The Online Library of Liberty

A project of Liberty Fund, Inc.

• Introduction
• Textual Introduction
• Preface to the Third Edition[*]
• Chapter I: Introductory Remarks
• Chapter II: The Relativity of Human Knowledge
• Chapter III: The Doctrine of the Relativity of Human Knowledge, As Held By Sir William Hamilton
• Chapter IV: In What Respect Sir William Hamilton Really Differs From the Philosophers of the Absolute
• Chapter V: What Is Rejected As Knowledge By Sir William Hamilton, Brought Back Under the Name of Belief
• Chapter VI: The Philosophy of the Conditioned
• Chapter VII: The Philosophy of the Conditioned, As Applied By Mr. Mansel to the Limits of Religious Thought
• Chapter VIII: Of Consciousness, As Understood By Sir William Hamilton
• Chapter IX: Of the Interpretation of Consciousness
• Chapter X: Sir William Hamilton’s View of the Different Theories Respecting the Belief In an External World
• Chapter XI: The Psychological Theory of the Belief In an External World
• Chapter XII: The Psychological Theory of the Belief In Matter, How Far Applicable to Mind
• Chapter XIII: The Psychological Theory of the Primary Qualities of Matter
• Chapter XIV: How Sir William Hamilton and Mr. Mansel Dispose of the Law of Inseparable Association
• Chapter XV: Sir William Hamilton’s Doctrine of Unconscious Mental Modifications
• Chapter XVI: Sir William Hamilton’s Theory of Causation
• Chapter XVII: The Doctrine of Concepts, Or General Notions
• Chapter XVIII: Of Judgment
• Chapter XIX: Of Reasoning
• Chapter XX: On Sir William Hamilton’s Conception of Logic As a Science. Is Logic the Science of the Laws, Or Forms, of Thought?
• Chapter XXI: The Fundamental Laws of Thought According to Sir William Hamilton
• Chapter XXII: Of Sir William Hamilton’s Supposed Improvements In Formal Logic
• Chapter XXIII: Of Some Minor Peculiarities of Doctrine In Sir William Hamilton’s View of Formal Logic
• Chapter XXIV: Of Some Natural Prejudices Countenanced By Sir William Hamilton, and Some Fallacies Which He Considers Insoluble
• Chapter XXV: Sir William Hamilton’s Theory of Pleasure and Pain
• Chapter XXVI: On the Freedom of the Will
• Chapter XXVII: Sir William Hamilton’s Opinions On the Study of Mathematics
• Chapter XXVIII: Concluding Remarks
• Appendices
• Appendix A: Manuscript Fragments
• Appendix B: Textual Emendations
• Appendix C: Corrected References
• Appendix D: Bibliographic Index of Persons and Works Cited In the Examination, With Variants and Notes

CHAPTER XXII

Of Sir William Hamilton’s Supposed Improvements in Formal Logic

of all Sir W. Hamilton’s philosophical achievements, there is none, except perhaps his “Philosophy of the Conditioned,” on account of which so much merit has been claimed for him, as the additions and corrections which he is supposed to have contributed to the doctrine of the Syllogism. These may be summed up in two principal theories, with their numerous corollaries and applications; the recognition of two kinds of Syllogism, Syllogisms in Extension and Syllogisms in Comprehension; and the doctrine of the Quantification of the Predicate. To the former of these, Sir W. Hamilton ascribed great importance. According to him, all previous logicians, “with the doubtful exception of Aristotle,” “have altogether overlooked the reasoning in Comprehension”—“have marvellously overlooked one, and that the simplest and most natural of these descriptions of reasoning,—the reasoning in the quantity of comprehension:” and he claims, in directing attention to it, to have “relieved a radical defect and vital inconsistency in the present logical system.”^* For the other theory, that of the Quantification of the Predicate, still loftier claims are advanced both by himself and by others. Mr. Baynes, with an enthusiasm natural and not ungraceful in a pupil, concludes his Essay on the subject (which still remains the clearest exposition of his master’s doctrine) with the following words:

Previous to discussing these additions to the Syllogistic Theory, it is necessary to revert to a doctrine which has been briefly stated in a former chapter,^[*] but did not then receive all the elucidation it requires, and which has a most important bearing on both of Sir W. Hamilton’s supposed discoveries. This is, that all Judgments (except where both the terms are proper names) are really judgments in Comprehension; though it is customary, and the natural tendency of the mind, to express most of them in terms of Extension. In other words, we never really predicate anything but attributes, though, in the usage of language, we commonly predicate them by means of words which are names of concrete objects.

When, for example, I say, The sky is blue; my meaning, and my whole meaning, is that the sky has that particular colour. I am not thinking of the class blue, as regards extension, at all. I am not caring, nor necessarily knowing, what blue things there are, or if there is any blue thing except the sky. I am thinking only of the sensation of blue, and am judging that the sky produces this sensation in my sensitive faculty; or (to express the meaning in technical language) that the quality answering to the sensation of blue, or the power of exciting the sensation of blue, is an attribute of the sky. When again I say, All oxen ruminate, I have nothing to do with the predicate, considered in extension. I may know, or be ignorant, that there are other ruminating animals besides oxen. Whether I do or do not know it, it does not, unless by mere accident, pass through my mind. In judging that oxen ruminate, I do not, unless accidentally, think under the notion ruminate (to borrow Sir W. Hamilton’s phraseology) any other notion than that of an ox. The Comprehension of the predicate—the attribute or set of attributes signified by it—are all that I have in my mind; and the relation of this attribute or these attributes to the subject, is the entire matter of the judgment.

In one of the examples above given, the predicate is an adjective, and in the other a verb, which, in a logical point of view, is classed with adjectives: but its being a noun substantive makes no difference. For reasons easily shown, a substantive is more strongly associated with the ideas of the concrete objects denoted by it, than an adjective or a verb is. But when we predicate a substantive—when we say, Philip is a man, or, A ^aherring^a is a fish—do the words man and fish signify anything to us but the bundles of attributes connoted by them? Do the propositions mean anything except that Philip has the human attributes, and a ^bherring^b the piscine ones? Assuredly not. Any notion of a multitude of other men, among whom Philip is ranked, or a variety of fishes besides ^cherrings^c , is foreign to the proposition. The proposition does not decide whether there is this additional quantity or no. It affirms the attributes of its own particular subject, and of no other.

Passing now from the predicate to the subject, we shall find that the subject also, if a general term or notion, is always construed in Comprehension, that is, by the attributes which constitute it, and has no other meaning in thought. When I judge that all oxen ruminate, what do I mean by all oxen? I have no image in my mind of all oxen. I do not, nor ever shall, know all of them, and I am not thinking even of all those I do know. “All oxen,” in my thoughts, does not mean particular animals—it means the objects, whatever they may be, that have the attributes by which oxen are recognised, and which compose the notion of an ox. Wherever these attributes shall be found, there, as I judge, the attribute of ruminating will be found also: that is the entire purport of the judgment. Its meaning is a meaning in attributes, and nothing else. It supposes subjects, but merely as all attributes suppose them.

But there is another mode of interpreting the same proposition, by considering it as ^da^d part of the statement of a classification and mental co-ordination of the objects which exist in nature. The proposition is then looked upon as an assertion respecting given objects; affirming what other individual objects they are classed among by the general scheme of human language. Thus interpreted, the proposition “all oxen ruminate” may be read as follows: If all creatures that ruminate were collected in a vast plain, and I were required to search the world and point out all oxen, they would all be found among the crowd on that plain, and none anywhere else. Moreover, this would have been the case in all past time, and will at any future, while the present order of nature lasts. This is the proposition “All oxen ruminate” interpreted in Extension. Will any one say that a process of thought like this passes in the mind of whoever makes the affirmation? It is a point of view in which the proposition may be regarded; it is one of the aspects of the fact asserted in the proposition. But it is not the aspect in which the proposition presents it to the mind.

It will, however, very naturally be objected—If the meaning in our mind is that the bovine attributes are always accompanied by the attribute of ruminating, why do we, except for the purposes of abstract logic or metaphysics, never say this, but always say “All oxen ruminate?” The reason is, that we have no other convenient and compact mode of speaking. Most attributes, and nearly all large “bundles of attributes,” have no names of their own. We can only name them by a circumlocution. We are accustomed to speak of attributes not by names given to themselves, but by means of the names which they give to the objects they are attributes of. We do not talk of the phænomena which accompany piscinity; we talk of the phænomena of fishes. We do not frame a definition of piscinity, but a definition of a fish. The definition, however, of a fish is exactly the same which the definition of piscinity would be; it is an enumeration of the same attributes. Language is constructed upon the principle of naming concrete objects first: it does not always name abstractions at all, and when it does, the names are almost always derived from those of concrete objects. The reasons are obvious. Objects—even classes of objects—being conceivable by a much less effort of abstraction than attributes, are in the necessary order of things conceived and named earlier, and remain always more familiar to the mind: attributes, even when they come to be conceived, cannot be conceived in a detached state, but are always (as may be said by an adaptation of the Hamiltonian phraseology) thought through objects of some sort. Consequently all familiar propositions are expressed in the language which denotes objects, and not in that which denotes attributes. Nor is this all. What is primarily important to us in our sensations and impressions, is their permanent groups. In our particular and passing sensations (unless in cases of exceptional intensity) the important thing to us is, not the sensation itself, but to what group it belongs; what concrete object, what Permanent Possibility of Sensation, it indicates the presence of. The mind consequently hurries on from the sensible impressions that proceed from an outward object, to the object itself, and its subsequent thoughts revolve round that. It is on the concrete object indicated, that the expectation of future sensations depends; and the concrete object, consequently, in most cases, exclusively engages our thoughts, and stimulates us to mark it by a name. The name, to answer its purpose, must remind ourselves, and inform others, of the sensations we or they have to expect: that is, it must connote an attribute, or set of attributes. And men did not at first name attributes in any other than this indirect manner. They gave no direct names to attributes, because they did not conceive attributes as having any separate existence. As they began by naming only concrete objects, so the first names by which they expressed even the results of abstraction, were not names of attributes in the abstract, regarded apart from their objects, but names of concrete objects signifying the presence of the attributes. Men talked of blue, or of blue things, before they talked of blueness. Even when they did talk of blueness, it was originally not as the attribute, but as an imaginary cause of the attribute, which cause they figured to themselves as itself a concrete thing, residing in the object.

It thus appears that though all judgments consist in ascribing attributes, the original and natural mode of expressing them was by general names denoting concrete objects, and only connoting attributes; and by the structure of language this remains the only concise mode, and the only one which, addressing itself to familiar associations, conveys the meaning at once, to minds not exercised in metaphysical abstraction. But this does not alter the obvious truth, that concrete objects are only known by attributes, are only distinguished by attributes, and that the concrete names by which we speak of them mean nothing but attributes, or “bundles of attributes.” Our representation in thought of a concrete object is but a representation of attributes, and our concept of a class of concrete objects is but a certain portion of those attributes, not, indeed, separately conceived or imaged, but exclusively attended to. There is, therefore, nothing in our mind when we affirm a general proposition, but attributes, and their coexistence or repugnance: and the position is made out, that all judgments, expressed by means of general terms, are judgments in Comprehension, though always, unless for some special purpose, expressed in Extension.

If this be the true doctrine of Judgments, what is meant by saying that there are two sorts of Judgment, one in Extension, the other in Comprehension, and two kinds of reasoning corresponding to these, one of which, that in Comprehension, had been overlooked by all logicians, except possibly Aristotle, up to the time of Sir W. Hamilton? All our ordinary judgments are in Comprehension only, Extension not being thought of. But we may, if we please, make the Extension of our general terms an express object of thought, and this may be called thinking in Extension, though it is rather thinking about Extension. When I judge that all oxen ruminate, I have nothing in my thoughts but the attributes and their coexistence. But when, by reflection, I perceive what the proposition implies, I remark, that other things may ruminate besides oxen; and that the unknown multitude of things which ruminate form a mass, with which the unknown multitude of things having the attributes of oxen is either identical, or is wholly comprised in it. Which of these two is the truth I may not know, and if I did, took no notice of it when I assented to the proposition “all oxen ruminate.” But I perceive, on consideration, that one or other of them must be true. Though I had not this in my mind when I affirmed that all oxen ruminate, I can have it now; I can make the concrete objects denoted by each of the two names an object of thought, as a collective though indefinite aggregate; in other words, I can make the Extension of the names (or notions) an object of direct consciousness. When I do this, I perceive that this operation introduces no new fact, but is only a different mode of contemplating the very fact which I had previously expressed by the words “all oxen ruminate.” The fact is the same, but the mode of contemplating it is different: the mental operation, the act of thought, is not only a distinct act, but an act of a different kind.

There is thus, in all propositions (save those in which both terms are Proper, that is, in significant, names) a judgment concerning attributes (called by Sir W. Hamilton a judgment in Comprehension), which we make as a matter of course, and a possible judgment in or concerning Extension, which we may make, and which will be true if the former is true. Nevertheless (as has just been shown), the conditions of primitive thought, and subsequent convenience, cause us generally to enunciate our propositions in terms appropriate to the derivative judgment which we seldom make, rather than to the primitive judgment which we always make. And this explains why, though the meaning of all propositions in which general terms are used is in Comprehension, writers on logic always explain the rules of the Syllogism in reference to Extension alone. It is because the framers of the rules did not concern themselves with propositions or reasonings as they exist in thought, but only as they are expressed in language. And in this they were justified. For the syllogism is not the form in which we necessarily reason, but a test of reasoning: a form into which we may translate any reasoning, with the effect of exposing all the points at which any unwarranted inference can have got in. According to this view of the Syllogism—for the justification of which I must refer to the Second Book of my System of Logic^[*] —the syllogistic theory is only concerned with providing forms suitable to test the validity of inferences; and it was not necessary that the forms in which reasoning was directed to be written, should be those in which it is carried on in thought, so long as they are practically equivalent, that is, so long as the propositions in words are always true or false according as the judgments in thought are so. The propositions in Extension, being, in this sense, exactly equivalent to the judgments in Comprehension, served quite as well to ground forms of ratiocination upon: and as the validity of the forms was more easily and conveniently shown through the concrete conception of comparing classes of objects, than through the abstract one of recognising coexistence of attributes, logicians were perfectly justified in taking the course, which, in any case, the established forms of language would doubtless have forced upon them. They are thus deserving of no blame, though their mode of proceeding has been attended with some practical mischief, by diverting the attention of thinkers from what really constitutes the meaning of Propositions. It has also been one of the causes of the prejudice so general in the last three centuries, against the syllogistic theory. For a doctrine which defined one of the two great processes of the discovery of truth as consisting in the operation of placing objects in a class and then finding them there, can never, I think, have really satisfied any competent thinker, however he may have acquiesced in it for want of a better. There must always have been a dormant sense of discontent, an obscure feeling that this was a description of the reasoning process by one of its accidents, though an inseparable accident.^*

Sir W. Hamilton distinguishes two kinds of Syllogism, Extensive and Comprehensive.

He acknowledges, however, that both syllogisms are identically the same argument; “every syllogism in the one quantity being convertible into a syllogism absolutely equivalent in the other quantity.”^* And what is the difference in form and language between the two syllogisms? According to our author it is merely a difference in the order of the premises. The following,

• “Every morally responsible agent is a free agent;
• Man is a morally responsible agent;
• Therefore man is a free agent,”^†

is, according to him, a syllogism in Extension. Transpose the premises, and write it thus,

• “Man is a responsible agent;
• But a responsible agent is a free agent;
• Therefore, man is a free agent,”^‡

and we have, according to him, a syllogism in Comprehension. Far, however, from constituting two kinds of reasoning, this does not even supply us with two different forms of it. He himself says elsewhere, that “the transposition of the propositions of a syllogism affords no modifications of form yielding more than a superficial character.”^§ And even this superficial difference he with his own hands abolishes, saying, that any syllogism whatever “can be perspicuously expressed not only by the normal, but by any of the five consecutions of its propositions which deviate from the regular order,” and that “a syllogism in Comprehension is equally susceptible of a transposition of its propositions as a syllogism in Extension.”^¶ So that the slight distinction of form which he seemed at first to contend for, does not exist; a Syllogism in Comprehension, and the corresponding Syllogism in Extension, are word for word the same. Instead of “every syllogism in the one quantity” being “convertible into a syllogism absolutely equivalent in the other quantity,” every syllogism is already a syllogism in both quantities.^∥

The distinction, therefore, is not between two kinds, or even between two forms, of syllogism, but between two modes of construing the meaning of the same syllogism. And what are these two modes? Sir W. Hamilton says, that they are distinguished by a difference in the meaning of the copula.

I cannot admit this to be a true analysis of the meaning of the proposition, either in Extension or in Comprehension. The statement that God is merciful I construe as an affirmation not concerning the notion God, but the Being God. Interpreted in Comprehension I hold it to mean, that this Being has the attribute signified by the word merciful, or, in our author’s language, comprehended in the concept. Interpreted in Extension I render it thus: The Being, God, is either the only being, or one of the beings, forming the class merciful, or, in other words, possessing the attribute mercifulness. Thus stated, who can doubt which of the two is the original and natural judgment, and which is a derivative and artificial mode of restating it? The difference between them is slight, but real, and consists in this, that the second construction introduces the idea of other possible merciful beings, an idea not suggested by the first construction. This suggestion gives rise to the idea of a class merciful, and of God as a member of that class: notions which are not present to the mind at all when it simply assents to the proposition that God is merciful. To make a distinction between Reasoning in Extension and in Comprehension, when the same syllogism serves for both, could only be admissible if we employed the same words having sometimes in our mind the meaning in Extension, sometimes that in Comprehension: but in reality all reasoning is thought solely in Comprehension, except when we, for a technical purpose, perform a second act of thought upon the Extension—which in general we do not, and have no need to, consider.

Nor is this the only objection to Sir W. Hamilton’s doctrine. There is another, less obvious, but equally fatal. The statement in Comprehension is, that A has the attributes comprehended in B. The statement in Extension is, that A belongs to the class of things which have the attributes comprehended in B. These statements are either, as I affirm them to be, one and the same assertion in slightly different words, or they are different assertions. If they are the same assertion, there is but one judgment, which is both in Extension and in Comprehension, and but one kind of reasoning, which is in both. But supposing them, for the sake of argument, to be two different assertions, the judgment respecting Extension is a corollary from that in Comprehension, expressing an artificial point of view in which we may regard the natural judgment. Now, on this supposition, that the judgment respecting Extension is not the same, but an additional judgment, it is, like all other judgments, a judgment in Comprehension. “A is part of class B” must be interpreted thus: The phænomenon A possesses, or the concept A comprehends, the attribute of being included in the class B. So that, while every judgment in Comprehension warrants, by way of immediate inference, a corresponding judgment respecting Extension, this very judgment respecting Extension is itself but a particular kind of judgment in Comprehension. Even, therefore, on the untenable doctrine that there are two different judgments in the case, the distinction between judgments in Extension and judgments in Comprehension is not sustainable; and the supposed addition to the theory of the Syllogism is a mere excrescence and incumbrance on it.

How great the incumbrance is, all are able to judge, who follow our author through the details of the syllogistic logic. He not only finds it necessary to expound and demonstrate every one of the doctrines twice over, as adapted to Extension and to Comprehension, but struggles to express all the fundamental principles in a manner combining both points of view; and is thereby compelled either to state those principles in terms too wide and abstract for easy apprehension, in order that what is laid down respecting wholes and their parts may be applicable to both kinds of wholes (in Extension and in Comprehension), or else to embarrass the learner with the necessity of carrying on two trains of thought at once, in the attempt to apprehend a single principle. I need not dwell on the additional error, of considering the relation of whole and parts as the foundation of the Syllogism in both aspects. To the point of view of Extension that relation is applicable. In every affirmative proposition, if true, the object or class of objects denoted by the subject is a part (when it is not the whole) of the class of objects denoted by the predicate. But no similar relation exists between the two “bundles of attributes” comprehended in the subject and in the predicate, except in the case of Analytical Judgments, that is, of merely verbal propositions. In Synthetical Judgments, that is, in all propositions which convey information about anything except the meaning of words, the relation between the two sets of attributes is not a relation of Whole and Part, but a relation of Coexistence.

I now pass to the doctrine of the Quantification of the Predicate; examining it by the light of the same principles which we have applied to the distinction between the supposed two kinds of Reasoning.

It will be desirable to state in Sir W. Hamilton’s own words, as first published in 1846, the claims he prefers in behalf of this doctrine, and the important consequences to which he considers it to lead.

The doctrine which leads to all these consequences, or rather, which necessitates all these changes of expression (for they are no more), is that the Predicate is always quantified in thought; that we always think it either as signifying the whole, or as signifying only a part, of the objects included in its Extension. “In reality and in thought, every quantity is necessarily either all, or some, or none.”^† The proposition, All A is B, must mean, in thought, either All A is all B, or All A is some B. When I judge that all oxen ruminate, it must not only be true, but I must mean, either that All ox is all ruminating, or that All ox is some ruminating. Logic, therefore, postulates to express in words what is already in the thoughts, and to write all^e propositions in one or other of these forms: which makes it necessary that all the rules for reasoning should be altered, at least in expression, and grounded on the relation of exact equality between the terms.

But if, as I have endeavoured to show, the predicate B is present in thought only in respect of its Comprehension; if it be an error to suppose that it is thought of as an aggregate of objects at all; still less is it thought of as an aggregate with a determinate quantity, as some or all. I repeat the appeal which I have already made to every reader’s consciousness: Does he, when he judges that all oxen ruminate, advert even in the minutest degree to the question, whether there is anything else which ruminates? Is this consideration at all in his thoughts, any more than any other consideration foreign to the immediate subject? One person may know that there are other ruminating animals, another may think that there are none, a third may be without any opinion on the subject: but if they all know what is meant by ruminating, they all, when they judge that every ox ruminates, mean exactly the same thing. The mental process they go through, as far as that one judgment is concerned, is precisely identical; though some of them may go on further, and add other judgments to it.^*

The fact, that the proposition “Every A is B” only means Every A is some B, far from being always present in thought, is not at first seized without some difficulty by the tyro in logic. It requires a certain effort of thought to perceive that when we say, All As are Bs, we only identify A with a ^hportion^h of the class B. When the learner is first told that the proposition All As are Bs can only be converted in the form “Some Bs are As,” I apprehend that this strikes him as a new idea; and that the truth of the statement is not quite obvious to him, until verified by a particular example in which he already knows that the simple converse would be false, such as, All men are animals, therefore all animals are men. So far is it from being true that the proposition, All As are Bs, is spontaneously quantified in thought as All A is some B.

The pretension, therefore, of the doctrine of a Quantified Predicate, to be a more correct representation and analysis of the reasoning process than the common doctrine of the syllogism, I hold to be psychologically false. And this is fatal to the doctrine, if we admit Sir W. Hamilton’s theory that Logic is the science of the laws according to which we must think in order that our thought may be valid. But according to the very different view I myself take of Formal Logic, this doctrine might still be a valuable addition to it: since, in my view, the Syllogistic theory altogether is not an analysis of the reasoning process, but only furnishes a test of the validity of reasonings, by supplying forms of expression into which all reasonings may be translated if valid, and which, if they are invalid, will detect the hidden flaw. In this point of view it might well be, that a form which always exhibited the quantity of the predicate might be an improvement on the common form. And I am not disposed to deny that for occasional use, and for purposes of illustration, it is so. The exposition of the theory of the syllogism is made clearer, by pointing out that All As are B only implies that All A is some B, while No As are B excludes A from the whole of B. This, in fact, is taught to all who learn logic in the common way, by what is called the doctrine of Suppositio; or (in the many books which leave this doctrine out) by the theory of Conversion, and the syllogistic rules against Undistributed Middle, and against proceeding à non distributo ad distributum. There is no harm, and some little good, in giving to these essential doctrines the more explicit expression demanded for them by Sir W. Hamilton. But to obtain any advantage from it, we must be content with quantifying such propositions as, in their unquantified form, are really asserted and used. To foist in any others, overlays and confuses, instead of illuminating, the theory. “All A is some B” is admissible, because it is the quantification really implied in All As are B; but “All A is all B” is inadmissible, because it is not the equivalent of any single proposition capable of being asserted in an unquantified form. As all reasoning, except in the process of teaching Logic, will always be carried on in the forms which men use in real life; and as the only purpose of providing other forms, is to supply a test for those which are really used; it is essential that the forms provided should be forms into which the propositions expressed in common language can be translated—that every proposition in logical form, should be the exact equivalent of some proposition in the common form. Now, there is no proposition capable of being expressed in the ordinary form, which is equivalent to the proposition, All A is all B. That form of expression combines the import of two propositions in common language, expressive of two separate judgments, All As are Bs, and All Bs are As.

If this had not been denied, I should have deemed it too obvious to require either proof or illustration. But Sir W. Hamilton does deny it, and therefore some enforcement of it is indispensable. When we make an assertion in the cramped and unnatural form, All man is all rational, can anything seem more evident than that to cover the whole ground occupied by this statement, two judgments are required; namely, first, that every man has the attribute reason; and secondly, that nothing which is not man has that attribute, or (which is the same thing) that every rational creature has the attributes of man? How is it possible to make only one judgment, out of an assertion divisible into two parts, one of which may be unknown and the other known, one unthought of and the other thought of, one false and the other true?^*

Unless Sir W. Hamilton was prepared to maintain that whenever the universal converse of an universal affirmative proposition would be true, we cannot know the one without knowing the other, it is in vain for him to contend that a form which asserts both of them at once is only one proposition. If in judging that “All equilateral triangles are equiangular,” we judge that all equilateral triangles are all equiangular, in what condition of judgment is the mind of the tyro to whom it has just been proved that all equilateral triangles are equiangular, but who does not yet know the proof of the converse proposition that all equiangular triangles are equilateral? If “All equilateral triangles are all equiangular” is only one judgment, what is the proposition that all equilateral triangles are equiangular? Is it half a judgment?^†

This is not the only case in which Sir W. Hamilton insists upon wrapping up two different assertions in one form of words, and demands that they shall be considered one assertion. He strenuously contends that the form “Some A is B,” or (in its quantified form) “Some A is some B,” ought in logical propriety to be used and understood in the sense of “some and someonly.”^* No shadow of justification is shown for thus deviating from the practice of all writers on logic, and of all who think and speak with any approach to precision, and adopting into logic a mere sous-entendu of common conversation in its most unprecise form. If I say to any one, “I saw some of your children to-day,” he might be justified in inferring that I did not see them all, not because the words mean it, but because, if I had seen them all, it is most likely that I should have said so: though even this cannot be presumed unless it is presupposed that I must have known whether the children I saw were all or not. But to carry this colloquial mode of interpreting a statement into Logic, is something novel. If Some A is B is to be understood of some only, it is a double judgment, compounded of the propositions, Some As are Bs, and Some As are not Bs. If quantified in our author’s manner, the propositions would run thus: Some A is some B, and Some (other) A is not any B. If two statements, one of which affirms and the other denies a different predicate of a different subject, are not two distinct judgments, it is impossible to say what are so. One of the great uses of discipline in Formal Logic, is to make us aware when something which claims to be a single proposition, really consists of several, which, not being necessarily involved one in another, require to be separated, and considered each by itself, before we admit the compound assertion. This separation may be called, with reason, stating explicitly in words what is implicitly in thought. But it is a new postulate of Logic to state implicitly in words what is explicitly in thought, and I do not think that Logic is at all enriched by the acquisition.

With these compound propositions falls the whole pretension of the quantified mode of expression to yield legitimate inferences which are not recognised by the old Logic. Whatever can be proved from “All A is all B,” can be proved in the old form from one or both of its elements, All As are Bs, and All Bs are As. Whatever can be proved from “Some, and only some, A is some (or all) B,” can be proved in the old form from its elements, Some As are Bs, Some As are not Bs, and (in the case last mentioned) All Bs are As. If we choose to alter the forms of all our propositions, the forms of our syllogisms naturally require alterations too; and there may be a greater number of forms in which quantified conclusions can be drawn from quantified premises, than in which unquantified conclusions can be drawn from unquantified premises. But there is not a single instance, nor is it possible in the nature of things that there should be an instance, in which a conclusion that is provable from quantified premises, could not be proved from the same premises unquantified, if we set forth all those which are really involved. If there could be such an instance, the quantified Syllogism would be a real addition to the theory of Logic: if not, not.

As I have already once remarked, it does not follow, because the quantified Syllogism is not a true expression of what is in thought, that ^jthe occasional^j writing the predicate with a quantification may not be a real help to the art of Logic. Though not a correct analysis of the reasoning process, it may, in some cases, enable us more readily to see whether the conclusion really follows from the premises. But without rejecting it as an available help for this purpose, I must observe that its use in this capacity appears to me extremely limited; for two reasons. First; the problem is, to test the validity of a reasoning as expressed in the language in which men ordinarily reason. We do this by taking the propositions as they are, and measuring the extent of the assertions made in the two premises and in the conclusion respectively, so as to ascertain whether the former are broad enough to cover and include the latter. This it requires some practice to do, but the task is not avoided by quantifying the predicate; on the contrary, it must have been actually performed before the predicate can be correctly quantified; so that by quantifying it in expression, no trouble is saved. My second reason is, that after the predicate has been quantified, it is often equally or more difficult to follow the consecution of the thought through the symbols, than as expressed in ordinary language. Take one of the common cases of invalid inference, a syllogism in the first figure with the major premise particular, such as this:

• Some Ms are Ps
• All Ss are Ms
• Therefore all Ss are Ps;

the inference fails, because the Ms which are identified with Ss may not be the same Ms which are Ps, but other Ms. Let us now quantify the predicates thus:

• Some Ms are some Ps
• All Ss are some Ms
• Therefore all Ss are some Ps;

is the invalidity of the inference at all clearer? Does it require less exertion of thought to perceive that “some Ms” may not mean the same some in both premises, than it did to recognise the equivalent truth as to M in the minor, and “some M” in the major premise? On the contrary, the quantified form is the more plausibly misleading of the two, since the middle term, though really ambiguous, is, in that form, verbally the same, which in the unquantified form it is not.

The general result of these considerations is, that the utility of the new forms is by no means such as to compensate for the great additional complication which they introduce into the syllogistic theory; a complication which would make it at the same time difficult to learn or remember, and intolerably tiresome both in the learning and in the using. The sole purpose of any syllogistic forms is to afford an available test for the process of drawing inferences in the common language of life from premises in the same common language; and the ordinary forms of Syllogism effect this purpose completely. The new forms do not, in any appreciable degree, facilitate the process, while they are chargeable, in a far greater degree than the common forms, with diverting the mind from the true meaning of propositions (the ascription of attributes to objects considered severally), and concentrating it upon the highly artificial, and generally unimportant, consideration of the relation of extent between classes of objects, considered not severally, but as collective wholes. The new forms have thus no practical advantage which can countervail the objection of their entire psychological irrelevancy; and the invention and acquisition of them have little value, except as one among many other feats of mental gymnastic, by which students of the science may exercise and invigorate their faculties. They should, in short, be dealt with as Sir W. Hamilton deals with Mr. De Morgan’s forms of “numerically definite” Syllogism, viz. “taken into account by Logic as authentic forms, but then relegated as of little use in practice, and cumbering the science with a superfluous mass of moods.”^*

[* ]Lectures, Vol. III, pp. 297, 304, 378; Vol. IV, App. v, p. 250.

[† ]An Essay on the New Analytic of Logical Forms, being that which gained the prize proposed by Sir William Hamilton in the year 1846 for the best exposition of the new Doctrine propounded in his Lectures. With an Historical Appendix. By Thomas Spencer Baynes, Translator of the Port Royal Logic (p. 80). [See also Antoine Arnauld and Pierre Nicole, The Port-Royal Logic, trans. Baynes, 3rd ed. (Edinburgh: Sutherland, Knox, 1854).]

[[*] ]See pp. 339-41 above.

[a-a]651, 652 dolphin

[b-b]651, 652 dolphin

[c-c]651, 652 dolphins

[d-d]+652, 67, 72

[[*] ]See Collected Works, Vol. VII, pp. 196-9 (Bk. II, Chap. iii, §5).

[* ][67] Dr. M‘Cosh has some partially just observations on this subject. He admits that “in by far the greater number of propositions, the primary and uppermost sense is in Comprehension.” ([Examination,] p. 292.) He says, however, that in some, “the uppermost thought is in Extension. Thus, when the young student of Natural History is told that the crocodile is a reptile, his idea is of a class, of which he may afterwards learn the marks.” (Ibid., p. 293.) And it is true that when the known purpose of the statement is to declare what place the object occupies in a classification, a fact of classification is the real meaning of the proposition. This is emphatically the exception which proves the rule. Dr. M‘Cosh adds, “the mind in its discursive operations tends to go on from Comprehension to Extension.” [Ibid.] This I admit; but the thought in Comprehension comes first: the thought in Extension rests on the thought in Comprehension, and follows it; but is so closely linked with it that it can hardly help following. The circumstance, however, that the proposition is familiarly expressed in concrete language, does not prove it to be thought in Extension. The practice of so expressing it must, no doubt, as Dr. M‘Cosh says, “proceed from some law of thought as applied to things;” but the law of thought it proceeds from is merely the obvious one, that concrete language, requiring for its formation a lower degree of abstraction, was earliest formed, took possession of the field, and is still the most familiar. [Ibid.] When Dr. M‘Cosh goes on to say that although “so far as propositions are concerned, spontaneous thought is chiefly in Comprehension,” the case is “different in regard to reasoning, the uppermost thought in which is always in Extension,” (ibid., p. 303,) I cannot agree with him. If the meaning, in consciousness, of the premises when separate, is in Comprehension, it is not natural that the derivative and subordinate meaning in Extension should leap to the front as soon as the premises are brought together. But if, instead of “in reasoning,” Dr. M‘Cosh had said “in the artificial formula of Reasoning called Syllogism,” I think he would have been right.

[* ]Lectures, Vol. III, pp. 286-7.

[† ]Ibid., p. 270.

[‡ ]Ibid., p. 273.

[§ ]Ibid., p. 399.

[¶ ]Ibid., pp. 397-8.

[∥ ]It is curious to observe with what facility Sir W. Hamilton drives two conflicting opinions together in a team. The passages quoted in the text are destructive of any notion of a different order of the premises in a Syllogism of Extension and in one of Comprehension. Yet this notion maintains full possession of our author’s mind. We have found him accusing all logical writers of overlooking Reasoning in Comprehension; but he thinks that they exceptionally recognised it in the case of the Sorites, and that in that case, by a contrary error, they “altogether overlooked the possibility of a Reasoning in Extension,” solely because, in the Sorites, they inverted the usual order of the premises. (Ibid., pp. 379 and ff.) On a similar foundation stands his charge against the Fourth Figure, of being “a monster undeserving of toleration,” [ibid., p. 424,] because instead of keeping to one of the two quantities, Extension and Comprehension, it reasons (he says) across from one of them to the other. This is merely because the Fourth Figure, while it draws the same conclusion which might have been drawn in the First, reverses the order of the premises. (Ibid., pp. 425-8.)

[* ]Ibid., p. 274.

[* ]Discussions, App. II [A], pp. 650-1.

[† ]Ibid., App. II [B], p. 691n. But the whole meaning of this assertion, as available for our author’s purpose, is destroyed by the statement which he is presently obliged to make, that “the Indesignate is thought, either precisely, as whole or as part, or vaguely, as the one or the other, unknown which, but the worse always presumed.” [Ibid.] The concession, though fatal to himself, is short of the truth; for the Indesignate is not necessarily thought either as a whole, or as part, or as “unknown which:” it is often not thought in any relation of quantity at all.

[e]651 other

[* ]Not only we do not (unless exceptionally for some special purpose) quantify the predicate in thought, but we do not even quantify the subject, in the sense which Sir W. Hamilton’s theory requires. Even in an universal proposition, we do not think of the fsubjectf as an aggregate whole, but as its several parts: we do not judge that all A is B, but that all As are Bs, which is a different thing. That what is true of the whole must be true of any part, only holds good when the whole means the parts themselves, and not when it means the aggregate of them. All A, is a very different notion from Each A. What is true of A only as a whole, forms no element of a judgment concerning its parts—even concerning all its parts. Sir W. Hamilton thinks that the relation of quantity in extension which the class A bears to the class B, is always present in my thoughts when I predicate B of A. This relation of quantity, however, does not belong to individual As, but specifically and solely to A as a whole, and as a whole I am not thinking of it. When I am predicating B of all As severally, I am not adverting to any property or relation which belongs to A as their aggregate. Accordingly we do not say, all ox ruminates, but all oxen ruminate. The distinction is of little importance when A is only coextensive with part of B; for if A altogether is but a part, still more must this be true of any particular A, and it is indifferent whether we say all A is some B, or each of the As is some B. But it is quite another matter when the assertion is that all A is all B. This, if true at all, is true only of A considered as a whole; and expresses a relation between the two classes as totals, not between either of them and its parts. Now, to affirm that when we judge every A to be a B, we always, and necessarily, recognise in thought a fact which is not true of every, or even of any A, but only of the aggregate composed of all As, seems to me as baseless a fancy as ever implanted itself in the intellect of an eminent thinker. gIt is, in short (as observed by one of my correspondents), a conclusive reason against the assimilation of a judgment to an equation, that in equations the terms are used collectively, and in judgments mostly distributively.g

[h-h]651 part

[* ]The only answer I can imagine to this is, that having the two concepts Man and Rational, and being engaged in actually comparing them with each other, we must perceive and judge whether the one is merely a part of the other, or a whole coinciding with it. But this answer it is not competent to Sir W. Hamilton, or any other Conceptualist, to make. An adversary of Sir W. Hamilton might make it. I have myself said, and have offered as a reductio ad absurdum of his analysis of Reasoning, that if we have two concepts and compare them, we cannot but perceive any relation of whole and part which exists between them. [See pp. 342ff. above.] Sir W. Hamilton however is precluded from making this reply; for all Reasoning, even to the longest process in Mathematics, consists, according to him, in discovering this relation of whole and part by circuitous means, when direct comparison does not disclose it. From his point of view, therefore, the argument is not tenable; and from mine it has no pertinence, since I do not admit that Reasoning is a comparison of Concepts at all.

[† ]Sir W. Hamilton goes the length of asserting that to a person who knows all trilateral figures to be triangular, the proposition “all triangles are trilateral” must, if expressed as understood, be written “All triangles are all trilateral:” as if every proposition which I affirm respecting a subject, must include all I know about it. (Appendix [v(f)] to Lectures, Vol. IV, pp. 292 and ff.)

That the proposition All A is all B is not a single judgment, but compounded of two, has already been urged against Sir W. Hamilton by Mr. De Morgan, and we are in possession of Sir W. Hamilton’s answer (Discussions, Appendix II, pp. 687-8). Unhappily Mr. De Morgan (by an oversight not usual with that able thinker) gave Sir W. Hamilton an apparent triumph, by mistaking the two judgments which the pretended single proposition is composed of. He appears to have said, that the proposition “All Xs are all Ys,” is compounded of the propositions “All Xs are some Ys,” and “Some Xs are all Ys.” [See Augustus De Morgan, “On the Symbols of Logic,” Proceedings of the Cambridge Philosophical Society, I (25 Feb., 1850), 92.] Sir W. Hamilton replies, that these two propositions are (in his own peculiar language) incompossible, inasmuch as we cannot think X both as some Y, that is, a part of Y, and as the whole. The argument is little better than a quibble, because other people do not (though Sir W. Hamilton does) mean by some, some only; they mean some at least; and if the first of Mr. De Morgan’s two propositions identifies X with only some of Y, the second superadds the remainder. But in reality the two judgments which go to the composition of “All A is all B,” are not judgments with quantified predicates at all. They are, All A is B, and All B is A. The one ascribes the attributes of B to every A, the other the attributes of A to every B. Judgments more distinct and independent of one another do not exist.

According to Sir W. Hamilton “ordinary language quantifies the Predicate as often as this determination becomes of the smallest import.” And he cites such instances as “Virtue is the only nobility;” “Of animals man alone is rational,” and the like. (Lectures, Vol. IV, App. [v], pp. 259-61.) The truth is, that ordinary language quantifies the predicate in the rare cases in which it is quantified in thought, and in no others. And even then the quantified proposition is an abbreviated expression of two judgments. The German logician Scheibler, to whom our author refers in a foot-note (ibid., p. 261), could have set him right here. [Christoph Scheibler, Opera philosophica, 2 vols. (Frankfurt: Wustii, 1665).]

i“Sir W. Hamilton,” says Mr. Grote, “insists on stating explicitly, not merely all that is thought implicitly, but a great deal more; adding to it something else, which may, indeed, be thought conjointly, but which more frequently is not thought at all. He requires us to pack two distinct judgments into one and the same proposition: he interpolates the meaning of the Propositio Conversa simpliciter into the form of the Propositio Convertenda (when an universal affirmative) and then claims it as a great advantage, that the proposition thus interpolated admits of being converted simpliciter, and not merely per accidens. . . . If a man is prepared to give us information on one Quæsitum, why should he be constrained to use a mode of speech which forces on his attention at the same time a second and distinct Quæsitum, so that he must either give us information about the two at once, or confess himself ignorant respecting the second?” ([“John Stuart Mill on the Philosophy of Sir William Hamilton,”] pp. 31-2.) Mr. Grote goes on to cite from Sir W. Hamilton’s own collection of authorities, an excellent passage from a Jewish philosopher of the fourteenth century, Levi Ben Gerson, which exactly confutes Sir W. Hamilton’s doctrine. “The cause why the quantitative note is not usually joined with thepredicate, is that there would thus be two quæsita at once; to wit, whether the predicate were affirmed of the subject, and whether it were denied of everything beside. For when we say, All Man is all Rational, we judge that all man is rational, and judge likewise that rational is denied of everything but man. But these are, in reality, two different quæsita; and therefore it has become usual to state them, not in one, but in two several propositions. And this is self-evident, seeing that a quæsitum in itself, asks only—Does or does not this inhere in that? and not, Does or does not this inhere in that, and at the same time inhere in nothing else.”i [Quoted by Grote, p. 32n, from Hamilton, Lectures, Vol. IV, App. v(g), pp. 310-11.]

Propositions in Extension have absolutely no meaning but what they derive from Comprehension. The Logic of the quantified predicate takes the Comprehension out of them, and leaves them a caput mortuum.

[* ]See, among many other places, Discussions, Appendix II[B], pp. 690n-1n, where he says, “Every quantity is necessarily either all, or none, or some; of these, the third is formally exclusive of the other two.”

[j-j]+67, 72

[* ]Lectures, Vol. IV, App. [vi], p. 355. [See De Morgan, Formal Logic (London: Taylor and Walton, 1847), p. 142.]

[* ]Not only we do not (unless exceptionally for some special purpose) quantify the predicate in thought, but we do not even quantify the subject, in the sense which Sir W. Hamilton’s theory requires. Even in an universal proposition, we do not think of the fsubjectf as an aggregate whole, but as its several parts: we do not judge that all A is B, but that all As are Bs, which is a different thing. That what is true of the whole must be true of any part, only holds good when the whole means the parts themselves, and not when it means the aggregate of them. All A, is a very different notion from Each A. What is true of A only as a whole, forms no element of a judgment concerning its parts—even concerning all its parts. Sir W. Hamilton thinks that the relation of quantity in extension which the class A bears to the class B, is always present in my thoughts when I predicate B of A. This relation of quantity, however, does not belong to individual As, but specifically and solely to A as a whole, and as a whole I am not thinking of it. When I am predicating B of all As severally, I am not adverting to any property or relation which belongs to A as their aggregate. Accordingly we do not say, all ox ruminates, but all oxen ruminate. The distinction is of little importance when A is only coextensive with part of B; for if A altogether is but a part, still more must this be true of any particular A, and it is indifferent whether we say all A is some B, or each of the As is some B. But it is quite another matter when the assertion is that all A is all B. This, if true at all, is true only of A considered as a whole; and expresses a relation between the two classes as totals, not between either of them and its parts. Now, to affirm that when we judge every A to be a B, we always, and necessarily, recognise in thought a fact which is not true of every, or even of any A, but only of the aggregate composed of all As, seems to me as baseless a fancy as ever implanted itself in the intellect of an eminent thinker. gIt is, in short (as observed by one of my correspondents), a conclusive reason against the assimilation of a judgment to an equation, that in equations the terms are used collectively, and in judgments mostly distributively.g

[† ]Sir W. Hamilton goes the length of asserting that to a person who knows all trilateral figures to be triangular, the proposition “all triangles are trilateral” must, if expressed as understood, be written “All triangles are all trilateral:” as if every proposition which I affirm respecting a subject, must include all I know about it. (Appendix [v(f)] to Lectures, Vol. IV, pp. 292 and ff.)

That the proposition All A is all B is not a single judgment, but compounded of two, has already been urged against Sir W. Hamilton by Mr. De Morgan, and we are in possession of Sir W. Hamilton’s answer (Discussions, Appendix II, pp. 687-8). Unhappily Mr. De Morgan (by an oversight not usual with that able thinker) gave Sir W. Hamilton an apparent triumph, by mistaking the two judgments which the pretended single proposition is composed of. He appears to have said, that the proposition “All Xs are all Ys,” is compounded of the propositions “All Xs are some Ys,” and “Some Xs are all Ys.” [See Augustus De Morgan, “On the Symbols of Logic,” Proceedings of the Cambridge Philosophical Society, I (25 Feb., 1850), 92.] Sir W. Hamilton replies, that these two propositions are (in his own peculiar language) incompossible, inasmuch as we cannot think X both as some Y, that is, a part of Y, and as the whole. The argument is little better than a quibble, because other people do not (though Sir W. Hamilton does) mean by some, some only; they mean some at least; and if the first of Mr. De Morgan’s two propositions identifies X with only some of Y, the second superadds the remainder. But in reality the two judgments which go to the composition of “All A is all B,” are not judgments with quantified predicates at all. They are, All A is B, and All B is A. The one ascribes the attributes of B to every A, the other the attributes of A to every B. Judgments more distinct and independent of one another do not exist.

According to Sir W. Hamilton “ordinary language quantifies the Predicate as often as this determination becomes of the smallest import.” And he cites such instances as “Virtue is the only nobility;” “Of animals man alone is rational,” and the like. (Lectures, Vol. IV, App. [v], pp. 259-61.) The truth is, that ordinary language quantifies the predicate in the rare cases in which it is quantified in thought, and in no others. And even then the quantified proposition is an abbreviated expression of two judgments. The German logician Scheibler, to whom our author refers in a foot-note (ibid., p. 261), could have set him right here. [Christoph Scheibler, Opera philosophica, 2 vols. (Frankfurt: Wustii, 1665).]

i“Sir W. Hamilton,” says Mr. Grote, “insists on stating explicitly, not merely all that is thought implicitly, but a great deal more; adding to it something else, which may, indeed, be thought conjointly, but which more frequently is not thought at all. He requires us to pack two distinct judgments into one and the same proposition: he interpolates the meaning of the Propositio Conversa simpliciter into the form of the Propositio Convertenda (when an universal affirmative) and then claims it as a great advantage, that the proposition thus interpolated admits of being converted simpliciter, and not merely per accidens. . . . If a man is prepared to give us information on one Quæsitum, why should he be constrained to use a mode of speech which forces on his attention at the same time a second and distinct Quæsitum, so that he must either give us information about the two at once, or confess himself ignorant respecting the second?” ([“John Stuart Mill on the Philosophy of Sir William Hamilton,”] pp. 31-2.) Mr. Grote goes on to cite from Sir W. Hamilton’s own collection of authorities, an excellent passage from a Jewish philosopher of the fourteenth century, Levi Ben Gerson, which exactly confutes Sir W. Hamilton’s doctrine. “The cause why the quantitative note is not usually joined with thepredicate, is that there would thus be two quæsita at once; to wit, whether the predicate were affirmed of the subject, and whether it were denied of everything beside. For when we say, All Man is all Rational, we judge that all man is rational, and judge likewise that rational is denied of everything but man. But these are, in reality, two different quæsita; and therefore it has become usual to state them, not in one, but in two several propositions. And this is self-evident, seeing that a quæsitum in itself, asks only—Does or does not this inhere in that? and not, Does or does not this inhere in that, and at the same time inhere in nothing else.”i [Quoted by Grote, p. 32n, from Hamilton, Lectures, Vol. IV, App. v(g), pp. 310-11.]

Propositions in Extension have absolutely no meaning but what they derive from Comprehension. The Logic of the quantified predicate takes the Comprehension out of them, and leaves them a caput mortuum.

[fsubjectf]652 object [printer’s error?]

[gIt is, in short (as observed by one of my correspondents), a conclusive reason against the assimilation of a judgment to an equation, that in equations the terms are used collectively, and in judgments mostly distributively.g]+72

[i“Sir W. Hamilton,” says Mr. Grote, “insists on stating explicitly, not merely all that is thought implicitly, but a great deal more; adding to it something else, which may, indeed, be thought conjointly, but which more frequently is not thought at all. He requires us to pack two distinct judgments into one and the same proposition: he interpolates the meaning of the Propositio Conversa simpliciter into the form of the Propositio Convertenda (when an universal affirmative) and then claims it as a great advantage, that the proposition thus interpolated admits of being converted simpliciter, and not merely per accidens. . . . If a man is prepared to give us information on one Quæsitum, why should he be constrained to use a mode of speech which forces on his attention at the same time a second and distinct Quæsitum, so that he must either give us information about the two at once, or confess himself ignorant respecting the second?” ([“John Stuart Mill on the Philosophy of Sir William Hamilton,”] pp. 31-2.) Mr. Grote goes on to cite from Sir W. Hamilton’s own collection of authorities, an excellent passage from a Jewish philosopher of the fourteenth century, Levi Ben Gerson, which exactly confutes Sir W. Hamilton’s doctrine. “The cause why the quantitative note is not usually joined with thepredicate, is that there would thus be two quæsita at once; to wit, whether the predicate were affirmed of the subject, and whether it were denied of everything beside. For when we say, All Man is all Rational, we judge that all man is rational, and judge likewise that rational is denied of everything but man. But these are, in reality, two different quæsita; and therefore it has become usual to state them, not in one, but in two several propositions. And this is self-evident, seeing that a quæsitum in itself, asks only—Does or does not this inhere in that? and not, Does or does not this inhere in that, and at the same time inhere in nothing else.”i]+67, 72