THE PHILOSOPHY OF CHANCE. 229 though not of course a numerically-measured, probability. And similarly in applying the Calculus of Probabilities, as the most distinguished astronomers have done, to the question whether the distribution of the fixed stars can be regarded as the result of a random sprinkling, do we not know something about the involved constant, the a priori probability that such a chance-distribution should have taken place ? Have we not experienced that chance does not certainly rule among the celestial phenomena, that the constants expressing d priori probability are not equal to unity, in the case of similar arguments which have been confirmed by fact, for instance, the argument which the Calculus of Probabilities has drawn from the apparent motion of all the fixed stars round the earth in favour of the earth's revolution, and other examples ad- duced by Professor Jevons in the Principles of Sci^n/ / Or, in leaving terrestrial phenomena, are we leaving the solid ground of experience ? In treating celestial constants as equally likely to have one value as another, are we enter- ing on a region peculiar to probability and not governed by the general analogy of mathematical physics ? As long as we have some approximate data, that hypothetical reasoning should be based upon imperfect data is agreeable to the experience of mathematical physics. But what is peculiar and paradoxical in probabilities is that our reasoning appears to become more accurate as our ignorance becomes com- plete ; that when we have embarked upon chaos we seem to drop down into a cosmos. Just when probability, founded upon statistical fact, material probability, as Boole calls it, 1 has reached the utmost degree of tenuity, we fall back upon intellectual probability. Such a turning-point we seem now to have reached in the progress of our illustrations from the more to the less accurate data. I submit that the ' intellectual ' probability is not essen- tially different from the ' material,' but only consists, so to speak, of a more diffused sort of matter; that the change which is made is not from experience into dreamland, but from a particular to a more general sort of experience. The case is paralleled, perhaps, and explained by a familiar and all- pervading arithmetical experience. Suppose we are evalu- ating a decimal. If we know nothing at all about the forth- coming ' place ' or digit, then one digit is as likely to occur as another. The ground of this belief is a very wide experi- ence, perhaps, of the unconscious and even ante-natal species, 1 Edinb. Roy. Soc. Proc., xx.
