premise is only this, adopts the theory in its essentials.
But I can not concede that this recognition of the sufficiency of the evidence—that is, of the correctness of the induction—is a part of the induction itself; unless we ought to say that it is a part of every thing we do, to satisfy ourselves that it has been done rightly. We conclude from known instances to unknown by the impulse of the generalizing propensity; and (until after a considerable amount of practice and mental discipline) the question of the sufficiency of the evidence is only raised by a retrospective act, turning back upon our own footsteps, and examining whether we were warranted in doing what we have provisionally done. To speak of this reflex operation as part of the original one, requiring to be expressed in words in order that the verbal formula may correctly represent the psychological process, appears to me false psychology.64 We review our syllogistic as well as our inductive processes, and recognize that [pg 155] they have been correctly performed; but logicians do not add a third premise to the syllogism, to express this act of recognition. A careful copyist verifies his transcript by collating it with the original; and if no error appears, he recognizes that the transcript has been correctly made. But we do not call the examination of the copy a part of the act of copying.
The conclusion in an induction is inferred from the evidence itself, and not from a recognition of the sufficiency of the evidence; as I infer that my friend is walking toward me because I see him, and not because I recognize that my eyes are open, and that eyesight is a means of knowledge. In all operations which require care, it is good to assure ourselves that the process has been performed accurately; but the testing of the process is not the process itself; and, besides, may have been omitted altogether, and yet the process be correct. It is precisely because that operation is omitted in ordinary unscientific reasoning, that there is any thing gained in certainty by throwing reasoning into the syllogistic form. To make sure, as far as possible, that it shall not be omitted, we make the testing operation a part of the reasoning process itself. We insist that the inference from particulars to particulars shall pass through a general proposition. But this is a security for good reasoning, not a condition of all reasoning; and in some cases not even a security. Our most familiar inferences are all made before we learn the use of general propositions; and a person of untutored sagacity will skillfully apply his acquired experience to adjacent cases, though he would bungle grievously in fixing the limits of the appropriate general theorem. But though he may conclude rightly, he never, properly speaking, knows whether he has done so or not; he has not tested his reasoning. Now, this is precisely what forms of reasoning do for us. We do not need them to enable us to reason, but to enable us to know whether we reason correctly.
In still further answer to the objection, it may be added that—even when the test has been applied, and the sufficiency of the evidence recognized—if it is sufficient to support the general proposition, it is sufficient also to support an inference from particulars to particulars without passing through the general proposition. The inquirer who has logically satisfied himself that the conditions of legitimate induction were realized in the cases A, B, C, would be as much justified in concluding directly to the Duke of Wellington as in concluding to all men. The general conclusion is never 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. Whenever there is ground for drawing any conclusion at all from particular instances, there is ground for a general conclusion; but that this general conclusion should be actually drawn, however useful, can not 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 legality of the smaller act, that he should make a formal assertion of his right to the greater one.
Some additional remarks, in reply to minor objections, are appended.65
[pg 156]
§ 9. The preceding considerations enable us to understand the true nature of what is termed, by recent writers, Formal Logic, and the relation [pg 157] between it and Logic in the widest sense. Logic, as I conceive it, is the entire theory of the ascertainment of reasoned or inferred truth. Formal Logic, therefore, which Sir William Hamilton from his own point of view, and Archbishop Whately from his, have represented as the whole of Logic properly so called, is really a very subordinate part of it, not being directly concerned with the process of Reasoning or Inference in the sense in which that process is a part of the Investigation of Truth. What, then, is Formal Logic? The name seems to be properly applied to all that portion of doctrine which relates to the equivalence of different modes of expression; the rules for determining when assertions in a given form imply or suppose the truth or falsity of other assertions. This includes the theory of the Import of Propositions, and of their Conversion, Æquipollence, and Opposition; of those falsely called Inductions (to be hereafter spoken of)66, in which the apparent generalization is a mere abridged statement of cases known individually; and finally, of the syllogism: while the theory of Naming, and of (what is inseparably connected with it) Definition, though belonging still more to the other and larger kind of logic than to this, is a necessary preliminary to this. The end aimed at by Formal Logic, and attained by the observance of its precepts, is not truth, but consistency. It has been seen that this is the only direct purpose of the rules of the syllogism; the intention and effect of which is simply to keep our inferences or conclusions in complete consistency with our general formulæ or directions for drawing them. The Logic of Consistency is a necessary auxiliary to the logic of truth, not only because what is inconsistent with itself or with other truths can not be true, but also because truth can only be successfully pursued by drawing inferences from experience, which, if warrantable at all, admit of being generalized, and, to test their warrantableness, require to be exhibited in a generalized form; after which the correctness of their application to particular cases is a question which specially concerns the Logic of Consistency. This Logic, not requiring any preliminary knowledge of the processes or conclusions of the various sciences, may be studied with benefit in a much earlier stage of education than the Logic of Truth: and the practice which has empirically obtained of teaching it apart, through elementary treatises which do not attempt to include any thing else, though the reasons assigned for the practice are in general very far from philosophical, admits of philosophical justification.
[pg 158]
Chapter IV.
Of Trains Of Reasoning, And Deductive Sciences.
§ 1. In our analysis of the syllogism, it appeared that the minor premise always affirms a resemblance between a new case and some cases previously known; while the major premise asserts something which, having been found true of those known cases, we consider ourselves warranted in holding true of any other case resembling the former in certain given particulars.
If all ratiocinations resembled, as to the minor premise, the examples which were exclusively employed in the preceding chapter; if the resemblance, which that premise asserts, were obvious to the senses, as in the proposition “Socrates is a man,” or were at once ascertainable by direct observation; there would be no necessity for trains of reasoning, and Deductive or Ratiocinative Sciences would not exist. Trains of reasoning exist only for the sake of extending an induction founded, as all inductions must be, on observed cases, to other cases in which we not only can not directly observe the fact which is to be proved, but can not directly observe even the mark which is to prove it.
§ 2. Suppose the syllogism to be, All cows ruminate, the animal which is before me is a cow, therefore it ruminates. The minor, if true at all, is obviously so: the only premise the establishment of which requires any anterior process of inquiry, is the major;
