"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—

 
'All men are mortal.
Socrates is a man;
THEREFORE
Socrates is mortal'—
 

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—

 
'All men are mortal.
The Duke of Wellington is a man;
THEREFORE
The Duke of Wellington is mortal.'
 

"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.

"When, therefore, we conclude, from the death of John and Thomas, and every other person we ever heard of in whose case the experiment had been fairly tried, that the Duke of Wellington is mortal like the rest, we may, indeed, pass through the generalization, All men are mortal, as an intermediate stage; but it is not in the latter half of the process—the descent from all men to the Duke of Wellington—that the inference resides. The inference is finished when we have asserted that all men are mortal. What remains to be performed afterwards is merely deciphering our own notes.

"Archbishop Whately has contended, that syllogizing, or reasoning from generals to particulars, is not, agreeably to the vulgar idea, a peculiar mode of reasoning, but the philosophical analysis of the mode in which all men reason, and must do so if they reason at all. With the deference due to so high an authority, I cannot help thinking that the vulgar notion is, in this case, the more correct. If, from our experience of John, Thomas, &c. who once were living, but are now dead, we are entitled to conclude that all human beings are mortal, we might surely, without any logical inconsequence, have concluded at once, from those instances, that the Duke Wellington is mortal. The mortality of John, Thomas, and Company, is, after all, the whole evidence we have for the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition. Since the individual cases are all the evidence we can possess; evidence which no logical form into which we choose to throw it can make greater than it is; and since that evidence is either sufficient in itself, or, if insufficient for one purpose, cannot be sufficient for the other; I am unable to see why we should be forbidden to take the shortest cut from these sufficient premisses to the conclusion, and constrained to travel the 'high priori road' by the arbitrary fiat of logicians. I cannot perceive why it should be impossible to journey from one place to another, unless 'we march up a hill and then march down again.' It may be the safest road, and there may be a resting-place at the top of the hill, affording a commanding view of the surrounding country; but for the mere purpose of arriving at our journey's end, our taking that road is perfectly optional: it is a question of time, trouble, and danger.

"Not only may we reason from particulars to particulars, without passing through generals, but we perpetually do so reason. All our earliest inferences are of this nature. From the first dawn of intelligence we draw inferences; but years elapse before we learn the use of general language. The child who, having burnt his fingers, avoids to thrust them again into the fire, has reasoned or inferred, though he has never thought of the general maxim—fire burns. He knows from memory that he has been burnt, and on this evidence believes, when he sees a candle, that if he puts his finger into the flame of it, he will be burnt again. He believes this in every case which happens to arise; but without looking, in each instance, beyond the present case. He is not generalizing; he is inferring a particular from particulars.—Vol. I. p. 244.

"From the considerations now adduced, the following conclusions seem to be established:—All inference is from particulars to particulars: General propositions are merely registers of such inferences already made, and short formulæ for making more: The major premiss 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 premisses being the particular facts from which the general proposition was collected by induction. * * *

"In the above observations, it has, I think, been clearly shown, that although there is always a process of reasoning or inference where a syllogism is used, the syllogism is not a correct analysis of that process of reasoning or inference; which is, on the contrary, (when not a mere inference from testimony,) an inference from particulars to particulars; authorized by a previous inference from particulars to generals, and substantially the same with it: of the nature, therefore, of Induction. But while these conclusions appear to me undeniable, I must yet enter a protest, as strong as that of Archbishop Whately himself, against the doctrine that the syllogistic art is useless for the purposes of reasoning. The reasoning lies in the act of generalisation, not in interpreting the record of that act; but the syllogistic form is all indispensable collateral security for the correctness of the generalisation itself."—P. 259.

By this explanation we are released from the dilemma into which the syllogistic and non-syllogistic party had together thrown us. We can acknowledge that the process of reason can be always exhibited in the form of a syllogism, and yet not be driven to the strange and perplexing conclusion that our reasoning can never conduct us to a new truth, never lead us further than to admit in one shape what we had already admitted in another. We have, or may have, it is true, a major in all our ratiocination, implied, if not expressed, and are so far syllogistic; but then the real premiss from which we reason is the amount of experience on which that major was founded, to which amount of experience we, in fact, made an addition in our minor, or conclusion.

But while we accept this explanation, and are grateful for the deliverance it works for us, we must also admit, (and we are not aware that Mr Mill would controvert this admission,) that there is a large class of cases in which our reasoning betrays no reference to this anterior experience, and where the usual explanation given by teachers of logic is perfectly applicable; cases where our object is, not the discovery of truth for ourselves, but to convince another of his error, by showing him that the proposition, which in his blindness or prejudice he has chosen to contradict, is part and parcel of some other proposition to which he has given, and is at all times ready to give, his acquiescence. In such cases, we frequently content ourselves with throwing before him this alternative—refuse your major, to which you have again and again assented, or accept, as involved in it, our minor proposition, which you have persisted in controverting.

It will have been gathered from the foregoing train of observation, that, in direct contradistinction to Archbishop Whately, who had represented induction (so far as it consisted of an act of ratiocination) as resolvable into deductive and syllogistic reasoning, our author has resolved the syllogism, and indeed all deductive reasoning whatever, ultimately into examples of induction. In doing this, he is encountered by a metaphysical notion very prevalent in the present day, which lies across his path, and which he has to remove. We allude to the distinction between contingent and necessary truths; it being held by many philosophical writers that all necessary and universal truths owe their origin, not to experience (except as occasion of their development,) and not, consequently, to the ordinary process of induction, but flow from higher sources—flow immediately from some supreme faculty to which the name of reason has by some been exclusively appropriated, in order to distinguish it from the understanding, the faculty judging according to sense. We will pause a while upon this topic.

Contingent and Necessary Truths.—Those who have read Mr Whewell's treatise on the Philosophy of the Inductive Sciences, will remember that there is no topic which that author labours more sedulously to inculcate than this same distinction between contingent and necessary truths; and it is against his statement of the doctrine in question, that Mr Mill directs his observations. Perhaps the controverted tenets would have sustained a more equal combat under the auspices of a more practised and more complete metaphysician than Mr Whewell; but a difficulty was probably experienced in finding a statement in any other well-known English author full and explicit. Referring ourselves to Mr Whewell's volumes for an extract, in order to give the distinction here contended against the advantage of an exposition in the words of one who upholds it, we are embarrassed by the number which offer themselves. From many we select the following statement:—

"Experience," says Mr Whewell, "must always consist of a limited number of observations. And, however numerous these may be, they can show nothing with regard to the infinite number of cases in which the experiment has not been made. Experience, being thus unable to prove a fact to be universal, is, as will readily be seen, still more incapable of proving a fact to be necessary. Experience cannot, indeed, offer the smallest ground for the necessity of a proposition. She can observe and record what has happened; but she cannot find, in any case, or in any accumulation of cases, any reason for what must happen. She may see objects side by side, but she cannot see a reason why they must be ever side by side. She finds certain events to occur in succession; but the succession supplies, in its occurrence, no reason for its recurrence. She contemplates external objects; but she cannot detect any internal bond which indissolubly connects the future with the past, the possible with the real. To learn a proposition by experience, and to see it to be necessarily true, are two altogether different processes of thought.