SECT. 11.] Modality. 305 



times in which the universal proposition would be correctly 

 made. And in this there is, so far, no difficulty. The only 

 difference is that whereas the justification of the former, viz. 

 the particular or individual kind of modal, was obtainable 

 within the limits of the universal proposition which included 

 it, the justification of the modality of a universal proposition 

 has to be sought in a group or succession of other propo 

 sitions. The proposition has to be referred to some group of 

 similar ones and we have to consider the proportion of cases 

 in which it will be true. But this distinction is not at all 

 fundamental. 



It is quite true that universal propositions from their 

 nature are much less likely than individual ones to be justi 

 fied, in practice, by such appeal. But, as has been already 

 frequently pointed out, we are not concerned with the way 

 in which our propositions are practically obtained, nor with 

 the way in which men might find it most natural to test 

 them ; but with that ultimate justification to which we ap 

 peal in the last resort, and which has been abundantly shown 

 to be of a statistical character. When, therefore, we say that 

 it is probable that all X is F, what we mean is, that in 

 more than half the cases we come across we should be right 

 in so judging, and in less than half the cases we should be 

 wrong. 



11. It is at this step that the possible ambiguity is 

 encountered. When we talk of the chance that All X is F, 

 we contemplate or imply the complementary chance that it is 

 not so. Now this latter alternative is not free from am 

 biguity. It might happen, for instance, in the cases of failure, 

 that no X is F, or it might happen that some X, only, is not 

 F; for both of these suppositions contradict the original pro 

 position, and are therefore instances of its failure. In prac 

 tice, no doubt, we should have various recognized rules and 

 v. 20 



