50 REMARKS ON THE FUNDAMENTAL PRINCIPLE 



is not readily expressed in any way, because in its own nature it 

 is negative and indefinite. The phrases I have just quoted imply 

 merely the absence of the limitations inseparable from individual 

 cases, or from any finite number of such 'cases, whether contem- 

 plated as actually existent or as about to be developed within 

 definite limits of space and time. 



When individual cases are considered, we have no conviction 

 that the ratios of frequency of occurrence depend on the circum- 

 stances common to all the trials. On the contrary, we recognise 

 in the determining circumstances of their occurrence an extra- 

 neous element, an element, that is, extraneous to the idea of the 

 genus and its species. Contingency and limitation come in (so 

 to speak) together ; and both alike disappear when we consider 

 the genus in its entirety, or (which is the same thing), in what 

 may be called an ideal and practically impossible realization of 

 all which it potentially contains. If this be granted, it seems to 

 follow that the fundamental principle of the theory of probabilities 

 may be regarded as included in the following statement ; "The 

 conception of a genus implies that of numerical relations among 

 the species subordinated to it." 



2. But in what relation, it may be asked, do these con- 

 ceptions stand to outward realities ? How can they be made the 

 foundation of a real science, that is, of a science relating to things 

 as they really exist? We are by such questions led back to 

 what was long the great controversy of philosophy ; I mean 

 the contest between the realists and the nominalists. The former 

 in asserting the reality of universals did not maintain that what 

 we think of when we use a general term is an actually existing 

 thing. Like every one else they admitted, that in one sense 

 nothing can exist but the individual, nevertheless they held that 

 universals are not mere figments of the mind, but that they have 

 a reality of their own which is the foundation of the truth of 

 general propositions. To assert therefore that the theory of pro- 

 babilities has for its foundation a statement touching genera 

 and their species, and is at the same time a real science, is to 

 take a realistic view of its nature. And this I believe is what, 

 on consideration, we cannot avoid doing. 



If it be said that the grouping phenomena together is merely 

 a mental act wholly disconnected from outward reality and alto- 



