Page:Mind (Old Series) Volume 9.djvu/235

 IV. THE PHILOSOPHY OF CHANCE. By F. Y. EDGE WORTH. THE first principles of the Calculus of Probabilities, the metaphysical roots rather than the mathematical branches of the science, are what I attempt here to examine. Underlying the whole subject, but at a philosophical depth below the reach of the present inquiry, is the definition of probability. Probability may be described, agreeably to general usa^e, as importing partial incomplete belief. What- ever belief is whether according to the doctrine of Hume, which has been much repeated but little improved, " belief is nothing but a more vivid, lively, forcible, firm, steady con- ception of an object than what the imagination alone is ever able to attain," related to mere imagination as the " idea of an enchanted castle " to actual sensations ; or whether, according to Professor Bain's doctrine, belief is something more or something different, being of the nature of volition, " preparedness to act," whether these things are so or whether not, and whatever the physiological pro- cesses accompanying the phenomenon of consciousness, pro- bability may be described, with sufficient accuracy for the present purpose, as differing somehow in degree from perfect belief or rather credibility. The Calculus of Probabilities is concerned with the estimation of degrees of probability ; not every species of estimate, but that which is founded on a particular standard. That standard is the phenomenon of statistical uniformity : the fact that a genus can very frequently be subdivided into species such that the number of individuals in each species bears an approximately con- stant ratio to the number of individuals in the genus. 1 Thus the object of the calculus is probability as estimated by sta- tistical uniformity : the partial belief about some unknown occurrence, as the throw of a die, together with the observed fact, or full belief, that any one face is thrown about as often as another. The foundation is regarded as an integral part of the whole structure ; and indeed it is the most solid part. The indispensability of this objective foundation has been established by Mr. Venn ; 2 with whom on this and all other 1 Cf. Cournot The'orie des Chances, and Ellis, Camb. Phil. Trans., viii. 2 Cf. Ellis, Camb. Phil. Trans, iii., and Mr. Venn's more full exposition, Logic of Chance, ch. 3.