Chapter 2

"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.

"But it may be said, that we do learn, by means of observation and experience, many universal truths; indeed, all the general truths of which science consists. Is not the doctrine of universal gravitation learned by experience? Are not the laws of motion, the properties of light, the general properties of chemistry, so learned? How, with these examples before us, can we say that experience teaches no universal truths?

"To this we reply, that these truths can only be known to be _general_, not universal, if they depend upon experience alone. Experience cannot bestow that universality which she herself cannot have, and that necessity of which she has no comprehension. If these doctrines are universally true, this universality flows from the _ideas_ which we apply to our experience, and which are, as we have seen, the real sources of necessary truth. How far these ideas can communicate their universality and necessity to the results of experience, it will hereafter be our business to consider. It will then appear, that when the mind collects from observation truths of a wide and comprehensive kind, which approach to the simplicity and universality of the truths of pure science; she gives them this character by throwing upon them the light of her own fundamental ideas."--_Whewell_, Vol. I. p. 60.

Accordingly, Mr Whewell no sooner arrives at any truth which admits of an unconditional positive statement--a statement defying all rational contradiction--than he abstracts it from amongst the acquisitions of experience, and throwing over it, we suppose, the light of these fundamental ideas, pronounces it enrolled in the higher class of universal and necessary truths. The first laws of motion, though established through great difficulties against the most obstinate preconceptions, and by the aid of repeated experiments, are, when surveyed in their present perfect form, proclaimed to be, not acquisitions of experience, but truths emanating from a higher and more mysterious origin.[2]

[2] Necessary truths multiply on us very fast. "We maintain," says Mr Whewell, "that this equality of _mechanical action and reaction_ is one of the principles which do not flow from, but regulate, our experience. A mechanical pressure, not accompanied by an equal and opposite pressure, can no more be given by experience than two unequal right angles. With the supposition of such inequalities, space ceases to be space, form ceases to be form, matter ceases to be matter." And again he says, "_That the parallelogram of forces is a necessary truth_;" a law of motion of which we surely can _conceive_ its opposite to be true. In some of these instances Mr Whewell appears, by a confusion of thought, to have given to the _physical fact_ the character of necessity which resides in the mathematical formula employed for its expression. Whether a moving body would communicate motion to another body--whether it would lose its own motion by so doing--or what would be the result if a body were struck by two other bodies moving in different directions--are questions which, if they could be asked us prior to experience, we could give no answer whatever to--which we can easily conceive to admit of a quite different answer to that which experience has taught us to give.

This distinction, which assigns a different mental origin to truths, simply because (from the nature of the subject-matter, as it seems to us) there is a difference with regard to the sort of certainty we feel of them, has always appeared to us most unphilosophical. It is admitted that we arrive at a general proposition through experience; there is no room, therefore, for quibbling as to the meaning of the term experience--it is understood that when we speak of a truth being derived from experience, we imply the usual exercise of our mental faculties; it is the step from a general to a universal proposition which alone occasions this perplexing distinction. The dogma is this--that experience can only teach us by a limited number of examples, and therefore can never establish a universal proposition. But if _all_ experience is in favour of a proposition--if no experience has occurred even to enable the imagination to conceive its opposite, what more can be required to convert the general into a universal proposition?

Strange to say, the attribution of these characteristics of universality and necessity, becomes, amongst those who loudly insist upon the palpable nature of the distinction we are now examining, a matter of controversy; and there are a class of scientific truths, of which it is debated whether they are contingent or necessary. The only test that they belong to the latter order is, the impossibility of conceiving their opposites to be the truth; and it seems that men find a great difference in their powers of conception, and that what is impossible with one is possible with another. But (wisely, too) passing this over, and admitting that there is a distinction (though a very ill-defined one) between the several truths we entertain of this nature; namely, that some we find it impossible, even in imagination, to contradict, whilst of others we can suppose it possible that they should cease to be truths--does it follow that different faculties of the mind are engaged in the acquisition of them? Does nothing depend on the nature of the subject itself? "That two sides of a triangle," says Mr Whewell, "are greater than the third, is a universal and necessary geometrical truth; it is true of all triangles; it is true in such a way that the contrary cannot be conceived. _Experience could not prove such a proposition._" Experience is allowed to prove it of this or that triangle, but not as an inseparable property of a triangle. We are at a loss to perceive why the same faculties of the mind that can judge, say of the properties of animal life, of organized beings, cannot judge of the properties of a figure--properties which must immediately be conceived to exist the moment the figure is presented to the imagination. We say, for instance, of any animal, not because it is this or that animal, a sheep or an ox, but simply _as_ animal, that it must sustain itself by food, by the process of assimilation. This, however, is merely a contingent truth, because it is in our power to conceive of organized beings whose substance shall not wear away, and consequently shall not need perpetual restoration. But what faculty of the mind is unemployed here that is engaged in perceiving the property of a triangle, that _as_ triangle, it must have two sides greater than the third? The truths elicited in the two cases have a difference, inasmuch as a triangle differs from an animal in this, that it is impossible to conceive other triangles than those to which your truth is applicable, and therefore the proposition relating to the triangle is called a necessary truth. But surely this difference lies in the subject-matter, not in the nature of our mental faculties.

But we had not intended to interpose our own lucubrations in the place of those of Mr Mill.

"Although Mr Whewell," says our author, "has naturally and properly employed a variety of phrases to bring his meaning more forcibly home, he will, I presume, allow that they are all equivalent; and that what he means by a necessary truth, would be sufficiently defined, a proposition the negation of which is not only false, but inconceivable. I am unable to find in any of Mr Whewell's expressions, turn them what way you will, a meaning beyond this, and I do not believe he would contend that they mean any thing more.

"This, therefore, is the principle asserted: that propositions, the negation of which is inconceivable, or in other words, which we cannot figure to ourselves as being false, must rest upon evidence of higher and more cogent description than any which experience can afford. And we have next to consider whether there is any ground for this assertion.