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 232 F. Y. EDGEWOETH : the result of a random selection, or whether we, or our in- formant, had once known, but completely forgotten, which was the preponderating colour. For in the latter case the constitution of our urn falls into the category of things which are experienced to happen just as often one way as another. As Ellis says, 1 " When we expect two events equally, we believe that they will recur equally in the long run ". This position appears to be intermediate between that of Mill 2 and Mr. Venn ; agreeing with Mr. Venn that for the significant employment of the Calculus of Probabilities, objective data are requisite ; but disagreeing from Mr. Venn's assertion that in most cases of inverse probability such data are not forthcoming. (3) The following is given by Boole 3 as the typical instance of ' intellectual ' probability. The material proba- bability of one event is x, of another is y. Of their con- currence nothing is known experientially. Then the intellec- tual probability of the double event is xy ; though of course, as a matter of fact, the statistical frequency of the double event may turn out to be different. In so far as the assigned value, xy, has any real value, I think it must be grounded on the experience that, in the long run, consisting of events in general occurrence, events are found to be independent of one another ; or that the connexions between events tending to increase the probability of the double event above xy are just balanced by the repugnancies tending to depress the true value below xy. Referring to our typical instance of arithmetical experience, let us consider the probability of two forthcoming decimal places (about which nothing is known) being, say, 73. In virtue of the general experience that these different figures of natural constants have no dis- cernible connexion distinguishing them on inspection from a chance aggregation of digits, it would be safe to say, I think, that the d priori probability of 73 is l-100th ; and I shall be prepared to find that about one in a hundred logarithms had, say, its sixth and seventh places respectively 7 and 3. And, if we take into account the second consideration above speci- fied as a ground for the value of xy, it would not, I think, affect the value as long as we range over the wider experi- ences, such as that of number ; though no doubt there may be particular departments of phenomena which may be corn- 1 Camb. Phil. Trans., viii. 2 Logic, bk. iii., ch. 18, 1. 8 Edinburgh Boy. Soc. Proc.