Blackwood's Edinburgh Magazine, No. CCCXXXVI. October, 1843. Vol. LIV.

MILL'S LOGIC. 1

These are not degenerate days. We have still strong thinkers amongst us; men of untiring perseverance, who flinch before no difficulties, who never hide the knot which their readers are only too willing that they should let alone; men who dare write what the ninety-nine out of every hundred will pronounce a dry book; who pledge themselves, not to the public, but to their subject, and will not desert it till their task is completed. One of this order is Mr John Stuart Mill. The work he has now presented to the public, we deem to be, after its kind, of the very highest character, every where displaying powers of clear, patient, indefatigable thinking. Abstract enough it must be allowed to be, calling for an unremitted attention, and yielding but little, even in the shape of illustration, of lighter and more amusing matter; he has taken no pains to bestow upon it any other interest than what searching thought and lucid views, aptly expressed, ought of themselves to create. His subject, indeed—the laws by which human belief and the inquisition of truth are to be governed and directed—is both of that extensive and fundamental character, that it would be treated with success only by one who knew how to resist the temptations to digress, as well as how to apply himself with vigour to the solution of the various questions that must rise before him.

"This book," the author says in his preface, "makes no pretence of giving to the world a new theory of our intellectual operations. Its claim to attention, if it possess any, is grounded on the fact, that it is an attempt not to supersede, but to embody and systematize, the best ideas which have been either promulgated on its subject by speculative writers, or conformed to by accurate thinkers in their scientific enquiries.

"To cement together the detached fragments of a subject, never yet treated as a whole; to harmonize the true portions of discordant theories, by supplying the links of thought necessary to connect them, and by disentangling them from the errors with which they are always more or less interwoven—must necessarily require a considerable amount of original speculation. To other originality than this, the present work lays no claim. In the existing state of the cultivation of the sciences, there would be a very strong presumption against any one who should imagine that he had effected a revolution in the theory of the investigation of truth, or added any fundamentally new process to the practice of it. The improvement which remains to be effected in the methods of philosophizing, [and the author believes that they have much need of improvement,] can only consist in performing, more systematically and accurately, operations with which, at least in their elementary form, the human intellect, in some one or other of its employments, is already familiar."

Such is the manly and modest estimate which the author makes of his own labours, and the work fully bears out the character here given of it. No one capable of receiving pleasure from the disentanglement of intricacies, or the clear exposition of an abstruse subject; no one seeking assistance in the acquisition of distinct and accurate views on the various and difficult topics which these volumes embrace—can fail to read them with satisfaction and with benefit.

To give a full account—to give any account—of a work which traverses so wide a field of subject, would be here a futile attempt; we should, after all our efforts, merely produce a laboured and imperfect synopsis, which would in vain solicit the perusal of our readers. What we purpose doing, is to take up, in the order in which they occur, some of the topics on which Mr Mill has thrown a new light, or which he has at least invested with a novel interest by the view he has given of them. And as, in this selection of topics, we are not bound to choose those which are most austere and repulsive, we hope that such of our readers as are not deterred by the very name of logic, will follow us with some interest through the several points of view, and the various extracts we shall present to them.

The Syllogism.—The logic of Induction, as that to which attention has been least devoted, which has been least reduced to systematic form, and which lies at the basis of all other modes of reasoning, constitutes the prominent subject of these volumes. Nevertheless, the old topic of logic proper, or deductive reasoning, is not omitted, and the first passage to which we feel bound, on many accounts, to give our attention, is the disquisition on the syllogism.

Fortunately for us it is not necessary, in order to convey the point of our author's observations upon this head, to afflict our readers with any dissertation upon mode or figure, or other logical technicalities. The first form or figure of the syllogism (to which those who have not utterly forgotten their scholastic discipline will remember that all others may be reduced) is familiar to every one, and to this alone we shall have occasion to refer.

Who has not met—what young lady even, though but in her teens, has not encountered some such charming triplet as this, which looks so like verse at a distance, but, like some other compositions, approximates nothing the more on this account to poetry? Who has not learnt from such examples what is a major, what a middle term, and what the minor or conclusion?

As no one, in the present day, advises the adoption, in our controversies, of the syllogistic forms of reasoning, it is evident that the value of the syllogism must consist, not in its practical use, but in the accurate type which it affords of the process of reasoning, and in the analysis of that process which a full understanding of it renders necessary. Such an analysis supplies, it is said, an excellent discipline to the mind, whilst an occasional reference to the form of the syllogism, as a type or model of reasoning, insures a steadiness and pertinency of argument. But is the syllogism, it has been asked, this veritable type of our reasoning? Has the analysis which would explain it to be such, been accurately conducted?

Several of our northern metaphysicians, it is well known—as, for example, Dr Campbell and Dugald Stewart—have laid rude hands upon the syllogism. They have pronounced it to be a vain invention. They have argued that no addition of knowledge, no advancement in the acquisition of truth, no new conviction, can possibly be obtained through its means, inasmuch as no syllogism can contain any thing in the conclusion which was not admitted, at the outset, in the first or major proposition. The syllogism always, say they, involves a petitio principii. Admit the major, and the business is palpably at an end; the rest is a mere circle, in which one cannot advance, but may get giddy by the revolution. According to the exposition of logicians themselves, we simply obtain by our syllogism, the privilege of saying that, in the minor, of some individual of a class, which we had said, in the major, already of the whole class.

Archbishop Whately, our most distinguished expositor and defender of the Aristotelian logic, meets these antagonists with the resolute assertion, that their objection to the syllogism is equally valid against all reasoning whatever. He does not deny, but, on the contrary, in common with every logician, distinctly states, that whatever is concluded in the minor, must have been previously admitted in the major, for in this lies the very force and compulsion of the argument; but he maintains that the syllogism is the true type of all our reasoning, and that therefore to all our reasoning, the very same vice, the very same petitio principii, may be imputed. The syllogism, he contends, (and apparently with complete success,) is but a statement in full of what takes place mentally even in the most rapid acts of reasoning. We often suppress the major for the sake of brevity, but it is understood though not expressed; just as in the same manner as we sometimes content ourselves with merely implying the conclusion itself, because it is sufficiently evident without further words. If any one should so far depart from common sense as to question the mortality of some great king, we should think it sufficient to say for all argument—the king is a man!—virtually implying the whole triplet above mentioned:—

"In pursuing the supposed investigation, (into the operation of reasoning,)" says Archbishop Whately, "it will be found that every conclusion is deduced, in reality, from two other propositions, (thence called Premisses;) for though one of these may be and commonly is suppressed, it must nevertheless be understood as admitted, as may easily be made evident by supposing the denial of the suppressed premiss, which will at once invalidate the argument; e.g. if any one, from perceiving that 'the world exhibits marks of design,' infers that 'it must have had an intelligent author,' though he may not be aware in his own mind of the existence of any other premiss, he will readily understand, if it be denied that 'whatever exhibits marks of design must have had an intelligent author,' that the affirmative of that proposition is necessary to the solidity of the argument. An argument thus stated regularly and at full length, is called a syllogism; which, therefore, is evidently not a peculiar kind of argument, but only a peculiar form of expression, in which every argument may be stated."—Whately's Logic, p. 27.

"It will be found," he continues, "that all valid arguments whatever may be easily reduced to such a form as that of the foregoing syllogisms; and that consequently the principle on which they are constructed is the Universal Principle of reasoning. So elliptical, indeed, is the ordinary mode of expression, even of those who are considered as prolix writers,—i.e. so much is implied and left to be understood in the course of argument, in comparison of what is actually stated, (most men being impatient, even to excess, of any appearance of unnecessary and tedious formality of statement,) that a single sentence will often be found, though perhaps considered as a single argument, to contain, compressed into a short compass, a chain of several distinct arguments. But if each of these be fully developed, and the whole of what the author intended to imply be stated expressly, it will be found that all the steps, even of the longest and most complex train of reasoning, may be reduced into the above form."—P. 32.

That it is not the office of the syllogism to discover new truths, our logician fully admits, and takes some pains to establish. This is the office of "other operations of mind," not unaccompanied, however, with acts of reasoning. Reasoning, argument, inference, (words which he uses as synonymous,) have not for their object our advancement in knowledge, or the acquisition of new truths.

"Much has been said," says Archbishop Whately, in another portion of his work, "by some writers, of the superiority of the inductive to the syllogistic methods of seeking truth, as if the two stood opposed to each other; and of the advantage of substituting the Organon of Bacon for that of Aristotle, &c. &c., which indicates a total misconception of the nature of both. There is, however, the more excuse for the confusion of thought which prevails on this subject, because eminent logical writers have treated, or at least have appeared to treat, of induction as a kind of argument distinct from the syllogism; which, if it were, it certainly might be contrasted with the syllogism: or rather the whole syllogistic theory would fall to the ground, since one of the very first principles it establishes, is that all reasoning, on whatever subject, is one and the same process, which may be clearly exhibited in the form of syllogisms.

"This inaccuracy seems chiefly to have arisen from a vagueness in the use of the word induction; which is sometimes employed to designate the process of investigation and of collecting facts, sometimes the deducing an inference from those facts. The former of these processes (viz. that of observation and experiment) is undoubtedly distinct from that which takes place in the syllogism; but then it is not a process of argumentation: the latter again is an argumentative process; but then it is, like all other arguments, capable of being syllogistically expressed."—P. 263.

"To prove, then, this point demonstratively, (namely, that it is not by a process of reasoning that new truths are brought to light,) becomes on these data perfectly easy; for since all reasoning (in the sense above defined) may be resolved into syllogisms; and since even the objectors to logic make it a subject of complaint, that in a syllogism the premises do virtually assert the conclusion, it follows at once that no new truth (as above defined) can be elicited by any process of reasoning.

"It is on this ground, indeed, that the justly celebrated author of the Philosophy of Rhetoric objects to the syllogism altogether, as necessarily involving a petitio principii; an objection which, of course, he would not have been disposed to bring forward, had he perceived that, whether well or ill founded, it lies against all arguments whatever. Had he been aware that the syllogism is no distinct kind of argument otherwise than in form, but is, in fact, any argument whatever stated regularly and at full length, he would have obtained a more correct view of the object of all reasoning; which is merely to expand and unfold the assertions wrapt up, as it were, and implied in those with which we set out, and to bring a person to perceive and acknowledge the full force of that which he has admitted; to contemplate it in various points of view; to admit in one shape what he has already admitted in another, and to give up and disallow whatever is inconsistent with it."—P. 273.

Now, what the Archbishop here advances appears convincing; his position looks impregnable. The syllogism is not a peculiar mode of reasoning, (how could it be?)—if any thing at all, it must be a general formula for expressing the ordinary act of reasoning—and he shows that the objections made by those who would impugn it, may be levelled with equal justice against all ratiocination whatever. But then this method of defending the syllogism, (to those of us who have stood beside, in the character of modest enquirers, watching the encounter of keen wits,) does but aggravate the difficulty. Is it true, then, that in every act of reasoning, we do but conclude in one form, what, the moment before, we had stated in another? Are we to understand that such is the final result of the debate? If so, this act of reasoning appears very little deserving of that estimation in which it has been generally held. The great prerogative of intelligent beings (as it has been deemed,) grants them this only—to "admit in one shape what they had already admitted in another."

From the dilemma in which we are here placed, the Archbishop by no means releases, or attempts to release us: he seems (something too much after the manner and disposition generally attributed to masters in logic-fence,) to have rested satisfied with foiling his opponents in their attack upon the exact position he had bound himself to defend. He saves the syllogism; what becomes, in the controversy, of poor human reason itself, is not his especial concern—it is as much their business as his. You do not, more than I, he virtually says to his opponents, intend to resign all reasoning whatever as a mere inanity; I prove, for my part, that all reasoning is capable of being put into a syllogistic form, and that your objection, if valid against the syllogism, is equally valid against all ratiocination. You must therefore either withdraw your objection altogether, or advance it at your peril; the difficulty is of your making, you must solve it as you can. Gentlemen, you must muzzle your own dog.

In this posture of affairs the author of the present work comes to the rescue. He shall speak in his own words. But we must premise, that although we do not intend to stint him in our quotation—though we wish to give him all the sea-room possible; yet, for a full development of his views, we must refer the reader to his volumes themselves. There are some disquisitions which precede the part we are about to quote from, which, in order to do complete justice to the subject, ought to find a place here, as well as in the author's work—but it is impossible.

"It is universally allowed, that a syllogism is vicious, if there be any thing more in the conclusion than was assumed in the premisses. But this is, in fact, to say, that nothing ever was, or can be, proved by syllogism, which was not known, or assumed to be known, before. Is ratiocination, then, not a process of inference? And is the syllogism, to which the word reasoning has so often been represented to be exclusively appropriate, not really entitled to be called reasoning at all? This seems an inevitable consequence of the doctrine, admitted by all writers on the subject, that a syllogism can prove no more than is involved in the premisses. Yet the acknowledgment so explicitly made, has not prevented one set of writers from continuing to represent the syllogism as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths, whether of science or of daily life, which we believe; while those who have avoided this inconsistency, and followed out the general theorem respecting the logical value of the syllogism to its legitimate corollary, have been led to impute uselessness and frivolity to the syllogistic theory itself, on the ground of the petitio principii which they allege to be inherent in every syllogism. As I believe both these opinions to be fundamentally erroneous, I must request the attention of the reader to certain considerations, without which any just appreciation of the true character of the syllogism, and the functions it performs in philosophy, appears to me impossible; but which seem to me to have been overlooked or insufficiently adverted to, both by the defenders of the syllogistic theory, and by its assailants.

"It must be granted, that in every syllogism, considered as an argument to prove the conclusion, there is a petitio principii. When we say—

it is unanswerably urged by the adversaries of the syllogistic theory, that the proposition, Socrates is mortal, is presupposed in the more general assumption, All men are mortal; that we cannot be assured of the mortality of all men, unless we were previously certain of the mortality of every individual man; that if it be still doubtful whether Socrates, or any other individual you choose to name, be mortal or not, the same degree of uncertainty must hang over the assertion, All men are mortal; that the general principle, instead of being given as evidence of the particular case, cannot itself be taken for true without exception, until every shadow of doubt which could affect any case comprised with it, is dispelled by evidence aliundè, and then what remains for the syllogism to prove? that, in short, no reasoning from generals to particulars can, as such, prove any thing; since from a general principle you cannot infer any particulars, but those which the principle itself assumes as foreknown.

"This doctrine is irrefragable; and if logicians, though unable to dispute it, have usually exhibited a strong disposition to explain it away, this was not because they could discover any flaw in the argument itself, but because the contrary opinion seemed to rest upon arguments equally indisputable. In the syllogism last referred to, for example, or in any of those which we previously constructed, is it not evident that the conclusion may, to the person to whom the syllogism is presented, be actually and bona fide a new truth? Is it not matter of daily experience that truth previously undreamt of, facts which have not been, and cannot be, directly observed, are arrived at by way of general reasoning? We believe that the Duke of Wellington is mortal. We do not know this by direct observation, since he is not yet dead. If we were asked how, this being the case, we know the Duke to be mortal, we should probably answer, because all men are so. Here, therefore, we arrive at the knowledge of a truth not (as yet) susceptible of observation, by a reasoning which admits of being exhibited in the following syllogism—

"And since a large portion of our knowledge is thus acquired, logicians have persisted in representing the syllogism as a process of inference or proof; although none of them has cleared up the difficulty which arises from the inconsistency between that assertion and the principle, that if there be any thing in the conclusion which was not already asserted in the premisses, the argument is vicious. For it is impossible to attach any serious scientific value to such a mere salvo, as the distinction drawn between being involved by implication in the premisses, and being directly asserted in them. When Archbishop Whately, for example, says that the object of reasoning is 'merely to expand and unfold the assertions wrapt up, as it were, and implied in those with which we set out, and to bring a person to perceive and acknowledge the full force of that which he has admitted,' he does not, I think, meet the real difficulty requiring to be explained; namely, how it happens that a science like geometry can be all 'wrapt up' in a few definitions and axioms. Nor does this defence of the syllogism differ much from what its assailants urge against it as an accusation, when they charge it with being of no use except to those who seek to press the consequence of an admission into which a man has been entrapped, without having considered and understood its full force. When you admitted the major premiss, you asserted the conclusion, 'but,' says Archbishop Whately, 'you asserted it by implication merely; this, however, can here only mean that you asserted it unconsciously—that you did not know you were asserting it; but if so, the difficulty revives in this shape. Ought you not to have known? Were you warranted in asserting the general proposition without having satisfied yourself of the truth of every thing which it fairly includes? And if not, what, then, is the syllogistic art but a contrivance for catching you in a trap, and holding you fast in it?'

"From this difficulty there appears to be but one issue. The proposition, that the Duke of Wellington is mortal, is evidently an inference, it is got at as a conclusion from something else; but do we, in reality, conclude it from the proposition—All men are mortal? I answer, No.

"The error committed is, I conceive, that of overlooking the distinction between the two parts of the process of philosophizing—the inferring part and the registering part; and ascribing to the latter the functions of the former. The mistake is that of referring a man to his own notes for the origin of his knowledge. If a man is asked a question, and is at the moment unable to answer it, he may refresh his memory by turning to a memorandum which he carries about with him. But if he were asked how the fact came to his knowledge, he would scarcely answer, because it was set down in his note-book.

"Assuming that the proposition, The Duke of Wellington is mortal, is immediately an inference from the proposition, All men are mortal, whence do we derive our knowledge of that general truth? No supernatural aid being supposed, the answer must be, from observation. Now, all which men can observe are individual cases. From these all general truths must be drawn, and into these they may be again resolved; for a general truth is but an aggregate of particular truths—a comprehensive expression, by which an indefinite number of individual facts are affirmed or denied at once. But a general proposition is not merely a compendious form for recording and preserving in the memory a number of particular facts, all of which have been observed. Generalization is not a process of mere naming, it is also a process of inference. From instances which we have observed, we feel warranted in concluding, that what we found true in those instances holds in all similar ones—past, present, and future, however numerous they may be. We, then, by that valuable contrivance of language, which enables us to speak of many as if they were one, record all that we have observed, together with all that we infer from our observations, in one concise expression; and have thus only one proposition, instead of an endless number, to remember or to communicate. The results of many observations and inferences, and instructions for making innumerable inferences in unforeseen cases, are compressed into one short sentence.