliged to you for your letter which though it does not remove my difficulties affords material which may perhaps help me towards resolving them.

How do we know that any energy has ever been expended in “separating the masses to the distance at which they begin to gravitate towards each other”? The new theory of the universe in relation to Force shews the same tendency from all past time to draw the masses nearer to one another instead of separating them, to which it is supposed that the present order of the universe will finally succumb. If by the masses are meant the molecules, & if what you say refers to the separation into different stellar bodies by cooling, of what was originally a nebula; I would say that the molecules of the nebula must have already gravitated towards one another. If they were ever too close together to do so, how have they ever emerged from that state? I cannot see what preexisting force can have been hoarded by gravitation.

“Elimination” in the chemical application which you mention, still seems to mean only getting rid of, and not picking out & retaining. . . .

4.

Bain to Mill

Inverurie, Aberdeen, Aug. 16, 1970

. . . The only answer to your difficulty as to the separation of gravitating bodies is that both theoretically, and in fact, a collision between two bodies, converts mechanical force into heat, which is expansive energy, and leads to the separation of a compact solid mass into a diffused aenal mass, which gravitation brings together again. The fall of another earth towards ours, under gravity, is calculated as discharging an amount of force that would vaporise the entire mass; and ages would be occupied in its re-consolidation. This is the only known mode of regenerating extinct solar systems.

There is a volume edited by Dr. Youmans, an American, containing the whole series of essays on the correlation of force.^[*] Some of them you have read, others are now past; but one or two would still be of use by suggesting illustrations and points of view. There is one by Mayer, and I think one by Helmholtz, which although out a good many years, have not been exhausted of their interest. I can send you my copy if the book is not in the London Library. . . .

Papers on the Conservation of Force

Mill’s Paper

1.

Potential Energy.

It appears to me that this is a misnomer, and that it produces unnecessary obscurity in the theory of the Conservation of Force. The theory being that all force consists in motion, either molar or molecular, & that motion is neither created nor destroyed but only transferred, it seems as if the force said to be laid up (for instance) in the coal were a contradiction to the theory, unless one supposes that an undiminished quantity of molecular motion continues to take place in the coal during the whole interval between its first deposition & its extrication, & in that case one does not see why it shd not produce heat. This difficulty is cleared up by the consideration that what is really potential is the motion. The motion, or other phenomenon interchangeable with motion, which caused the formation of the coal, has not been stored up, but has ceased & been annihilated: but the coal which has been generated will, under suitable allocations, reproduce a quantity of motion or other equivalent phenomenon, which quantity not being indefinite, but exactly equal to the quantity previously expended, justifies the expression that a definite quantity of force has been stored up. Force, therefore, must be defined not as real motion, no more than as an occult cause of motion, but as a potentiality or permanent possibility of motion, just as matter is a permanent possibility of sensation. Hence it is not proper to speak of potential force, or potential energy. Potential means (vide Hamilton) that which is not, but may be: but the energy is; that which sometimes is not, but always may be, is the motion itself: & instead of speaking of potential energy, we should define the energy itself as potential motion.

2.

Gravitation.

The interchangeability, in the case of gravitation, of force not merely with other forms of force but with what is called a “position of advantage,” is a great puzzle, & seems to be so far a surrender of the theory of Conservation of Force. For the purpose of saving the theory it is denied that gravity creates any force, & even Mr. Bain accepts this doctrine, giving as the ground of it that “what is gained in power is lost in position; to restore the position would require the power to be given back.” But surely this is merely the equivalent of what is true of all force. The force expended in chemical decomposition is restored in recomposition; & the power must be given back to replace things as they were before. The heat given out in freezing must be restored in melting. It seems to me that what requires force to overcome it must be allowed to be force. This difficulty however is removed by the change of language I have proposed. We should then say as is usually said, that a stationary body resting on the earth exerts a present force equal to its weight; but besides an actual moving power equal to that of the weight necessary to balance it, it has a latent potentiality of motion equal to the whole of the motion which it would go through if it, with the whole earth, were to fall into the sun. Now when this body is lifted or thrown up to a higher position & remains there, it has added to its former potentiality of motion, in the direction of gravity, a quantity equal to the additional motion which it would have to perform in first falling back to its original position; & this quantity is exactly equal to the quantity of force which was expended in raising it. We may therefore say, without impropriety, that this amount of energy has not perished, but has been stored up in the body by the fact of elevating its position.

3.

Light.

I do not see the difficulty which others appear to see in the relation of light to the theory of Conservation. I do not see why that theory should make us expect that when a body by heating becomes luminous the light should be produced at the expense of heat. It ought to be so if light were itself a force; but my solution would be that light, like the sensation of heat, is purely subjective: what is objective, if the theory be true, is the vibrations of the medium. Now though there are vibrations which produce only heat, or only chemical action, there are, if I remember right, none which produce only light; all the rays of the spectrum are I believe also calorific, though in unequal degrees. I shd therefore surmise that light is merely a concomitant, due to a physiological action of those vibrations, & that the chemical influence said to be exerted by light is really exerted by the vibrations themselves. Any other supposition seems inconsistent with the fact that there are rays, not luminous, which produce the chemical effect in a still higher degree than those which are luminous. Then, when a body is heated to luminousness, there would be an increased extrication of the form of force which is represented by heat, but no transmutation of any of it into another form represented by light; the sensation of light would be merely an incidental effect on our optic nerve of the increased vibratory motion in the medium, & there would be no expenditure of force except what takes place at the transition from the ether to the optic nerve, which would be parallel with the similar expenditure of force that there must be in putting our nerves into the condition which gives the sensation of heat.

4.

Force expended without result.

Here seems still to lurk the only real imperfection of the theory. It appears that force expended in altering the mere allocations of objects, as in moving stones from the quarry to the place where they are to be used, is wholly lost, no potentiality of reproducing equivalent motion being stored up. If this be so, then, according to the theory, the quantity of force in the universe must be constantly diminishing, since every change in the position of objects consumes some of it, &, unless when a “position of greater advantage” has been obtained, none is reproduced. This is a more serious matter than even the dissipation of energy by the solar radiation into space, since that is a transfer of the force to the interstellar ether from which for aught we know it may be capable of being again collected about points. But if the Conservation theory be true ought not the force expended in altering allocations to be still preserved in a similar manner to the force radiated from the sun, viz by being transferred to the ether? As a matter of fact is not much of it converted into heat? I shd much like to know what scientific authorities would say to this.

5.

Attraction & Repulsion.

There still remain many questions, which may or may not have been settled, respecting the application of the Conservation of Force to those internal forces by which bodies are supposed to be held in their existing state, viz. molecular attractions & repulsions balancing one another. Here is apparently a vast store of potential motion, prevented from being actual by opposite potentialities. Is this store of latent force also derived from the Sun? & if so how? When air is condensed by pressure heat is evolved. Is this heat a numerical equivalent of the motion, real or potential, which is expended? Take off all pressure, & the particles of the air fly apart, until they are stopped by gravity: the expansive force I suppose is the force which was stored up in the air; but then air, in rarifying, absorbs a great quantity of heat. What is the explanation of this phenomenon by the Conservation of Force? It is not that the heat is transformed into expansive motion, as when heat applied to water converts it into elastic steam: on the contrary, the expansion comes first, & the absorption follows as its effect just as if a vacuum had been made in the ocean of force & other force rushed in to fill it; but this is not a transformation of force. I do not know whether these questions have been resolved, or what are the exact relations between the theorem of the Persistence of Force & these particular kinds of molecular action.

Bain’s Paper

The phrase, Potential Energy, must not be too closely criticised. It covers a gap that at present we know not how to fill up. The difficulty does not occur in regard to the molecular force of chemical action, although the phrase is used for that case. The force supposed to be stored up in coal is not potential, but real movement existing in the Oxygen. As compared with Carbonic Acid, Oxygen contains in the shape of the high molecular movement all the force given out in combustion; and the lowered condition of molecular force in Carbonic Acid expresses the amount of change.

It is with gravity that the real difficulty occurs, in finding the suitable expression of equivalence. When force is expended to raise a body against gravity, we know only that the body on falling again would acquire the force equal to what had been expended, but we are unable to assign any molecular movement which represents the force expended, when the body has attained its height. If gravity could be explained in the form of some ethereal action of the intervening medium, doubtless the agitation of such a medium might be a molecular equivalent for the force expended in raising a body against gravity. But as this seems to be a hopeless attempt, we must just express the fact as we find it, and allow a break in the continuity of molecular and molar movement as respects force.

Another case very much resembling gravity is the action of a spring, which is the case of attraction or repulsion in the small scale of molecules. This is equally heterogeneous with the idea of matter in motion as representing the type of force. At the present moment we must treat these attractions and repulsions exactly like gravity as a break in the line of force considered as matter in motion. A distended spring is a position to attain which force is expended, and the recovery from which by molecular attraction restores the force into moving matter. But we cannot say that the tension of the spring is itself moving matter.

In the case of the transference of bodies from one place to another, the force consumed all turns to radiant heat through the medium of friction or of collision. A heavy body set in motion would of course move for ever, and retain the force expended on it. It would go through space, and might be found, as it were, at all distances without any waste. That is the very nature of motion to treat space and distance as nothing. But now, if we wish to arrest and to localize this body, we must apply a counter force to stop it. This counter force might be another body free to move, and to take on the equivalent momentum, so that nothing would be lost. But, in point of fact, we oppose bodies in motion by a dead obstacle, or a drag, which converts all the movement into sensible heat, raises the temperature of bodies, and, consequently, in cooling all the heat and force are wasted by the usual mode of ultimate dissipation.

As to the question of light. The subjective aspect of the phenomenon does not exhaust its bearings. We must view light as well as heat both on the objective and on the subjective sides. Objectively, heat is supposed to be a mode of molecular motion capable of imparting motion molar or molecular at a definite rate of commutation. The difficulty lies in making good the same fact regarding light. No amount of mere light has ever yet been transformed into force in any of the other modes: yet light plays a part in the disturbance of molecular equilibrium. It is the occasion of combinations and of decompositions as in the well-known facts culminating in Photography. As causing combination it displays no molecular force in the sense of imparting a definite quantity of its own to another body. It merely puts the particles in a position to bring their own forces into play, and to begin a molecular change in the bodies combined. A mechanical disturbance and many other things would have the very same efficacy. The testing case of the transference of power is chemical decomposition. Heat is a decomposing agent because it can supply, or restore, the molecular power that was given forth when the elements first combined. Light is incapable of this. If it ever causes decomposition, it is in the presence of some other power that supplies the needful molecular force that was given out in the previous combination. The action of light upon the retina is apparently of this disturbing kind, and its great efficiency is due to the extreme instability of nervous matter.

The change of phrase from Potential Energy to Potential Motion is certainly an improvement, in respect of exchanging the vague word “Energy” for the definite fact “Motion”, which is the word that is supposed to generalize, and, at the same time, embody the fact called “Energy” and “force”. The gain of the new theory is from never losing sight of the “moving matter” as the cardinal circumstance, and the true meaning of what we call “force”, “Energy”, “power”, and the like.

Appendix E

Book III, Chapter xiii (“Miscellaneous Examples of the Explanation of Laws of Nature”) §§1-3, in MS, and 1st (1843) through 5th (1862) editions

[These sections were replaced in the 6th edition (1865) by the present §§1-3. The 1862 version is printed below, with variants to the earlier editions and the MS.]

§ 1. [Liebig’s theory of the contagiousness of chemical action] Some of the most remarkable instances which have occurred since the great Newtonian generalization, of the explanation of laws of causation subsisting among complex phenomena, by resolving them into simpler and more general laws, are to be found among the^a speculations of Liebig in organic chemistry. These speculations, though they have not yet been sufficiently long before the world to entitle us positively to assume that no well-grounded objection can be made to any part of them, afford, however, so admirable an example of the spirit of the Deductive Method, that I may be permitted to present some specimens of them here.

It has been observed in certain cases, that chemical action is, as it were, contagious; that is to say, a substance which would not of itself yield to a particular chemical attraction, (the force of the attraction not being sufficient to overcome cohesion, or to destroy some chemical combination in which the substance was already held,) will nevertheless do so if placed in contact with some other body which is in the act of yielding to the same force. Nitric acid, for example, does not dissolve pure platinum, which may “be boiled with this acid without being oxidized by it, even when in a state of such fine division that it no longer reflects light.”^[*] But the same acid easily dissolves silver. Now if an alloy of silver and platinum be treated with nitric acid, the acid does not, as might naturally be expected, separate the two metals, dissolving the silver, and leaving the platinum; it dissolves both: the platinum as well as the silver becomes oxidized, and in that state combines with the undecomposed portion of the acid. In like manner, “copper does not decompose water, even when boiled in dilute sulphuric acid; but an alloy of copper, zinc, and nickel, dissolves easily in this acid with evolution of hydrogen gas.”^[*] These phenomena cannot be explained by the laws of what is termed chemical affinity. They point to a peculiar law, by which the oxidation which one body suffers, causes another, in contact with it, to submit to the same change. And not only chemical composition, but chemical decomposition, is capable of being similarly propagated. The peroxide of hydrogen, a compound formed by hydrogen with a greater ^bamount^b of oxygen than the quantity necessary to form water, is held together by a chemical attraction of so weak a nature, that the slightest circumstance is sufficient to decompose it; and it even, though very slowly, gives off oxygen and is reduced to water spontaneously (being, I presume, decomposed by the tendency of its oxygen to absorb heat and assume the gaseous state). Now it has been observed, that if this decomposition of the peroxide of hydrogen takes place in contact with some metallic oxides, as those of silver, and the peroxides of lead and manganese, it superinduces a corresponding chemical action upon those substances; they also give forth the whole or a portion of their oxygen, and are reduced to the metal or to the protoxide; though they do not undergo this change spontaneously, and there is no chemical affinity at work to make them do so. Other similar phenomena are mentioned by^c Liebig. “^dNo^d other explanation,” he observes, “of these phenomena can be given, than that a body in the act of combination or decomposition enables another body, with which it is in contact, to enter into the same state.”^[†]

Here, therefore, is a law of nature of great simplicity, but which, owing to the extremely special and limited character of the phenomena in which alone it can be detected experimentally (because in them alone its results are not intermixed and blended with those of other laws), had been very little recognised by chemists, and no one could have ventured, on experimental evidence, to affirm it as a law common to all chemical action; owing to the impossibility of a rigorous employment of the Method of Difference where the properties of different kinds of substance are involved, an impossibility^e noticed and characterized in a previous chapter.^* Now this ^fextremely^f special and apparently precarious generalization has, in the hands of Liebig, been converted, by a masterly employment of the Deductive Method, into a law pervading all nature, in the same way as gravitation assumed that character in the hands of Newton; and has been found to explain, in the most unexpected manner, numerous detached generalizations of a more limited kind, reducing the phenomena concerned in those generalizations into mere cases of itself.

The contagious influence of chemical action is not a powerful force, and ^gis^g only capable of overcoming weak affinities: we may, therefore, expect to find it principally exemplified in the decomposition of substances which are held together by weak chemical forces. Now the force which holds a compound substance together is generally weaker, the more compound the substance is; and organic products are the most compound substances known, those which have the most complex atomic constitution. It is, therefore, upon such substances that the self-propagating power of chemical action is likely to exert itself in the most marked manner. Accordingly, first, it explains the remarkable laws of fermentation, and some of those of putrefaction. “A little leaven,” that is, dough in a certain state of chemical action, impresses a similar chemical action upon “the whole lump.”^[*] The contact of any decaying substance, occasions the decay of matter previously sound. Again, yeast is a substance actually in a process of decomposition from the action of air and water, evolving carbonic acid gas. Sugar is a substance which, from the complexity of its composition, has no great energy of coherence in its existing form, and is capable of being easily converted (by combination with the elements of water) into carbonic acid and alcohol. Now the mere presence of yeast, the mere proximity of a substance of which the elements are separating from each other, and combining with the elements of water, causes^h sugar to undergo the same change, giving out carbonic acid gas, and becoming alcohol. It is not the elements contained in the yeast which do this. “An aqueous infusion of yeast may be mixed with a solution of sugar, and preserved in vessels from which the air is excluded, without either experiencing the slightest change.”^[†] Neither does the insoluble residue of the yeast, after being treated with water, possess the power of exciting fermentation. ⁱ(Here we have the Method of Difference.)ⁱ It is not the yeast itself, therefore; it is the yeast in a state of decomposition. The sugar, which would not decompose and oxidize by the mere presence of oxygen and water, is induced to do so when another oxidation is at work in the midst of it.

By the same principle Liebig is enabled to explain ^jmany cases of^j malaria; the pernicious influence of putrid substances; a variety of poisons; contagious diseases; and other phenomena.^[*] Of all substances, those composing the animal body are the most complex in their composition, and ^kare^k in the least stable condition of union. The blood, in particular, is the most unstable compound known. ^lIt is, therefore, not surprising^l that gaseous or other substances, in the act of undergoing the chemical changes which constitute, for instance, putrefaction, should, when brought into contact with the tissues by respiration or otherwise, and still more when introduced by inoculation into the blood itself, impress upon some of the particles a chemical action similar to its own; which is propagated in like manner to other particles, until the whole system is placed in a state of chemical action more or less inconsistent with the chemical conditions of vitality.

Of the three modes in which we observed in the last chapter that the resolution of a special law into more general ones may take place, this speculation^m exemplifies the second. The laws explained are such as this, that yeast puts sugar into a state of fermentation. Between the remote cause, the presence of yeast, and the consequent fermentation of the sugar, there has been interpolated a proximate cause, the chemical action between the particles of the yeast and the elements of air and water. The special law is thus resolved into two others, more general than itself: the first, that yeast is decomposed by the presence of air and water; the second, that matter undergoing chemical action has a tendency to produce similar chemical action in other matter in contact with it. But while the investigation thus aptly exhibits the second mode of the resolution of a complex law, it no less happily exemplifies the third; the subsumption of special laws under a more general law, by gathering them up into one more comprehensive expression which includes them all. For the curious fact of the contagious nature of chemical action ⁿisⁿ only raised into a law of all chemical action by these very investigations: just as the Newtonian attraction was only recognised as a law of all matter when it was found to explain the phenomena of terrestrial gravity. Previously to Liebig’s investigations, the property in question had only been observed in a few special cases of chemical action; but when his deductive reasonings ^ohave^o established that innumerable effects produced upon weak compounds, by substances none of whose known peculiarities would account for their having such a power, might be explained by considering the supposed special property to exist in all those cases, ^pthese numerous generalizations on separate substances^qare^q brought together into one law of chemical action in general^p: the peculiarities of the various substances being, in fact, eliminated, just as the Newtonian deduction eliminated from the instances of terrestrial gravity the circumstance of proximity to the earth.

§ 2. [Liebig’s theory of respiration] Another “speculation of the same chemist^a, which, if it should ultimately be found to agree with all the facts of the extremely complicated phenomenon to which it relates, will constitute one of the finest examples of the Deductive Method on record, is his theory of respiration.^[*]

The facts of respiration, or in other words the special laws which ^bit is^b attempted to explain from, and resolve into, more general ones, are, that the blood in passing through the lungs absorbs oxygen and gives out carbonic acid gas, changing thereby its colour from a blackish purple to a brilliant red. The absorption and exhalation are evidently chemical phenomena; and the carbon of the carbonic acid must have been derived from the body, that is, must have been absorbed by the blood from the substances with which it came into contact in its passage through the organism. ^cIt is required^c to find the intermediate links—the precise nature of the two chemical actions which take place; first, the absorption of the carbon or of the carbonic acid by the blood, in its circulation through the body; next, the excretion of the carbon, or the exchange of the carbonic acid for oxygen, in its passage through the lungs.

Dr. Liebig believes himself to have found the solution of this vexata quæstio in a class of chemical actions in which scarcely any less acute and ^dpenetrating^d inquirer would have thought of looking for it.

Blood is composed of two parts, the serum and the globules. The serum absorbs and holds in solution carbonic acid in great quantity, but has no tendency either to part with it or to absorb oxygen^e . The globules, therefore, are concluded to be the portion of the blood which is operative in respiration. These globules contain a ^fcertain quantity of iron, which from^f chemical tests is inferred to be in the state of oxide.

Dr. Liebig recognised, in the known chemical properties of the oxides of iron, laws which, if followed out deductively, would lead to the prediction of the precise series of phenomena which respiration exhibits.

There are two oxides of iron, a protoxide and a peroxide. ^gIn the arterial blood the iron is in the form of peroxide: in the venous blood we have no direct evidence which of the oxides is present, but the considerations to be presently stated^hlead to the conclusion^h that it is the protoxide.^g As arterial and venous blood are in a perpetual state of alternate conversion into one another, the question arises, ⁱinⁱ what circumstances the protoxide of iron is capable of being converted into the peroxide, and vice versâ. Now the protoxide readily combines with oxygen in the presence of water, forming the hydrated peroxide: these conditions it finds in passing through the lungs; it derives oxygen from the air, ^jand finds water in the blood itself. This would already explain one portion of the phenomena of respiration.^j But the arterial blood, in quitting the lungs, is charged with hydrated peroxide: in what manner is the peroxide brought back to its former state?

The chemical conditions for the reduction of the hydrated peroxide into the state of protoxide, are precisely those which the blood meets with in circulating through the body; namely, contact with organic compounds.

Hydrated peroxide of iron, when treated with organic compounds (where no sulphur is present) gives forth oxygen and water, which oxygen, attracting the carbon from the organic substance, becomes carbonic acid; while the peroxide, being reduced to the state of protoxide, combines with the carbonic acid, and becomes a carbonate. Now this carbonate needs only come again into contact with oxygen and water to be decomposed; the carbonic acid being given off, and the protoxide, by the absorption of oxygen and water, becoming again the hydrated peroxide.

The mysterious chemical phenomena connected with respiration can ^kthus^k , by a beautiful deductive process, be completely explained. The arterial blood, containing iron in the form of hydrated peroxide, passes into the capillaries, where it meets with the decaying tissues, receiving also in its course certain non-azotised but highly carbonised animal products, in particular the bile. In these it finds the precise conditions required for decomposing the peroxide into oxygen and the protoxide. The oxygen combines with the carbon of the decaying tissues, and forms carbonic acid, which, though insufficient in amount to neutralize the whole of the protoxide, combines with a portion ^l(one-fourth) of it,^l and returns in the form of a carbonate, along with the other three-fourths of the protoxide,^m through the venous system into the lungs. There it again meets with oxygen and water: the free protoxide becomes hydrated peroxide: the carbonate of protoxide parts with its carbonic acid, and by absorbing oxygen and water, enters also into the state of hydrated peroxide. The heat evolved in the transition from protoxide to peroxide, as well as in the previous oxidation of the carbon contained in the tissues, is considered by Liebig as the cause which sustains the temperature of the body. But into this portion of the speculation we need not enter.^*

This example displays the second mode of resolving complex laws, by the interpolation of intermediate links in the chain of causation; and some of the steps of the deduction exhibit cases of the first mode, that which infers the joint effect of two or more causes from their separate effects; but to trace out in detail these exemplifications may be left to the intelligence of the reader. The third mode is not employed in this example, since the simpler laws into which those of respiration are resolved (the laws of the chemical action of the oxides of iron) were ^rlaws already known, and do^r not acquire any additional generality from their employment in the present case.

§ 3. [Other^achemical speculations^a ] ^bThe property which salt possesses of preserving animal substances from putrefaction is^cresolved by Liebig^c into two more general laws, the strong attraction of salt for water, and the necessity of the presence of water as a condition of putrefaction.^[*] The intermediate phenomenon which is interpolated between the remote cause and the effect, can here be not merely inferred but seen; for it is a familiar fact, that flesh upon which salt has been thrown is speedily found swimming in brine.

The second of the two factors (as they may be termed) into which the preceding law has been resolved, the necessity of water to putrefaction, itself affords an additional example of the Resolution of Laws. The law itself is proved by the Method of Difference, since flesh completely dried and kept in a dry atmosphere does not putrefy, as we see in the case of dried provisions, and human bodies in very dry climates. A deductive explanation of this same law results from Liebig’s speculations. The putrefaction of animal and other azotised bodies is a chemical process, by which they are gradually dissipated in a gaseous form, chiefly in that of carbonic acid and ammonia; now to convert the carbon of the animal substance into carbonic acid requires oxygen, and to convert the azote into ammonia requires hydrogen, which are the elements of water. The extreme rapidity of the putrefaction of azotised substances, compared with the gradual decay of non-azotised bodies (such as wood and the like) by the action of oxygen alone, ^dhe explains^d from the general law that substances are much more easily decomposed by the action of two different affinities upon two of their elements, than by the action of only one.^b

The purgative effect of salts with alkaline bases, when administered in concentrated solutions, is explained^e from the two following principles: Animal tissues (such as the stomach) do not absorb concentrated solutions of alkaline salts; and such solutions do dissolve the solids contained in the intestines. The simpler laws into which the complex law is here resolved, are the second of the two foregoing principles, combined with a third, namely, that the peristaltic contraction acts easily upon substances in a state of solution. The negative general proposition, that animal substances do not absorb these salts, contributes to the explanation by accounting for the absence^f of a counteracting cause, namely, absorption by the stomach; which in the case of other substances possessed of the requisite chemical properties, interferes to prevent them from reaching the substances which they are destined to dissolve.

Appendix F

Book III, Chapter xviii (“Of the Calculation of Chances”), in the MS and 1st (1843) edition

[This chapter was so extensively revised for the 2nd (1846) edition that JSM had it (and Book III, Chapter xxv; see Appendix G below) offprinted from the 2nd edition as a pamphlet (see the Textual Introduction, lxxxi above). The 1843 version is printed below, with variant notes giving the MS readings. Passages that were substantially retained in later editions are surrounded by square brackets, with footnoted references to the text of the 8th edition as printed above.]

§ 1. [The foundation of the doctrine of chances, as taught by Laplace, defective] [“Probability,” says Laplace,^* “has reference partly to our ignorance, partly to our knowledge. We know that among three or more events, one, and only one, must happen; but there is nothing leading us to believe that any one of them will happen rather than the others. In this state of indecision, it is impossible for us to pronounce with certainty on their occurrence. It is, however, probable that any one of these events, selected at pleasure, will not take place; because we perceive several cases, all equally possible, which exclude its occurrence, and only one which favours it.”]^[1]

Such is this great mathematician’s statement of the logical foundation upon which rests, according to him, the theory of chances: and if his unrivalled command over the means which mathematics supply for calculating the results of given data, necessarily implied an equally sure judgment of what the data ought to be, I should hardly dare give utterance to my conviction, that in this opinion he is entirely wrong; that his foundation is altogether insufficient for the superstructure erected upon it; and that there is implied, in all rational calculation of the probabilities of events, an essential condition, which is either overlooked in Laplace’s statement, or so vaguely indicated as neither to be suggested to the reader, nor kept in view by the writer himself.

[To a calculation of chances,]^[2] [according to Laplace, two things are necessary: we must know that of several events some one will certainly happen, and no more than one; and we must not know, nor have any reason to expect, that it will be one of these events rather than another.]^[3] I contend [that these are not the only requisites, and that]^[4] another supposition is necessary. This supposition it might be imagined that Laplace intended to indicate, by saying that all the events must be equally possible (également possibles). But his next sentence shows that, by this expression, he did not mean to add anything to the two conditions which he had already suggested. “The theory of chances consists in reducing all events of the same kind to a certain number of cases equally possible, that is, such that we are equally undecided as to their existence; and to determine the number of these cases which are favourable to the event of which the probability is sought.” By “events equally possible,” then, he only means events “such that we are equally undecided as to their existence;” ^athat we^a have no reason to expect one rather than another; which is not a third condition, but the second of the two previously specified. I, therefore, feel warranted in affirming that [Laplace has overlooked, in]^[5] this [general theoretical statement, a necessary part of the foundation of the doctrine of chances.]^[6]

§ 2. [The real foundation, what] [To be able]^[1] [to pronounce two events equally probable, it is not enough that we should know that one or the other must happen, and should have no]^[2] ground [for conjecturing which. Experience must have shown that the two events are of equally frequent occurrence. Why, in tossing up a halfpenny, do we reckon it equally probable that we shall throw cross or pile? Because]^[3] experience has shown [that in any great number of throws, cross and pile are thrown about equally often; and that the more throws we make, the more nearly the equality is perfect. We]^[4] call the chances even, because if we stake equal sums, and play a certain large number of times, experience proves that our gains and losses will about balance one another; and will continue to do so, however long afterwards we continue playing: while on the contrary, if we give the slightest odds, and play a great number of times, we are sure to lose; and the longer we continue playing, the greater losers we shall be. If experience did not prove this, [we should proceed as much at haphazard in staking equal sums]^[5] [as in laying odds]^[6] ; we should have no more reason for expecting not to be losers by the one wager than by the other.

It would indeed require strong evidence to persuade any rational person that by a system of operations upon numbers, our ignorance can be coined into science; and it is doubtless this strange pretension which has driven a profound thinker, M.^a Comte, into the contrary extreme of rejecting altogether a doctrine which, however imperfectly its principles may sometimes have been conceived, receives daily verification from the practice of insurance, and from a great mass of other positive experience. The doctrine itself is, I conceive, sound, but the manner in which its foundations have been laid by its great teachers is most seriously objectionable. Conclusions respecting the probability of a fact rest not upon a different, but upon the very same basis, as conclusions respecting its certainty; namely, not our ignorance, but our knowledge: knowledge obtained by experience, of the proportion between the cases in which the fact occurs, and those in which it does not occur. Every [calculation of chances is grounded on an induction: and to render the calculation legitimate, the induction must be a valid one. It is not less an induction, though it does not prove that the event occurs in all cases of a given description, but only that out of a given number of such cases, it occurs in about so many. The fraction which mathematicians use to designate the probability of an event, is the ratio of these two numbers; the ascertained proportion between the number of cases in which the event occurs, and the sum of all the cases, those in which it occurs and in which it does not occur taken together. In playing at cross and pile, the description of cases concerned are throws, and the probability of cross is one half, because]^[7] it is found that [if we throw often enough, cross is thrown about once in every two throws]^[8] ; and because this induction is made under circumstances justifying the belief that the proportion will be the same in other cases as in the cases examined. [In the cast of a die, the probability of ace is one-sixth; not]^[9] , as Laplace would say, [because there are six possible throws, of which ace is one, and because we do not know any reason why one should turn up rather than another;]^[10] [but because we do]^[11] [know]^[12] [that in a hundred, or a million of throws, ace]^[13] will be [thrown]^[14] [about one-sixth of that number, or once in six times.]^[15]

Not only is this third condition indispensable, but if we have that, we do not want Laplace’s two. It is not necessary that we should know how many possibilities there are, or that we should have no more reason for expecting one of them than another. If a north wind blows one day in every ten, the probability of a north wind on any given day will be one-tenth, even though of the remaining possibilities a west wind should be greatly the most probable. If we know that half the trees in a particular forest are oaks, though we may be quite ignorant how many other kinds of trees it contains, the chance that a tree indiscriminately selected will be an oak is an even chance, or, in mathematical language, one-half. So that the condition which Laplace omitted is not merely one of the requisites for the possibility of a calculation of chances; it is the only requisite.

In saying that he has omitted this condition, I am far from meaning to assert, that he does not frequently take it into consideration in particular instances; nor indeed could he fail to do so, since whenever any experience bearing upon the case really exists, he would naturally consult that experience to assure himself of the fulfilment of his second condition, that there be no reason for expecting one event rather than another. When experience is to be had, he takes that experience as the measure of the probability: his error is only in imagining that there can be a measurement of probability where there is no experience. The consequence of this error has been his adoption of conclusions not indeed contrary to, but unsupported by, experience. He has been led to push the theory and its applications beyond the bounds which confine all legitimate inferences of the human mind; by extending them to subjects on which the absence of any ground for determining between two suppositions, does not arise from our having equal grounds for presuming both, but from our having an equal absence of grounds for presuming either.

According to his views, indeed, the calculation of chances should be much more universally applicable to things of which we are completely ignorant, than to things of which we have partial knowledge. Where we have some experience of the occurrence of each of the conflicting possibilities, it may often be difficult, according to the prescriptions of the theory, to reduce those possibilities to a definite number of cases, all equally probable; but when the case is out of the reach of all experience, so that we have no difficulty in being “equally undecided” respecting the possibilities, there is nothing to make us halt or waver in applying the theory. If the question be whether the inhabitants of Saturn have red hair, we need only know the number of the prismatic colours, and of their more marked compounds, and we can at once assign the fraction corresponding to the probability! It is evident that probability, in any sense in which it can operate upon our belief or conduct, has nothing to do with such chimerical evaluations, and that entire suspension of judgment, where we have no evidence, is the only course befitting a rational being. To entitle us to affirm anything positive about uncertain facts, whether ^bit be^b that one supposition is more probable than another, or only that it is equally probable, we must have the testimony of experience, that, taking the whole of some class of cases, the one guess will be oftener right, or as often right as the other. The estimation, in short, of chances, like that of certainties, is only rational when grounded upon a complete induction by observation or experiment.^*

§ 3. [Theorem of the doctrine of chances, which relates to the cause of a given event] [From]^[1] these principles [it is easy to deduce the demonstration of that theorem of the doctrine of probabilities, which is the foundation of its]^[2] principal [application to]^[3] judicial or other [inquiries for ascertaining the occurrence of a given event, or the reality of an individual fact. The signs or evidences by which a fact is usually proved, are some of its consequences: and the inquiry hinges upon determining what cause is^a most likely to have produced a given effect. The theorem applicable to such investigations is the Sixth Principle in Laplace’s Essai Philosophique sur les Probabilités, which is described by him as]^[4] “the [fundamental principle of that branch of the Analysis of Chances, which consists in ascending from events to their causes.”^*

Given an effect to be accounted for, and there being several causes which might have produced it, but of the presence of which, in the particular case, nothing is known; the probability that the effect was produced by any one of these causes is as the antecedent probability of the cause, multiplied by the probability that the cause, if it existed, would have produced the given effect.

Let M be the effect, and A, B, two causes, by either of which it might have been produced. To find the probability that it was produced by the one and not by the other, ascertain which of the two is most likely to have existed, and which of them, if it did exist, was most likely to produce the effect M: the probability sought is a compound of these two probabilities.

Case I. Let the causes be both alike in the second respect; either A or B, when it exists, being supposed equally likely (or equally certain) to produce M; but let A be in itself twice as likely as B to exist, that is, twice as frequent a phenomenon. Then it is twice as likely to have existed in this case, and to have been the cause which produced M.

For, since A exists in nature twice as often as B; in any 300 cases in which one or other existed, A has existed 200 times and B 100. But either A or B must have existed wherever M is produced: therefore in 300 times that M is produced, A was the producing cause 200 times, B only 100, that is, in the ratio of 2 to 1. Thus, then, if the causes are alike in their capacity of producing the effect, the probability as to which actually produced it, is in the ratio of their antecedent probabilities.

Case II. Reversing the last hypothesis, let us suppose that the causes are equally frequent, equally likely to have existed, but not equally likely, if they did exist, to produce M: that in three times]^[5] that [A occurs, it produces that effect twice, while B, in three times, produces it only once. Since the two causes are equally frequent in their occurrence; in every six times that either one or the other exists, A exists three times and B three times. A, of its three times, produces M in two; B, of its three times, produces M in one. Thus, in the whole six times, M is only produced thrice; but of that thrice it is produced twice by A, once only by B. Consequently, when the antecedent probabilities of the causes are equal, the chances that the effect was produced by them are in the ratio of the probabilities that if they did exist they would produce the effect.

Case III. The third case, ^bthat in which^b the causes are unlike in both respects, is solved by what has preceded. For, when a quantity depends upon two other quantities, in such a manner that while either of them remains constant it is proportional to the other, it must necessarily be proportional to the product of the two quantities, the product being the only function of the two which obeys that]^[6] particular [law of variation. Therefore, the probability that M was produced by either cause, is as the antecedent probability of the cause, multiplied by the probability that if it existed it would produce M. Which was to be demonstrated.

Or we may prove the third case as we proved the first and second. Let A be twice as frequent as B; and let them also be unequally likely, when they exist, to produce M: let A produce it twice in four times, B thrice in four times. The antecedent probability of A is to that of B as 2 to 1; the probabilities of their producing M are as 2 to 3; the product of these ratios is the ratio of 4 to 3],^[7] which therefore, if the theorem be true, [will be the ratio of the probabilities that A or B was the producing cause in the given instance.]^[8] And such will that ratio really be. For, since A is twice as frequent as B, out of twelve cases in which one or other exists, A exists in 8 and B in 4. But of its eight cases, A, by the supposition, produces M in only 4, while B of its four cases produces M in 3. M, therefore, is only produced at all in seven of the twelve cases; but in four of ^cthese^c it is produced by A, in three by B; hence, the probabilities of its being produced by A and by B are as 4 to 3, and are expressed by the fractions 4/7 and 3/7. Which was to be demonstrated.]^[9]

It is here necessary to point out another serious oversight in Laplace’s theory. When he first introduces the foregoing theorem, he characterises it correctly, as the principle for determining to which of several causes we are to attribute a known fact. But after having conceived the principle thus accurately, when he comes to its applications he no longer restricts it to the ascertainment of causes alone, but, without any previous notice substitutes for the idea of causes that of hypotheses, or suppositions of any kind. In this extended sense, I do not conceive the proposition to be tenable. The hypotheses must be either causes, or at least signs showing the existence of causes. If we could be permitted to substitute mere suppositions affording no ground for concluding that the effect would be produced, in the room of causes capable of producing it, the theorem thus extended would stand as follows. A fact, M, having happened, the probability of the truth of any arbitrary supposition altogether unconnected with M, is as the antecedent probability of the supposition, multiplied by the probability that if the supposition was true M would happen; that is, multiplied by the antecedent probability of M, since M is neither more ^dnor^d less probable on account of a supposition which has nothing to do with the causes of it. Now the proposition, as thus stated, is an absurdity. The probability that when M happened A had previously happened, is not the antecedent probability of M multiplied by that of A, but the antecedent probability of A only. The antecedent probability of M cannot be an element of a question into which the occurrence of M enters not as a contingency but as a certainty. What the product of the antecedent probabilities of A and M does give, is, not the probability of the one when the other is a known past event, but the antecedent probability of the two together, considered as future events.

This error of Laplace has not been harmless. We shall see hereafter, in treating of the Grounds of Disbelief, that he has been led by it into serious practical mistakes when attempting to pronounce upon the circumstances which render any statement incredible.

§ 4. [In what cases the doctrine is practically applicable] ^aFrom the preceding view of the foundation of the doctrine of chances, its general principles may be seen to be applicable in a rough way to many subjects which are by no means amenable to its precise calculations. To render these applicable, there must be numerical data, derived from the observation of a very large number of instances. The probabilities of life at different ages, or in different climates; the probabilities of recovery from a particular disease; the chances of the birth of male or female offspring; the chances of the loss of a vessel in a particular voyage; all these admit of estimation sufficiently precise to render the numerical appreciation of their amount a thing of practical value; because there are bills of mortality, returns from hospitals, registers of births, of shipwrecks, &c., founded on cases sufficiently numerous to afford average proportions which do not materially vary from year to year, or from ten years to ten years. But where observation and experiment have not afforded a set of instances sufficiently numerous to eliminate chance, and sufficiently various to eliminate all non-essential specialities of circumstance, to attempt to calculate chances is to convert mere ignorance into dangerous error by clothing it in the garb of knowledge.^a

[It remains to examine the bearing of the doctrine of chances upon the peculiar problem]^[1] for the sake of which we have on this occasion adverted to it, [namely, how to distinguish coincidences which are casual from those which are the result of law; from those in which the facts which accompany or follow one another are somehow connected through causation.]^[2]

§ 5. [How the doctrine is applicable to the elimination of chance] [The doctrine of chances affords means by which, if we knew the average number of coincidences to be looked for between two phenomena connected only casually, we could determine how often any given deviation from that average will occur by chance. If the probability of any casual coincidence, considered in itself, be , the probability that the same coincidence will be repeated n times in succession is . For example, in one throw of a die the probability of ace being ⅙; the probability of throwing ace twice in succession will be 1 divided by the square of 6, or . For ace is thrown at the first throw once in six, or six in thirty-six times: and of those six, the die being cast again, ace will be thrown but once; being altogether once in thirty-six times. The chance of the same cast three times successively is, by a similar reasoning, or : that is, the event will happen, on ^aa^a large average, only once in two hundred and sixteen throws.

We have thus a rule ^bby which^b to estimate the probability that any given series of coincidences arises from chance; provided we can measure correctly the probability of a single coincidence. If we]^[1] could [obtain an equally precise expression for the probability that the same series of coincidences arises from causation, we should only have to compare the numbers. This, however, can rarely be done. Let us see what degree of approximation can practically be made to the necessary precision.

The question falls within Laplace’s sixth principle,]^[2] of which, a short distance back, we gave the demonstration. [The given fact, that is to say, the series of coincidences, may have originated either in a casual conjunction of causes or in a law of nature. The probabilities, therefore, that the fact originated in these two modes, are as their antecedent probabilities, multiplied by the probabilities that if they existed they would produce the effect. But the particular combination of chances if it occurred, or the law of nature if real, would certainly produce the series of coincidences. The probabilities, therefore, that the coincidences are produced by the two causes in question, are as the antecedent probabilities of the causes. One of these, the antecedent probability of the combination of mere chances which would produce the given result, is an appreciable quantity. The antecedent probability of the other supposition may be susceptible of a more or less exact estimation, according to the nature of the case.

In some cases, the coincidence, supposing it to be the result of causation at all, must be the result of a known cause; as the succession of aces, if not accidental, must arise from the loading of the die. In such cases we may be able to form a conjecture as to the antecedent probability of such a circumstance, from the characters of the parties concerned, or other such evidence; but it would]^[3] clearly [be impossible to estimate that probability with anything like numerical precision. The counter-probability, however, that of the accidental origin of the coincidence, dwindling so rapidly as it does at each new trial; the stage is soon reached at which the chance of unfairness in the die, however small in itself, must be greater than that of a casual coincidence: and on this ground, a practical decision can generally be come to without much hesitation, if there be the power of repeating the experiment.

When, however, the coincidence is one which cannot be accounted for by any known cause, and the connexion between the two phenomena, if produced by causation, must be the result of some law of nature hitherto unknown; which is the case we had in view in the last chapter; then, although the probability of a casual coincidence may be capable of appreciation, that of the counter-supposition, the existence of an undiscovered law of nature, is clearly unsusceptible of even an approximate]^[4] evaluation. [In order to have the data which such a case would require, it would be necessary to know what proportion of all the individual sequences or co-existences occurring in nature are the result of law, and what proportion are]^[5] the result of chance. [It being evident that we cannot form any plausible conjecture as to this proportion, much less appreciate it numerically, we cannot attempt any precise estimation of the comparative probabilities. But of this we are sure, that the detection of an unknown law of nature—of some previously unrecognised constancy of conjunction among phenomena—is no uncommon event. If, therefore, the number of instances in which a coincidence is observed, over and above that which would arise on the average from the mere concurrence of chances, be such that so great an amount of coincidences from accident alone would be an extremely uncommon event; we have reason to conclude that the coincidence is the effect of causation, and may be received (subject to correction from further experience) as an empirical law. Further than this, in point of precision, we cannot go; nor, in most cases, is greater precision required, for the solution of any practical doubt.]^[6]

Appendix G

Book III, Chapter xxv (“Of the Grounds of Disbelief”), § 5, in the MS and 1st (1843) edition

[This section was rewritten as §6 for the 2nd (1846) edition, the final §5 being added at the same time. Though JSM had the whole of Chapter xxv offprinted from the 2nd edition, with Book III, Chapter xviii (see headnote to Appendix F above), the major revisions were only in this section, and therefore the variants to the rest of the chapter are given in the normal way in the text above. The 1843 version of this section is printed below, with variant notes giving the MS readings. Passages that were substantially retained in later editions are surrounded by square brackets, with footnote references to the text of the 8th edition as printed above.]

§ 5. [An opinion of Laplace examined] While the defenders of Christianity against Hume have thus confounded two different meanings of the word improbability, contending that because improbability of the one kind is not necessarily a ground of disbelief, neither therefore is the other, and that nothing supported by credible testimony ought ever to be disbelieved; Laplace, again, falling into the same confusion between the two meanings, contends on the contrary, that because improbability of the one kind is a sufficient ground for disbelief, the other is so too; and that what is improbable before the fact, is therefore (not indeed in all cases, but in a peculiar class of cases which I am about to specify), incredible after it.

[If, says Laplace, there]^[1] are [one thousand tickets in a box, and one only has been drawn out; then if an eye-witness affirms that the number drawn was 79, this, though the chances were 999 in 1000 against it, is not]^[2] incredible, because the chances were equally great against every other number. But (he continues) if there are [in the box 999 black balls and only one white, and the witness affirms that the white ball was drawn,]^[3] this is incredible; because there was but one chance in favour of white, and 999 in favour of some black ball.

This appears to me entirely fallacious. It is evident, both from general reasoning and specific experience, that the white ball will be drawn out exactly as often, in any large number of trials, as the ticket No. 79 will; the two assertions, therefore, are precisely on the same level in point of credibility. There is one way of putting the case which, I think, must carry conviction to every one. Suppose that the thousand balls are numbered, and that the white ball happens to be ticketed 79. Then the drawing of the white ball, and the drawing of No. 79, are the very same event; how then can the one be credible, the other absolutely incredible? A witness sees it drawn, and makes his report to us: if he says ^athat^a No. 79 was drawn, according to Laplace he may be believed; if he says a white ball was drawn, we are bound to disbelieve him. Is this rational? Is it not clear, on the contrary, that the only difference there could be in the credit due to him would arise from moral causes, namely, from the influence which (if the witness knew that there was but one white ball in a thousand) might be assigned to the greater apparent wonder in the latter case? which to one kind of person would be a temptation to deceive, or to take up a hasty impression, while to another, the same thing would be a motive for assuring himself more positively of the fact, and would therefore actually increase the credit due to his testimony.

The mathematical reasoning which misled Laplace into this logical error, is too long to be here quoted. It is found in the section of his Essai Philosophique sur les Probabilités entitled De la Probabilité des Témoignages, and is founded upon a misapplication, noticed by us in a former place, of his own sixth theorem of the doctrine of chances; a theorem which he himself describes as that by which we determine the probability that a given effect was produced by one or by another of several causes capable of producing it. The substance of his argument may be briefly stated as follows: Treating the assertion of the witness as the effect, he considers as its two possible causes, the veracity or mendacity of the witness on the particular occasion, that is, the truth or falsity of the fact. According to the theorem, the probability that the effect was produced by a particular cause, is as the antecedent probability of the cause, multiplied by the probability that the cause, if it existed, would produce the given effect. Accordingly (says ^bLaplace^b ) in the case of the thousand tickets, the cause mendacity might produce any one of 999 untrue statements, while in the case of the balls, there being only two statements to make, viz., white or black, and one of these being true, the cause mendacity could only produce one untrue statement: and consequently (the antecedent probability of mendacity from the character of the witness being supposed the same in both cases) mendacity was 999 times less likely to have produced the particular assertion made, and is therefore 999 times less likely to have existed, in the former case than in the latter.

The error of this argument seems to be ^cthe same which^c we pointed out in a former chapter,^* that of applying a theorem, only true of the degrees of probability of causes, to the probability of what are neither causes nor indications of causes, nor in any other way specially connected with the effect. The point in question is, the comparative probability of two suppositions, that the witness lies, and that he speaks truth. But these are not two possible causes of the given effect (the witness’s assertion); they are merely two possible qualities of it. The truth of the assertion is, indeed, on the supposition of veracity, the cause of its being made; but the falsity of it is not, on any supposition, a cause of its being made. It is not incompatible with the dishonesty of the witness, that he should have spoken the truth: the difference between the two suppositions of honesty and dishonesty is, that on the one he would certainly speak the truth, while on the other he was just equally likely to speak that or anything else. If the falsity of the proposition were a real cause for his asserting it, and there were no possible mode of accounting for a false assertion but by supposing that it is made precisely because of its falsity, I do not see how Laplace’s argument could be resisted. The case where there are 999 possible false assertions, and that in which there is but one, would then present a vast difference in the probability that the assertion actually made proceeded from falsity; because in the one case a mendacious witness was sure to assert the one false fact, in the other there would be an equal chance of his asserting any one of the 999. But as it is, the falsity was a mere accident of the assertion, not the cause of it; and even on the supposition of dishonesty, the statement is as likely to be true as false, while on the supposition of honesty it is certain to be true. The assertion, therefore, is credible.

[With these remarks we]^[4] shall [close the discussion of the Grounds of Disbelief; and along with it, such exposition as]^[5] our space admitted, [and as the writer]^[6] had [it in his power to furnish, of the Logic of Induction.]^[7]

Appendix H

Book VI, Chapter xi (“Of the Logic of Practice, or Art; including Morality and Policy”), §6, in MS, 1st (1843), and 2nd (1846) editions

[This section was replaced by §§6 and 7 of the 3rd (1851) and subsequent editions (the chapter itself became no. xii with the addition of a new Chapter xi in the 5th [1862] edition). The 1846 version is printed below, with variant notes giving the readings of the MS and 1st edition.]

§ 6. [Application of the preceding principles to Morality] After these observations on the Logic of Practice in general, little needs here be said of that department of Practice which has received the name of Morality; since it forms no part of the appropriate object of this work to discuss how far morality depends, like other arts, upon the consideration of means and ends, and how far, if at all, upon anything else.

This, however, may be said; that questions of practical morality are partly similar to those which are to be decided by a judge, and partly to those which have to be solved by a legislator or administrator. In some things our conduct ought to conform itself to a prescribed rule; in others, it is to be guided by the best judgment which can be formed of the merits of the particular case.

Without entering into the disputed questions respecting the foundation of morality, we may consider as a conclusion following alike from all systems of ethics, that, in a certain description of cases at least, morality consists in the simple observance of a rule. The cases in question are those in which, although any rule which can be formed is probably (as we remarked on maxims of policy) more or less imperfectly adapted to a portion of the cases which it comprises, there is still a necessity that some rule, of a nature simple enough to be easily understood and remembered, should not only be laid down for guidance, but universally observed, in order that the various persons concerned may know what they have to expect: the inconvenience of uncertainty on their part being a greater evil than that which may possibly arise, in a minority of cases, from the imperfect adaptation of the rule to those cases.

Such, for example, is the rule of veracity; that of not infringing the legal rights of others; and so forth: concerning which it is obvious that although many cases exist in which a deviation from the rule would in the particular case produce more good than evil, it is necessary for general security, either that the rules should be inflexibly observed, or that the license of deviating from them, if such be ever permitted, should be confined to definite classes of cases, and of a very peculiar and extreme nature.

With respect, therefore, to these cases, practical ethics must, like the administration of positive law, follow a method strictly and directly ratiocinative: whether the rules themselves are obtained, like those of other arts, from a scientific consideration of tendencies, or are referred to the authority of intuitive consciousness or express revelation.

In cases, however, in which there does not exist a necessity for a common rule, to be acknowledged and relied on as the basis of social life; where we are at liberty to inquire what is the most moral course under the particular circumstances of the case, without reference^a, or without exclusive reference,^a to the authorized expectations of other people; there the Method of Ethics cannot differ materially from the method of every other department of practice. Like other arts, it sets out from a general principle, or original major premiss, enunciative of its particular end: whether that end be the greatest possible happiness, as is contended by some, or ^b(as others hold) the conformity of our character to ideal perfection according to some particular standard^b . But on this as on other subjects, when the end has been laid down, it belongs to Science to inquire what are the kinds of actions by which this end, this happiness or this perfection of character, is capable of being realized. When Science has framed propositions, which are the completed expression of the whole of the conditions necessary to the desired end, these are handed over to Art, which has nothing further to do but to transform them into corresponding rules of conduct.

Appendix I

Typographical Errors in the 8th Edition

the list below gives those errors that are silently corrected in the text. Typographical errors in earlier editions are ignored;¹ slips of the pen in the Press-copy Manuscript are listed in a note below.² The intention is to err on the cautious side: except when the error is visually manifest, the evidence of other editions (and the source, in the case of quotations) is given, to support the choice of readings; on the other hand, evidence of editorial suspicion about retained variant readings is indicated by “[printer’s error?]” at the end of the relevant variant notes in the text. An example will be seen at 659^c-c, where in the MS “conceptions” was altered to “conception,” but “conceptions” appears in 43 and 46, with “conception” restored in 51. Another, much less common case of retention, as a variant, of a probable printer’s error, because it led to another textual change, may be seen at 686^c-c, where the original “applied” became “implied” in 51, and “employed” in 56 (cf. 688^b-b, where a faintly interlined “a” before “separate assertion” in the MS does not appear in 43, and in 46 “assertion” is changed to “assertions”). In a few places Greek accents have been regularized.

The entries are in the following form: Page and line reference to the present text. Reading in the 8th edition] Corrected reading in the present edition [Evidence for the corrected reading]. In the evidence, “as in MS,43” means that the corrected reading is found in the manuscript and 1st edition; “as in 51—62” means that the corrected reading is found in the 3rd to the 5th editions inclusive.

The first five entries are from the Table of Contents.

Appendix J

The Press-Copy Manuscript of the Logic

the holograph manuscript from which the 1st edition of the Logic was printed is in the British Museum (Add. MSS 41624-7). It was “bequeathed by Mill to a friend, Mr. William Fidler of the India Office, from whose daughters, the last of whom died in 1928, it came to Lady Magnay from whom the Museum acquired it.”¹ Bound in four volumes, it was folioed by the Museum staff in 1937 as follows: Vol. I, ff. 1-322; Vol. II, ff. 1-231; Vol. III, ff. 1-365; Vol. IV, ff. 1-294.² An earlier foliation, evidently entered for the most part by Mill currently, shows some evidence of the rewriting process; this foliation is based on the division of the work into Books.³ There is much evidence of the printing process, including compositors’ signatures,⁴ marked equivalents to the paging of the first edition, and folds.⁵

Following his most common practice,⁶ Mill wrote the text recto only, reserving the opposite versos for notes, additions, and corrections, and collected the folios into “gatherings” (estimated equivalents to the signatures of the printed volumes) lettered from A-Z, Aa-Zz, and 3A-3E; these gatherings, normally of twenty folios each, were originally sewn together.⁷ The paper is of five makes and dates, as follows: J. Coles (1836), G. Wilmot (1839), Ruse & Turners (1841), Munn & Co. (n.d., one folio only), and Towgood’s Superfine (n.d.).⁸ As indicated in the Textual Introduction, the different papers, the length of the gatherings, and other evidence of rewriting, enable one to reconstruct some details of the process of composition. Among the signs of rewriting one may note that Mill evidently did not intend to use section divisions originally, but added them fairly late in the rewriting, probably before the original submission of the manuscript to Murray. Often the section number is quite obviously squeezed into a paragraph indentation (sometimes subsequent to an earlier revision). In other places, where there is rewriting on the verso, a section number appears with no evidence that it was added later; presumably before that stage (or at that stage) of the rewriting Mill had decided on sectioning. In the final revisions further alterations in section divisions were made, as cancellations demonstrate.

It does not seem possible to date the inks or pens; all that can safely be said is that prima facie, as one would expect, there are many revisions current with the first inditing of the manuscript (even though it presumably was adapted from an earlier, not extant, manuscript), and that later revisions were made not in isolated single passages, but in a more thorough way. The judgments based on a closer look at particular passages support the other evidence (placing and kind of revision, short pages, cancellations that do not continue from the end of one page to the next, etc.), and have been taken into account in the description of the process of revision in the Textual Introduction.

Given our attempt in this edition to give all substantive variant readings, it may seem odd to some that we do not give manuscript cancellations. Whatever one’s desires, however, a glance at any of the heavily revised folios of the manuscript conclusively demonstrates the impracticability of such a practice. Even an extended reproduction of the longer cancellations would be inutile, especially because intelligibility demands parallel presentation of the various levels. It is appropriate, however, to give some examples of rewritten passages, with the sole intention of illustrating various kinds of revision. They should not be taken as indications of the relative importance, complexity, or density of the revisions.

There are relatively few places in the final manuscript where Mill cancelled a passage without replacing it; two of these may be taken as illustrative. The first, a deleted paragraph (MS Vol. IV, f.129; cancelled between the paragraphs on p. 827 above), shows two stages of composition before the cancellation.⁹ The first reading is:

By cancellation and interlineation, Mill altered the passage to read:

The following cancelled passage, one of the longest in the MS, occurs at the end of the second paragraph of Bk. V, Chap. 5, §5 (p. 792; MS Vol. IV, ff. 80-1):

The most frequent kind of rewriting, of course, is that which replaces single words and short phrases, with a view to clarity and precision. One such passage is interesting because of its content, and also because it comes at a place where the incompleteness of the first version demonstrates that a folio (or more) was cancelled and removed. The original wording, which concludes at the end of MS Vol. IV, f.207, was:

This was altered to:

Then the whole passage was cancelled, presumably along with its continuation on the next folio, and another folio was substituted, beginning with a new paragraph, the second sentence of which is the final version:

Examples of this kind occur on virtually every folio of the manuscript, and need not be exemplified at length, though one more typical illustration of Mill’s concern for the correct degree of qualification may be useful. In describing Victor Cousin’s lectures on Locke, Mill finally settled on this wording (MS Vol. IV, f.50; p. 770^e-e above): “which as a resumé of the objections of the opposite school to that great man’s doctrines is a work of eminent merit”; originally “all” appeared before “the objections”, and “eminent merit”, which originally read “extraordinary merit”, in an intermediate stage read “unrivalled merit”.

Two passages may be cited as of potential interest to students of Mill’s moral philosophy. The opening sentence of Bk. VI, Chap. xii, §2 (pp. 943-4 above), went through some intricate revision, including many current cancellations that did not lead to complete syntactical units. What he first wrote, however, may be reconstructed thus: “In doing this” (i.e., characterizing the general method of Art, as distinguished from Science) “it is necessary to commence by making a distinction according as we are bound”; he then broke off, and tried to substitute “between two different” for the last five words, and broke off again, beginning there a new sentence, starting “In some cases we are bound to conform our practice to a preestablished rule; in others it is part of our task to find the rule, by which we are to govern our conduct.” The final version, again involving current cancellations not here given, reads: “In all branches of practical business there are cases in which an individual is bound to conform his practice to a preestablished rule, while there are others in which it is part of his task to find or construct the rule, by which he is to govern his conduct.” (MS Vol. IV, f.284.)

The second passage has a relation to the much debated question of Mill’s quantity-quality distinction in Utilitarianism. In his discussion (p. 73 above) of the difference between water and wine, Mill’s final manuscript reading of one sentence is: “In the first case however we say that the difference is only in quantity; in the last, there is a difference in quality, while the quantity of the water & of the madeira is the same.” This sentence originally concluded “there is a difference in quality, but none in quantity” and the passage continued with the following sentences, which were currently cancelled:

It is a matter of regret that Mill never developed his thoughts on the Science of Ethology that he sketches in Bk. VI, Chap. v. A cancelled paragraph (replaced by the first paragraph of §6, pp. 872-3 above) suggests one line of approach that might well have been interesting. Having compared the current states of development in Psychology and Ethology, he says:

(It is possible that the confused syntax of the fourth sentence, which bridges the two folios, indicates that a full folio was cancelled and extracted at this point.)

There is almost no limit to the number of examples that might be chosen to illustrate different points. For instance, the discussion of Coleridge’s distinction between the “conceivable” and the “imaginable,” which eventually appeared in Bk. V, Chap. iii, §3 (p. 755^e), originally was a heavily revised note to Bk. II, Chap. v, §1 (p. 225; MS Vol. I, f.296v); and at MS Vol. I, f.290 (p. 220), a cancelled passage concerning the effect of acids and alkalis on vegetable substances suggests yet another intervention by Bain to correct a scientific example. Unfortunately, consultation of the manuscript remains essential for those interested in specific passages that may have been rewritten. To substantiate the earlier assertion that full reproduction is impossible, here is one example, certainly not among the most complicated.

In the reconstruction, the final version is given in boldface; italic type indicates current cancellations during both the original composition and the rewriting that did not produce coherent syntax; and roman type indicates cancellations in the rewriting.

In thoseIn allsubjects which are atonethe same time familiar & complicated, & especiallyin that which is bothon those which areboth those in soso muchso as high a degree as theof both these things asmoral and socialsubjects are, itphenomenais matter of common remark how manyof theimportant propositions are believed & repeated from habit, whileno account could be given andno sense is practically manifested& no account could be givenof the truths which they convey.

Reconstructed, the process probably was as follows: Mill first wrote “In all subjects which are at one” (cancel “one”) “the same time familiar & complicated,

>Folio from Book VI, Chapter v, of the Press-copy Manuscript British Museum

& especially in that which is both” (cancel “in that which is both”) “on [sic] those which are both those in so high a degree as the moral & social phenomena” (cancel “phenomena” and interline the next three words) “subjects are, it is matter of common remark how many of the important propositions are believed & repeated from habit, while no sense is practically manifested & no account could be given of the truths which they convey.” In the later rewriting, Mill cancelled “In all” and interlined “In those”; cancelled “both those in so high a degree as” and interlined “so much so as”; then cancelled the interlined “so as” and the original “the” before “moral”, and interlined “of both these things as”; cancelled “of the”; and by cancellation and interlineation altered “no sense is practically manifested & no account could be given” to “no account could be given and no sense is practically manifested”. The final reading is, then: “In those subjects which are at the same time familiar & complicated, & especially on those which are so much of both these things as moral & social subjects are, it is matter of common remark how many important propositions are believed & repeated from habit, while no account could be given and no sense is practically manifested of the truths which they convey.” (MS Vol. III, f. 297; p. 681 above.)

It must be realized that even such a complex and unsatisfactory reconstruction would be further complicated by the introduction of the variants in the printed versions. In this case the slip of the pen (“on”) was corrected to “in” in all the editions; “so much of both these things” became “both these things in so great a degree” in the 2nd edition, and “so in as great a degree” in the 3rd and subsequent editions; and an “a” appears before “matter of common remark” in the final three editions.

Trusting that the inutility of such a reproduction has been demonstrated, let us close with a brief example of a rather different kind.

It is often (and correctly) asserted that Mill is a highly impersonal writer, and what evidence there is of his manuscript revisions (most notably in the “Early Draft” of his Autobiography) indicates that he strove for this impersonality. One cancellation in the Logic, illustrated in the facsimile opposite, helps bear out the assertion. The passage occurs where, in Bk. VI, Chap. v (p. 890 above), Mill turns to a discussion of the “interest-philosophy of the Bentham school.” As will be seen, Mill altered “generally” to “commonly”, and deleted the following: “(& to one of the most eminent of whom the present writer owes as deep a debt, as a son ever owed to a father) have”, interlining the two “a”s before cancellation.

Appendix K

Bibliographic Index of Persons and Works cited in the Logic, with Variants and Notes

mill, like most nineteenth-century authors, is very cavalier in his approach to sources, often not identifying them with sufficient care, and very frequently quoting them inaccurately. This Appendix is intended to help correct these deficiencies, and also to serve as an index of names and titles (which are consequently omitted in the Index proper). The material is arranged in alphabetical order, with an entry for each author and work quoted or referred to in the Logic and in Appendices A-H. References to the “Early Draft” (Appendix A) and to the other Appendices are in italic; when the reference in the “Early Draft” corresponds to one in the final text, the reference to the “Early Draft” appears in parentheses immediately following the equivalent reference in the final text; when the reference in the “Early Draft” is not paralleled by a reference in the final text, the reference is given in normal sequence, separated by a semicolon from the other entries.

The entries take the following form:

1. Identification: author, title, etc., in the usual bibliographic form.

2. Notes (if required) giving information about JSM’s use of the source, and any other relevant information.

3. A list of the places in the Logic where the author or work is quoted, and a separate list of the places where there is reference only.

4. A list of the substantive variants between the Logic and the source, in this form: Page and line reference to the Logic. Reading in the Logic] Reading in the source (page reference in the source).

The list of substantive variants also places quoted remarks in their contexts by giving the beginnings and endings of sentences. Omissions of two sentences or less are given in full; only the length of other omissions is given. Following the page reference to the source, cross-references to substantive variants within editions (i.e., those recorded in footnotes to the present text) are given, where applicable. (These help identify places where inaccuracies may be blamed on the printer; in a few places the inaccuracies are accepted as typographical errors, and so noted.) Only surnames are given in cases of simple reference. Translated material is given in the original language.

Anaxagoras. Referred to: 365

Anaximenes. Referred to: 359, 361, 364-5

note: the references at 364 are in quotations by the anonymous reviewer of Tulloch’s Theism, Cicero, and St. Augustine.

Anon. “Mill’s System of Logic,” British Quarterly Review, IV (August, 1846), 1-38.

quoted: 147n, 206n, 207n; 1112-13, 1115-16referred to:1111-16

147.n7 ‘there is] Now we should have thought it perfectly plain that there is (16)

206.n15-16 “Whatever is true of a class, is true of everything included in the class,”] The maxim [dictum de omni et nullo], as commonly expressed, is, that whatever can be affirmed (or denied) of a class, may be affirmed (or denied) of everything included in the class. (27)

206.n18-19 “Whatever . . . class:”] The axiom should be stated thus: that whatever . . . class. (27)

207.n2 “we] If it did [i.e., if the major premise included the conclusion], we (22)

1112-13 [see entries for 206-7 above]

1115.2-4 “inference,” . . . “our] The mortality of A, B, C, &c., does not become evidence except by a process of inference, the result of which inference at least must be interpolated; and our (25)

1116.n10 “the . . . premiss.”] Our readers may exercise their ingenuity in trying to find out how, if, in the case of the unlucky syllogism, the . . . premiss, we can, according to the corrected type, have evidence enough to prove that very major premiss, while the conclusion is still something to be inferred from that evidence. (20)

Anon. “Theism,” Westminster Review, LXIV (Oct., 1855), 319-53.

note: the review is of Tulloch’s Theism.

quoted: 364 referred to: 368

364.5 Mill:] Mill in support of this position; (328)

364.9 to have . . . inconceivability.] to “have . . . inconceivability.” (328) [the reviewer is paraphrasing JSM’s words; see 360 above]

364.14 action on] action of mind on (328)

Antoninus. Referred to: 197 (1073)

The Arabian Nights. Tr. Edward Forster. 5 vols. London: Miller, 1802.

note: in JSM’s library, Somerville College. The reference is to “The History of Ali Baba, and of the Forty Robbers, Killed by One Slave,” V, 140-201.

referred to: 35(980)

Arago. Referred to: 427

note: the reference is in a quotation from Herschel.

Aranda. Referred to: 940

Archimedes. Referred to: 760

note: the reference is in a quotation from Playfair.

Arfwedson. Referred to: 427

note: the reference is in a quotation from Herschel.

Aristotle. Referred to: 46, 48n, 60n, 79 (970-1), 95, 111n, 144 (1046), 566, 658n, 678, 788, 802, 938; 1043

note: the reference at 658n is in a quotation from Whewell.

— The “Art” of Rhetoric. (Greek and English.) Tr. J. H. Freese. London: Heinemann; New York: Putnam’s Sons, 1926.

note: this ed. used for ease of reference. The quotation occurs in a passage from Whately.

quoted: 828

— De Anima. (Greek and English.) Tr. R. D. Hicks. Cambridge: Cambridge University Press, 1907.

note: this ed. used for ease of reference.

referred to: 365n

— De Coelo. (Greek and English.) Tr. W. K. C. Guthrie. London: Heinemann; Cambridge, Mass.: Harvard University Press, 1939.

note: this ed. used for ease of reference. The reference at 761 is in a quotation from Whewell.

quoted: 798 referred to: 761

— Metaphysics. (Greek and English.) 2 vols. Ed. Hugh Tredennick. London: Heinemann; New York: Putnam’s Sons, 1933, 1935.

note: this ed. used for ease of reference. The reference at 761 is in a quotation from Whewell.

quoted: 365-6; 1112nreferred to: 761

— Organon. Ed. Harold P. Cooke and Hugh Tredennick. London: Heinemann; Cambridge, Mass.: Harvard University Press, 1938.

note: this ed., which includes The Categories, On Interpretation, and the Prior Analytics, is used for ease of reference.

— The Categories.

referred to: 46 (989), 47n-48n, 77, 112n, 119 (1030); 990, 1002

— Prior Analytics.

quoted: 156 referred to: 171n

— Physics. (Greek and English.) 2 vols. Tr. Phillip H. Wicksteed and Francis M. Cornford. London: Heinemann; Cambridge, Mass.: Harvard University Press, 1929, 1934.

note: this ed. used for ease of reference. The quotation and references at 761-2 and 823 are in quotations from Whewell. Those at 762 and 823 are identical.

quoted: 761 referred to: 657, 761-2, 823

— Treatise On the Heavens. See De Coelo.

Arnauld, Antoine, and Pierre Nicole.La Logique ou l’Art de penser : contenant outre des règles communes, plusieurs observations nouvelles, propres à former le jugement. Dernière édition. Amsterdam: Wolfgank, 1775.

note: this ed. in JSM’s library, Somerville College, as is the translation by Thomas Spencer Baynes, The Port-Royal Logic. 3rd ed. Edinburgh: Sutherland and Knox, 1854.

referred to: 5 (962)

Arnott. Referred to: 480, 498n

Aurelius.See Antoninus.

Averroes. Referred to: 938

Avicenna. Referred to: 938

Bacon, Francis. Referred to: cxii, 305, 313, 433, 482, 835, 879-80, 886

— De Augmentis Scientiarum. In The Works of Francis Bacon. 14 vols. Ed. James Spedding, Robert Leslie Ellis, and Douglas Denon Heath. London: Longman, et al., 1857-74, I, 415-840.

note: for ease of reference this ed., which is in JSM’s library, Somerville College, is used, though JSM’s references antedate it. Most of JSM’s phrasal quotations are paraphrases, and that at 312 is undoubtedly summary, so no collation is given; the phrase “per enumerationem simplicem” appears in Novum Organum, Works, I, 205.

quoted: 312 (1109)

referred to: 10 (965), 312 (1109), 381, 763-5

— “Filum Labyrinth, sive formula inquisitionis.” In The Works of Francis Bacon. 14 vols. Ed. James Spedding, Robert Leslie Ellis, and Douglas Denon Heath. London: Longman, et al., 1857-74, III, 493-504.

note: for ease of reference, this ed., which is in JSM’s library, Somerville College, Oxford, is used. The quotation is indirect; the same image is used in “Of the Interpretation of Nature,” ibid., 227.

quoted: 801

— “Of the Interpretation of Nature.” In The Works of Francis Bacon. 14 vols. Ed. James Spedding, Robert Leslie Ellis, and Douglas Denon Heath. London: Longman, et al., 1857-74, III, 215-52.

note: For ease of reference this ed., which is in JSM’s library, Somerville College, is used. The quotation is indirect; the same image is used in “Filum Labyrinth,” ibid., 503.

quoted: 801

— Novum Organum. In The Works of Francis Bacon. 14 vols. Ed. James Spedding, Robert Leslie Ellis, and Douglas Denon Heath. London: Longman, et al., 1857-74, I, 119-365.

note: for ease of reference this ed., which is in JSM’s library, Somerville College, is used, though JSM’s references antedate it. Also in his library is 2nd ed. Amsterdam: Ravensteiny, 1660. Most of the phrasal quotations are paraphrases, so no collation is given. JSM habitually, like other philosophers (e.g., Hume), uses Robert Hooke’s term “experimentum crucis” for Bacon’s “instantia crucis”; see under Hooke, below.

quoted: 312 (1109), 313 (1109), 660, 661, 763, 776, 788, 802; 1077n

referred to: 254 (1093), 272, 382, 582-3, 677, 763-5, 769, 870-1, 872n, 875

763.2-4 “Calorem . . . posse:” . . . “Compositionem] Hinc opiniones illæ in activa et operativa parte; calorem . . . posse. Hinc illud: compositionem (184)

776.19 “Is] Quinetiam licet abfuerit ea quam diximus delectatio et vanitas, is (166)

788.15 “Inductio quæ] Inductio enim quæ (205)

788.22 concludere.”] concludere; quod adhuc factum non est, nec tentatum certe, nisi tantummodo a Platone, qui ad excutiendas definitiones et ideas, hac certe forma inductiones aliquatenus utitur. (205)

802.8-9 temere . . . abstractae,] Aut enim sunt rerum nomina quæ non sunt (quemadmodum enim sunt res quæ nomine carent per inobservationem, ita sunt et nomina quæ carent rebus per suppositionem phantasticam); aut sunt nomina rerum quæ sunt, sed confusa et male terminata, et temere . . . abstractæ. [JSM’s italics] (171)

802.11 “Invenietur] Exempli gratia, accipiatur aliquod verbum (Humidum, si placet), et videamus quomodo sibi constent quæ per hoc verbum significantur; et invenietur (171)

802.17 quum] cum (171) [JSM’s reading occurs in other eds.]

1077.n2 “qui naturam rei in ipsa re perscrutantur”] Nemo enim alicujus rei naturam in ipsa re fœliciter perscrutatur, sed amplianda est inquisitio ad magis communia (I, 180)

Bailey, Samuel.Essays on the Pursuit of Truth, on the Progress of Knowledge, and on the Fundamental Principle of all Evidence and Expectation. By the Author of Essays on the Formation and Publication of Opinions. London: Hunter, 1829.

note: the reference is to the third essay, “On the Fundamental Principle of All Evidence and Expectation,” 193ff.

referred to: 307

— Letters on the Philosophy of the Human Mind. First Series. London: Longman, Brown, Green, and Longmans, 1855.

note: a Second Series (London: Longman, Brown, Green, Longmans, and Roberts, 1858) was published in time for JSM’s reference in 1862, but as his quotations are from the First Series, it is cited. A Third Series (London: Longman, Green, Longman, Roberts, and Green) was published in 1863.

quoted: 342, 649n referred to: 62n, 63n

342.8 “Those] [paragraph] Those (219)

342.9 events] events (219)

649.n1 “The] [paragraph] There is indeed, it may be alleged, this difference between the two cases, that the proper name ties me down to a particular image, while the general name leaves me at liberty to vary the image within certain limits; or, to describe the matter with greater precision, the proper name raises up the image of one individual object, while the (189)

— A Review of Berkeley’s Theory of Vision, designed to show the unsoundness of that celebrated speculation. London: Ridgway, 1842.

referred to: 8n

— The Theory of Reasoning. 2nd ed. London: Longman, Brown, Green, and Longmans, 1852.

quoted: 664n-665n referred to: 170n, 203

664n13-665.n1 “from . . . observation,”] On examining them [all cases of reasoning] they all agree in this, that from . . . observation. (27)

Bain, Alexander.

note: the quotation at 663 (which antedates the press-copy MS of the Logic, and may be from an unpublished paper) has not been located; the same ground is covered in Bain’s “On the Abuse of Language, in Science and in Common Life,” Fraser’s Magazine, 36 (Feb., 1847), 127-40, which is based on his Blackwell Prize Essay (1845), which in turn was based on his earlier logical studies.

quoted: 663 referred to: 410n

— The Emotions and the Will. London: Parker, 1859.

note: Bain’s chapter on Belief, cited by JSM at 204n, actually runs from 568-98.

referred to: 204n, 410n, 853

— Logic. 2 Parts. London: Longmans, Green, Reader, and Dyer, 1870.

note: the quotations at 100n (the first quotation), 166n (the first syllogism), and 227n are indirect.

quoted: 38n, 47n-48n, 76n, 85n, 86, 95n, 100n-101n, 104, 141n-142n, 166n-167n, 181n-182n, 227n, 236, 279n, 375n, 377n, 448n-449n, 451, 453n, 487n-488n, 577, 589n, 676n referred to: cxvii 41n, 81, 159n, 352, 353, 587, 948n.

47.n1 “The] [paragraph] The (I, 265)

48.n4 predication.] predication, including Verbal as well as Real predication. (I, 265)

48.n6 or other] or any other (I, 265)

76.n1-2 “points . . . among classes.”] [section 8] General Names are said to be Connotative; that is, they denote objects, and connote or imply attributes, or points . . . among objects. (I, 49)

85.n3 “the contrast] [paragraph] The reason why “Universal” and “Particular” are not suitable names, for the two modes of quantity, is that these names designate also the inductive contrast (I, 82)

86.2 “with] The chief examples [of Indefinite forms of the proposition] occur with (I, 82)

86.8 metal.] metal collectively. (I, 83)

95.n2 “the] But the word “class” has two meanings—the (I, 50)

95n.4 planets . . . . The] [ellipsis indicates 4-sentence omission with paragraph break before The] (I, 50)

95n.6 virtuous . . . . In] [ellipsis indicates 5-sentence omission with paragraph break before In]

101n.1 “are] Indeed, all such propositions [as predicate Existence] are (I, 107)

101n.5 and succession] and of succession (I, 107)

101n.10 concrete form] correcter form (I, 107) [treated as typographical error]

101n.16 “fictitious and unmeaning language”] Indeed, when we talk of these two departments [the portions of knowledge called the Object world and the Subject world] as dividing between them the universe of existence, we are using fictitious and unmeaning language; the ultimate universe, according to the law of Relativity, is a couple; the highest real grouping of things is this two-fold grouping, called Object and Subject, &c. (I, 255-6) [The remark referred to by JSM at 100.n1 occurs in the second sentence following.]

104.21 “This] [paragraph] This (I, 105)

104.27 substance . . . . The] substance. Every blood corpuscle has a plurality of relations, indivisible and inseparable. [paragraph] The (I, 105)

104.29-30 exercise. The] exercise. Every pleasurable feeling has its power of acting on the will and of impressing the memory; all the attributes are joined in the unity of the mental being. [paragraph] A wide range of Scientific knowledge is comprised under the present head. The (I, 105)

141.n2 “the] The (I, 71)

141.n8 each,”] each. (I, 75)

166.n6 Socrates is wise,/Socrates is poor, therefore] Socrates is poor/Socrates is wise (I, 159)

166.n9 “one . . . wise.” “Now [paragraph] Properly, the conclusion is, “one . . . wise.” Now (I, 159)

167.n16 “a single meaningless] One form [of the Singular Name], exhibited in the above examples, is a single meaningless (I, 48)

181.n3 “unworkable] [paragraph] Notwithstanding so many advantages, this form of the axiom now described is unworkable (I, 157)

181.n8 at once] whence (I, 157) [treated as typographical error]

181.n8 A carries C] A carries B (I, 157) [printer’s error in Source?]

182.24 “The] [paragraph] It is only the same objection, otherwise put, that the (I, 158)

236.12 conclusion. . . . When] conclusion. When we know a fact, we know it, even when called by another name, which is all that is meant, at present, by necessary truth. When (I, 222)

236.14 affirmation that two . . . space. No] affirmation, “two . . . space.” [paragraph] No (I, 222)

236.15 in such cases. . . . We] for such cases. Our ordinary intellectual powers enable us to pronounce, in more than one form, that an object is everything or anything that we have found it to be. We (I, 222)

236.21 “the] It [the dictum de omni et nullo] is not intelligible without much familiarity with examples of the generalizing process; and, as, in the case of all other first principles, the (I, 226)

279.n2-3 “everything . . . affirmation;”] By the law of Relativity, every thing . . . affirmation; to the thing that we call a ‘straight’ line, there corresponds a negative or opposite called a “bent” or crooked line. (I, 16)

375.n2-4 “The . . . solid;”] [paragraph:] Many other laws might be cited:—The celebrated law of Berthollet, regarding the double decomposition of salts; the . . . solid. (II, 254)

448.n4 alone: a cause] alone, and cause (II, 83)

448.n6 these] those (II, 83)

448.n7 direction. The] direction. [paragraph] The (II, 83)

449.n2 variations] variation (II, 83)

449.n3 attractive] attracting (II, 83)

449.n3 bodies. By] bodies. [paragraph] By (II, 83)

449.n4 nitrogen from] nitrogen in (II, 83)

451.23-24 “quinine . . . oil,”] The Specifics that have been discovered for particular diseases, as quinine . . . oil, are affirmed as independent facts, resting on no deductive inferences from Cause and Effect in Disease, but on the experience of their efficacy. (II, 360)

453.n4 “when] This source of ambiguity [from the many unseen operations effecting change] is practically overcome when (II, 336)

453.n5 changes,] change; (II, 336)

453.n6 day by] day with (II, 336)

487.n2 “scientific . . . Induction,”] [section 6] Scientific . . . Induction. (II, 121)

487.n4 “the] [section 7] The (II, 121)

487.n5 facts. Induction] facts. [paragraph] Induction (II, 121)

488.n5 agency. . . . If] agency [paragraph] So remarkable have been the achievements of modern times, in the direction of lofty generalities, that some countenance seems to be lent to the ancient dream of attaining an ultimate centralized unity in the midst of the seeming boundless diversity of nature. [paragraph] It depends purely on actual investigation, how far all phenomena are resolvable into one or into several ultimate laws; whether inductive finality leaves us with one principle, with two, or with twenty principles. [paragraph] Thus, if (II, 121)

577.24 “leap in the dark”] It is always more congenial to make leaps in the dark, than to abide strictly by what we actually know. (II, 378)

589.n3 “the] [paragraph] With an exception to be noticed presently, these are perhaps the (II, 13)

589.n5 “a law connecting] [sub-section 1] A law has been discovered connecting (II, 13)

589.n7 product. The] product. Thus, for sulphur, the atomic weight (32), multiplied by the specific heat (0.1776), gives 5.68; the atomic weight of platinum (197), multiplied by its specific heat, (0.0324), gives 6.38. The (II, 13)

589.n9 “between] [sub-section 2] A law obtains between (II, 13)

589.n10 weights. The] Weights. Thus, the specific gravity of oxygen is 16, its atomic weight 16; hydrogen, specific gravity 1, atomic weight 1; phosphorus, specific gravity 62, atomic weight 31 (the relation here is 2 to 1); steam, specific gravity 9, atomic weight 18 (relation of 1 to 2). The (II, 13)

589.n10 is in] is thus, in (II, 13)

676.n7 “The] [paragraph] The (II, 173)

676.n8 humid] husnid [sic] (II, 173)

676.n12 further] farther (II, 173)

676.n15 containing water] containing no water (II, 173) [treated as typographical error in text above, and so corrected]

676.n19 unpaved. “Impertinent”] unpaved. [paragraph] Impertinent (II, 174)

— The Senses and the Intellect. London: Parker, 1855.

note: the 3rd ed. (London: Longmans, 1868) is in JSM’s library, Somerville College.

referred to: 62n, 410n, 853

Bentham, Jeremy. Referred to: 876n, 890

— The Book of Fallacies. London: Hunt, 1824.

note: in Works, ed. John Bowring. Edinburgh: Tait, 1843, II. The work was edited by Peregrine Bingham. The term quoted at 742 is the title of Part IV, “Fallacies of Confusion”; those quoted at 695 and 823 derive from the title of chap. i, “Question-Begging Appellatives,” of Part IV.

quoted: 695, 742, 823

— A Fragment on Government; being an examination of what is delivered on the subject of government in general in the introduction to Sir William Blackstone’s Commentaries; with a preface, in which is given a critique on the work at large. London: Payne, 1776.

note: in Works, ed. John Bowring. Edinburgh: Tait, 1843, I.

referred to: 732

— Rationale of Judicial Evidence, specially applied to English Practice. Ed. J. S. Mill. 5 vols. London: Hunt and Clarke, 1827.

note: in JSM’s library, Somerville College. In Works, ed. John Bowring. Edinburgh: Tait, 1843, VI & VII. The quotations are indirect; the passage referred to at 627 concludes with a long note by JSM.

quoted: 598, 627

Bentley. Referred to: 754

Berkeley, George. Referred to: 58, 59 (994), 203, 203n, 649, 829-30; 1020, 1088

note: the reference at 203 is in an indirect quotation from Herschel; JSM’s comment (203n) that the doctrine is not in Berkeley would appear to be correct.

— A Treatise Concerning the Principles of Human Knowledge, wherein the chief causes of error and difficulty in the sciences, with the grounds of scepticism, atheism, and irreligion, are inquired into. In Works. 3 vols. London: Priestley, 1820, I, 1-106.

note: this edition in JSM’s library, Somerville College. The quotation is from the title.

quoted: 815-16

Berthollet. Referred to: 375

Biber, George Edward.Christian Education, in a course of lectures, delivered in London, in Spring 1829. London: Effingham Wilson, 1830.

referred to: 257n (1095)

Bible. Referred to: 193

— New Testament. Referred to: 626n

— I Corinthians.

quoted: 626n

626.n7 “Christ, and him crucified,”] For I determined not to know any thing among you, save Jesus Christ, and him crucified. (2:2; cf. ibid., 1:23)

— Galatians.

quoted:1134

1134.16-18 “A little leaven,” . . . “the whole lump.”] A little leaven leaveneth the whole lump. (5:9; cf. I Corinthians, 5:6)

— Psalms.

quoted: 862

862.1 “said in his haste that all men are liars,”] I said in my haste, All men are liars. (116.11) [cf. 862^d-d]

— St. John.

quoted: 150 (1048)

Bichat. Referred to: 473

Biel. Referred to: 753n

Blainville, Henri Marie Ducrotay de.De l’Organisation des animaux, ou Principes d’anatomie comparée. Paris: Levrault, 1822.

referred to: 656, 675, 715, 730

Boe. Referred to: 793

note: the reference is in a quotation from Paris.

Borda. Referred to: 405

Boswell, James.Life of Johnson. Ed. George Birkbeck Hill and L. F. Powell. 6 vols. Oxford: Clarendon Press, 1934.

note: the reference is simply to Johnson’s “refutation” of Berkeley at I, 471; this ed. used for ease of reference.

referred to: 829

Bowen, Francis.Lowell Lectures, on the Application of Metaphysical and Ethical Science to the Evidences of Religion. Boston: Little and Brown, 1849.

quoted: 354, 356n

354.12-13 “of . . . causative.”] Thus, if I will to move a limb which has been paralyzed, though the limb does not move, I am conscious of making an effort to move it, and this consciousness of effort is a consciousness of . . . causative, though in this instance too weak, or too little, for the end proposed. (84)

354.24 agent. Let] agent; we cannot speak of the doings of matter, as we could if the word action were applicable to it in any other than a figurative sense. Let (88)

354.25 matter.”] matter,—a stone, for instance,—except this merely negative one, that it always and necessarily remains in its present state, whether this be of rest or motion. (88)

356.n11-13 “In . . . experience.”] But in . . . experience; the volition succeeds, which is a true effort, or a power in action; and this, if the power be sufficient, is necessarily followed by the effect. (85)

Brahe. Referred to: 652

Brandis, Christian August.Handbuch der Geschichte der Griechisch-Römischen Philosophie. Vol. I. Berlin: Reimer, 1835.

note: it is likely that George Grote supplied JSM with this reference. In his copy of Brandis (University of London Library), Grote has written “X Thales conceived ψυχὴ as = motive power” at the top of 119. (Cf. note to Preller and Ritter, Historia, below.)

quoted: 364

364.28 “augenscheinlich . . . berichten;”] Cicero, nachdem er an einer Stelle jene Worte als Ermahnung zur Frömmigkeit gefasst wiedergegeben, legt an einer andern Stelle augenscheinlich . . . berichten, dem Thales die Annahme eines göttlichen Geistes bei, der aus dem Wasser Alles bilde: wogegen die lehre von der Weltseele ihm von Griechischen Schriftstellern zugeeignet wird. (118-19) [footnotes omitted]

Bridgewater Treatise. See Chalmers, and Prout.

Broussais. Referred to: 497

Brown, John. “An Essay on Satire: Occasion’d by the Death of Mr. Pope,” in A Collection of Poems. By Several Hands. 3 vols. London: Dodsley, 1748.

note: in MS, 43, 46 JSM wrongly attributes the quotation to Pope.

quoted: 829

829.n2 “And . . . with a grin.”] Truth’s sacred prize the loudest horse-laugh win;/ And . . . by a grin. (Pt. 2, ll. 53-4; III, 124) [The passage is usually quoted from the 2nd ed., corrected and enlarged (London: Dodsley, 1849), Pt. II; ll. 223-4, where the reading is: “Truth’s sacred Forth th’ exploded laugh shall win;/ And . . . .”]

Brown, Dr. John.The Elements of Medicine. Vols. II and III of The Works of Dr. John Brown. 3 vols. London: Johnson, and Symonds; Edinburgh: Ballantyne, 1804.

note: the reference derives from a quotation from Paris.

referred to: 793

Brown, Thomas. Referred to: 61n (994), 335, 649, 830

— Inquiry into the Relation of Cause and Effect. 3rd ed. Edinburgh: Constable, 1818.

note: this edition in JSM’s library, Somerville College.

referred to: cxiv, 356n, 625, 758, 817, 838

— Lectures on the Philosophy of the Human Mind. 4 vols. Edinburgh: Tait, 1820.

note: the reference at 200-1 is to Vol. II, Lecture xlix; that at 769 is to Vol. II, Lecture xxvi, “On Dr. Reid’s Supposed Confutation of the Ideal System. . . .”

referred to: cxiv, 62n, 200-1 (1075-6), 769; 995, 1077

Browne, Thomas.Pseudodoxia Epidemica: or, Enquiries into very many received tenents, and commonly presumed truths. 2nd ed. London: Dod and Ekins, 1650.

note: this edition in JSM’s library, Somerville College.

quoted: 750

Brown-Séguard, Charles E. Course of Lectures on the Physiology and Pathology of the Central Nervous System. Philadelphia: Collins, 1860.

note: in JSM’s library, Somerville College. The quotations are indirect, and are taken from Lecture x, “On the Influence of the Nervous System upon Nutrition and Secretion. . . .”

quoted: 476-7

— “On the Relations between Muscular Irritability, Cadaveric Rigidity, and Putrefaction,” Proceedings of the Royal Society of London, XI (1860-62), 204-14.

note: the Croonian Lecture, delivered 16 May, 1861.

quoted: 421, 422, 424, 425 referred to: 421-5

422.2 “comparing] I have ascertained this fact in various ways; but the most decisive method consists in comparing (205)

422.4 “often] I have often (205) [this sentence follows immediately on the one last quoted]

424.17 “death] Death (208)

424.20 in the brain;”] of the brain. (208)

424.23 “a] But lightning may kill in another way: it may destroy life as galvanism does, by producing such a (208)

424.24-5 body,” . . . “muscular] body that muscular (208)

424.25 once.”] once; and the ensuing rigidity may then be of so short duration as to escape notice. (208)

425.15 “That] The facts I have mentioned show that (213)

425.21 slowly:” but “that] slowly. The facts mentioned also clearly show that (213)

Buckle, Henry Thomas.History of Civilization in England. 2 vols. London: Parker and Son, 1857, 1861.

quoted: 933 referred to: 931-2, 934-5, 935n-936n

Bunsen. Referred to: 408

note: the reference is in a quotation from Liebig.

Butler, Joseph.The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature. To which are added two brief dissertations: I. Of Personal Identity. II. Of the Nature of Virtue. London: Knapton, 1736.

referred to: 630

Caesar, Julius. Referred to: 321n, 605, 749, 937, 941; see also Suetonius.

note: the references at 941 are in quotations from Stephen.

Campbell, George.A Dissertation on Miracles: containing an Examination of the principles advanced by David Hume, Esq; in an Essay on Miracles. Edinburgh: Kincaid and Bell, 1762.

referred to: 631

Candolle, Augustin Pyramus de.Théorie élémentaire de la botanique, ou exposition des principes de la classification naturelle et de l’art de décrire et d’étudier les végétaux. 2nd ed. Paris: Deterville, 1819.

note: the translated quotation appears in a quotation from Whewell’s History of Scientific Ideas; as JSM follows Whewell’s translation, no collation is given.

quoted: 700

Capel, George. Letter to Mill. A.l.s., 3 November, 1866, British Library of Political and Economic Science (London School of Economics), Mill-Taylor Collection, I, 98.

quoted: 935n-936n

935.n4-936.n2 “In . . . alone,”] [paragraph] Now to do what he [Buckle] might to ascertain this order [of human progression], was what he addressed himself to, and in . . . alone. (f.2v)

936.n4 “He desired] He claimed (f.3r)

Carlyle, Thomas. “Characteristics,” Edinburgh Review, LIV (Dec., 1831), 351-83.

note: Mill disputed the matter in question (“we do not learn to use our muscles by studying their anatomy”) with Carlyle, and so, though there is no direct reference to Carlyle in the passage, the reference to his “Characteristics” is given. He says, e.g., “Is it the skilfullest Anatomist that cuts the best figure at Sadler’s Wells? or does the Boxer hit better for knowing that he has a flexor longus and a flexor brevis?” (355)

quoted: 13

— “Corn Law Rhymes,” Edinburgh Review, LV (July, 1832), 338-61.

quoted: 800n

800.n2 “strength does not] Strength, if that be the thing aimed at, does not (351)

— “Novalis.” In his Critical and Miscellaneous Essays. 5 vols. London: Fraser, 1840, II.

note: this ed. probably was in JSM’s library, Somerville College. The quotation is from Novalis, but as there can be little doubt that JSM took the passage from Carlyle, it is entered here. It is found in the ed. Carlyle used, Ludwig Tieck and Friedrich Schlegel, eds. Novalis Schriften. 2 vols. Berlin: Realschulbuchhandlung, 1805, II, 336.

quoted: 843

843.3 will:”] will (vollkommen gebildeter Wille). (242) [In Novalis the full sentence is: “Ein Charakter ist ein vollkommen gebildeter Wille.”]

Carpenter, William Benjamin.Principles of General and ComparativePhysiology, intended as an introduction to the study of human physiology, and as a guide to the philosophical pursuit of natural history. London: Churchill, 1839.

note: the 2nd ed. (London: Churchill, 1841) was reviewed by JSM in the Westminster Review, XXXVII (Jan., 1842), 254.

referred to: 374n; 1121n

— Principles of Human Physiology, with their chief applications to pathology, hygiene, and forensic medicine. London: Churchill, 1842.

referred to: 374n

Cato. Referred to: 799, 824

note: the reference at 824 is to Cicero’s presentation of Cato in his De finibus.

Chalmers, Thomas.On the Power Wisdom and Goodness of God as Manifested in the Adaptation of External Nature to the Moral and Intellectual Constitution of Man. 2 vols. London: Pickering, 1833.

note: Bridgewater Treatise I. The general title of the Bridgewater Treatises is On the Power Wisdom and Goodness of God as Manifested in the Creation; on the halftitle page (where this appears), Chalmers’ work is identified as On the Adaptation of External Nature to the Moral and Intellectual Constitution of Man.

referred to: 367n, 465

— On the Use and Abuse of Literary and Ecclesiastical Endowments. Glasgow: Collins, 1827.

referred to: 703n

Chares. Referred to: 941

Charles i (of England). Referred to: 778

Charles iii (of Spain). Referred to: 940

Christ. See Jesus.

Chillingworth. Referred to: 5n

Cicero.De finibus bonorum et malorum. Ed. H. Rackham. London: Heinemann; New York: Macmillan, 1914.

note: this ed. used for ease of reference; the collations are not given, as there is no indication which ed. JSM used.

quoted: 771, 797, 812-13, 823-5

— De natura deorum. Ed. H. Rackham. London: Heinemann; New York: Putnam’s Sons, 1933.

note: this ed. used for ease of reference; there is no indication of which ed. JSM used, but the collation is given to establish context.

quoted: 364

364.32-3 “Anaximenes . . . statuit.”] Post Anaximenes . . . statuit, eumque gigni esseque inmensum et infinitum et semper in motu: quasi aut aer sine ulla forma deus esse possit, cum præsertim deum non modo aliqua sed pulcherrima specie deceat esse, aut non omne quod ortum sit mortalitas consequatur. (28; Bk. I, Chap. x)

Clairaut. Referred to: 222

Coleridge, Samuel Taylor. Referred to: 685, 755n, 792n, 830

note: the reference at 685 is too general for precise identification, but the substance is reflected in the MS passage on language included in Alice D. Snyder, Coleridge on Logic and Learning (New Haven: Yale University Press, 1929), 138.

— Aids to Reflection in the Formation of a Manly Character on the Several Grounds of Prudence, Morality, and Religion: Illustrated by select passages from our elder Divines, especially Archbishop Leighton. 2nd ed. London: Hurst, Chance, 1831.

note: the 1st ed. (London: Taylor and Hessey, 1825) is in JSM’s library, Somerville College, but this is the edition cited in his “Coleridge”; both references are given in the collation below. See also the reference to Biographia Literaria at 755n, which might also refer to Aids to Reflection, 65.

quoted: 814

814.9-10 “the man . . . motive, not . . . man;” . . . “what] [paragraph] He needs only reflect on his own experience to be convinced, that the Man . . . motive, and not . . . Man. What (2nd ed., 59; 1st ed., 67)

— Biographia Literaria; or Biographical Sketches of My Literary Life and Opinions. 2 vols. in 1. London: Rest Fenner, 1817.

note: in JSM’s library, Somerville College. The reference at 755n might also be to Coleridge’s Aids to Reflection, 2nd ed., 65.

quoted: 770, 885 referred to: 755n

770.19 “evident truth,” that “the] Yet the apparent action of each [soul and body] on the other pressed heavy on the philosopher on the one hand; and no less heavily on the other hand pressed the evident truth, that the (I, 129)

770.21 property,” and therefore “cannot . . . opposite:”] property; and cannot . . . opposite. (I, 129)

885.4 whenever] wherever (I, 214) [cf. 885^b-b]

885.6 subtracting] substracting [sic] (I, 214)

885.8 different. As, for instance, in] different. In (I, 214) [treated as typographical error; MS reading given in text]

885.8 series of] series of* [footnote omitted, giving Coleridge’s identification of the articles as appearing in the Morning Post and Courier, and designed to appear in The Friend] (I, 214-15)

885.10-11 Bourbons.’ The] Bourbons,” I feel myself authorized to affirm, by the effect produced on many intelligent men, that were the dates wanting, it might have been suspected that the essays had been written within the last twelve months. The (I, 215)

— Second Lay Sermon [Blessed are ye that sow beside all waters]. 2nd ed. In On the Constitution of Church and State, and Lay Sermons. London: Pickering, 1839.

note: in JSM’s library, Somerville College. The same passage is quoted in JSM’s “Coleridge,” Collected Works, X, 155n.

quoted: 807

807.33 “which might be taken as a] Thus instead of the position, that all things find, it would be less equivocal and far more descriptive of the fact to say, that things are always finding, their level: which might be taken as the (403)

— The Friend: A series of Essays, in three volumes, to aid in the formation of fixed principles in politics, morals, and religion, with literary amusements interspersed. 3 vols. London: Rest Fenner, 1818.

note: in JSM’s library, Somerville College.

quoted: 774-5

774.32-3 “which . . . Europe,” viz., “Fortune favours fools.”] “Does fortune favor fools? Or how do you explain the origin of the proverb, which . . . Europe?” (III, 269)

774.n4 “admits] [paragraph] This proverb admits (III, 269)

774.n4 explanations. . . . It] explanations according to the mood of mind in which it is used. It (III, 269)

774.34 “tendency] [see 774^c-c] (III, 270)

775.40 whole.”] [see 775^f] (III, 277)

Columna. Referred to: 700

note: the reference is in a quotation from Whewell.

Columbus. Referred to: 302n, 819

Commodus. Referred to: 197 (1073)

Comte, Auguste. Referred to: 341-2, 495, 504, 560n, 859, 915; 1142

— Cours de philosophie positive. 6 vols. Paris: Bachelier, 1830-42.

note: in JSM’s library, Somerville College. Vol. I (Les Préliminaires généraux et la philosophie mathématique) was published in 1830; Vol. II (La Philosophie astronomiqueet la philosophie de la physique) in 1835; Vol. III (La Philosophie chimique et la philosophie biologique) in 1838; Vol. IV (La Philosophie sociale et les conclusions générales: première partie) in 1839; Vol. V (La Partie historique de la philosophie sociale, en tout ce qui concerne l’état théologique et l’état métaphysique) in 1841; and Vol. VI ( Le Complément de la philosophie sociale, et les conclusions générales) in 1842. Comte’s text is highly repetitive, and some of the references are therefore typical rather than specific.

quoted: 299, 488-9, 497, 621, 640, 832, 918-19 referred to: 284n, 375n, 393, 456n, 458n, 499, 504, 508n, 571n, 614n, 615-16, 619n, 620, 620n, 713n, 715, 726, 730n, 731n, 830, 851n, 895n, 897, 903n, 910n, 914n, 915, 915n, 917, 928, 929n, 930n, 942, 948, 948n, 950n; 1118-19

299.4 “L’astronomie] Quoi qu’il en soit, on voit clairemont par là que l’astronomie (II, 202)

488.6-489.3 “evidently primordial” . . . “la . . . substance,”] Je veux parler des efforts, nécessairement illusoires, qu’on a si souvent tentés pour expliquer, soit par le système émissif, soit par le système vibratoire, le phénomène primordial, évidemment inexplicable, de la . . . substance.” (II, 655-6)

489.3-6 “No . . . primordial?”] [translated from:] Personne n’entreprend plus aujourd’hui d’expliquer la pesanteur spécifique particulière à chaque substance ou à chaque structure. Pourquoi en serait-il autrement, quant à la couleur spécifique, dont la notion n’est pas, sans doute, moins primordiale?” (II, 656-7)

497.6-11 “Some . . . supposition.”] [translated from:] Tel fait est encore peu connu, ou telle loi est ignorée: on forme alors à cet égard une hypothèse, le plus possible en harmonie avec l’ensemble des données déjà acquises; et la science, pouvant ainsi se développer librement, finit toujours par conduire à de nouvelles conséquences observables, susceptibles de confirmer ou d’infirmer, sans aucune équivoque, la supposition primitive.” (II, 437-8)

497.12-15 “if . . . inquiry.”] [translated from:] Or, l’une et l’autre [induction and deduction] voie seraient certainement insuffisantes, même à l’égard des plus simples phénomènes, aux yeux de quiconque a bien compris les difficultés essentielles de l’étude approfondie de la nature, si l’on ne commençait souvent par anticiper sur les résultats, en faisant une supposition provisoire, d’abord essentiellement conjecturale, quant à quelques-unes des notions mêmes qui constituent l’objet final de la recherche.” (II, 434)

621.5 “at . . . inquiry:”] [translated from:] Il ne s’agirait néanmoins ici que de prolonger convenablement les réflexions que doivent naturellement suggérer les questions inorganiques susceptibles de solutions mathématiques, et dans lesquelles on voit, d’une manière si prononcée, ces solutions devenir graduellement plus difficiles et plus imparfaites à mesure que le sujet se complique davantage en rapprochant peu à peu l’état abstrait de l’état concret, à tel point que, au-delà des phénomènes purement astronomiques ou de leurs anologues les plus immédiats, une semblable perfection logique ne s’obtient presque jamais, comme nous l’avons constaté, qu’aux dépens de la réalité des recherches, même sans sortir des études générales de la physique proprement dit. (III, 414-15)

621.6-10 “notwithstanding . . . influences.”] [translated from:] En effet, lors même que l’on supposerait exactement connues les lois mathématiques propres aux différentes actions élémentaires dont le concours détermine l’accomplissement des phénomènes vitaux, leur extrême diversité et leur multiplicité inextricable ne pourraient aucunement permettre à notre faible intelligence d’en poursuivre avec efficacité les combinaisons logiques, comme le témoignent déjà si clairement les questions astronomiques elles-même malgré l’admirable simplicité de leurs élémens mathématiques, lorsqu’on veut considérer simultanément plus de deux ou trois influences essentielles. (II, 415-16)

918.7-919.33 “making . . . another.”] [translated from:] Ainsi conçue, cette sorte d’anatomie sociale, qui constitue la sociologie statique, doit avoir pour objet permanent l’étude positive, à la fois expérimentale et rationnelle, des actions et réactions mutuelles qu’exercent continuellement les unes sur les autres toutes les diverses parties quelconques du système social, en faisant scientifiquement, autant que possible, abstraction provisoire du mouvement fondamental qui les modifie toujours graduellement. Sous ce premier point de vue, les prévisions sociologiques, fondées sur l’exacte connaissance générale de ces relations nécessaires, seront proprement destinées à conclure les unes des autres, en conformité ultérieure avec l’observation directe, les diverses indications statiques relatives à chaque mode d’existence sociale, d’une manière essentiellement analogue à ce qui se passe habituellement aujourd’hui en anatomie individuelle. Cet aspect préliminaire de la science politique suppose donc évidemment, de toute nécessité, que, contrairement aux habitudes philosophiques actuelles, chacun des nombreux élémens sociaux, cessant d’être envisagé d’une manière absolue et indépendante, soit toujours exclusivement conçu comme relatif à tous les autres, avec lesquels une solidarité fondamentale doit sans cesse le combiner intimement. Il serait, à mon gré, superflu de faire expressément ressortir ici la haute utilité continue d’une telle doctrine sociologique: car, elle doit d’abord servir, évidemment, de base indispensable à l’étude définitive du mouvement social, dont la conception rationnelle suppose préalablement la pensée continue de la conservation indispensable de l’organisme correspondant; mais, en outre, elle peut être, par elle-même, immédiatement employée à suppléer souvent, du moins provisoirement, à l’observation directe, qui, en beaucoup de cas, ne saurait avoir lieu constamment pour certains élémens sociaux, dont l’état réel pourra néanmoins se trouver ainsi suffisamment apprécié, d’après leurs relations scientifiques avec d’autres déjà connus. L’histoire des sciences peut surtout donner, dès ce moment, quelque idée de l’importance habituelle d’un tel secours, en rappelant, par exemple, comment les vulgaires aberrations des érudits sur les prétendues connaissances en astronomie supérieure attribuées aux anciens Egyptiens ont été irrévocablement dissipées, avant même qu’une plus saine érudition en eût fait justice, par la seule considération rationnelle d’une relation indispensable de l’état général de la science astronomique avec celui de la géométrie abstraite, alors évidemment dans l’enfance; il serait aisé de citer une foule de cas analogues, dont le caractère philosophique serait irrécusable. On doit d’ailleurs noter, à ce sujet, pour ne rien exagérer, que ces relations nécessaires entre les divers aspects sociaux ne sauraient être, par leur nature, tellement simples et précises que les résultats observés n’aient pu jamais provenir que d’un mode unique de coordination mutuelle. Une telle disposition d’esprit, déjà évidemment trop étroite en biologie, serait surtout essentiellement contraire à la nature encore plus complexe des spéculations sociologiques. Mais il est clair que l’exacte appréciation générale de ces limites de variation, normales et même anormales, constitue nécessairement alors, au moins autant qu’en anatomie individuelle, un indispensable complément de chaque théorie de sociologie statique, sans lequel l’exploration indirecte dont il s’agit pourrait souvent devenir erronée.

N’écrivant point ici un traité spécial de philosophie politique, je n’y dois point méthodiquement établir la démonstration directe d’une telle solidarité fondamentale entre tous les aspects possibles de l’organisme social, sur laquelle d’ailleurs il n’existe guère maintenant, au moins en principe, de divergences capitales parmi les bons esprits. De quelque élément social que l’on veuille partir, chacun pourra aisément reconnaître, par un utile exercise scientifique, qu’il touche réellement toujours, d’une manière plus ou moins immédiate, à l’ensemble de tous les autres, même de ceux qui en paraissent d’abord le plus indépendans. La considération dynamique du développement intégral et continu de l’humanité civilisée permet, sans doute, d’opérer avec plus d’efficacité cette intéressante vérification du consensus social, en montrant avec évidence la réaction universelle, actuelle ou prochaine, de chaque modification spéciale. Mais cette indication pourra constamment être précédée, ou du moins suivie, par une confirmation purement statique; car, en politique, comme en mécanique, la communication des mouvemens prouve spontanément l’existence des liaisons nécessaires. Sans descendre, par exemple, jusqu’à la solidarité trop intime des diverses branches de chaque science ou de chaque art, n’est-il pas évident que les différentes sciences sont entre elles, ou presque tous les arts entre eux, dans une telle connexité sociale, que l’état bien connu d’une seule partie quelconque, suffisamment caractérisée, permet de prévoir, à un certain degré, avec une vraie sécurité philosophique, l’état général correspondant de chacune des autres, d’après les lois d’harmonie convenables? Par une considération plus étendue, on conçoit également l’indispensable relation continue qui lie aussi le système des sciences à celui des arts, pourvu qu’on ait toujours soin de supposer, comme l’exige clairement la nature du sujet, une solidarité moins intense à mesure qu’elle devient plus indirecte. Il en est évidemment de même quand, au lieu d’envisager l’ensemble des phénomènes sociaux au sein d’une nation unique, on l’examine simultanément chez diverses nations contemporaines, dont la continuelle influence réciproque ne saurait être contestée, surtout dans les temps modernes, quoique le consensus doive être ici, d’ordinaire, moins prononcé, à tous égards, et décroître d’ailleurs graduellement avec l’affinité des cas et la multiplicité des contacts, au point de s’effacer quelquefois presque entièrement, comme, par exemple, entre l’Europe occidentale et l’Asie orientale, dont les divers états généraux de société paraissent jusqu’ici à peu près indépendans. (IV, 325-9)

832.n1 “Une propriété] [paragraph] Enfin, une quatrième et dernière propriété (I, 47)

832.n6 civilisées. . . . Tant] civilisées. [ellipsis indicates 1-page omission] Tant (I, 48-9)

— Synthèse subjective, ou Système universel des conceptions propres à l’état normal de l’humanité. Tome premier, contenant le Système de logique positive, ou Traité de philosophie mathématique. Paris: Comte, Dalmont, 1856.

note: in JSM’s library, Somerville College. This work was only forecast at the time of JSM’s first reference to it; the reference was deleted (in 1846) before the work appeared.

referred to: 615n-616n

Condillac, Etienne Bonnot de. Referred to: 29 (976), 175-6, 606; 1020

— La Logique, ou les premiers developpemens de l’art de penser. In Oeuvres complètes. 31 vols. Paris: Dufart, 1803, XXX, 131-51.

note: this edition in JSM’s library, Somerville College. The quotation is indirect.

quoted: 176 (1061) referred to: 134 (1041)

Condorcet, Marie Jean Antoine Nicolas Caritat, marquis de.Esquisse d’un tableau historique des progrès de l’esprit humain. Paris: Agasse, 1795.

quoted: 832

832.3 l’expérience,] l’expérience du passé, (327)

832.6 histoire?] histoire. (327)

832.11 l’expérience . . . sont] l’expérience du passé, sur des objets du même ordre, sont (328)

— Vie de Monsieur Turgot. London: n.p., 1786.

quoted: 18

18.1 “La scolastique, qui] La conservation de la Langue Latine & d’une partie des ouvrages des anciens; l’étude de la Scolastique, qui du moins préserva d’une stupidité absolue les Etats des barbares destructeurs de l’Empire Romain, & qui (8-9)

18.4 philosophie.”] philosophie; l’établissement d’une Morale plus universelle, plus propre à rapprocher les hommes de tous les pays, fondée sur une fraternité générale entre tous les individus de l’espece humaine, tandis que la Morale payenne sembloit tendre à les isoler, à ne rapprocher que les membres d’une même cité, & sur-tout ne s’occupoit que de former des citoyens ou des philosophes, au lieu de former des hommes; la destruction de l’esclavage domestique & de celui de la Glebe, qui est peut-être autant l’ouvrage des maximes du Christianisme que de la Politique des Souverains, interessés à créer un peuple pour le faire servir à l’abaissement des Grands; cette patience, cette soumission que le Christianisme inspire, & qui, détruisant l’esprit inquiet & turbulent des peuples anciens, rendit les Etats Chrétiens moins sujets aux orages, apprit à respecter les Puissances établies, & à ne point sacrifier à l’amour, même légitime, de l’indépendance, la paix, le repos & la sûreté de ses freres: Tels furent les principaux bien-faits du Christianisme [according to Turgot’s Latin Discourse of 1750]. (9-10)

Confucius. Referred to: 938

Copernicus. Referred to: 272, 776-7

Copleston. Referred to: 797

Courier, Paul Louis. Quoted: 693n

note: quotation not located.

Cousin, Victor. “Argument philosophique,” Gorgias. In Oeuvres de Platon. Tr. Victor Cousin. 13 vols. Paris: Bossange, 1832-40, V, 129-80.

note: the reference is specifically to 167-8.

referred to: 780; 1061

— Cours d’histoire de la philosophie morale au dix-huitieme siècle. Seconde partie: Ecole écossaise. Ed. Danton and Vacherot. Paris: Ladrange, 1840.

note: the edition of 1841 (Brussels: Hauman) of Cousin’s Cours d’histoire is bound with the three vols. of Cousin’s Cours de philosophie (Brussels: Hauman, 1836) in JSM’s library, Somerville College.

quoted: 60n-61n referred to: 60, 62n

61.n4 évidemment. . . . Je] [ellipsis indicates ¾ page omission; “ici je” follows on a question mark] (230-1)

— Philosophie de Locke. 4th ed. Paris: Didier, 1861.

note: there is no indication of the ed. used by JSM.

quoted: 770

770.12-13 “Tout . . . cause.”] Si à cette expérience trompeuse vous ajoutez le principe, que tout . . . cause, il vous faudra admettre dans la cause ce qui est dans l’effet, c’est-à-dire non-seulement de l’intelligence, de la sagesse et de la puissance, mais des imperfections dégradantes, comme a fait plus d’un peuple, sous la domination exclusive de l’expérience, et dans l’enfance de l’humanité. (395)

Crassus. Referred to: 941

note: the reference is in a quotation from Stephen.

Cromwell. Referred to: 778

Cuvier, Georges. Referred to: 119, 128 (1035), 523n

— Le Règne animal distribué d’après son organisation. 4 vols. Paris: Deterville, 1817.

note: the quotation at 139 is summary.

quoted: 139 (1044), 640

referred to: 656, 730

139.1-2 “Man . . . hands.”] Première ordre des mammifères./Les bimanes ou l’homme. (I, 81)

640.11 que ceux] que de ceux (I, 11) [Source as 51, 56, 62, 65; treated as typographical error]

640.12 que ceux] que de ceux (I, 11) [Source as 51, 56, 62, 65; treated as typographical error]

D’Alembert, Jean le Rond. Referred to: 800

— “Doutes et questions sur le calcul des probabilités,” in Melanges de littérature, d’histoire, et de philosophie. 4th ed. 5 vols. Amsterdam: Chatelain, 1767, V, 273-304.

note: the ed. of 1759 (4 vols. Amsterdam: Chatelain), which does not contain this essay, is in JSM’s library, Somerville College. The quotations are indirect; D’Alembert’s example is based on tossing a coin, not throwing dice. (Bowen, in his Lowell Lectures [see above], translates a French note from Dugald Stewart’s Dissertation on the Progress of Metaphysical, Ethical, and Political Philosophy, concerning an anecdote of Abbé Galiani citing the throwing of sixes with loaded dice; JSM must have known the passage, and may have unconsciously conflated the two. Curiously, though Bowen is citing the anecdote for its original purpose, i.e., to show that God has loaded Nature’s dice, he goes on to cite JSM on chance.)

quoted: 632-4, 637

Dalton. Referred to: 221 (1086), 375, 473

Darwin, Charles.On the Origin of Species by Means of Natural Selection, or the preservation of favoured races in the struggle for life. London: Murray, 1859.

note: a copy of the 1861 ed. was formerly in JSM’s library, Somerville College.

referred to: 498n-499n

Darwin, Erasmus.Zoonomia; or, the Laws of Organic Life. 3rd ed. 4 vols. London: Johnson, 1801.

note: this edition (which was in JSM’s possession) in the library of Somerville College, without the usual bookplate.

quoted: 769

769.24 metaphysics] metaphysic (I, 11) [treated as typographical error in 72]

769.27 a motion] or motion (I, 11)

769.28 sense.”] sense; which will be explained at large in another part of the work. (I, 12)

769.32-770.1 “our . . . sense.”] [sub-section] V. Another method of discovering that our . . . sense, is from considering the great analogy they bear to the motions of the larger muscles of the body. (I, 28; variants of the quoted passage occur frequently in Section III)

Davy. Referred to: 265, 479, 775

note: the reference at 775 is in a quotation from Coleridge.

Decandolle. See Candolle.

Democritus. Referred to: 786

De Morgan, Augustus.The Differential and Integral Calculus. London: Baldwin and Cradock, 1842.

note: the reference is to De Morgan’s “profound treatises” on algebra and calculus; see also his Elements of Algebra.

referred to: 615

— The Elements of Algebra Preliminary to the Differential Calculus. London: Taylor, 1835.

note: the reference is to De Morgan’s “profound treatises” on algebra and calculus; see also his Differential and Integral Calculus.

referred to: 615

— Formal Logic: or, The Calculus of Inference, Necessary and Probable. London: Taylor and Walton, 1847.

note: in JSM’s library, Somerville College, Oxford. The quotations at 592n and the second and third at 808n are indirect.

quoted: 143n, 171n, 173n, 207n, 239n, 592n, 808n; 1113referred to: 170n, 171n-173n

171.n22 “numerically definite propositions,”] A numerically definite proposition is of this kind. (142)

171.n23-4 “45 Xs . . . 70 Ys,” . . . “45 Xs . . . 70 Ys,”] Then an affirmative proposition of the sort in question is seen in ‘45 Xs . . . 70 Ys’: and a negative proposition in ‘45 Xs . . . 70 Ys.’ (142) [4-sentence footnote omitted]

173.n18 “numerically definite Syllogism,”] [see collation at 171.n22 above]

207.n5-6 Socrates . . . Socrates] Plato . . . Plato (259) [cf. JSM’s note to the passage]

1113.19 [see 207 above]

De Morgan, George Campbell.

note: for the identification of De Morgan as the “mathematical friend,” see LL, CW, XVI, 1084.

referred to: 599n-600n

Descartes, René. Referred to: 87, 222, 260 (1097), 263, 300n, 318, 364, 368, 368n, 490, 499, 752, 771-2, 813

note: the reference at 364 is in a quotation from the reviewer of Tulloch’s Theism; that at 368n is in a quotation from Fontenelle; that at 813 is an inaccurate version of the proof for the existence of God in Meditation III.

— Dissertatio de methodo. Amsterdam: Elzevir, 1677.

note: in JSM’s library, Somerville College, bound together with Meditationes. Against the passage quoted JSM has pencilled “non sequitur.”

quoted: 751

751.25-7 “Credidi me,” . . . “pro . . . esse;”] Et quia notabam, nihil plane contineri in his verbis, Ego cogito, ergo sum, quod me certum redderet eorum veritatis, nisi quod manifestissime viderem fieri non posse ut quis cogitet nisi existat, credidi, me pro . . . esse; et tantummodo difficultatem esse nonnullam, ad recte advertendum quidnam sit quod distincte percipimus. (21)

— Meditationes de prima philosophia. Amsterdam: Elzevir, 1654.

note: in JSM’s library, Somerville College, bound together with Principia Philosophiae. See also the note above, under Descartes, referring to 813.

quoted: 771

771.13-15 “Si . . . nihilo;”] Hinc autem sequitur nec posse aliquid a nihilo fieri, nec etiam id quod magis perfectum est, hoc est, quod plus realitatis in se continet, ab eo quod minus: atque hoc non modo perspicue verum est de iis effectibus quorum realitas est actualis sive formalis; sed etiam de ideis in quibus consideratur tantum realitas objectiva; hoc est non modo non potest, exempli causa, aliquis lapis qui prius non fuit, nunc incipere esse, nisi producatur ab aliqua re, in qua totum illud sit vel formaliter, vel eminenter quod ponitur in lapide; neo potest calor in subjectum quod prius non calebat induci, nisi a re quae sit ordinis saltem aeque perfecti atque est calor, & sic de caeteris; sed praeterea etiam non potest in me esse idea caloris, vel lapidis, nisi in me posita sit ab aliqua causa in qua tantundem ad minimum sit realitatis quantum esse in calore, vel lapide concipio: nam quamvis ista causa nihil de sua realitate actuali, sive formali in meam ideam transfundat, non ideo putandum est illam minus realem esse debere, sed talem esse naturam ipsius ideae, ut nullam aliam ex se realitatem formalem exigat praeter illam quam mutuatur a cogitatione mea cujus est modus; quod autem haec idea realitatem objectivam hanc vel illam contineat potius quam aliam, hoc profecto habere debet ab aliqua causa in qua tantumdem sit ad minimum realitatis formalis, quantum ipsa continet objectivae; si . . . nihilo; atqui quantumvis imperfectus sit iste essendi modus quo res est objective in intellectu per ideam, non tamen profecto plane nihil est, nec proinde a nihilo esse potest. (18-19)

Digby, Kenelm.A Late Discourse made in a solemne assembly of Nobles and Learned Men at Montpellier in France, touching the Cure of Wounds by the Powder of Sympathy; with instructions how to make the said powder; whereby many other secrets of nature are unfolded. Tr. R. White. 2nd ed. London: Lowndes, and Davies, 1658.

note: this is the ed. cited by Paris, from whom JSM takes the reference.

referred to: 779

Diogenes. Referred to: cxiii

Diogenes of Apollonia. Referred to: 365

Domitian. Referred to: 197 (1073)

Eldon. See Scott.

Elizabeth i (of England). Referred to: 602-3, 892

Ellis, Thomas Flower. “Whewell’s Mechanical Euclid—Principles of Mathematical Reasoning,” Edinburgh Review, LXVII (April, 1838), 81-102.

note: author identified in Walter E. Houghton, ed. The Wellesley Index to Victorian Periodicals, Vol. I (Toronto: University of Toronto Press, 1966), 485. There is no doubt that this is the article referred to (Whewell gives a precise reference), but JSM, in ascribing it to “a writer of great scientific eminence,” may have been misled by an article in Edinburgh Review, LXVI (Oct., 1837), 110-51, “Whewell’s History of the Inductive Sciences,” by David Brewster, who had more “scientific eminence” than Ellis.

referred to: 228n

Empedocles. Referred to: 365

Encke. Referred to: 426, 499

note: the reference at 426 is in a quotation from Herschel.

Epaminondas. Referred to: 941

Epicurus. Referred to: 49 (991)

Euclid. See Playfair, Elements of Geometry.

Euler, Leonhard.Elements of Algebra. Tr. M. Bernoulli. 2 vols. London: Johnson, 1797.

note: there is no indication of which of the many editions of Euler JSM used, and the quotation is indirect, but accurately gives the sense of Part I, Section I, Chap. i, Article 33.

quoted: 826

Faraday, Michael.Experimental Researches in Electricity. London: Taylor, 1839.

referred to: 411, 413, 477

— “On the Condensation of several Gases into Liquids.” In his Experimental Researches in Chemistry and Physics. London: Taylor and Francis, 1859, 89-95.

note: reprinted from Philosophical Transactions, 1823, 189ff.

referred to: 580

Ferguson, Adam. Referred to: 554

— Principles of Moral and Political Science; being chiefly a retrospect of lectures delivered in the College of Edinburgh. 2 vols. Edinburgh: Creech; London: Strahan and Cadell, 1792.

note: the opinion referred to is also in Ferguson’s Institutes of Moral Philosophy. Edinburgh: Kincaid and Bell, 1769, 63 (I, ii, 6).

referred to: 801

Ferrier, James F. Institutes of Metaphysic: The Theory of Knowing and Being. Edinburgh: Blackwood, 1854.

note: author’s gift copy in JSM’s library, Somerville College.

referred to: 63n

Fontenelle, Bernard le Bovier de. “Eloge de Monsieur Leibnitz,” in Oeuvres. New ed. 11 vols. Paris: Brunet, 1758-61, V, 492-57.

note: this ed. gives the same page reference as that given by JSM to the Paris ed. of 1767, which was not available; the Paris ed. of 1766 (10 vols. Paris: Libraires Associés), which has different pagination, is in his library, Somerville College; in it the “Eloge” is in V, 447-506.

quoted: 368n

368.n1 “les] “Les (534)

Fothergill. Referred to: 780

note: the reference is in a quotation from Paris.

Fourcroy. Referred to: 793n

note: the reference is in a quotation from Paris.

Frederick i (of Prussia). Referred to: 603

Fresnel. Referred to: 502

Gall. Referred to: 498n, 860

Geminus. Referred to: 498

note: the reference is in a quotation from Whewell.

Gilbert. Referred to: 498n

Glauber. Referred to: 428

note: the reference is in a quotation from Herschel.

Goethe, Johann Wolfgang von.Versuch die Metamorphose der Pflanzen. In Werke. Stuttgart: Cotta, 1828, III, 92ff.

note: this ed. in JSM’s library, Somerville College.

referred to: 523n

Graham, George John. Referred to: 816n

Graham, Thomas. “Liquid Diffusion applied to Analysis,” Philosophical Transactions of the Royal Society of London, CLI (1861), 183-224.

note: as JSM notes, reprinted in the Journal of the Chemical Society of London, XV (1862), 216-70. An offprint of the earlier version is in the University of London Library; this is probably the “pamphlet” JSM refers to at 475n. The paper also appears in Graham’s Chemical and Physical Researches (Edinburgh: Constable [for presentation only], 1876), 552-600. JSM gives 1862 rather than 1861 for its first publication (corrected in text above).

quoted: 475

referred to: 474-5

475.11-15 “while . . . insipid,” . . . “are . . . membrane,” . . . “it] [paragraph] While insipid. It may be questioned whether a colloid, when tasted, ever reaches the sentient extremities of the nerves of the palate, as the latter are . . . membrane, impermeable to soluble substances of the same physical constitution. [paragraph] It (220)

— “Notice of the Singular Inflation of a Bladder.” In his Chemical and Physical Researches. Edinburgh: Constable [for presentation only], 1876, 40-1.

note: reprinted from Quarterly Journal of Science, II (1829), 88-9.

referred to: 478

Grant, Horace.Arithmetic for Young Children. London: Charles Knight, 1835.

note: this book was reviewed by Mill in an unsigned article in The Globe and Traveller 23 October, 1835, p. 3.

referred to: 257n (1095n)

— Second Stage of Arithmetic. New ed. London, 1861.

note: the 1st ed. has not been located.

referred to: 257n

Grote, George.A History of Greece. 12 vols. London: Murray, 1846-56.

note: in JSM’s library, Somerville College.

referred to: 942

Grote, John.Exploratio Philosophica: Rough notes on modern intellectual science. Part I. Cambridge: Deighton, Bell, 1865.

note: in JSM’s library, Somerville College. Part II, edited by Joseph B. Mayor, was published posthumously in 1900.

referred to: 63n

Grove, William Robert.On the Correlation of Physical Forces: being the substance of a course of lectures delivered in the London Institution, 1843. London: London Institution, 1846.

note: the 3rd ed. (London: Longman, Brown, Green and Longman, 1855) is in JSM’s library, Somerville College.

referred to: 333n; 1120n, 1121n, 1122n

Guyton-Morveau. Referred to: 704

Haig, James.Philosophy; or, The Science of Truth. A Treatise on first principles, mental, physical, and verbal. London: Saunders, Otley, 1861.

referred to: 34n-35n

Hall. Referred to: 389

Haller. Referred to: 732n

Hamilton, William. Referred to: 63n, 206, 277-8

— Discussions on Philosophy and Literature, Education and University Reform, chiefly from the Edinburgh Review. 2nd ed. London: Longman, Brown, Green and Longmans; Edinburgh: Maclachlan and Stewart, 1853.

note: See also “On the Philosophy of the Unconditioned.” “New Analytic of Logical Forms” is the running title of App. II (A), pp. 650-75, the title of which is “Of Syllogism, Its Kinds, Canons, Notations, Etc.”; this is true also of the 1st ed., ibid., 1852, where the Appendix is briefer (pp. 614-20). Hamilton’s first publication of his prospectus for the “New Analytic” is in his ed. of Reid’s Works, II, 1-4. In quoting from the version in Discussions, 2nd ed., JSM at 172-3 omits the 1st, 16th, 17th, and 18th of the “results” of the statement previously quoted, and omits the numbers (2nd to 15th) of those he quotes. The quotation at 251n is of Leslie’s Rudiments of Plane Geometry, q.v. below.

quoted: 18n, 59, 59n-60n, 170n, 172-3, 251n, 276 referred to: 160n, 171n

18.n1 “To the] The exact distinction of subject and object was first made by the schoolmen; and to the (5n)

59.33 unknown.] unknown.* [3-sentence footnote omitted] (643-4)

59.n12 “It] Nor is this [that the philosopher is an ignorant admirer of the world of matter and mind] denied; for it (644)

60.n13 school.”] school; and, as has so frequently been done, to attribute any merit, or any singularity to its recognition by any individual thinker, more especially in modern times, betrays only the ignorance of the encomiasts. (644)

172.17 “Logically] From the consistent application of this postulate [To state explicitly what is thought implicitly], on which Logic ever insists, but which Logicians have never fairly obeyed, it follows:—that, logically, (650)

276.31 “There] And as the one or the other of contradictions must be true, whilst both cannot; it proves, that there (624)

276.33 “Things] But practically, the fact, that we are free, is given to us in the consciousness of an uncompromising law of duty, in the consciousness of our moral accountability; and this fact of liberty cannot be redargued on the ground that it is incomprehensible, for the philosophy of the Conditioned proves, against the necessitarian, that things (624)

— Lectures on Metaphysics and Logic. Ed. H. L. Mansel and J. Veitch. 4 vols. Edinburgh: Blackwood and Sons, 1859-60.

note: the “New Analytic of Logical Forms” (pp. 249-317), referred to at 171n, is a collection of fragments; see also Hamilton, Discussions, above.

quoted: 15n, 355-6 referred to: 171n, 817

15.n4 “the . . . Thought”] This last condition [that a form of thought be a law], likewise, enables us to give the most explicit enunciation of the object-matter of Logic, in saying that Logic is the science of the Laws of Thought as Thought, or the . . . Thought, or the science of the Laws of the Form of Thought; for all these are merely various expressions of the same thing. (III, 25-6)

355.31 “is] [paragraph] This reasoning, in so far as regards the mere empirical fact of our consciousness of causality, in the relation of our will as moving and of our limbs as moved, is (II, 391)

— “Note D: Distinction of the Primary and Secondary Qualities of Body,” in The Works of Thomas Reid. Ed. William Hamilton. Edinburgh: Maclachlan and Stewart; London: Longman, Brown, Green and Longmans, 1846, 825-75.

note: Hamilton is commenting on Whewell’s “Demonstration that all Matter is Heavy,” Transactions of the Cambridge Philosophical Society, VII.2; JSM takes his reference from Whewell’s reply in his Philosophy of Discovery. See also Hamilton’s Discussions, above.

quoted: 503n-504n

504.n1-2 “which,” . . . “we can neither denude of their . . . nor clothe] Nay, more; there are, in fact, obtruded on our observation a series of apparent fluids, (as Light or its vehicle, the Calorific, Electro-galvanic and Magnetic agents,) which, in our present state of knowledge, we can neither, on the one hand, denude of the . . . nor, on the other, clothe (854n)

— “On the Philosophy of the Unconditioned; in reference to Cousin’s Infinito-Absolute.” In Discussions, 1-38.

note: a review of Cousin’s Cours, reprinted from the Edinburgh Review, L (Oct., 1829), 194-221.

quoted: 734n referred to: 60n

Hartley, David. Referred to: 14 (967), 57 (993), 787n, 854

— Observations on Man, his Frame, his Duty, and his Expectations. 2 pts. London: Hitch and Austen, 1749.

note: in JSM’s library, Somerville College.

quoted: 560

560.16 “any] And as the false and imperfect Keys, which turn up to the Decypherer in his Researches, prepare the Way for the Discovery of the true and complete one, so any (I, 16)

560.16 which] that (I, 16) [cf. 560^l-l]

Hegel. Referred to: 60n, 101n

Helvétius. Referred to: 866, 1020

Heraclitus. Referred to: 365

Hermotimus. Referred to: 365

Herodotus. Tr. Henry Cary. London: Bohn, 1849.

note: this ed. used for ease of reference. Two Greek and Latin eds. (Glasgow: Foulis, 1761; and Edinburgh: Laing, 1806) formerly in JSM’s library, Somerville College.

referred to: 749

Herschel, John Frederick William. Referred to: cxiv, 341, 498n

note: for an elucidation of the reference at cxiv, see Textual Introduction, lxxx-lxxxi.

— Outlines of Astronomy. London: Longman, Brown, Green, and Longmans; and Taylor, 1849.

note: this is, in Herschel’s words, an “extension” and “improvement” of his Astronomy (London: Longman, Rees, Orme, Brown, Green, and Longman; and Taylor, 1833), which appeared as no. 43 of Dionysius Lardner’s Cabinet Cyclopaedia. The reference at 427n (added in 1865) is to the 7th “conclusion” of §570, which is not in the edition cited above, but is in the 5th ed. (London: Longman, Brown, Green, Longmans, and Roberts, 1858), 383-4.

quoted: 428 referred to: 427n

428.8 of residual phenomena] of what we have elsewhere termed residual phænomena*, [footnote:] *Discourse on the Study of Natural Philosophy. Cab. Cyclopædia, No. 14 (584)

428.9 kind. . . . It] kind, that is to say, of such portions of the numerical or quantitative results of observation as remain outstanding and unaccounted for after subducting and allowing for all that would result from the strict application of known principles. It (584)

— A Preliminary Discourse on the Study of Natural Philosophy. London: Longman, Rees, Orme, Brown, and Green, 1831.

note: Dionysius Lardner’s Cabinet Cyclopaedia, No. 14.

quoted: 250n-251n, 406, 414-17, 420, 426-8, 484n referred to: 284n

406.4-5 subjects,” . . . “have] subjects have (179)

414.10-12 “one . . . specimens” . . . “of . . . compass;”] [section] (168.) We have purposely selected this theory of dew, first developed by the late Dr. Wells, as one . . . specimens we can call to mind of . . . compass. (163)

414.15 “Suppose] [section] (163.) Let us now exemplify this inductive search for a cause by one general example: suppose (159)

414.16-17 place” . . . “We] place, we (159)

415.9-11 on.” . . . “all] on: all (159)

415.12 point,] point (Rule 2. §147.), (159)

415.14 “Is] [section] (164.) But, in the case of the night dew, is this a real cause—is (160)

415.16 But . . . the] But the analogies are cogent and unanimous; and, therefore, (pursuant to Rule 3. §148.) we are not to discard their indications; and, besides, the (160)

415.27 must collect] must, therefore, collect (160) [cf. 415^i-i]

415.30 cases,] cases (Rule 4. §150.), (160)

415.30 produced:”] produced. (160)

416.1 dewed.”] dewed; which last circumstance (by Rule 1. §146.) excludes [as in 416^l] (160)

416.20 obvious.] obvious (Rule 5. §152.). (161)

416.30 “But] [no paragraph] But (161)

416.31 with.] with (Rule 5. §152.) (161)

416.34-35 surface,” . . . “and] surface (Rule 7. §156.), and (161)

417.2 copiously.”] copiously: and thus we have detected another law of the same generality with the former, by a comparison of two classes of fact, one relating to dew, the other to the radiation of heat from surfaces. (161)

417.11 “Again] [no paragraph] Again (161)

417.15 velvet, wool] wool, velvet (161) [cf. 417^n-n]

417.16-22 dew.” . . . “are] dew: and these are (161)

417.25 within;”] within. (162)

420.7 “It] [section] (166.) Lastly, among the negative instances, (§150.) it (162) [this section follows immediately on the passage last quoted]

420.10 increasing. . . . Dew] increasing. [2-sentence omission] This is so much the case, that dew (162)

420.11-12 overcast.] overcast (Rule 4. §150.). (162)

426.23 “It] [no paragraph] It (156)

426.28 “For] [section] (159.) For (156)

426.35 reappearance,] reappearances (156)

427.2-3 resistance. [paragraph] M. Arago] resistance. [section] (160.) This 9th observation is of such importance in science, that we shall exemplify it by another instance or two. M. Arago (157)

427.21 “Unexpected] [section] (181.) Unexpected (171)

427.32 in great] in a great (171) [treated as typographical error]

427.39 “Many] [section] (161.) Many (158)

— “Quetelet on Probabilities,” in Essays from the Edinburgh and Quarterly Reviews, with Addresses and Other Pieces. London: Longman, Brown, Green, Longmans, & Roberts, 1857, 365-465.

note: reprinted from the Edinburgh Review, XCII (July, 1850), 1-57.

quoted: 203, 531

203.16-20 “a discovery,” having been anticipated by Berkeley, to be “one . . . Logic.” “When . . . winds,”] [paragraph] One . . . Logic—a step which may almost be termed a discovery when . . . winds—is that recently taken by Mr. Mill*, in showing that all reasoning (meaning thereby the investigation of truth as distinguished from the mere interpretation of a formula) is from particulars to particulars, and in thence assigning to general propositions their true character, and to the syllogism its true office. [footnote:] *System of Logic, 2nd ed. chap. iii., on the functions and logical value of the Syllogism. Perhaps Mr. Mill may be considered as only following out more emphatically the views originally taken by Berkeley on this subject, but which seem to have dropped so far out of notice as to give their revival all the force of novelty. (366-7)

531.n11 “that] The theory of Probabilities affords a ready and precise rule, applicable not only to this, but to far more intricate cases: it is this: that (395)

531.n13 individual aberrations,” or deviations, “shall] individual errors or aberrations from exactness which the observations imply, shall (395)

— “Whewell on the Inductive Sciences,” in Essays from the Edinburgh and Quarterly Reviews, with Addresses and Other Pieces. London: Longman, Brown, Green, Longmans, & Roberts, 1857, 142-256.

note: reprinted from the Quarterly Review, LXVIII (June, 1841), 177-238. The article is a review of Whewell’s History of the Inductive Sciences (1837) and his Philosophy of the Inductive Sciences (1840). For ease of reference the version in Essays, which does not differ in the passages quoted, except at 249.44, q.v., is cited in the collation.

quoted: 248n-250, 257n referred to: 344

248.n17 “The] And after all, the (198)

248.n18 axioms. . . . Let] axioms. The definitions we need not consider, but let (198)

248.n22 enunciation. . . . Those] enunciation. Of those which expressly relate to space, the axiom which declares magnitudes equal which exactly fill the same space, is clearly only a rule of interpretation declaring how the word equal is to be understood when space is the object of reference, and how the measurement of space is to be executed, and is only the ordinary practical process of measurement embodied in words. Those (199)

249.17 experience, . . . including] [ellipsis indicates 5⅓-page omission] (200, 206)

249.17-23 including . . . relations] [not in italics, except for “intuition” (23)] (206)

249.28 view. Let] view. As we conceive matter to have been created, and to admit of annihilation, we can of course conceive the non-existence of force, and if so, it certainly does appear a violent inroad on the liberty and power of thought to maintain that we may not, or cannot, conceive the laws of force to have been otherwise established than as we find them. But let (216)

249.44 exerted] excited (217) [exerted in original version in QR, 217]

249.50 its own half] [in italics] (217)

250.2 lever? The] lever? [paragraph] The (218)

250.4 weights . . . is] weights, is derived by Mr. Whewell, from the principle of reaction. [9-sentence omission in which Whewell is refuted] It is (218)

250.7 sustains it] sustains a body (219)

250.10 weights.’ . . . But] weights. Certainly no person, with clear mechanical conceptions, ever wanted such a trial to convince him of its truth, or thought the truth clearer after the trial had been made.” [paragraph] But (219)

250.17 “paradox . . . experience,”] [cited by Herschel from Whewell] (220)

250.19 truths expressible] truths (which we unconditionally admit) expressible (220)

250.26 locomotion. . . . There] [ellipsis indicates 1-paragraph omission] (220-1)

250.41 imagination. . . . All] imagination. If that sentiment be wanting, the picture is unfaithful: it is, in fact, no picture at all. It is, therefore, impracticable for us to frame any logically true and consistent proposition concerning such object, in which that sentiment is not at least implicitly involved, much less one in which it is explicitly contradicted. All (223)

250.42 if . . . axioms] if necessary axioms (223)

257.n9 “Number,” . . . “we] Number, therefore, we (205)

Hippasus. Referred to: 365

Hippo. Referred to: 359, 365

note: at 365 JSM uses the French form, Hippon.

Hobbes, Thomas. Referred to: 112n, 175 (1061), 827, 889

— Computatio sive logica. In Thomæ Hobbes Opera Philosophica quæ latine scripsit omnia. Ed. William Molesworth. 5 vols. London: Bohn, 1839-54, I, 1-80.

note: in JSM’s library, Somerville College. See also “Computation or Logic,” below.

quoted: 734

— “Computation or Logic,” Part I of Elements of Philosophy: The First Section, Concerning Body. In The English Works of Thomas Hobbes, I. Ed. William Molesworth. London: Bohn, 1839.

note: in JSM’s library, Somerville College. The references at 90-3 are all to iii, 2 (30-1). See also Computatio sive logica above.

quoted: 24, 95n, 96n, 96-7

referred to: 79, 90-3 (1010-12), 95 (1013), 99, 144 (1046), 176-7, 817; 1014, 1023n-1024n, 1028

24.1-5 “A . . . mind.”] [section 4] A . . . mind. (16)

24.5 had before] had, or had not before (16) [cf. JSM’s footnote to the passage]

24.15 “But] [section 5] But (17)

95.n13 “From] [paragraph] From (36)

95.n16 these] those (36)

96.n1 “Men] [section 1] “Men (55)

96.n2 cogitation. . . . Tacit] [ellipsis indicates 3-sentence omission] (55-6)

96.n2 sense.”] sense; and yet the deception proceeds neither from our senses, nor from the things we perceive; but from ourselves while we feign such things as are but mere images to be something more than images. (56)

96.22 “Abstract] For concrete is the name of any thing which we suppose to have a being, and is therefore called the subject, in Latin suppositum, and in Greek ὑποκέιμενον; as body, moveable, moved, figurate, a cubit high, hot, cold, like, equal, Appius, Lentulus, and the like; and, abstract (31-2)

96.23 name. . . . And] [ellipsis indicates 6½-sentence omission with concluding paragraph break]

97.1 accidents.”] accidents; I say accidents, not in that sense in which accident is opposed to necessary; but so, as being neither the things themselves, nor parts thereof, do nevertheless accompany the things in such manner, that (saving extension) they may all perish, and be destroyed, but can never be abstracted. (33)

— Leviathan, or the Matter, Form, and Power of a Commonwealth Ecclesiastical and Civil. In The English Works of Thomas Hobbes, III. Ed. William Molesworth. London: Bohn, 1839.

note: in JSM’s library, Somerville College.

referred to: 827

— “Physics, or the Phenomena of Nature,” Part IV of Elements of Philosophy: The First Section, Concerning Body. In The English Works of Thomas Hobbes, I. Ed. William Molesworth. London: Bohn, 1839.

note: in JSM’s library, Somerville College. JSM’s reference is vague, but the doctrine referred to is covered in the passage cited.

referred to: 101n

Hooke, Robert.Micrographia. London, 1665.

note: Mill, like most other philosophers (including Hume, and following Newton) attributes “experimentum crucis” to Bacon, whose term actually is “instantia crucis”; see Bacon’s Novum Organum, 294.

quoted: 254 (1093)

Hooker, Richard.Of the Laws of Ecclesiastical Polity. Book VIII, ed. Raymond Aaron Houk. New York: Columbia University Press, 1931.

note: as no edition is cited, none is in JSM’s library, and Book VIII is usually omitted in editions of Hooker, this modern ed. is cited for ease of reference.

quoted: 796

796.28 “As] [section] 1. First, as (280)

796.30 immovable] unmoveable (280)

Hooker, William Jackson.The British Flora; comprising the Phænogamous, or Flowering Plants, and the Ferns. London: Longman, Rees, Orme, Brown, and Green, 1830.

note: the quotation is in a quotation from Whewell’s History of Scientific Ideas, where Whewell refers to this ed.

quoted: 701

701.8 spinuloso-serrate.’] spinuloso-serrate, involucres axillary solitary ovate inflated quite entire, rachis only slightly margined towards the extremity. (450)

Hume, David. Referred to: 457, 769; 1119

— An Inquiry Concerning Human Understanding, in Essays and Treatises on Several Subjects. 2 vols. Edinburgh: Cadell, 1793, II.

note: in JSM’s library, Somerville College. Until 1758 entitled Philosophical Essays Concerning Human Understanding. Another copy of Hume’s Essays, annotated by JSM, was bought from the Avignon bookseller, Romanille, in March, 1906, by the American novelist Thomas Nelson Page; its present location is unknown. The reference at 838 is to Section VII, “Of the Idea of Necessary Connection,” II, 74-93; that at 852 is to Section II, “Of the Origin of Ideas,” II, 30-5; the remainder are to Section X, “Of Miracles,” II, 124-47.

referred to: 623, 625, 627, 630-1, 838, 852; 1151

Hutton, R. H. “Mill and Whewell on the Logic of Induction,” Prospective Review, VI (Feb., 1850), 77-111.

note: a review of the 2nd ed. (1849) of the Logic, and Whewell’s Of Induction; with especial reference to Mr. John Stuart Mill’s System of Logic (1849).

quoted: 331n-333n, 354, 359-60, 541, 541n-542n

referred to: 629n, 664n

331.n5 “we] But to take Mr. Mill on his own ground: even in external nature, we (104)

331.n9-13 “every . . . feel” . . . “allurement . . . surprise.”] So, too, every . . . feel Mr. Mill’s example, that “the cause of a surprise was the sentinel’s being off his post,” [see 330^p-pabove] as incorrect; the allurement . . . surprise: but by common consent “cause” is always reserved for the active element, or the prominently active element, in producing an effect; and in matters of personal causation, mental or physical, where the consciousness of effort comes home, no one ever misapplies the term to the passive conditions; no one calls the cause [see entry for 332.n22-6 below] . . . necessary to . . . it (which . . . condition); there is quite enough consent amongst men in their employment of the term, to prove that it does denote a distinct element, the active element in the production of phenomena; and its misapplication in physical nature is easily accounted for by the impossibility of being able to perceive or understand the active element in processes quite external to our own consciousness. (105-6)

332.n22-6 “call the cause . . . necessary for . . . it, which . . . condition.”] [see entry for 331.n9-13 above] (106)

333.32 “there] Such cases are unfair, and only complicate the question; that we do really reserve the word and the idea “cause” for active force, wherever that element can be detected and separated, is clear enough; the reason that in physical science this is so difficult to do, is, that all matter is probably resolvable into force, so that there is no phenomenon physically caused which is not the result of conflicting forces, and we can only select the one whose tendency is most obvious to produce the phenomenon; but there (105)

333.n34 arrested] corrected (105)

354.19 “It] To us, indeed, it (87)

354.20 creation. We] creation, as we (87)

354.22 mind.”] mind: we know the kind of reply that Mr. Mill would make to such a notion; we know that he would say in his majestic, judicial way—“Inquiries of this kind have no relation to Logic; they belong to the science of transcendental Metaphysics; but I must renew my protest against adducing as proof of a fact in external nature, any necessity which the human mind may be conceived to be under, of believing in it.” (87)

359.8 “Their] But their (108)

359.9 conviction.’ . . . They] conviction. Accustomed to the inductions of mental science,—where no cause could even be suggested that did not contain something capable of deduction into a very similar effect, where the probability of a suggestion was seen even before it could be thrown out at all, and the mind knew before it began its search what kind of cause it must look for,—they looked out for the same kind of evidence for a physical cause before they even thought of trying it, and expected to find some evidence in a mental comparison, although neither the operation of the cause nor the nature of the effect were accessible to their consciousness: they (108-9)

359.10 only their] only to know their (109)

359.12 feel after] feel often (109)

359.14 mind. . . . They] mind, as the suggestion of mental causes for mental effects were [sic] accustomed to do. They (109)

360.10-12 “wanted . . . consequent,” . . . “which . . . mind.”] [see 359.13-15]

541.8 “what] To take then the simplest case first; what (100)

541.12 conditions] conditions* [footnote:] *We do not say “causes” for reasons we shall afterwards give. But if the word “cause” be used generally, to include all the conditions, it would not be incorrect. (100)

541.9 it. . . . After] [ellipsis indicates the omission of 2½ sentences, with a footnote] (101-2)

542.n4 future?”] [½-page footnote, partly quoted at 542n7, here omitted] (102)

542.n7 “would . . . erroneous,” and “is] Besides this, Mr. Mill’s method (see Vol. II. c. xviii, p. 78 [2nd ed.], of obtaining the chance, by comparing the cases in which the event occurs, and those in which it does not occur, and regarding the numbers so found as the ratio of the chances of success and failure, would . . . erroneous. It is (102n-103n)

542.n11 “would] This would (103n)

Huygens. Referred to: 799

Iphicrates. Referred to: 941

Jesus. Referred to: 938

Johnson, Samuel. Referred to: 5n, 829 (see Boswell, Life of Johnson)

— The History of Rasselas, Prince of Abissinia. In The Works of Samuel Johnson. London: Buckland, Rivington, et al., 1787, XI, 1-144.

quoted: 26

26.29 “The] [paragraph] The (1)

26.30 princes,”] princes, was a spacious valley in the kingdom of Amhara, surrounded on every side by mountains, of which the summits overhang the middle part. (2)

Jussieu. Referred to: 732

Kant. Referred to: 14 (967), 59 (994), 60n, 116n, 830

Kepler. Referred to: 292-8, 300n, 302, 303-4, 317, 342-3, 461, 490, 492, 494-5, 517, 647-8, 651-2, 798, 863, 872

note: the reference at 300n is in a quotation from Whewell.

Knight, Richard Payne.An Analytical Inquiry into the Principles of Taste. London: Payne, and White, 1805.

note: JSM takes the reference from Stewart.

referred to: 676

Koran. Referred to: 186

Lambert, Johann Heinrich.Neues Organon, oder Gedanken über die Erforschung und Bezeichnung des Wahren und dessen Unterscheidung vom Inthum und Schein. Leipzig: Wendler, 1764.

quoted: 170n

170.n1-4 “The . . . genus”] [translated and adapted from] (1) Die erste Figur eignet der Sache zu, was wir von ihrer Eigenschaft wissen. Sie schliesst von der Gattung auf die Art. (2) Die zweyte Figur führt auf die Unterscheid der Dinge, und hebt die Verwirrung in den Begriffen auf. (3) Die dritte Figur giebt Beispiele und Ausnahmen a [sic] Sätzen, die allgemein scheinen. (4) Die vierte Figur findet Arten zu der Gattung in Baralip und Dibatis. Sie zeigt, dass die Art die Gattung nicht erschöpfe, in Fesapo und Fresison; und läugnet die Gattung von dem, was von dem, was von der Gattung geläugnet wird, in Calentes. (138-9)

Laplace, Pierre Simon de. Referred to: 427

note: the reference is in a quotation from Herschel.

— Essai philosophique sur les probabilités. 5th ed. Paris: Bachelier, 1825.

quoted: 534, 543; 1140-1, 1145referred to: 546, 553, 630n, 634-8; 1142-3, 1146-7, 1149, 1151-3

534.2-17 “Probability . . . possible.”] [translated from:] La probabilité est relative en partie à cette ignorance, en partie à nos connaissances. Nous savons que sur trois ou un plus grand nombre d’évènemens, un seul doit arriver; mais rien ne porte à croire que l’un d’eux arrivera plutôt que les autres. Dans cet état d’indécision, il nous est impossible de prononcer avec certitude sur leur arrivée. Il est cependant probable qu’un de ces évènemens pris à volunté, n’arrivera pas; parce que nous voyons plusieurs cas également possible qui excluent son existence, tandis qu’un seul la favorise.

La théorie des hasards consiste à réduire tous les évènemens du même genre, à un certain nombre de cas également possibles, c’est-à-dire, tels que nous soyons également indécis sur leur existance; et à déterminer le nombre de cas favorables à l’évènement dont on cherche la probabilité. Le rapport de ce nombre à celui de tous les cas possibles, est la mesure de cette probabilité que n’est ainsi qu’une fraction dont le numérateur est le nombre des cas favorables, et dont le dénominateur est le nombre de tous les cas possibles. (7)

543.10-11 “fundamental . . . causes.”] [translated from:] C’est le principe fondamental de cette branche de l’Analyse des hasards, qui consiste à remonter des évènemens aux causes. (18-19)

— Exposition du systême du monde. 2 vols. Paris: Cercle-Social, 1796.

referred to: 507-8, 508n, 517n

Lavoisier. Referred to: 441, 704

Leibniz, Gottfried Wilhelm.

note: the quotation at 368 has not been located. JSM’s invariable spelling, Leibnitz, perhaps points to his use of French texts.

quoted: 368 referred to: 87, 95 (1013), 364, 367-9, 752, 758n, 771

— Esprit de Leibnitz, ou Recueil de pensées choisies, sur la religion, la morale, les langues, l’histoire, &c. 2 vols. Lyons: Bruyset, 1772.

note: this edition is the only Leibniz now in JSM’s library, Somerville College; the volumes are (for JSM) heavily annotated on the back fly leaves, where, in Vol. II, there is the following reference to the passage here cited: “508 Motion only produced by motion”.

referred to: 767

— Nouveaux essais sur l’entendement humain. In Oeuvres de Leibnitz. New ed. 2 vols. Ed. A. Jacques. Paris: Charpentier, 1846.

note: JSM’s reference, which antedates this ed., is to the Paris ed. of 1842, which was not available; his reference is therefore left in the text, with the 1846 reference added.

quoted: 756

756.1 “Je] [paragraph] Sur tout cela je remarquerai, avant que de venir à l’explication de mon opinion, qu’il est sûr que la matière est aussi peu capable de produire machinalement du sentiment que de produire de la raison, comme notre auteur en demeure d’accord; qu’à la vérité je (I, 79)

756.3 ce que] ce qui (I, 79)

756.4 aussi . . . qu’enfin] aussi que les substances (matérielles ou immatérielles) ne sauraient être conçues dans leur essence nue sans activité; que l’activité est de l’essence de la substance en général, et qu’enfin (I, 79)

— Opera Omnia. Ed. L. Dutens. 6 vols. Geneva: Fratres de Tournes, 1768.

referred to: 360

quoted: 239n

239.n11 “Tout] J’ai fait voir autrefois à Mr. Bayle, que tout (III, 446)

Leonidas. Referred to: 333n

Leslie, John.The Philosophy of Arithmetic; exhibiting a progressive view of the theory and practice of calculation. Edinburgh: Constable; London: Longman, Hurst, Rees, Orme, and Brown, 1817.

referred to: 257n (1095n)

— Rudiments of Plane Geometry, including Geometrical Analysis and Plane Trigonometry. Edinburgh: Oliver and Boyd, 1828.

note: JSM is following Hamilton’s quotation from Leslie.

quoted: 251

Liebig, Justus von. Referred to: 479

— Animal Chemistry, or Organic Chemistry in its Applications to Physiology and Pathology. Ed. William Gregory. London: Taylor and Walton, 1842.

note: JSM probably used this ed., though a 2nd ed. appeared (ibid.), in 1843.

referred to:1136-8

— Organic Chemistry in its Applications to Agriculture and Physiology. Ed. Lyon Playfair. London: Taylor and Walton, 1840.

note: the wording of the quotation at 408 identifies this as the ed. used by JSM; revised 2nd (1842) and 3rd eds. (1843) were issued by Taylor and Walton, with “Organic” deleted from the title-page, and with “Application” substituted for “Applications” in the 2nd. The work corresponds to the lengthy “Introduction” in Vol. I of Liebig’s Traité de chimie organique (3 vols. Ed. Charles Gerhardt. Paris: Fortin, Massin, 1841-44), which JSM may also have seen.

quoted: 408; 1132, 1133, 1134referred to: 220, 407-10, 475-6; 1132-6, 1138-9

408.23 “many] Many (338)

1132.23-5 “be . . . light.”] Platinum, for example, does not decompose nitric acid; it may be . . . light (black spongy platinum). (220-1)

1133.3 “copper] [paragraph] Copper (221)

1133.23 “No] [paragraph] Now no (225) [cf. 1133^d-d]

Lindley, John.An Introduction to the Natural System of Botany: or, A Systematic view of the organisation, natural affinities, and geographical distribution of the whole vegetable kingdom. London: Longman, Rees, Orme, Brown, and Green, 1830.

note: in JSM’s library, Somerville College. The reference is in a quotation from Whewell.

referred to: 717

Linnæus. Referred to: 129 (1037), 700, 705, 713, 725, 732

note: the reference at 700 is in a quotation from Decandolle; that at 725 is in a quotation from Whewell.

Locke, John. Referred to: 14 (967), 29 (976), 57 (993), 59 (994), 87, 110 (1017), 112, 175 (1061), 305, 606, 649, 769, 770, 822-3; 1119

— Essay Concerning Human Understanding. In Works. New ed. 10 vols. London: Tegg, Sharpe, Offor, Robinson, and Evans, 1823, I-III.

note: in JSM’s library, Somerville College.