78 Modes of establishing the Groups or Series. [CHAP. IV. 



portion of Psychology, confined therefore to considering states 

 of mind in themselves, rather than in their reference to facts, 

 viz. as being true or false. We should, that is, be ceasing 

 to make it a science of inference about things. This point 

 will have to be gone into more thoroughly in another chap 

 ter ; but it is impossible to direct attention too prominently 

 to the fact that Logic (and therefore Probability as a branch 

 of Logic) is not concerned with what men do believe, but 

 with what they ought to believe, if they are to believe 

 correctly. 



(2) In the other form of reply the explanation of the 

 phrase in question would be sought, not in a state of mind, 

 but in a quality of the things contemplated. We might assign 

 the following as the meaning, viz. that the events really 

 would occur with equal frequency in the long run. The 

 ground of this assertion would probably be found in past ex 

 perience, and it would doubtless be impossible so to frame 

 the answer as to exclude the notion of our belief altogether. 

 But still there is a broad distinction between seeking an 

 equality in the amount of our belief, as before, and in the 

 frequency of occurrence of the events themselves, as here. 



4. When we have got as far as this it can readily be 

 shown that an appeal to experience cannot be long evaded. 

 For can the assertion in question (viz. that the throws of the 

 penny will occur equally often) be safely made a priori? 

 Those who consider that it can seem hardly to have fully 

 faced the difficulties which meet them. For when we begin 

 to enquire seriously whether the penny will really do what 

 is expected of it, we find that restrictions have to be in 

 troduced. In the first place it must be an ideal coin, with 

 its sides equal and fair. This restriction is perfectly intelli 

 gible ; the study of solid geometry enables us to idealize a 

 penny into a circular or cylindrical lamina. But this condition 



