480 THE LIFE OF JAMES D. FORBES. [CHAP. 



be the precise size that it is of all the infinite variety of 

 possible sizes, &c. 



' Consequently the improbability 4hat the actual angular 

 distance between Aldebaran and Arcturus should be 

 within certain limits may, if the limits be taken narrow 

 enough, be made to exceed as much as we please the 

 improbability that there should be 91 cases of stars 

 lying within 4" of each other. If, therefore, in the case 

 of double stars we are bound to believe in physical con- 

 nection because of the d priwi improbability of what 

 is observed to exist, I do not see how the wit of man 

 can escape from the conclusion that we are bound also to 

 believe in a physical connection between Arcturus and 

 Aldebaran. If it be said that the cases are not parallel 

 except quoad the numerical calculation, I answer that 

 this is undoubtedly true ; but then the remark admits 

 that the numerical calculation is in itself no ground for 

 inference in either case. And so, as they used to say in 

 the schools, cadit qucestio. 



' Avec des cliiffres onpeut tout demontrer, ought to be 

 the motto of most of the philosophical applications of 

 the theory of probabilities which in its own nature and 

 according to the plain view of it, is only a development 

 of the theory of combinations. To attempt to constitute 

 it into the philosophy of science, is, in effect, to destroy 

 the philosophy of science altogether. . . .' 



' MY DEAR FORBES, * BELGRAVE PLACE, October 8th. 



'. . . I am greatly pleased with your argunn-nt 

 in general ; it expresses what I have long thought. The 

 foundation of all the confusion is the notion that the 

 numerical expression of a chance expresses the force of 

 expectation, whereas it only expresses the proportion of 

 frequency with which such and such an event occurs on 

 the long run. From this notion that chances express 

 something mental or subjective, is derived the assump- 

 tion that the force of belief touching past events admits 

 of numerical evaluation as well as the force of expecta- 

 tion touching future. If this were true, it would 1 



