Page:Mind (Old Series) Volume 9.djvu/247

THE PHILOSOPHY OF CHANCE. 235 as they may be called, with reference to the law of causation on the one hand and particular laws on the other such as the constancy of chemical laws, the constancy of anatomi- cal forms, the inconstancy of certain psychical phenomena which contribute important, though unnoticed, 1 foundations to the fabric of inductive logic. I would not undertake to indicate the exact points at which the sustaining forces are applied to that substructure, which, in Mr. Venn's words, " is not so much to be compared to the solid foundations of an ordinary building as to the piles of the houses of Rotterdam, which rest somehow in a deep bed of soft mud ". I only submit that the Rule of Succession may constitute, if not one of the piles, at least an important cross-beam, in that mysterious structure. Having now found that indeterminate probabilities, con- sidered as statements of statistical fact, are respectably grounded upon experience, let us look at the subjective side which, on entering this department of the science, we agreed to postpone. Let us examine the paradox that there should be an accurate measure of ' quantity of belief ' as claimed by some for the constants of inverse probability in the absence of accurate statistics. The paradox disappears in our view that the precise quantity of belief does rest upon precise experience, such as that one digit occurs as often as another in nature. Where this conception of an exact, how- ever general, experience is inappropriate, there the precise measurement of quantity of belief is impossible. The con- sideration of quantity of belief does not present any peculiar difficulty in the case of imperfect statistics any difficulty essentially different from those which we have already dis- cussed, with special reference to the case of perfectly deter- minate statistical data. The relation between the fact of statistics and the feeling of belief is not much more obscure because the things related are not precisely measurable. So far as to the pure science of Probabilities. I have else- where - attempted to treat of the mixed science of Probability and Utility : of what Laplace calls esperance, the product of probability upon utility ; that quantity which to maximise is the main problem of the Art of Measurement of the art proper, which is described by its founder as the most advan- tageous method of combining observations, and of fju-rprjTiKr] in a wider sense. 1 There are some excellent remarks on the concatenation of our different beliefs in Cournot, Throne des Chances, p. 229. Philosophical Magazine, for November, 1883, and February, 1884.