Mill’s System of Logic: Selected Works vol. VII
Source: Editor's introduction to The Collected Works of John Stuart Mill, Volume VII - A System of Logic Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation (Books I-III), ed. John M. Robson, Introduction by R.F. McRae (Toronto: University of Toronto Press, London: Routledge and Kegan Paul, 1974).
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john stuart mill’sSystem of Logic is his principal philosophical work. Its subject matters cost him more effort and time to think through than those of his other writings, including the Political Economy, which, though of comparable scope, was, he says, far more rapidly executed. He believed that the System of Logic was destined to survive longer than anything else he had written, than even, perhaps, the essay On Liberty. In so far as it introduces technical material, it has contributed the Four Experimental Methods—though usually criticised in one way or another—to almost every later textbook on logic which treats of induction. Mill would appear, therefore, to have succeeded in his intention of doing for inductive arguments what Aristotle, in originating the rules of syllogism, did for ratiocination or deduction. The survival of Mill’s System of Logic as a philosophical work is a consequence of other features. It was conceived in controversy, and on many subjects it still remains pertinent to controversy because of the classic formulation it gives to one of a set of alternative theses, whether at the very beginning of the book in the theory of meaning, or at the end in the idea of a social science. It consequently has a survival value greatly extending beyond any that can be estimated by the number of adherents to its doctrines. The System of Logic has survived also in a third, and ghostly, fashion under the labels “empiricism” and “psychologism,” with the varying connotations which these have. Mill himself was not in the least averse to labels. He saw himself as protagonist in a conflict of “schools.” If, however, some general, undistorted, view is to be taken of his System of Logic, it becomes necessary to give precision to the applicability of these two labels, often interconnected as they are, as, for example, in a recent description of it as an “attempt to expound a psychological system of logic within empiricist principles.”1
R. P. Anschutz has forcefully drawn attention to the fact that Mill did not regard himself as an empiricist but as in fundamental opposition to empiricism.2 By empiricism Mill meant “bad generalization” and “unscientific surmise.” His own position he identified with “the School of Experience.” It may have been natural enough for Mill to have retained the term “empiricism” in its ordinary, as well as in its older philosophical use, and in any case, it aptly covered the type of political theory associated with Mackintosh and Macaulay. The latter’s attack on his father’s Essay on Government caused Mill to see that Macaulay “stood up for the empirical mode of treating political phenomena, against the philosophical; that even in physical science, his notion of philosophizing . . . would have excluded Newton and Laplace.”3 However, the members of what Mill called “the School of Experience” are today more generally called the British empiricists, and he is counted among them. To speak of Mill’s empiricism is to speak of his adherence to what he described as “the prevailing theory in the eighteenth century,” a theory which had its starting point, as he believed every system of philosophy should, with two questions, one about the sources of human knowledge, and the other about the objects which the mind is capable of knowing. With regard to the first question, the answer of this school was that “all knowledge consists of generalizations from experience. . . . There is no knowledge à priori; no truths cognizable by the mind’s inward light, and grounded on intuitive evidence. Sensation, and the mind’s consciousness of its own acts, are not only the exclusive sources, but the sole materials of our knowledge.” With regard to the second question their answer was, “Of nature, or anything whatever external to ourselves, we know . . . nothing, except the facts which present themselves to our senses, and such other facts as may, by analogy, be inferred from these.”4 This means that the “nature and laws of Things in themselves, or of the hidden causes of the phenomena which are the objects of experience,” are “radically inaccessible to the human faculties.” Nothing “can be the object of our knowledge except our experience, and what can be inferred from our experience by the analogies of experience itself. . . .”5
In general, the term “experience” refers in the System of Logic to observation that something is the case and to experimentation as an adjunct of such observation. When Mill states the empirical thesis that “all knowledge consists in generalization from experience,” he is using the term in this sense. For example, he asks about the proposition, All men are mortal, “whence do we derive our knowledge of that general truth? Of course from observation. Now all that man can observe are individual cases. From these all general truths are drawn, and into these they may again be resolved.” But Mill also uses “experience” to refer to the undergoing of sensations and feelings, or having what he calls collectively “states of consciousness.” It is this sense of “experience” which is indicated when he says that “sensation and the mind’s consciousness of its own acts are . . . the sole materials of our knowledge.” This too is a familiar empirical thesis, but by virtue of the kind of experience to which it refers, it is different from the first thesis, and it constitutes the basis of Mill’s phenomenalism. Both senses of the term “experience” are common and philosophically neutral, but the first of them, observation that something is the case, ceases to be taken in neutral fashion when it is reduced to, or considered to mean the same in the end as the second, namely, having sensations. While acknowledging in the System of Logic that he is here on disputed philosophical territory, Mill does perform this reduction, as in the following example which he gives of something which can be observed to be the case.
Let us take, then, as our example, one of what are termed the sensible qualities of objects, and let the example be whiteness. When we ascribe whiteness to any substance, as, for instance, snow; when we say that snow has the quality whiteness, what do we really assert? Simply, that when snow is present to our organs, we have a particular sensation, which we are accustomed to call the sensation of white. But how do I know that snow is present? Obviously from the sensations which I derive from it, and not otherwise. I infer that the object is present, because it gives me a certain assemblage or series of sensations. And when I ascribe to it the attribute whiteness, my meaning is only, that, of the sensations composing this group or series, that which I call the sensation of white colour is one.6
We must then distinguish two levels of empiricism in Mill, one in which “experience” refers to observation of what is the case and to experimentation as related to it, and the other more radical level, that of his phenomenalism, in which all experience is reduced to one kind, namely, undergoing sensations, feelings, and other “states of consciousness.” On which of these levels of empiricism are Mill’s logical doctrines constructed?
On the relation of logic to experience Mill appears to take two contradictory positions, one in his Autobiography and the other in the Introduction to the System of Logic. In the Autobiography he says, “The German, or à priori view of human knowledge, and of the knowing faculties, is likely for some time longer (though it may be hoped in a diminishing degree) to predominate among those who occupy themselves with such inquiries, both here and on the Continent. But the ‘System of Logic’ supplies what was much wanted, a text-book of the opposite doctrine—that which derives all knowledge from experience, and all moral and intellectual qualities principally from the direction given to the associations.”7 In the Introduction to the System of Logic, however, Mill proclaims the philosophical neutrality of logic. “Logic is common ground on which the partisans of Hartley and of Reid, of Locke and Kant, may meet and join hands. Particular and detached opinions of all these thinkers will no doubt occasionally be controverted, since all of them were logicians as well as metaphysicians; but the field on which their principal battles have been fought, lies beyond the boundaries of our science”(14). Mill concludes the Introduction with this remark: “. . . I can conscientiously affirm that no one proposition laid down in this work has been adopted for the sake of establishing, or with any reference to its fitness for being employed in establishing, preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided” (14-15).
Mill’s claim for the neutrality of logic derives from a distinction which he makes between two ways in which truths may be known. Some are known directly, that is, by intuition; some are known by means of other truths, that is, are inferred. Logic has no concern with the former kind of truths, nor with the question whether they are part of the original furniture of the mind or given through the senses. It is concerned only with inferred truths. Moreover, while there is much in our knowledge which may seem to be intuited, but which may actually be inferred, the decision as to what part of our knowledge is intuitive and what inferential is something which also falls outside the scope of logic. It belongs to what Mill calls Metaphysics, a term he uses in such a way as to include psychology and theory of knowledge. It is clear from his description of metaphysics in the Introduction that it is this science, not logic, which decides the issue which separates “the German, or à priori view of human knowledge” from that which “derives all knowledge from experience.” In the Autobiography, however, Mill looked to his Logic to settle the issue.
The notion that truths external to the mind may be known by intuition or consciousness, independently of observation and experience, is, I am persuaded, in these times, the great intellectual support of false doctrines and bad institutions. . . . And the chief strength of this false philosophy in morals, politics, and religion, lies in the appeal which it is accustomed to make to the evidence of mathematics and of the cognate branches of physical science. To expel it from these, is to drive it from its stronghold. . . . In attempting to clear up the real nature of the evidence of mathematical and physical truths, the “System of Logic” met the intuitive philosophers on ground on which they had previously been deemed unassailable. . . .8
The apparent contradiction dissolves, however, as the course of Mill’s argument reveals that it rests on no assumptions about the nature of direct knowledge, and reaches a conclusion which, if valid, would subvert the àpriori school. The argument also reveals the nature and extent of Mill’s empiricism.
Because twentieth-century empiricists, with their predominantly Viennese background, express their doctrine in the language, not of the British empiricists, but of Leibniz and Kant, it will be useful to state Mill’s argument in this latter, more familiar language. Leibniz distinguished between two kinds of propositions, truths of reason and truths of fact. Truths of reason are necessary and their opposites are impossible, that is, contain a contradiction. A necessary truth can be shown to be so by a mere analysis of its terms; the analysis will reveal the concept of the predicate to be contained within the concept of the subject. A truth of fact, on the other hand, is not necessary but contingent. By this Leibniz means, not that the predicate is not contained within the concept of the subject, but that no finite analysis, however far it is pursued, can ever show the concept of the predicate to be contained within that of the subject, for the required analysis is infinite. Only by experience can it be known that the subject and predicate are connected. Kant modified Leibniz’s division in an important way by introducing a further distinction, one between analytic and synthetic judgments. Analytic judgments, like Leibniz’s truths of reason, are those in which the concept of the predicate is contained within that of the subject. Synthetic judgments, a type not recognized by Leibniz, are, on the other hand, those in which the concept of the predicate is not contained within that of the subject. No analysis of the concept of the subject can extract it. Where an analytic judgment is merely explicative of the concept of the subject, a synthetic judgment is ampliative; it extends our knowledge of the subject. Kant now enlarged Leibniz’s class of necessary truths so that it should include not only propositions which were analytical, but also some which were synthetic, that is, some whose negation did not contain a contradiction. These synthetic propositions, being necessary, could only be known to be true independently of sense experience. Modern empiricists have adopted the Kantian distinction between the analytic and the synthetic as so basic that it has been labelled one of the “dogmas of empiricism.”9 But while accepting Kant’s distinction, they of course rule out the possibility of the class of synthetic propositions which are necessary. Like Leibniz they hold that all necessary truths are analytical.
Mill makes a distinction which, he says, corresponds to “that which is drawn by Kant and other metaphysicians between what they term analytic, and synthetic, judgments; the former being those which can be evolved from the meaning of the terms used” (116n). Mill’s distinction is between propositions which are merely verbal or relate to the meaning of terms, and propositions which assert matters of fact. Verbal propositions, those “(. . . in which the predicate connotes the whole or part of what the subject connotes, but nothing besides) answer no purpose but that of unfolding the whole or some part of the meaning of the name, to those who did not previously know it” (113). Every man is a corporeal being, or Every man is rational, would be examples. Real propositions, on the other hand, “predicate of a thing some fact not involved in the signification of the name by which the proposition speaks of it. . . . Such are . . . all general or particular propositions in which the predicate connotes any attribute not connoted by the subject. All these, if true, add to our knowledge: they convey information, not already involved in the names employed” (115-16).
But while Mill accepts the distinction between analytic and synthetic propositions, this is not for him one between two kinds of truths. Verbal propositions are “not, strictly speaking, susceptible of truth or falsity, but only of conformity or disconformity to usage or convention; and all the proof they are capable of, is proof of usage . . .” (109). Analytic propositions are not, then, as they are for Leibniz, Kant, and modern empiricists, necessary truths, for they are not truths at all. Some examples of what Mill considered to be true propositions, that is, propositions asserting matters of fact, would be: All men are mortal, Two straight lines cannot enclose a space, Two and one is equal to three, Every fact which has a beginning has a cause, The same proposition cannot at the same time be false and true. All these assert something about what is the case in this world. They do not assert what would be, in the language of Leibniz, true in all possible worlds. In the case of two of these propositions, the arithmetical one and the principle of contradiction, Mill considered, and rejected, the possibility that they were not assertions of matters of fact, and therefore neither true nor false, but were merely verbal or analytical. Indeed, he acknowledged great plausibility in the view that the “proposition, Two and one is equal to three . . . is not a truth, is not the assertion of a really existing fact, but a definition of the word three; a statement that mankind have agreed to use the name three as a sign exactly equivalent to two and one; to call by the former name whatever is called by the other more clumsy phrase” (253). Mill did not, however, consider the possibility of looking at geometry in this way; “that science cannot be supposed to be conversant about non-entities” (225). Geometrical theorems add to our knowledge of the world. Consequently he thought it fatal to the view that the science of numbers is merely a succession of changes in terminology, that it is impossible to explain by it how, when a new geometrical theorem is demonstrated by algebra, the series of translations brings out new facts. Mill takes note also—again with some degree of sympathy—of those who regard the principle of contradiction as “an identical proposition; an assertion involved in the meaning of terms; a mode of defining Negation, and the word Not” (277), and indeed he is willing to go part way with this. “If the negative is true the affirmative is false,” is merely an identical proposition, for what the negative means is only the falsity of the affirmative. But the statement that the same proposition cannot at the same time be false and true, is not a merely verbal one but a generalization about facts in the world. The principle of contradiction states a truth.
The distinction between verbal, or analytic, and real, or synthetic, propositions has an important bearing on Mill’s conception of the nature of logic. For him logic is primarily concerned with real propositions, that is, assertions of matters of fact, or propositions which are either true or false. It is, in his words, a “logic of truth.” But there are two ways in which truths are known. Some are known directly, some are known by inference from other truths. Logic is concerned only with the second of these two ways. This means that Mill’s logic is concerned with the way in which we infer from some truths other truths which are quite distinct from them. Such inference Mill calls “real,” in order to contrast it with merely “apparent” inference. The latter kind occurs in instances of equivalence or implication, for in these the conclusion asserts no new truth, but only what is already asserted in the premises: “the conclusion is either the very same fact, or part of the fact asserted in the original proposition.” Moreover, the logic of truth requires an interpretation of the syllogism different from any it has traditionally received. Mill finds it unanimously admitted that a syllogism is invalid if there is anything in the conclusion which is not contained in the premises. This being so, syllogism cannot, then, be inference at all, though it may perform some important function in relation to inference. This function Mill sought to determine. In short, formal logic, which some have taken to be the whole of logic, is not concerned with inference, and must be sharply contrasted with the logic of truth. Its sole aim is consistency. As a logic of consistency it performs a subordinate, but indispensable, role in relation to the logic of truth, for consistency is a condition for truth.
If thought be anything more than a sportive exercise of the mind, its purpose is to enable us to know what can be known respecting the facts of the universe: its judgments and conclusions express, or are intended to express, some of those facts: and the connexion which Formal Logic, by its analysis of the reasoning process, points out between one proposition and another, exists only because there is a connexion between one objective truth and another, which makes it possible for us to know objective truths which have never been observed, in virtue of others which have. This possibility is an eternal mystery and stumbling-block to Formal Logic. The bare idea that any new truth can be brought out of a Concept—that analysis can ever find in it anything which synthesis has not first put in—is absurd on the face of it: yet this is all the explanation that Formal Logic, as viewed by Sir W. Hamilton, is able to give of the phænomenon; and Mr. Mansel expressly limits the province of Logic to analytic judgments—to such as are merely identical. But what the Logic of mere consistency cannot do, the Logic of the ascertainment of truth, the Philosophy of Evidence in its larger acceptation, can. It can explain the function of the Ratiocinative process as an instrument of the human intellect in the discovery of truth, and can place it in its true correlation with the other instruments.10
But Mill’s logic is not only a logic of truth; it is intended to be a “logic of experience,” and as such to subvert the doctrines of the German or à priori school.11 Its single most important thesis, that on which the whole conception of the logic of experience rests, is that all inference is from particulars to particulars. This is by no means advanced by Mill as a dogma. It is given as the conclusion of an argument in which he examines the nature of the syllogism. It is to be observed that in doing so, Mill adopts as his example of the syllogism, one in which the major premise, All men are mortal, is obviously a generalization from observation. The minor premise asserts that the Duke of Wellington is a man, and the conclusion is drawn that the Duke, who was alive at the time, is mortal. Mill points out that the conclusion is not inferred from the generalization stated in the major premise, for it is already included in that generalization. The evidence for the mortality of the Duke of Wellington is the same as that for all men, namely John and Thomas and other known individual cases. It is on the basis of this instance of the syllogism that Mill maintains his general principle that all inference is from particulars to particulars. But what the argument presupposes is that all universal propositions are empirical generalizations, as in his example, All men are mortal. This, however, is just the issue which separated Mill from the German or à priori school. The latter maintained that there are some propositions which are necessary, and that necessary propositions cannot be got by empirical generalization. They must therefore be à priori. Of the five examples which were cited earlier of propositions which Mill regarded as truly asserting matters of fact, four would have been regarded by Kant as necessary, namely, the arithmetical and geometrical propositions, the causal axiom, and the principle of contradiction, although he would not, as Mill did, have considered this last to be an assertion of fact.12 As necessary, they cannot be derived from experience. But Mill is not only opposing the German or à priori school. In the case of mathematics he felt that he was opposing almost everyone. “Why,” he asks, “are mathematics by almost all philosophers, and (by some) even those branches of natural philosophy which, through the medium of mathematics, have been converted into deductive sciences, considered to be independent of the evidence of experience and observation, and characterized as systems of Necessary Truth?” (224.)
Because it is the deductive sciences which give rise to the illusion that there are systems of necessary truth, an important part of Mill’s defence of the main thesis of his logic of experience is to consider the nature of deduction and of the deductive sciences, in order to get rid altogether of the distinction between induction and deduction as two opposed types of inference. There is only one kind of inference. Mill’s account of deduction is clear in spite of the fact that his key word in the account, “reasoning,” is sometimes used in a broad sense, sometimes in a more narrow and technical sense, without notice of change from one to the other being given. In what Mill calls “the most extensive sense of the term,” reasoning is a synonym of inference, and he frequently couples the words “reasoning or inference.” In its narrower sense it is the process which is exemplified in the syllogism, and is alternatively called by him ratiocination or deduction. But syllogism or ratiocination or deduction is not inference; it is rather what in theology and law is called interpretation. “All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formulae for making more: The major premise of a syllogism, consequently, is a formula of this description: and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula: the real logical antecedent, or premise, being the particular facts from which the general proposition was collected by induction” (193). Just as in a case of law or of theological dogma, the
only point to be determined is, whether the authority which declared the general proposition, intended to include this case in it; and whether the legislator intended his command to apply to the present case among others, or not. This is ascertained by examining whether the case possesses the marks by which, as those authorities have signified, the cases which they meant to certify or to influence may be known. The object of the inquiry is to make out the witness’s or the legislator’s intention, through the indication given by their words. This is a question, as the Germans express it, of hermeneutics. The operation is not a process of inference, but a process of interpretation.
In this last phrase we have obtained an expression which appears to me to characterize, more aptly than any other, the functions of the syllogism in all cases.
The term induction applies equally to inference from particulars to a general proposition or formula, and to inference from particulars to particulars according to the formula. Usage, however, tends to limit the term induction to the former, and to call the interpretation of the formula deduction. Hence, Mill will speak of an inference to an unobserved case as consisting of “an Induction followed by a Deduction; because, although the process needs not necessarily be carried on in this form, it is always susceptible of the form, and must be thrown into it when assurance of scientific accuracy is needed and desired” (203).
The task of determining whether Socrates or the Duke of Wellington have the marks which justify bringing them under the general formula, All men are mortal, is easily accomplished by observation, and the result stated in the minor premise. But not all cases are so simple. The minor premise may by itself have to be established by an induction followed by a deduction or interpretation, that is, by a syllogism. The succession of deductions or interpretations may, as required, be extended indefinitely, and this is pre-eminently the case in the mathematical sciences, where the inductions themselves may be obvious, while yet it may be far from obvious whether particular cases come under these inductions. Geometry rests on a very few simple inductions, the formulae of which are expressed in the axioms and a few of the so-called definitions.
The remainder of the science is made up of the processes employed for bringing unforeseen cases within these inductions; or (in syllogistic language) for proving the minors necessary to complete the syllogisms; the majors being the definitions and axioms. In those definitions and axioms are laid down the whole of the marks, by an artful combination of which it has been found possible to discover and prove all that is proved in geometry. The marks being so few, and the inductions which furnish them being so obvious and familiar; the connecting of several of them together, which constitutes Deductions, or Trains of Reasoning, forms the whole difficulty of the science, and with a trifling exception, its whole bulk; and hence Geometry is a Deductive Science.
Every science aspires to the condition of mathematics, that is, to be a deductive science, resting on a small number of inductions of the highest generality.13 A science begins as almost wholly observational and experimental, each of its generalizations resting on its own special set of observations and experiments. Some sciences, however, by being rendered mathematical, have already advanced to the stage of becoming almost entirely “sciences of pure reasoning; whereby multitudes of truths, already known by induction from as many different sets of experiments, have come to be exhibited as deductions or corollaries from inductive propositions of a simpler and more universal character” (218). But they are not, says Mill, to be regarded as less inductive by virtue of having become more deductive.
A deductive science is, then, one which is distinguished from an experimental science, not as being independent of observation and experiment, thereby constituting a system of necessary truth, but one whose conclusions are arrived at by successive interpretations of inductions of great generality, instead of resting directly on observation and experiment. Whewell, who was for Mill the chief spokesman for the à priori school in matters of science, found him to be much too optimistic—in the light of the history of the sciences—about the efficacy of deduction in their progress. Whewell was, however, prepared to accept Mill’s account of the nature of deduction as being the interpretation of the formula contained in the major premise.
I say then that Mr. Mill appears to me especially instructive in his discussion of the nature of the proof which is conveyed by the syllogism; and that his doctrine, that the force of the syllogism consists in an inductive assertion, with an interpretation added to it, solves very happily the difficulties which baffle other theories of this subject. I think that this doctrine of his is made still more instructive, by his excepting from it the cases of Scriptural Theology and of Positive Law, as cases in which general propositions, not particular facts, are our original data.14
Thus, while the main thesis of Mill’s logic of experience, that all inference is from particulars to particulars, is derived from an analysis of the syllogism, that analysis is inconclusive for Mill’s purpose; Whewell is quite happy to accept the analysis, since it allows that the general proposition expressed in the major premise may be an original datum not derivative from particular facts. In this class Whewell would put the axioms of geometry, which he would say are necessary truths and hence incapable of being inductively arrived at. To complete the case for his main thesis Mill must dispose of the doctrine that there are necessary truths, such as, Two straight lines cannot enclose a space. Because we cannot, according to Mill, look at any two straight lines which intersect without seeing that they continue to diverge, he asks what reason there is for maintaining that our knowledge of the axiom is grounded in any other way than through that evidence of the senses by which we know other things. This experiential evidence is quite sufficient. “The burden of proof lies on the advocates of the contrary opinion: it is for them to point out some fact, inconsistent with the supposition that this part of our knowledge of nature is derived from the same sources as every other part” (232). Mill finds that the à priori case is made to rest on two arguments, both of which he takes from Whewell.
The first argument is that we are able to perceive in intuition that two straight lines cannot enclose a space. Whewell calls it “imaginary looking,” and maintains that by means of it alone, and without any real looking, that is independently of, and prior to, visual perception, we can “see” that the two straight lines cannot enclose a space. But for Mill this is easily explainable by the abundantly experienced fact that spatial forms in the imagination can exactly resemble those given to visual perception. Hence it is possible to conduct experiments with lines and angles in the imagination, and to know that the conclusions hold for observable lines and angles in the external world. Whether we work with mental diagrams or real figures, the conclusions are inductions.15 Mill must be counted among those philosophers who believe that geometry rests on intuition, if we include under this heading what he calls “inspection” or “contemplation,” whether in imagination or visually. He sees no reason for maintaining that such intuition has any à priori form. Against such a position as Kant’s, who maintains that there must be à priori forms of intuition if the necessity which characterizes mathematical propositions is to be accounted for, Mill would simply deny that there is any necessity in the mathematical propositions to be accounted for.
This brings us to the second argument for the apriority of certain truths, namely that they are necessary, and must, therefore, be know independently of experience. Whatever force this argument has depends on what is meant by the term “necessary,” and in particular what meaning it has for those who use it to qualify the term “truth.”
Mill recognized that in popular usage there were two kinds of necessity which were referred to, logical necessity and causal necessity. The latter he variously calls philosophical or metaphysical or physical necessity. He remarks in one of his letters, “You are probably, however, right in thinking that the notion of physical necessity is partly indebted for the particular shape it assumes in our minds to an assimilation of it with logical necessity.”16 In his Autobiography Mill writes:
during the later returns of my dejection, the doctrine of what is called Philosophical Necessity weighed on my existence like an incubus. I felt as if I was scientifically proved to be the helpless slave of antecedent circumstances; as if my character and that of all others had been formed for us by agencies beyond our control, and was wholly out of our own power. . . . I pondered painfully on the subject, till gradually I saw light through it. I perceived, that the word Necessity, as a name for the doctrine of Cause and Effect applied to human action, carried with it a misleading association; and that this association was the operative force in the depressing and paralysing influence which I had experienced.17
Thereafter, Mill says, he discarded altogether “the misleading word Necessity.” The theory which released him from his dilemma is contained in the chapter of the Logic entitled “Of Liberty and Necessity,” and which he described to de Tocqueville as “the most important chapter” in that work. There he writes, “The application of so improper a term as Necessity to the doctrine of cause and effect in the matter of human character, seems to me one of the most signal instances in philosophy of the abuse of terms, and its practical consequences one of the most striking examples of the power of language over our associations. The subject will never be generally understood, until that objectionable term is dropped.” (841.)
Hume had maintained that necessity, or necessary connection, is an essential part of our idea of cause and effect. He claimed to have shown just what our idea of necessity is, or what we mean when we use the term. Mill does not at all agree with Hume as to what the term means, but he agrees that the term is used with meaning.18 He himself, however, uses an expression which he regards as less objectionable. He points out that when we define the cause of a thing as the antecedent which the thing invariably follows, we do not mean that which the thing invariably has followed in our past experience, but that which it invariably will follow. Thus we would not call night the cause of day. The sun could cease to rise without, for all we know, any violation of the laws of nature. “Invariable sequence . . . is not synonymous with causation, unless the sequence, besides being invariable, is unconditional.” “This is what writers mean when they say that the notion of cause involves the idea of necessity. If there be any meaning which confessedly belongs to the term necessity, it is unconditionalness. That which is necessary, that which must be, means that which will be, whatever supposition we may make in regard to all other things.” (339.)
Thus the word necessity is eliminated from the treatment of causation, and a synonym will also be found for the word when used in its logical sense, namely certainty.19 The conclusions of a deductive science are said to be necessary as following certainly or correctly or legitimately from the axioms and definitions of the science, whether these latter, either as inductions or as assumptions, are true or false. But the à priori school refers to the axioms or principles of a science themselves as necessary truths. In what sense are they said to be necessary? For this sense Mill turns to Whewell as representative of the school. According to Whewell the necessity of a necessary truth lies in the impossibility of conceiving the reverse. “Now I cannot but wonder,” says Mill, “that so much stress should be laid on the circumstance of inconceivableness, when there is such ample experience to show, that our capacity or incapacity of conceiving a thing has very little to do with the possibility of the thing in itself; but is in truth very much an affair of accident, and depends on the past history and habits of our own minds” (238). Psychological impossibilities are contingent facts with a fluctuating history, and Mill points out that the history of science has abounded with “inconceivabilities” which have become actualities.
It has been noted that Mill denies that there are two kinds of inference, inductive and deductive. All inference is inductive. In this regard he stands in direct contrast with those who hold that all inference is deductive, an inference being valid by virtue of the relation of implication which holds between propositions. If the latter view of the nature of inference is taken, then according to some, Hume included, induction could be justified only if every induction could be put in deductive form with one supreme premise, such as the principle of the uniformity of nature or the causal axiom. Only then would inductive conclusions be implied, and hence logically valid.
It is sometimes said that not only did Mill share this view as to what is required to make inductions valid, but he also undertook to justify the one supreme premise by induction. To assert that the principle which justifies induction is itself an induction from experience is, of course, to argue in a circle. Hume’s conclusion was, therefore, that inductive inference cannot be justified, that is to say, converted into a deductive inference. But Mill, it is widely thought, happily committed himself to the circle. Let us consider, then, Mill’s position in relation to what is variously called the problem of induction, or Hume’s problem, or the justification of induction. Mill says:
the proposition that the course of nature is uniform, is the fundamental principle, or general axiom, of Induction. . . . I hold it to be itself an instance of induction. . . . Far from being the first induction we make, it is one of the last, or at all events one of those which are latest in attaining strict philosophical accuracy. . . . The truth is, that this great generalization is itself founded on prior generalizations. The obscurer laws of nature were discovered by means of it, but the more obvious ones must have been understood and assented to as general truths before it was ever heard of. . . . In what sense, then, can a principle, which is so far from being our earliest induction, be regarded as our warrant for all the others? In the only sense, in which . . . the general propositions which we place at the head of our reasonings when we throw them into syllogisms, ever really contribute to their validity. As Archbishop Whately remarks, every induction is a syllogism with the major premise suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism, by supplying a major premise. If this be actually done, the principle which we are now considering, that of the uniformity of the course of nature, will appear as the ultimate major premise of all inductions, and will, therefore, stand to all inductions in the relation in which . . . the major proposition of a syllogism always stands to the conclusion; not contributing at all to prove it, but being a necessary condition of its being proved; since no conclusion is proved, for which there cannot be found a true major premise.
This makes it clear that Mill is not seeking to solve Hume’s problem, for the latter rests on the assumption that inductive inference is justified only if it can be shown to be a deductive inference. But since for Mill there is no such thing as deductive inference, and since the major premise of the syllogism into which any induction can be formulated, forms no part of the proof for the inductive conclusion, he cannot be considered to mean by “the warrant” for induction, what those who have concerned themselves with Hume’s problem have called the “justification” of induction. The formulation of an induction syllogistically or deductively does not, for Mill, relate an inference to the evidence for it. It is rather the interpretation of an induction, in which the major premise, as we have seen, is a formula, not from which the conclusion is inferred, but in accordance with which the conclusion is inferred. It is, in Mill’s language, a warrant or authorization for inferring the conclusion from the particulars which constitute the evidence for it. It warrants the inference because it states in, for example, the proposition, All men are mortal, that having the attributes of a man is satisfactory evidence for the inference to the attribute mortality. The function of the minor premise in turn is to state that in the particular case in question, that of the Duke of Wellington, this evidence does exist for the inference that he will die. According to this account of the syllogism it is not necessary that inductions or inferences in order to be sound should be warranted. It is the evidence from the particular facts alone, and not they together with a general warrant, which makes an induction or inference valid, and this will be no less true for the induction to the principle of the uniformity of nature than for any other induction. Of course, as the ultimate warrant for all other inductions, the principle cannot itself as an induction be warranted by a formula. But its validity, like that of other inductions, is independent of any general warrant. Contrary to a common misunderstanding there is no circle in Mill’s account of “the ground of induction.”
This throws some light on the way in which Mill conceived the nature of scientific explanation. Although in the deductively ordered sciences major premises state general matters of fact (either the uniformities of coexistence in the case of the axioms of mathematics, or of succession in the case of the laws of physical science), they nevertheless function as formulae or rules for making inferences from particular facts to particular facts, as well as providing security that the inferences have been correctly made. To explain a particular fact is, for Mill, to show that the way in which it came about is an instance of a causal law. The fact is explained when its mode of production is deduced from a law or laws. To explain a law is in turn to deduce it from another law or laws more general than itself, and the ultimate goal of the sciences is to find “the fewest general propositions from which all the uniformities existing in nature could be deduced” (472). Viewed in terms of the directional function for inference which Mill assigns to major premises in deductions, this means that scientific explanation consists not in dispelling the mysteries of nature, but in bringing the formulae for inferring particulars from particulars under the fewest and most general formulae for inferring. So far as laws are viewed in their character as statements of general matters of fact, Mill says, “What is called explaining one law of nature by another, is but substituting one mystery for another; and does nothing to render the general course of nature other than mysterious; we can no more assign a why for the more extensive laws than for the partial ones” (471).
The case against the à priori school is for Mill complete when he has established that all inference is from particulars to particulars. It is this which makes his logic a logic of experience, for he could consider himself to be on philosophically neutral ground in asserting that particular facts, not known inferentially, can be known only by observation. The empiricism of Mill’s logic is solely of that kind in which “experience” refers to observation that something is the case. So far as the more radical type of empiricism is concerned, in which “experience” refers to feelings and states of consciousness, and on which his phenomenalism is built, Mill scrupulously seeks to avoid resting his logical theory on it, in order that the partisans of Hartley and of Reid, of Locke and of Kant, can meet on common ground. However conspicuous the appearance of Mill’s phenomenalism in the System of Logic, it is never used for grounding his logical theory, nor on the other hand is it in any respect the outcome of his argument. When Mill introduces phenomenalist doctrines they are accompanied by expressions of the following sort:
here the question merges in the fundamental problem of metaphysics properly so called: to which science we leave it (59).
For the purposes of logic it is not of material importance which of these opinions we adopt (65).
But, as the difficulties which may be felt in adopting this view of the subject cannot be removed without discussions transcending the bounds of our science, I content myself with a passing indication, and shall, for the purposes of logic, adopt a language compatible with either view of the nature of qualities
Among nameable things are:
. . . Bodies, or external objects which excite certain of those feelings, together with the powers or properties whereby they excite them; these latter (at least) being included rather in compliance with common opinion, and because their existence is taken for granted in the common language from which I cannot prudently deviate, than because the recognition of such powers or properties as real existences appears to be warranted by a sound philosophy
As a logic of truth whose concern is with propositions asserting observable matters of fact in a world of things denoted by names, Mill’s logic rests on a certain ontology which is reflected in “common language,” and which as such provides neutral ground for metaphysicians of different schools. For Mill as a phenomenalist metaphysician the only constituents of matters of fact are individual sensations and permanent groups of possible individual sensations, some of which on occasion become actual. However, common language, he observes, allows for no designation of sensations other than by circumlocution. It cannot designate them by attribute-words. On the other hand for Mill, author of the logic of experience, the constituents of the observed matters of fact from which inferences are made are of quite a different nature, and they are of two kinds, either substances or the attributes by which substances are designated. The substances are individuals, and the attributes are universals. While a sensation is always individual, “a quality, indeed, in the custom of the language, does not admit of individuality; it is supposed to be one thing common to many.”
In his various discussions of universals Mills rejects each of realism, conceptualism, and nominalism. Of realism he has this to say,
Modern philosophers have not been sparing in their contempt for the scholastic dogma that genera and species are a peculiar kind of substances, which general substances being the only permanent things, while the individual substances comprehended under them are in a perpetual flux, knowledge, which necessarily imports stability, can only have relation to those general substances or universals, and not to the facts or particulars included under them. Yet, though nominally rejected, this very doctrine . . . has never ceased to poison philosophy.
It is, however, important to take note of the kind of realism which Mill was rejecting. In order to do so we must look first at his distinction between general names and individual or singular names, and also at his distinction between concrete and abstract names. A general name is one which can be affirmed of an indefinite number of things because they possess the attributes expressed by that name; an individual name is one which can be truly affirmed, in the same sense, of only one thing. A concrete name is one which stands for a thing or things. Thus “white” is a concrete name, for it is the name of all things which are white. “Whiteness” on the other hand is an abstract name, for it is the name of the attribute possessed by those things. By realism Mill means the doctrine according to which “concrete general terms were supposed to be, not names of indefinite numbers of individual substances, but names of a peculiar kind of entities termed Universal Substances” (757). But, while Mill’s concrete general names do not refer to real universals, but only to individual things, the attributes to which his abstract names refer perform the functions of real universals in his theory of inference. He warns the reader that in using the term “abstract name” he is not following the unfortunate practice initiated by Locke of applying it to names which are the result of abstraction or generalization. He is retaining the sounder scholastic usage, according to which an abstract name refers to an attribute as opposed to a thing or object. A concrete general name denotes many different objects, but in the case of an abstract name, “though it denotes an attribute of many different objects, the attribute itself is always conceived as one, not many” (30). And so it is in Mill’s account of the import of propositions and of the syllogism:
Every proposition which conveys real information asserts a matter of fact. . . . It asserts that a given object does or does not possess a given attribute; or it asserts that two attributes, or sets of attribues, do or do not (constantly or occasionally) co-exist. . . .
Applying this view of propositions to the two premises of a syllogism, we obtain the following results. The major premise, which . . . is always universal, asserts, that all things which have a certain attribute (or attributes) have or have not along with it, a certain other attribute (or attributes). The minor premise asserts that the thing or set of things which are the subject of that premise, have the first-mentioned attribute; and the conclusion is, that they have (or that they have not), the second.
The realism involved in this did not escape Herbert Spencer. Mill’s reply to his criticism is instructive:
Mr. Herbert Spencer . . . maintains, that we ought not to say that Socrates possesses the same attributes which are connoted by the word Man, but only that he possesses attributes exactly like them. . . .
The question between Mr. Spencer and me is merely one of language; for neither of us . . . believes an attribute to be a real thing, possessed of objective existence; we believe it to be a particular mode of naming our sensations, or our expectations of sensation, when looked at in their relation to an external object which excites them.
But Mill says that he has chosen to use the phraseology “commonly used by philosophers” because it seems best. As he goes on, however, he indicates the unavoidability of regarding attributes as real universals if there is to be any such thing as language at all:
Mr. Spencer is of opinion that because Socrates and Alcibiades are not the same man, the attribute which constitutes them men should not be called the same attribute; that because the humanity of one man and that of another express themselves to our senses not by the same individual sensations but by sensations exactly alike, humanity ought to be regarded as a different attribute in every different man. But on this showing, the humanity even of any one man should be considered as different attributes now and half-an-hour hence; for the sensations by which it will then manifest itself to my organs will not be a continuation of my present sensations, but a repetition of them; fresh sensations, not identical with, but only exactly like the present. If every general conception, instead of being “the One in the Many,” were considered to be as many different conceptions as there are things to which it is applicable, there would be no such thing as general language. A name would have no general meaning if man connoted one thing when predicated of John, and another, though closely resembling, thing when predicated of William.
Thus language prohibits Mill from basing his theory of inference on phenomenalism.
The principal characteristics of Mill’s empiricism, so far as it is related to his logical doctrines, can be summed up. It is observational, not sensational as in his phenomenalism. It is metaphysically neutral, in the sense of being based on an ontology embedded in “common language,” even though the terms it uses, like attributes, powers, states, are for Mill, as a phenomenalist, “not real things existing in objects” but “logical fictions.”20 Mill’s empiricism differs from that of Hume and modern empiricists in general in that in his all inference is inductive, while in theirs all valid inference is deductive. It is more radical than theirs in that it includes mathematics within its scope, and that on the ground, which they reject, that mathematical propositions assert matters of fact. They prefer to regard them as necessary, or, in Mill’s language, as merely “verbal.” Finally, it is an empiricism in which the ideal of any science is to become deductive instead of directly experimental, or “empirical” in the old sense of the term. It achieves this ideal to the extent that less general warrants to infer (or major premises) can be brought under more general warrants.
We come now to the second way in which Mill’s logic has been characterized. It has been said, for example, that “Mill is the one great logician of the school which, following Hume, tried to rest logic upon psychology.”21 Mill’s own often quoted words appear to give ample justification for taking this view. He says of logic, “It is not a Science distinct from, and coordinate with, Psychology. So far as it is a science at all, it is a part, or branch, of Psychology; differing from it, on the one hand as a part differs from the whole, and on the other, as an Art differs from a Science. Its theoretic grounds are wholly borrowed from Psychology, and include as much of that science as is required to justify the rules of the art.”22
There are four distinct views which are, or might be, taken as to the sense in which Mill’s logic is grounded in psychology. First, we may consider a statement by Ernest Nagel: “What is characteristic of Mill is his conception of what the basic facts are to which beliefs should be subjected for testing, and what are the essential requirements for the process of testing them. The theoretical grounds of logic, he explicitly argued, are ‘wholly borrowed from Psychology’; and it is the psychological assumptions of sensationalistic empiricism that are made to support the principles of evidence which emerge in the Logic.”23 Mill’s sensationalistic empiricism is given in the important chapter of The System of Logic, “Of the Things denoted by Names,” which incorporated much of what he was later to say in “The Psychological Theory of the Belief in an External World.”24 It is a chapter which is decisive for his account of the import of propositions and for his theory of syllogism. But while “the psychological theory” is incorporated in the chapter, it does not exhaust it. Moreover, as we have already observed, not only does Mill maintain that “for the purposes of logic it is not of material importance” whether we adopt the psychological theory or not, but his logic is also, in fact, entirely independent of the psychological theory. The basic facts to which beliefs should be subjected for testing are those of an observational, not a sensationalistic, empiricism.
Secondly, we can consider Husserl’s reference to “the misled followers of British empiricism,” according to whose point of view “concepts, judgments, arguments, proofs, theories, would be psychic occurrences; and logic would be, as John Stuart Mill said it is, a ‘part or branch of psychology.’ This highly plausible conception is logical psychologism.”25 But does this cover Mill’s own case? It would at first appear so. “Our object,” he says, “will be, to attempt a correct analysis of the intellectual process called Reasoning or Inference, and of such other mental operations as are intended to facilitate this. . . .” (12). In turning to the subject of inference in Book II, Mill says, “The proper subject, however, of Logic is Proof” (157). To understand what proof is, it is necessary first to understand the nature of what is proved, namely, propositions, for it is propositions which are believed or disbelieved, affirmed or denied, as true or false. In inquiring into the nature of propositions we must, says Mill, distinguish, as all language recognizes, between “the state of mind called Belief” and “what is believed”; between “an opinion” and “the fact of entertaining the opinion”; between “assent” and “what is assented to”:
Logic . . . has no concern with the nature of the act of judging or believing; the consideration of that act, as a phenomenon of the mind, belongs to another science. Philosophers, however, from Descartes downward, and especially from the era of Leibnitz and Locke, have by no means observed this distinction and would have treated with great disrespect any attempt to analyse the import of Propositions, unless founded on an analysis of the act of Judgment. A proposition, they would have said, is but the expression in words of a Judgment. The thing expressed, not the mere verbal expression, is the important matter. When the mind assents to a proposition, it judges. Let us find out what the mind does when it judges, and we shall know what propositions mean, and not otherwise.
Mill observed that almost every writer on logic in the two previous centuries had treated the proposition as a judgment in which one idea or conception is affirmed or denied of another, as a comparison of two ideas, or, in the language of Locke, as perception of the agreement or disagreement of ideas. But, Mill points out, an account of the process occurring in the mind is irrelevant to determining the nature of propositions, for propositions are not about our ideas but about things. “The notion that what is of primary importance to the logician in a proposition, is the relation between the two ideas corresponding to the subject and predicate, (instead of the relation between the two phenomena which they respectively express), seems to me one of the most fatal errors ever introduced into the philosophy of Logic; and the principal cause why the theory of the science has made such inconsiderable progress during the last two centuries” (89).
Mill has said that to understand the nature of proof it is necessary to understand the nature of propositions, for it is these which are proved. But, in turn, to understand the nature of propositions, or the meaning of what is asserted, it is necessary to consider the nature of the meanings of names, for in every proposition one name is asserted of another name, the predicate of the proposition being the name which denotes what is affirmed or denied, and the subject being the name which denotes the person or thing of which something is affirmed or denied. It is because the import of propositions is determined by the import of names that the consideration of the latter becomes the starting point for the analysis of reasoning or inference. In treating of the import of names one of Mill’s principal intentions is to depsychologize the theory of meaning in radical fashion. A meaning of a name is not an idea in the mind; it is not a mental phenomenon. This forms the basis of his attack on conceptualism. Mill says, “. . . I consider it nothing less than a misfortune, that the words Concept, General Notion, or any other phrase to express the supposed mental modification corresponding to a class name, should ever have been invented. Above all, I hold that nothing but confusion ever results from introducing the term Concept into Logic, and that instead of the Concept of a class, we should always speak of the signification of a class name.”26 Nor is the meaning of a name the thing or things denoted by the name. Its meaning is what the name connotes—that attribute or set of attributes by the possession of which things can be said to be denoted by that name. A meaning is a real universal. So far as concepts and judgments are concerned, Mill’s logic is not an exemplification of what Husserl calls psychologism, but, rather, a forceful condemnation of it.27
Thirdly, it has been said of Mill that “In his view logical and mathematical necessity is psychological; we are unable to conceive any other possibilities than those which logical and mathematical propositions assert.”28 Mill denied that logical principles (the so-called laws of thought) and mathematical axioms possessed necessity. It was those whom he opposed who attributed necessity to them, and the necessity which they attributed was, according to Mill, nothing but the psychological inability to conceive their negation. Such psychological inability could be fully accounted for by the laws of association, and it had no bearing on the truth or falsehood of the logical or mathematical propositions asserted. These are true only as they are generalizations from the facts of experience. When Sir William Hamilton says of the laws of identity, contradiction, and excluded middle, “To deny the universal application of the three laws is, in fact, to subvert the reality of thought; and as this subversion is itself an act of thought, it in fact annihilates itself. When, for example, I say that A is, and then say that A is not, by the second assertion I sublate or take away what, by the first assertion, I posited or laid down; thought, in the one case, undoing by negation what, in the other, it had by affirmation done,” Mill simply comments, “This proves only that a contradiction is unthinkable, not that it is impossible in point of fact.”29 This third version of psychologism attributed to Mill’s conception of logic is repudiated by him in his criticisms of Spencer in Book II, Chapter vii. In Book V, “On Fallacies” it appears among the first in the five classes of fallacies.
Fourthly, it might be said that Mill’s statement that logic is a branch of psychology confuses questions of validity with questions of fact. This is perhaps what is most often meant by the term psychologism as applied to a theory of logic. Mill’s statement occurs in his analysis of Sir William Hamilton’s conception of logic as a science, and it is important to consider it within that context. Hamilton had said that logic is both a science and an art, without, however, in Mill’s view finding any satisfactory basis for distinguishing between the science and the art. As science its subject matter is stated to be “the laws of thought as thought.” Mill finds that by this Hamilton means that the laws are “the conditions subject to which by the constitution of our nature we cannot but think.” But it soon turns out that this is “an entire mistake”; that they are not laws which by its nature the mind cannot violate, but laws which it ought not to violate if it is to think validly. Laws now mean precepts or rules.
So that, after all, the real theory of Thought—the laws, in the scientific sense of the term, of Thought as Thought—do not belong to Logic, but to Psychology: and it is only the validity of thought which Logic takes cognisance of. It is not with Thought as Thought, but only as Valid thought, that Logic is concerned. There is nothing to prevent us thinking contrary to the laws of Logic: only, if we do, we shall not think rightly, or well, or conformably to the ends of thinking, but falsely, or inconsistently, or confusedly. This doctrine is at complete variance with the saying of our author in his controversy with Whately, that Logic is, and never could have been doubted to be, in Whately’s sense of the terms, both a Science and an Art. For the present definition reduces it to the narrowest conception of an Art—that of a mere system of rules. It leaves Science to Psychology, and represents Logic as merely offering to thinkers a collection of precepts, which they are enjoined to observe, not in order that they may think, but that they may think correctly, or validly.30
Nevertheless Mill thinks that with this Hamilton is nearer the mark. Logic is not the theory of thought as thought, but the theory of valid thought, not of thinking, but of valid thinking. At the same time he does not agree with Hamilton’s final position, or that into which Mill drives him, in so far as it implies that logic is merely an art. The art, the set of rules, does have theoretical grounds, and these belong to psychology, though constituting a very limited part of it; that is, it “includes as much of that science as is required to justify the rules of art.” Here Mill is using the term psychology in the broadest sense, to include everything that comes under the heading of thinking; it includes not only what, by the definition of psychology given in the System of Logic, would be an inquiry into the laws or uniformities according to which one mental phenomenon succeeds another; it also includes “a scientific investigation into the requisites of valid thinking,” or the conditions for distinguishing between good and bad thinking. The first kind of inquiry, concerned as it is with what is common to all thinking, good or bad, valid or invalid, “is irrelevant to logic, unless by the light it indirectly throws on something besides itself.” Logic for Mill borrows nothing from it. Logic is concerned only with the second kind of inquiry. If Mill calls this latter a branch of psychology, it is solely because “the investigation into the requisites of valid thinking” is theory of valid thinking, a type of theory which is essential for the grounding of rules, or of logic as an art. Not only does Mill’s statement that logic is “a part or branch of Psychology” not imply a confusion of questions of justification or validity with questions of fact, the statement occurs within a discussion dominated by the great importance which he attaches to keeping separate the two kinds of questions.
For Mill there were in logic two sets of rules: the rules of the syllogism for deduction, and the four experimental methods for induction. The former he considered to be available in “the common manuals of logic.” The latter he considered himself to be formulating explicitly for the first time. The question as to how these rules of art can be viewed as grounded in the science of valid thinking must be brought under the larger question as to how rules of art in general are grounded in science. For Mill, the way in which they are grounded is universally the same for all arts in which there are rules. He distinguishes two kinds of practical reasoning. One is typified in the reasoning of a judge, the other in that of a legislator. The judge’s problem is to interpret the law, or to determine whether the particular case before him comes under the intention of the legislator who made the law. Thus the reasoning of the judge is syllogistic, for syllogism or deduction consists in the interpretation of a formula. The legislator’s problem, on the other hand, is to find rules. This depends on determining the best means of achieving certain desired ends. It is science alone which can determine these means, for the relation between means and ends is the relation between causes and effects. In this second kind of practical reasoning, art prescribes the end, science provides the theorem which shows how it is to be brought about, and art then converts the theorem into a rule. In this way propositions which assert only what ought to be, or should be done, are grounded on propositions which assert only matters of fact.
The task of finding the rules of logic, whether of deduction or of induction, is of the same type as the legislator’s. Knowledge of what ought to be done, as expressed in the rules of art, must be grounded on knowledge of what is the case, as expressed in the theorems of science. The rules of the syllogism are the rules for interpreting an induction; the rules of induction are the rules for “discovering and proving general propositions.” What then are the theoretical foundations of these two classes of rules? So far as the rules for interpreting inductions are concerned Mill has nothing to say, for he is not concerned with the task of finding them. They exist already in the manuals of logic as the rules of the syllogism. But he sees himself as confronted with the task of stating in “precise” terms or, “systematically and accurately,” the rules or canons of induction for the first time, and the problem of their derivation does concern him, for he had both to find them and to justify them.31 In accordance with his own account of the logic of practice Mill looks to matter of fact to ground his rules for “discovering and proving general propositions.” “Principles of Evidence and Theories of Method are not to be constructed à priori. The laws of our rational faculty, like those of every other natural agency, are only learnt by seeing the agent at work.” (833.) In the Preface to the 1st edition, in which he describes what he had undertaken to do in the System of Logic, Mill says, “On the subject of Induction, the task to be performed was that of generalizing the modes of investigating truth and estimating evidence, by which so many important and recondite laws of nature have, in the various sciences, been aggregated to the stock of human knowledge” (cxii). He found that what metaphysicians had written on the subject of logic had suffered from want of sufficient acquaintance with the processes by which science had actually succeeded in establishing general truths, and even when correct they had not been specific enough to provide rules. On the other hand scientists, who had only to generalize the methods which they themselves use to get at the theoretical basis for the rules, had not thought it worthwhile to reflect on their procedures.
This suggests that Mill considered that the rules of induction are to be got by generalizing or reconstructing the procedures which the history of science reveals scientists actually to have used. It would appear as though Mill shared exactly Whewell’s conception of how we arrive at a theory of scientific method. Whewell says:
We may best hope to understand the nature and conditions of real knowledge by studying the nature and conditions of the most certain and stable portions of knowledge which we already possess: and we are most likely to learn the best methods of discovering truth, by examining how truths, now universally recognized, have really been discovered. Now there do exist among us doctrines of solid and acknowledged certainty, and truths of which the discovery has been received with universal applause. These constitute what we commonly term Sciences and of these bodies of exact and enduring knowledge, we have within our reach so large and varied a collection, that we may examine them, and the history of their formation, with a good prospect of deriving from their study such instruction as we seek.32
Whewell criticized Mill’s four experimental methods on the ground that they were not derived from the actual procedures of scientists as revealed in the history of science. “Who will tell us,” he asks, “which of the methods of inquiry those historically real and successful inquiries exemplify? Who will carry these formulæ through the history of the sciences, as they have really grown up; and show us that these four methods have been operative in their formation; or that any light is thrown upon the steps of their progress by reference to these formulæ?” (Quoted by Mill, 430.)
If Mill found his canons of induction by generalizing and reconstructing the procedures successfully followed by natural scientists, their derivation from this source does not appear in the System of Logic itself. Illustrations are given, but it is evidently not on these that the generalizations are based, for the illustrations were sought after the canons were formulated. When his publisher’s referee had suggested that more of these be added to the text, Mill replied, “I fear I am nearly at the end of my stock of apt illustrations. I had to read a great deal for those I have given. . . .”33 His debt to Bain for producing examples was considerable.34 How Mill actually arrived at his rules indicates, however, that he means by “generalization” something other than Whewell’s induction from the history of science. The groundwork for Mill’s rules is to be found in the chapters on causation which precede the enunciation of the rules, for he says, “The notion of Cause being the root of the whole theory of Induction, it is indispensable that this idea should, at the very outset of our inquiry be, with the utmost practicable degree of precision, fixed and determined” (326).
In the means-end relation, with which the rules of induction are concerned, the desired end is the solution of a problem—“the discovering and proving general propositions”—the means consists in the way in which the problem is solved. The generalizing which Mill performs lies not in generalizing the means used by scientists, but in generalizing and reconstructing what he considered to be the nature of their problem, or of reducing their inquiries to one fundamental type. The problem in its full generality having in his view been ascertained, Mill then proceeds to solve it. Indeed the very statement of the problem dictates the solution; there is no need to consult the history of science for its solution. The method of solution once found can then be formulated in canons; or in the language of Mill’s logic of practice, “Art . . . converts the theorem into a rule or precept.”35 In so far as the “Four Methods” can be said to be a generalization of scientists’ actual modes of investigation, it is not because Mill has taken those modes of investigation themselves as his data, but because the scientist must, in successfully solving his problem as subsumed under the general form given by Mill, have used the method of solution dictated by that general problem. Nor is Mill’s generalization of the problem of scientific investigation in any direct sense an induction from the history of science, but rests on a conception of the whole course of nature as one in which the general uniformity is made up out of separate threads of uniformity holding between single phenomena. The course of nature is a web composed of separate fibres, a “collective order . . . made up of particular sequences, obtaining invariably among the separate parts” (327). These separate threads are the laws of nature or the laws of causation. The task of the scientist, and the main business of induction, is to discover these separate threads, or “to resolve this complex uniformity into the simpler uniformities which compose it, and assign to each portion of the vast antecedent the portion of the consequent which is attendant on it” (379). The antecedents in the complex having been discriminated from one another, and the consequents also, it remains to be determined which antecedents and consequents are invariably connected. That being the nature of the problem, it is solved by methods of elimination, which are described by Mill as “the successive exclusion of the various circumstances which are found to accompany a phenomenon in a given instance, in order to ascertain what are those among them which can be absent consistently with the existence of the phenomenon. . . . [W]hatever can be eliminated, is not connected with the phenomenon by any law. . . . [W]hatever cannot be eliminated, is connected with the phenomenon by a law.” (392.)
To return now to the definition of logic as the science as well as the art of reasoning, in which the science consists of an analysis of the mental process which takes place when we reason, and the art consists of the rules grounded on that science, it can be said that in the case of induction the mental process consists in the solving of a problem stated in its full generality. Mill discovers what this mental process is by directly solving the problem himself. The account of this process constitutes the theoretical part of the logic of induction and is found in the chapters on causation; it reveals the means-end relation which provides the foundation for the rules of discovering the solution for any particular problem which can be subsumed under the general problem of induction. In basing the rules of art on the theoretical relation between means and end no more confusion arises here between questions of validity and questions of fact than in any other sphere of practice concerned with the means to a desired end.
In conclusion it may be remarked that any logic which deals with inference, as well as any which deals with scientific method, is concerned with a psychological process. Only persons with mental capacities infer or are governed by methods. In so far as Mill considered the principal subject matter of logic to be inference, and not implication, he was quite correct in asserting it to be a branch of psychology. This, and no more, constitutes the psychologism of his System of Logic. But Mill, in taking inference to be his subject, is in so numerous a company—one, moreover, composed of such varied types of logical theorists—that one wonders why he should have been so singled out in this regard, if not for merely having called a spade a spade.
[1 ]Philosophy of Recent Times, ed. J. B. Hartmann (New York: McGraw-Hill, 1967), I, 14.
[2 ]The Philosophy of J. S. Mill (Oxford: Oxford University Press, 1953), 73-7.
[3 ]Autobiography, ed. Jack Stillinger (Boston: Houghton Mifflin, 1969), 95.
[4 ]“Coleridge,” in Essays on Ethics, Religion, and Society, ed. J. M. Robson, Collected Works, X (Toronto: University of Toronto Press, 1969), 125.
[5 ]Ibid., 128-9.
[6 ]Logic, 65 below. Henceforth references to the present edition of the Logic are given in parentheses in the text.
[7 ]Autobiography, 134.
[8 ]Ibid., 134-5.
[9 ]W. V. Quine, “Two Dogmas of Empiricism,” From a Logical Point of View (New York: Harper and Row, 1963), 20ff.
[10 ]An Examination of Sir William Hamilton’s Philosophy, 4th ed. (London: Longmans, 1872), 477-8.
[11 ]“But mine professes to be a logic of experience only, & to throw no further light upon the existence of truths not experimental, than is thrown by shewing to what extent reasoning from experience will carry us.” Letter to John Sterling, 4 Nov., 1839, in Earlier Letters, ed. F. E. Mineka, Collected Works, XIII (Toronto: University of Toronto Press, 1963), 412. Hereafter cited as EL, CW.
[12 ]The principle of contradiction belongs for Kant to logic, and he does not speak of logical principles as true.
[13 ]In the physical sciences these inductions would not be of uniform coexistences, as they are in the mathematical sciences, but of uniform successions, that is, causal laws. The “whole problem of the investigation of nature” consists in this: “What are the fewest assumptions, which being granted, the order of nature as it exists would be the result? What are the fewest general propositions from which all the uniformities existing in nature could be deduced?” (472.)
[14 ]On the Philosophy of Discovery (London: Parker, 1860), 289-90.
[15 ]For Mill it is merely a fact of our experience that space in our part of the universe is uniformly the same. He believed that there was ample evidence that it was the same also in the region of the fixed stars, but he accepts the possibility of space being differently constituted elsewhere. It would appear that, if the notion of non-Euclidean geometries were to make sense for Mill, it would have to be in terms of the possibility of experiencing elsewhere alternative kinds of actual space.
[16 ]To Thomas Squire Barrett (6/5/72), in Later Letters, ed. F. E. Mineka and D. Lindley, Collected Works, XVII (Toronto: University of Toronto Press, 1972), 1890.
[17 ]Autobiography, 101-2.
[18 ]Hume says, “Necessity may be defined two ways, conformably to the two definitions of cause, of which it makes an essential part. It consists in the constant conjunction of like objects, or in the inference of the understanding from one object to another.” (An Enquiry concerning Human Understanding [Oxford: Clarendon Press, 1894], 97.) By the latter Hume means the psychological compulsion to make the inference. Mill would reject both these definitions. He would reject the first on the grounds that causation is not mere uniformity, but unconditional uniformity, unconditional being for Mill a synonym of necessary; and the second on the ground that it has no relevance to facts in the external world.
[19 ]See the Textual Introduction, xci below, for references to successive revisions involving “necessity.”
[20 ]While there would seem to be no escape from the ontology embedded in “common language” so long as we are compelled to speak, Mill is completely hostile to the conception of language as a reflection of, and a clue to, the nature of things. He considered this notion to be a very extended and ancient prejudice: “scientific investigation among the Greek schools of speculation and their followers in the middle ages, was little more than a mere sifting and analysing of the notions attached to common language. They thought that by determining the meaning of words, they could become acquainted with facts.” (760.) According to Whewell, whom Mill here quotes with approval, it was Thales who was the founder of this method of doing philosophy. “When he was asked,” says Whewell, “ ‘What is the greatest thing?’ he replied ‘Place; for all other things are in the world, but the world is in it.’ In Aristotle we have the consummation of this mode of speculation. The usual point from which he starts in his inquiries is, that we say thus or thus in common language.” (Quoted by Mill, 761.) Mill’s case against this use of common language is the same as his case against conceptualism. “The propensity to assume that the same relations obtain between objects themselves, which obtain between our ideas of them, is here seen [with language] in the extreme stage of its development” (762).
[21 ]Brand Blanshard, The Nature of Thought (London: Allen and Unwin, 1948), I, 468.
[22 ]An Examination of Sir William Hamilton’s Philosophy, 461-2.
[23 ]John Stuart Mill’s Philosophy of Scientific Method, ed. Ernest Nagel (New York: Hafner, 1950), xxxii.
[24 ]Chapter xi of An Examination of Sir William Hamilton’s Philosophy.
[25 ]Edmund Husserl, Formal and Transcendental Logic, tr. Dorion Cairns (The Hague: Martinus Nijhoff, 1969), 153-4.
[26 ]An Examination of Sir William Hamilton’s Philosophy, 1st ed. (London: Longman, Green, Longman, Roberts, and Green, 1865), 331-2. In the 3rd ed. (London: Longmans, Green, Reader, and Dyer, 1867), the first of the two sentences quoted was revised to read: “. . . I think that the words Concept, General Notion, and other phrases of like import, convenient as they are for the lighter and every-day uses of philosophical discussion, should be abstained from where precision is required” (388).
[27 ]Mill’s criticism is less harsh in the Examination of Sir William Hamilton’s Philosophy than in the System of Logic. “Many writers have given good and valuable expositions of the principles and rules of Logic, from the Conceptualist point of view. The doctrines which they have laid down respecting Conception, Judgment, and Reasoning, have been capable of being rendered into equivalent statements respecting Terms, Propositions, and Arguments; these, indeed, were what the writers really had in their thoughts, and there was little amiss except a mode of expression which attempted to be more philosophical than it knew how to be. To say nothing of less illustrious examples, this is true of all the properly logical part of Locke’s Essay. His admirable Third Book requires hardly any other alteration to bring it up to the scientific level of the present time, than to be corrected by blotting out everywhere the words Abstract Idea, and replacing them by ‘the connotation of the class-name.’ ” (414.)
[28 ]D. W. Hamlyn, “Empiricism,” Encyclopaedia of Philosophy (New York: Macmillan, 1967), II, 503.
[29 ]An Examination of Sir William Hamilton’s Philosophy, 492-3.
[30 ]Ibid., 460-1.
[31 ]The extent of the novelty which Mill attributed to his formulation of the canons is indicated in a letter to Sir John Herschel, 1 May, 1843: “You will find that the most important chapter of the book, that on the four Experimental Methods, is little more than an expansion & a more scientific statement of what you had previously stated in the more popular manner suited to the purpose of your ‘Introduction’ ” EL, CW, XIII, 583). As for Bacon, it was he who recognized elimination as “the foundation of experimental inquiry.” For his criticism of the ancients’ inductio per enumerationem simplicem he “merited the title . . . of Founder of the Inductive Philosophy. The value of his own contributions to a more philosophical theory of the subject has certainly been exaggerated.” (Below, 392, 313.) “A revolution is peaceably and progressively effecting itself in philosophy, the reverse of that to which Bacon has attached his name. That great man changed the method of the sciences from deductive to experimental, and it is now rapidly reverting from experimental to deductive.” (482.) On the failure of Bacon’s inductive logic to produce any actual scientific results, Mill says, “But this, though not unfrequently remarked, has scarcely received any plausible explanation; and some, indeed, have preferred to assert that all rules of induction are useless, rather than suppose that Bacon’s rules are grounded on an insufficient analysis of the inductive process. Such, however, will be seen to be the fact, as soon as it is considered, that Bacon entirely overlooked Plurality of Causes.” (763.) It is not uncommon to link Mill’s conception of induction not only with Bacon’s but also with Hume’s, as given in the section of his Treatise of Human Nature entitled, “Rules by which to judge of causes and effects.” However, Mill makes no mention of Hume in this regard.
[32 ]The Philosophy of the Inductive Sciences (London: Parker, 1847), I, 1.
[33 ]EL, CW, XIII, 514.
[34 ]For examples of Bain’s assistance, see the Textual Introduction, lxviii and lxxi ff. below.
[35 ]Logic, 945. Mill provides five canons, with the titles, the Method of Agreement, the Method of Difference, the Joint Method of Agreement and Difference, the Method of Residues, and the Method of Concomitant Variations, but he calls them collectively “the Four Methods of Experimental Inquiry” without giving any direct explanation of this anomaly. For an explanation, see the Textual Introduction, n49 on lxviii below.
John Stuart Mill
- A Guide to JS Mill Online
- Ashley’s Introduction to Mill’s Principles of Political Economy
- Hayek on Mill’s early letters: Collected Works vol. XII
- Mill and Liberty as the Cardinal Moral Virtue
- Mill and Taylor
- Mill and Taylor on Women
- Mill on England, Ireland, Empire: Collected Works vol. VI
- Mill on Equality, Law, Education: Collected Works vol. XXI
- Mill on Ethics & Religion: Collected Works vol. X
- Mill on French History: Collected Works vol. XX
- Mill on Hamilton’s Philosophy: Collected Works vol. IX
- Mill on India: Collected Works vol. XXX
- Mill on Philosophy & Classics: Collected Works vol. XI
- Mill on Political Economy: Collected Works vol. II
- Mill on Politics & Society: Collected Works vol. XVIII
- Mill’s Additional Letters: Collected Works vol. XXXII
- Mill’s Autobiography, Literary Essays: Collected Works vol. I
- Mill’s Essays on Economics: Collected Works vol. IV
- Mill’s Journals & Debating Speeches: Collected Works vol. XXVIII
- Mill’s Later Letters: Collected Works vol. XIV
- Mill’s Newspaper Articles: Collected Works vol. XXII
- Mill’s Parliamentary Speeches: Collected Works vol. XXVIII
- Mill’s System of Logic: Selected Works vol. VII
- Mill’s The Spirit of the Age (1831)
- Mill’s Utilitarianism: Collected Works vol. X
- Mill, Collected Works, Table of Contents
- Mill: A Bibliographical Essay by John Gray
- Stephen’s Critique of Mill’s Idea of Liberty