722 Miss Wrinch and Dr. H. Jeffreys on some 



propositions other than those expressible in this way ; and it- 

 is habitually employed in scientific practice and everyday 

 life in cases where it seems likely that such expression is im- 

 possible. Most of the problems of inverse probability, for 

 instance, seem to introduce propositions not so decomposable. 

 If then we wish to retain the customary applications of the 

 theory (and this seems desirable at any cost), we must assume 

 that axiom 2 is correct. The assumption that information 

 can be obtained from the notion of " equally probable " alone 

 without that of " more probable," which seems as intelligible 

 a priori anyhow, demands that propositions can be decomposed 

 in this way in all these cases, whether there is any warrant 

 for assuming this possibility or not. Thus axiom 2 is prefer- 

 able to the principle of sufficient reason as a primitive 

 proposition, since it covers as much ground and involves 

 fewer assumptions. 



The use of the principle of sufficient reason in the cases 

 where it is applicable leads to a proof of another proposition 

 which is an axiom in Jevons's theory. Suppose we have a 

 class of n propositions, of which we know that one and only 

 one is true, and any one is as likely to be true as any other. 

 Then if any m of them are selected, the probability that ono 

 of these m is true is m/n. Let q then denote the proposition 

 that one of these m is true. Consider another class of the 

 original propositions, and let p denote the probability that 

 some member of this class is true. The probability that p 

 and q are both true is then the probability that some member 

 of the common part of the two sub-classes is true. Let the 

 number of propositions in this common part be /. Then if /* 

 denote the data we have at the beginning, we have 



P(p.q:h) = l/n 



I 7)1 



m * n 

 = ?(p:q.],).T( q :h). 



We see that all cases where the probabilities of propositions 

 can be determined by decomposing a certain proposition into 

 a finite number of equally probable alternatives can be 

 treated in this way, so that the relation 



V(p.q:h)=-p{p:q.h).V{q:h) ... (2) 



is always true when the principle of sufficient reason is. 

 applicable. 



But is there any reason to suppose that this relation still 



