THE PHILOSOPHY OF CHANCE. 233 pared to persons whose appearances on any scene may be regarded as in general independent, but who, in so far as they do influence each other's movements, exercise only an attractive influence, x and y then being the respective sta- tistical probability of appearance for two persons, the proba- bility of their meeting would not be xy, but rather xy + c. (4) The preceding instance belongs to, and may fitly intro- duce Boole's method of probabilities, the peculiar feature of which is that it deals with probabilities which are not deter- mined by statistics. What is to be said of these mysteri- ously evolved probabilities? I do not feel able to say with Jevons that they are the most probable probabili- ties consistent with the data. I only see that they are con- sistent with the data, and that there is some analogy, I know not of what weight, between the method of attaining these values by the logical calculus and the procedure in the simple case just considered of xy, which does seem to rest upon actual experience. I should not be surprised if others more quick-sighted were able to intuit the connexion of the Boolian solutions with actual experience ; to ground them " upon reasonableness of hypothesis viewed in the light of that general analogy of nature which experience tends daily to confirm " (Donkin). At any rate the values in question are possible values consistent with the data, as Boole has shown by a most remarkable mathematical investigation, 1 which certainly seems to remove his calculus from the sphere of mere guess- work. Accordingly the Boolian calculus may subserve what is probably the principal use of ' intellectual ' probabilities : namely, to afford an hypothesis which may serve as a starting point for further observation. This is a use more important than the only role which Cournot will allow to subjective probability, as he calls it : namely, to regulate the conditions of a bet. At the risk of appearing visionary, I will suggest another possible role. I have elsewhere argued that, as the regime of contract becomes predominant, there will arise a wide-spread need for a principle of adjustment between self-interested contractors, whether in commerce or in politics; 2 and that the required basis can be no other than the utility of all con- cerned. Well, then, in the absence of definite calculations of utility, it may be found necessary often to fall back upon those analogies confirmed by general experience which con- 1 Transactions of the Royal Society, 1862. -Mathematical Psychics, p. 55. 16
