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to these truths reduce themselves to two : they are à priori, they are necessary.

Axioms are not a priori; they are experimental truths, generalizations of observation. The proposition, two right lines cannot enclose a space,' is a deduction resulting from the testimony of the senses. No doubt experience gives us only an actual knowledge of this truth, and thence it seems insufficient to found an axiom; but, let us observe, that the imagination supplies for it; we make for ourselves a mental image of two lines, and we see that as soon as they meet each other they cease to be right lines. It is, therefore, upon an internal production and reproduction of experience that the truths called à priori rest.

Then there is the character of necessity. What is a necessary truth? It is a proposition, the negation of which is not only false, but also inconceivable. Mr. Mill categorically rejects this criticism of inconceivability. He absolutely denies that we can say such a thing is not, since it is inconceivable by us. adds, he has only to open the history of the sciences in order to justify his assertion. A number of propositions have been held to be inconceivable, which have now passed into science as uncontested truths, such as the existence of the antipodes, and the existence of gravitation, which the Cartesians repelled, because they regarded motion without contact as impossible. The inconceivability of the negative is but a case of inseparable association. We experience the greatest difficulty in uniting two ideas for the first time; then, by habit and repetition, they become so thoroughly associated that their disunion appears inconceivable, even to enlightened minds.

. Axioms are then experimental truths of which there is superabundant evidence, whose basis is experience, and whose criterion is verification. • They are only a class, the most universal class, of inductions

And, he

1 Mr. Mill has maintained, on several occasions, and without any variation, that the truth of a proposition is not sufficiently established by the inconceivability of its negative. On this point he combats Messrs. Spencer and Lewes.-See Mill's Logic, and An Examination, etc., Spencer's Principles of Psychology, and Lewes's History of Philosophy.

from experience, the easiest and simplest generalizations of the facts furnished by the senses and the consciousness.'1


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The preceding discussion has led us to the confines of logic, beyond which we will not go. Not that we hold the barrier to be impassable; it is even a little conventional, seeing that logic is contained in psychology, as the part is contained in the whole. We regret that Mr. Mill, with his great philosophical authority, should not have treated in some of his works of the relations between psychology and logic. This question is not so idle as it may appear ; because clearly to determine the relations between two neighbouring sciences is to define their object with precision, afterwards to define their method, and so to render their progress possible. It is so much the more important because psychology, which is hardly constituted as an independent science, has hitherto been absorbed, now by metaphysics, and then by logic, the one debating substances and first causes, and the other considering human faculties in abstracto only, the science of facts, experimental psychology, was stifled, or merely vegetated.

If, placing ourselves at the point of view of the school which we are considering (or even of any other, provided it gives a large share to facts), we examine the relations of psychology to logic, we shall see that logic is only a branch broken off from psychology. In fact, the latter has for its object the facts of consciousness, their immediate causes and their laws; it ought to embrace them all, whilst logic occupies itself only with the single faculty of inference and its mechanism. Besides, psychology ought to study our faculties in the entire series of their evolution, in their variations, ethnological or otherwise, whilst logic considers the faculty of reasoning only under its adult, impersonal, scientific form, and rejects the exceptions. Psychology is concrete, whilst logic, even when understood in the modern fashion—that is to say, stripped of scholastic formalism remains abstract; a me



Logic, book ii. chap. vi.

Among ancients, Aristotle must be excepted. He frequently proceeds as a naturalist, and his psychology is astonishing, considering the epoch.

chanism of reasoning being much more important to it than the matter to which it is applied. Logic is, then, only a small portion of psychology. Nevertheless it constitutes, as it is justly entitled to do, a science apart, because it can be studied separately, and because, by reason of the simplicity of its object, it is much more advanced than psychology.

We shall, therefore, lay logic aside, although we are now dealing with one of the most celebrated logicians of the nineteenth century, and we shall explain his psychological theory of reasoning only.

On this point the opposition of empiricism and idealism is remarkable. Idealism, which considers deduction as the fundamental operation, because it starts from the general, sees nothing in induction except an operation which brings it back thither. For empiricism induction is everything, because it starts from the facts, and is the experimental process; deduction supposes it, and is in many other respects no other than verification. We shall not therefore be surprised at the preponderance which Mr. Mill assigns to the inductive process.

In order to reason, that is to say, in order to go from what one knows to what one does not know, a point of departure, a foundation, is necessary. This point of departure, says Mr. Mill, is the particular. “To infer or reason is the process of the mind by which one starts from known truths to arrive at others really distinct from the first.'—(Logic, B. ii. p. 1.) It is generally divided into two kinds, induction and syllogism. But there is a third kind of reasoning, distinct from the preceding two, 'and which, nevertheless, is not only valid, but is the foundation of the two others. This is inference, which goes from the particular to the particular.

Let us consider the first mode of reasoning. Logicians err in considering the dictum de omni et multo as the basis of all reasoning; in reality, “every inference is from the particular to the particular.

: 2 Not only may we reason from particulars to particulars without passing through generals, but we perpetually do so reason.'

· See Ravaisson, La Philosophie en France au XIXme Siècle, $ 15, 33.
? Logic, book ii. chap. iii.

• 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 and inferred, though he has never thought of the general maxim, Fire burns. . . . He is not generalizing; he is inferring a particular from particulars. In the same way also brutes reason.'1

Mr. Mill thinks that, when we draw consequences from our personal experience, we conclude more often from the partiticular to the particular, than by the intermediary of a general proposition.

Among the higher order of practical intellects, there have been many of whom it was remarked how admirably they suited their means to their ends, without being able to give any sufficient reasons for what they did ; and applied, or seemed to apply, recondite principles, which they were wholly unable to state. This is the natural consequence of having a mind stored with appropriate particulars, and having been long accustomed to reason at once from these to fresh particulars, without practising the habit of stating to one's-self or to others the corresponding general propositions.?

General propositions are simple registers of inferences already effectuated, and of short formulas for the formation of others.3 We store up our experiences in them, as it were, that we may use them at need. Reasoning from the particular to the particular bring us then naturally to induction.

Induction is, in fact, the mode of reference which goes from the particular to the general, from the known to the unknown. It may be defined as a generalization of experience, or as 'the means of discovering and proving general propositions.' Its foundation is not, as the Scotch pretend, our belief in the uniformity of the course of nature, seeing that this belief itself is an example of induction, and of an induction not the easiest or most evident, since, before we reach it, we must have conceived the particular uniformities, whose general uniformity is the resultant and the synthesis. What then is the foundation of induction ? It is the idea of causality. " The notion of cause is the root of all the theory of induction.' We have already seen that, according to Mr. Mill, cause is the invisible antecedent, and that the relation of causality is unconditional succession. Hence, if two facts or groups of facts are such as experience has shown them to us, up to this time (without any known exception) in a relation of irreversible and unconditional succession, it results from this, that one of the terms gives the other, with which it is indissolubly united; that if we hold the cause, we can infer the effect; that, if we know the effect, we can infer the cause; and that the passage is thus legitimately performed between the known and the unknown; and that, besides, the uniformity of causes supposing that of effects, and vice verså, we pass thus from the particular to the general.

1 Mill's Logic, vol. i. p. 212, 4th edition.
3 Ibid. book iii. chap. iii.

2 Ibid. vol. i. p. 213.
4 Ibid. book iii. chap. iii.

“The inductive process is essentially an inquiry into cases of causation. ... If we could determine what causes are correctly assigned to what effects, and what effects to what causes, we should be virtually acquainted with the whole course of nature. All those uniformities which are mere results of causation, might then be explained and accounted for, and every individual fact or event might be predicted. ... To ascertain, therefore, what are the laws of causation which exist in nature, to determine the effects of every cause, and the causes of all effects, is the main business of induction.' 2

Deduction is thus relegated to a secondary rank. Whilst certain logicians see in it the universal type of reasoning, and think that every discursive process is reduced by final analysis to the drawing of ideas one from the others, Mr. Mill says, “the employment of the syllogism is in reality only the employment of general propositions in reasoning.' Now, a general proposition is only a memorandum, a 'condensation' of a number of instances drawn from particular cases. • We can reason without them, and

SO, in the more simple cases; they are only necessary to the advance and progress of the reasoning. They simplify it, and permit

we do


Logic, book iii. chap. v.

2 Ibid. vol. i. p. 407.

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