III.

HYPOTHESIS.

I. TREATMENT OF HYPOTHESIS BY ENGLISH LOGICIANS.

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EVONS begins his chapter on Hypothesis 1 with the remark that "All inductive investigation consists in the marriage of hypothesis and experiment." This has not always been the view of English logicians. Bacon's objections to hypothetical anticipations of nature, and to the deductive method in general, are well known. Newton's statement of the law of gravitation was accompanied with a self-denying ordinance in respect to hypothetical causes. Along with the great discoverers of his own and the succeeding age, he would undoubtedly have disclaimed the a priori method of medieval thought, and would have identified with it a process, the essence of which was to start with an unverified assumption, and go on to deduce consequences from it. And this view was thought, at a later date, to be established on a sound philosophical basis by the speculations of Locke and Hume as to the source of all our knowledge. It is true that, try as he would, Bacon was unable to exclude deduction from his own method, that his great contemporaries and successors, who had already entered on the modern epoch of scientific discovery, consistently employed methods which the prevailing 1 Principles of Science, p. 504.

philosophy renounced, and that Newton himself propounded hypotheses in the light of which his celebrated disclaimer bears the appearance of irony. But this only shows that the methods these investigators employed were in advance of the means they possessed of analysing them. And it remains true that the attitude of English logicians towards hypothesis during this whole period was one of suspicion and hostility. It is not till we come to our own time that the important place in all scientific investigations of the preliminary assumption, the deduction of the consequences which must flow from it, and the comparison of these with actual fact, was recognised.

The reaction against the purely empirical method is clearly marked in J. S. Mill, who devotes a large section in the middle of his Logic to a description of the deductive method, and to defining the place of hypothesis in science. Jevons gives him credit for the part he took in initiating this reaction, but justly observes that his conclusions in this part of his system are inconsistent with his disparagement of the deductive process in the early part of his work, and his continual appeal to inference from particular to particular as the true type of reasoning. "Mill," he concludes, "would have saved much confusion of thought had he not failed to observe that the inverse use of deduction constitutes induction."

Jevons himself, as we have already seen, cannot be accused of undervaluing the "inverse method." He is too much of a mathematician to permit his psychological empiricism to invade the sphere of geometry and formal logic. In his view the deductions of these abstract sciences take their place beside the direct intuitions of experience as types of certainty. Similarly,

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he has too keen an insight into the real processes of scientific thought to assign to the deductive method any subordinate place in physical investigation. "There are four different steps," he says, "in inductive reasoning: first, preliminary observation; second, the making of hypothesis; third, deductive reasoning; fourth, verification." On the other hand, Jevons shares with Mill the philosophical assumptions of Locke and Hume, and we cannot be surprised if, in spite of the above contentions, his own theory of hypothesis turns out in its later stages to be infected by them. His difference with Mill is founded on no thorough-going analysis of the nature of truth and the grounds of certainty. Accordingly when, leaving mathematical and quasi-mathematical science, we come to the application of induction to concrete nature, we not only find no attempt to reconcile the acknowledged hypothetical character of scientific method with the appeal of the Empirical Philosophy to simple intuition as the only test of truth, but have the contradiction emphasised in a theory which gives up certainty in physical science as an unrealisable ideal. According to this theory, Perfect or Complete Induction is not to be looked for (as we might expect from the abovequoted views as to the nature of induction in general) in the establishment of hypothesis by deduction and verification, but in that process of complete enumeration which Mill rejected as the mere summation of singular propositions. As compared with the certainty achieved by this latter process, the result of induction in Mill's sense ("proper," as opposed to "perfect," induction) can never amount to more than a balance of probabilities. "Nature," to quote a well-known 1 Logic, p. 79.

passage, "is to us like an infinite ballot-box, the contents of which are being continually drawn ball after ball, and exhibited to us. Science is but the

careful observation of the succession in which balls of various character present themselves; we register the combinations, notice those which seem to be excluded from occurrence, and from the proportional frequency of those which appear we infer the probable character of future drawings." In other words, the truth of even the best - supported hypothesis is problematical. It could only be finally established by the exhaustive consideration and rejection of an infinite number of all possible rivals. Even then there would still remain another ground of uncertainty; for there is always the possibility that the Power which created the universe at the first may introduce a change into the order hitherto established in the experience of men. What we call the uniformity of nature is merely an assumption, and like all other assumptions in this field, rests in the last instance on a comparison of conflicting probabilities.

Beginning with a rooted distrust of hypothesis, English logic seems thus to end in establishing it as the only scientific method, but in doing so comes very near denying the possibility of scientific knowledge altogether. Jevons saved himself from this conclusion by appealing to the deductions of geometry and formal logic, and to the intuitions of sense as a ground of certainty. But it is easy to see that he has no right to these exceptions. For it is evident that mathematics and formal logic rest upon assumptions in just the same sense as do the natural sciences. It was Mill's merit to see that this followed from his premises. 1 Principles of Science, p. 150.

It is no merit in Jevons, but merely indicates confusion of thought to ignore it. No proof can be offered of the axioms of geometry or the formal laws of identity, contradiction, and excluded middle, that cannot be claimed for the uniformity of nature and for well-grounded hypotheses. No doubt can attach to the latter which does not infect the former. If, for instance, it be said that we cannot conceive of a thought which is not governed by these axioms and by the formal laws, this undoubtedly is true, but it is equally impossible to conceive of a world in which uniformity does not exist, or of a knowledge of it which does not rest on hypothetical interpretations. And if, giving up the deductive sciences, Jevons falls back with Mill on the intuitions of sense, it may be shown that these, equally with the generalisations of science, rest upon conceptions of the mind, and are hypothetical in the same sense. The world of sense which, to the early English psychologists, seemed to be an immediate datum is in reality a construction by the aid of conceptions whose only ultimate justification is that they are necessary to give coherence and consistency to our experience. Spatial position, temporal succession, substance and attribute, cause and effect, the identity of the object of intuition with itself, are such conceptions. They are assumptions in Jevons's sense, and if we were to adopt his criterion of truth, would merely at best be the most probable of an infinite number of possible ones.

Having reached this point, which the reader may construe at pleasure as the destruction either of the possibility of certainty, or of the ballot-box theory of the nature of hypothesis, we are in a position to approach the subject for ourselves.