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From these inductive laws we deduce the conclusion that any man or woman will, on examination, present these anatomical details. The inference is of very high probability, but is only an inference, and only probable; and because of this we name it a deduction. In the course of actual Experience we now and then stumble upon cases which prove the conclusion at fault; we find human organisms in other respects similar to the organisms we have known, but having the viscera transposed; and (but more rarely) we meet with women having three, and even four, breasts.* Now, since it is impossible that we could ever know what is the structure of all human organisms, any assertion we may venture on respecting an unobserved organism must be hypothetical; and although we may rely on the deduction, owing to its great probability, we cannot be said to know what has not been proved, and may be erroneous. Our induction, "All substances expand when heated," if employed deductively to prove that this india-rubber will expand when heated, would manifestly lead to error. Unless the stretched india-rubber be one of the all, what is affirmed of the all cannot be affirmed of it; and if we assume it to be one of the all, this assumption requires verification.

48. The ordinary notion of Deduction fails to distinguish it from that of simple Intuition, or from the restatement in a particular of what has been stated in general. It is said to be a conclusion from the all or many to the one; and this is correct, if we understand the conclusion to be a restatement of the assumed inclusion, - i. e. if the one is assumed to be one of the all or many. But this assumption, which is the ground of the inference, the justification of the inclusion, is excluded

* Nay, there are authentic cases of even men with four breasts; and in one case there was an abundant secretion of milk, which had to be arrested by medical treatment. See Journal of Anatomy, 1872, p. 56.

from the type of Deduction presented in logical textbooks as that of Perfect Deduction. I shall touch on this presently. Here it must suffice to say, that Deduction ceases when Inference is excluded, precisely as in the inverse process of Induction; both are guesses; both are applications of what is, or has been, to what may, or will be. If we have found that 2 + 2 = 4, we do not infer that whenever 4 is divided into halves each half will equal 2; we intuite it; there is no possibility of doubt when the terms are clearly seen. In like manner, when we have all the particular facts expressed in a general fact, the statement that any one of these facts is one included in the general fact, is not an inference at all, not a deduction, but an intuition: we see the relation in seeing the terms.

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Deduction can only be certain through the intuition of the law, or, as I have termed it, through intuition of its invariants. We are certain that any numbers composed of three consecutive integers (e. g. 123 or 567), and three figures in a progression by equal differences (e. g. 579 or 159), are divisible by 3; we are likewise certain that all numbers ending in 5, being multiples of 5, are divisible by 5. But this certainty is not attainable simply by trying particular cases, unless we know that in each particular case the ratios are in all respects a repetition of the one originally proved. We may have found that fifty different numbers ending in 7 are what is called prime; but we cannot conclude from these cases that any number ending in 7 is prime; we may infer it; but we soon stumble upon numbers ending in 7 which are not prime; and on then comparing the two sets we find that they are not similar throughout. The laws of our decimal scale are such that every number ending in 5 must be divisible by 5, because it is a multiple of 5. But the laws of number are not such that every number ending

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in 7 must be prime; because prime numbers are multiples only of unity, and there are many ending in 7 which are not multiples only of unity.

The application of a general expression to any one of the particulars it expresses is a tautology, not a deduction; the application to new particulars, not expressed but assumed to be identical, is deduction, because it is inference.

49. Here we meet with the common mistake of supposing that an axiom or general truth gives validity to any special truth inferred from it. The fact is precisely the reverse: the particular truths constitute the sole validity of the axiom or general truth, which condenses them in a brief expression; and any further inference needs verification to assure us that it does come within the formula. When, for example, we assert that Mr. B― is mortal, we do not affirm this as a derivative from the general truth, "All men are mortal" (although this is commonly implied, because any doubt raised respecting Mr. B's mortality would be answered by the general statement); we affirm it because we believe Mr. B― to be a man, and in our idea of man is inBcluded the idea of mortality. The truth that "all men are mortal" is only admissible on the assumption that no men are included in the "all," save such as are of the same kind as those included in the class "mortal." We have no difficulty in imagining a man resembling other men in every outward character, yet so peculiarly constructed that the waste and repair of his tissues should preserve a perfect balance, and that his body should be incapable of fractures, lesions, and other destructive changes, in a word, an organism which would not follow the universal law of other organisms, and would survive amid the ruins of its descendants. But by the very exclusion from the class designated," all men," this man is not one to whom our general truth referred. If Mr. B

has

such an organism, he is not one of the all men who are affirmed to be mortal. Further, when Mr. BB- dies, it will not be because all other men resembling him have died or will die, but because Death is one of the cycle of phenomena constituting the individual existence of an organism which is momently dying. An unsupported body does not fall because Gravitation is a Law; it falls because there is a particular concurrence of conditions; and the Law is simply the generalization of such concurrent conditions. If the unsupported body rise in the air instead of falling, this also is due to the concurrent conditions, and not to Levitation. In the same way one man dies not because of the Law of Mortality (which is abstracted from the particular facts of mortality), nor because other men die, but because Death is the terminal phenomenon in the series of vital phenomena. A man dies because the living organism is chemically unstable, and only living when its instability alternates with stability. The structure is forever changing: assimilation of new material and destruction of the old are incessant; and among the consequences of this incessant change there are inequalities which lead to differentiations, and these finally to Death.

50. Not until we have ascertained the physiological conditions of Death, has the induction " All men are mortal" a probative character. As a matter of fact, we know that the idea of Mortality is one which rises late in human consciousness. The early races did not, and many savage races of the present time do not, believe in it; they believe death would never take place unless some evil-disposed demon, instigated by a witch or magician, exercised a spell. The disease which destroys an organism is held to be the action of this demon; and were there no such demonic influence, men would, they believe, continue forever on their hunting-grounds.

CHAPTER V.

SOME ERRORS RESPECTING INDUCTION AND DEDUCTION.

51. To complete the foregoing exposition of the psychological processes, we must consider certain views expressed in works on Logic which are irreconcilable with its leading arguments.

In the first place, note the misleading phrase, "Induction passes from particular truths to general truths." We have seen that this is not so, but that Induction passes from particular truths or assumptions to an inferred correspondence between them and the untested cases which resemble them; and when these correspondences are proved, Induction ceases.

In the second place, note the classical division into Perfect and Imperfect Inductions and Deductions. Whatever justification there may be for this division in Formal Logic, it is certainly not justifiable in Psychology.

52. Induction is defined by De Morgan as "the inference of a universal proposition by the separate inference of all the particulars of which it is composed."* This use of the word inference is not the one adopted by me, but accepting it as equivalent to "conclusion," I still object to the definition, since it does not express the mental process which takes place in what is called Imperfect Induction. Hamilton declares the division of Perfect and Imperfect Induction to be absurd, and will only recognize logical Induction as "that which infers the whole from

* DE MORGAN, Formal Logic, p. 211.

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