F. T. EDGEWORTH: stitute intellectual probability. And in fact something of this sort appears to be unconsciously performed by the utili- tarian who thinks it ' fair ' to treat as equals those between whom no material difference is discerned. As Jevons says, with direct reference to the external world, but with that deep undertone of harmony with the things of soul which pervades his chapters upon Probability and Measurement, we must treat as equals things which are not known to be unequal. The preceding examples, especially the first, may show that the assumptions connected with ' Inverse Probability,' far from being arbitrary, constitute a very good working hypothesis. They suggest that the particular species of inverse probability called the ' Eule of Succession ' may not be so inane as Mr. Venn would have us believe. Admitting that the metaphor of nature's urn l does not much aid us in the work of Induction, may we not still say with Sir John Herschel, "It is never without its instruction to trace this sort of parallel between mental impressions and abstract numerical relations"? 2 Consider a chemical law which may be established by two or three careful experiments. To say that our certitude is here measured by 3-4ths or 4-5ths would be absurd. But the ground of our belief is not simply the two or three occurrences. There is the substratum established by a wide experience, that what has held good in two or three such chemical experiments will hold good generally. The case is not like drawing balls out of a jar about the constitution of which we know nothing but that one constitution is as likely as another ; but rather like drawing a little jar out of a big jar, the constitution of which big jar is such that the contained jars contain each balls of one colour. When, then, we have ascertained the colour of any little jar, we know that all the future drawings from that jar will present the same colour. But how did we ascertain the character of the big jar's contents? By a simple induc- tion to which the idea of sortition may not be irrelevant. The fact that upon so many trials there occurred no instance contradicting the generalisation in question does seem analo- gous to the continual drawing of balls of the same colour from an urn of whose contents before the drawing we were completely ignorant. The mathematical conceptions of the Kule of Succession do appear applicable to the inductions of simple enumeration ; in particular to those axiomata media, 1 Of. Jevons's Principles of Science, ch. 11, end. 2 " On an Application of the Rule of Succession," Edinburgh Revieiv, 1850.
