established generalisations of mechanics, optics, or chemistry, simply as conclusions possessing a high degree of probability.

Still, Mr. Jevons, appearing not in the character of a physicist, but of a logician, tells us that the law of gravitation itself is only probably true ".' It would be interesting to learn what is the exact amount of this 'probability,' or, if it be meant that we can only be certain that the force of gravity is acting here and now, it would be an interesting enquiry to ascertain what is the exact value of the 'probability' that it is at this moment acting in Manchester as well as in Oxford, or that it will be acting at this time to-morrow as well as to-day.

6

But, if the conclusions of Induction are thus uncertain, where, according to Mr. Jevons, are we to find certainty? Certainty belongs only to the deductive process and to the teachings of direct intuition.' Does it then belong to the conclusions of deduction? Apparently not, for, at the very beginning of the work 9, we are told that 'in its ultimate origin or foundation, all knowledge is inductive,' and Mr. Jevons is, of course, too practised a logician to suppose that the conclusion 9 p. 14.

7 p. 300.

8

P. 309.

can be more certain than the premisses. The conclusions of geometry, therefore, partake of the same 'uncertainty' as the results of the physical sciences, and the region of 'certainty' is confined to our direct intuitions and to the rules of syllogism (supposing, that is, a difference to be intended between the 'deductive process' and deductive results). We venture to suggest that this small residuum of 'certainty' would soon yield to solvents as powerful as those which Mr. Jevons has applied to the results of induction (and apparently also of deduction); and that, therefore, its inherent uncertainty' is no special characteristic of that method, but one which it shares with all our socalled knowledge.

The fact is that in all reasoning, whether inductive or deductive, we make, and must make, assumptions which may theoretically be questioned, but of the truth of which no man, in practice, entertains the slightest doubt. Thus, in syllogistic reasoning, we assume at every step the trustworthiness of memory; we assume, moreover, the validity of the premisses, which, as Mr. Jevons acknowledges, must ultimately be guaranteed either by induction or direct observation; lastly, we assume the validity of the primary axioms of reasoning, b ·

which, according to different theories, are either obtained by induction or assumed to be necessary laws of the human mind. In this sense, all reasoning and all science is hypothetical, and the assumption of the Uniformity of Nature does not render inductive reasoning hypothetical in any special sense of the term. For, if the Laws of the Uniformity of Nature and of Universal Causation admit of exceptions or are liable to ultimate frustration, so, for aught we know, may the axioms of syllogistic reasoning or the inductions by which we have established the trustworthiness of our faculties. And, if the conceptions of uniformity and causation be purely relative to man, so, for aught we know, may Induction

be the so-called laws of thought themselves 10.

would only be hypothetical in a special sense, if we had any reasonable ground for doubting the truth of the hypotheses on which it rests.

11

10 According to the view of the nature and ultimate origin of human knowledge, accepted both by Mr. Jevons and myself, it is, in fact, no paradox but a mere truism to say that the fundamental axioms of reasoning are themselves only particular uniformities of nature, arrived at by the same evidence and depending for their justification on the same grounds as those ultimate generalisations on causation to which we give the special names of the Law of Universal Causation and the Law of the Uniformity of Nature.

11 I need hardly say that I am not here using the word 'hypothesis' in the sense of an unverified assumption. Reasoning, both inductive and

But, as in its ultimate origin or foundation, all knowledge' (including, of course, that of the laws which govern the syllogistic process itself) is inductive,' Professor Jevons must either employ the word 'certain ’ in a variety of senses, or he must be prepared with the philosophers of the New Academy to maintain the uncertainty of all knowledge whatsoever.

Such, as it appears to me, are the inconsistences and paradoxes into which a very able writer has been led by a tendency to over-refinement, and, still more perhaps, by a desire to apply the ideas and formulæ of mathematics to the explanation of logical problems.

I must further express my dissidence from Mr. Jevons' statement that all inductive inference is preceded by hypotheses 12, from his theory that Induction is simply the Inverse Method of Deduction, and, above all, from what appears to me to be the exceedingly misleading

deductive, is found on analysis to depend, in the last resort, on certain assumptions or hypotheses, but then the truth of these assumptions or hypotheses is guaranteed by the whole experience of the human race, past and present, and beyond this guarantee we conceive that there is no other attainable. In other words, all truth is relative to our faculties of knowing, and this condition it is in vain for us to attempt to transcend. 12 See chap. i, pp. 11, 12, of this work.

parallel drawn between Nature and a ballot-box. 'Events,' says Mr. Jevons, 'come out like balls from the vast ballot-box of Nature 13. Now the balls were placed in the ballot-box by human hands; the number and character of them may have been due merely to caprice or chance; moreover, they are all isolated entities having no connection with each other. Would it be possible to find a stronger contrast to the works of nature? If natural phenomena did indeed admit only of the same kind of study as the drawing of balls from a ballot-box, Mr. Jevons' conception of Induction would undoubtedly be the true one, and we should agree with him that no finite number of particular verifications of a supposed law will render that law certain.' But, just because we believe that the operations of Nature are conducted with an uniformity for which we seek in vain amongst the contrivances of men, do we regard ourselves as capable, in many cases, of predicting the one class of events with certainty, while the other affords only matter for more or less probable conjecture.

Intimately connected with Mr. Jevons' depreciation of the value of the inductive inference is his statement

13 Vol. i. p. 275.