In order to connect this proposition with the conclusion, Socrates is mortal, the additional link necessary is such a proposition as the following: “Socrates resembles my father, and my father's father, and the other individuals specified.” This proposition we assert when we say that Socrates is a man. By saying so we likewise assert in what respect he resembles them, namely, in the attributes connoted by the word man. And from this we conclude that he further resembles them in the attribute mortality.
§ 7. We have thus obtained what we were seeking, an universal type of the reasoning process. We find it resolvable in all cases into the following elements: Certain individuals have a given attribute; an individual or individuals resemble the former in certain other attributes; therefore they resemble them also in the given attribute. This type of ratiocination does not claim, like the syllogism, to be conclusive from the mere form of the expression; nor can it possibly be so. That one proposition does or does not assert the very fact which was already asserted in another, may appear from the form of the expression, that is, from a comparison of the language; but when the two propositions assert facts which are bonâ fide different, whether the one fact proves the other or not can never appear from the language, but must depend on other considerations. Whether, from the attributes in which Socrates resembles those men who have heretofore died, it is allowable to infer that he resembles them also in being mortal, is a question of Induction; and is to be decided by the principles or canons which we shall hereafter recognise as tests of the correct performance of that great mental operation.
Meanwhile, however, it is certain, as before remarked, that if this inference can be drawn as to Socrates, it can be drawn as to all others who resemble the observed individuals in the same attributes in which he resembles them; that is (to express the thing concisely), of all mankind. If, therefore, the argument be conclusive in the case of Socrates, we are at liberty, once for all, to treat the possession of the attributes of man as a mark, or satisfactory evidence, of the attribute of mortality. This we do by laying down the universal proposition, All men are mortal, and interpreting this, as occasion arises, in its application to Socrates and others. By this means we establish a very convenient division of the entire logical operation into two steps; first, that of ascertaining what attributes are marks of mortality; and, secondly, whether any given individuals possess those marks. And it will generally be advisable, in our speculations on the reasoning process, to consider this double operation as in [pg 229] fact taking place, and all reasoning as carried on in the form into which it must necessarily be thrown to enable us to apply to it any test of its correct performance.
Although, therefore, all processes of thought in which the ultimate premisses are particulars, whether we conclude from particulars to a general formula, or from particulars to other particulars according to that formula, are equally Induction; we shall yet, conformably to usage, consider the name Induction as more peculiarly belonging to the process of establishing the general proposition, and the remaining operation, which is substantially that of interpreting the general proposition, we shall call by its usual name, Deduction. And we shall consider every process by which anything is inferred respecting 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.
NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.
This theory of the syllogism, (which has received the important adhesion of Dr. Whewell,[33]) has been controverted by a writer in the “British Quarterly Review.”[34] The doctrine being new, discussion respecting it is extremely desirable, to ensure that nothing essential to the question escapes observation; and I shall, therefore, reply to this writer's objections with somewhat more minuteness than their strength may seem to require.
The reviewer denies that there is a petitio principii in the syllogism, or that the proposition, All men are mortal, asserts or assumes that Socrates is mortal. In support of this denial, he argues that we may, and in fact do, admit the general proposition that all men are mortal, without having particularly examined the case of Socrates, and even without knowing whether the individual so named is a man or not. But this of course was never denied. That we can and do draw conclusions concerning cases specifically unknown to us, is the datum from which all who discuss this subject must set out. The question is, in what terms the evidence, or ground, on which we draw these conclusions, may best be designated—whether it is most correct to say, that the unknown case is proved by known cases, or that it is proved by a general proposition, including both sets of cases, the unknown and the known? I contend for the former [pg 230] mode of expression. I hold it an abuse of language to say, that the proof that Socrates is mortal, is that all men are mortal. Turn it in what way we will, this seems to me to be asserting that a thing is the proof of itself. Whoever pronounces the words, All men are mortal, has affirmed that Socrates is mortal, though he may never have heard of Socrates; for since Socrates, whether known to be so or not, really is a man, he is included in the words, All men, and in every assertion of which they are the subject. If the reviewer does not see that there is a difficulty here, I can only advise him to reconsider the subject until he does: after which he will be a more competent judge of the success or failure of an attempt to remove the difficulty.[35] That he had reflected very little on the point when he wrote his remarks, is shown by his oversight respecting the dictum de omni et nullo. He acknowledges that this maxim as commonly expressed,—“Whatever is true of a class, is true of everything included in the class,” is a mere identical proposition, since the class is nothing but the things included in it. But he thinks this defect would be cured by wording the maxim thus,—“Whatever is true of a class, is true of everything which can be shown to be a member of the class:” as if a thing could “be shown” to be a member of the class without being one. If a class means the sum of all the things included in the class, the things which “can be shown” to be included in it are a part of these; it is the sum of them too, and the dictum is as much an identical proposition with respect to them as to the rest. One would almost imagine that, in the reviewer's opinion, things are not members of a class until they are called up publicly to take their place in it—that so long, in fact, as Socrates is not known to be a man, he is not a man, and any assertion which can be made concerning men does not at all regard him, nor is affected as to its truth or falsity by anything in which he is concerned.
The reviewer says that if the major premiss included the conclusion, “we should be able to affirm the conclusion without the intervention of the minor premiss; but every one sees that that is impossible.” It does not follow, because the major premiss contains the conclusion, that the words themselves must show all the conclusions which it contains, and which, or evidence of which, it presupposes. The minor is equally required on both theories. It is respecting the functions of the major premiss that the theories differ; whether that premiss merely affirms the existence of proof, or is itself part of the proof—whether the conclusion follows from the minor and major, or from the minor and the [pg 231] particular instances which are the foundation of the major. On either supposition, it is necessary that the new case should be perceived to be one coming within the description of those to which the previous experience is applicable; which is the purport of the minor premiss. When we say that all men are mortal, we make an assertion reaching beyond the sphere of our knowledge of individual cases; and when a new individual, Socrates, is brought within the field of our knowledge by means of the minor premiss, we learn that we have already made an assertion respecting Socrates without knowing it: our own general formula is, to that extent, for the first time interpreted to us. But according to the reviewer's theory, it is our having made the assertion which proves the assertion: while I contend that the proof is not the assertion, but the grounds (of experience) on which the assertion was made, and by which it must be justified.
The reviewer comes much nearer to the gist of the question, when he objects that the formula in which the major is left out—“A, B, C, &c., were mortal, therefore the Duke of Wellington is mortal,” does not express all the steps of the mental process, but omits one of the most essential, that which consists in recognising the cases A, B, C, as sufficient evidence of what is true of the Duke of Wellington. This recognition of the sufficiency of the induction he calls an “inference,” and says, that its result must be interpolated between the cases A, B, C, and the case of the Duke of Wellington; and that “our final conclusion is from what is thus interpolated, and not directly from the individual facts that A, B, C, &c. were mortal.” On this it may first be observed, that the formula does express all that takes place in ordinary unscientific reasoning. Mankind in general conclude at once from experience of death in past cases, to the expectation of it in future, without testing the experience by any principles of induction, or passing through any general proposition. This is not safe reasoning, but it is reasoning; and the syllogism, therefore, is not the universal type of reasoning, but only a form in which it is desirable that we should reason. But, in the second place, suppose that the enquirer does logically satisfy himself that the conditions of legitimate induction are realized in the cases A, B, C. It is still obvious, that if he knows the Duke of Wellington to be a man, he is as much justified in concluding at once that the Duke of Wellington is mortal, as in concluding that all men are mortal. The general conclusion is not legitimate, unless the particular one would be so too; and in no sense, intelligible to me, can the particular conclusion be said to be drawn from the general one.[36] That the process of testing the sufficiency of an inductive inference is an operation of a general character, I readily concede to the reviewer; I had myself said as much, by laying down as a fundamental law, that whenever there is ground for drawing any conclusion at all from particular [pg 232] instances, there is ground for a general conclusion. But that this general conclusion should be actually drawn, however useful, cannot be an indispensable condition of the validity of the inference in the particular case. A man gives away sixpence by the same power by which he disposes of his whole fortune; but it is not necessary to the lawfulness of his doing the one, that he should formally assert, even to himself, his right to do the other.
The reviewer has recourse for an example, to syllogisms in the second figure (though all are, by a mere verbal transformation, reducible to the first), and asks, where is the petitio principii in this syllogism, “Every poet is a man of genius, A B is not a man of genius, therefore A B is not a poet.” It is true that in a syllogism of this particular type, the petitio principii is disguised. A B is not included in the terms, every poet. But the proposition, “every poet is a man of genius” (a very questionable proposition, by the way), cannot have been inductively proved, unless the negative branch of the enquiry has been attended to as well as the positive; unless it has been fully considered whether among persons who are not “men of genius,” there are not some who ought to be termed poets, and unless this has been determined in the negative. Therefore, the case of A B has been decided by implication, as much as the case of Socrates in the first example. The proposition, Every poet is a man of genius, is confessedly æquipollent with “No one who is not a man of genius is a poet,” and in this the petitio principii, as regards A B, is no longer implied, but express, as in an ordinary syllogism of the first figure.