SECT. 3.] On certain kinds of Groups or Series. 3 



the general proposition may be, that of the particulars is 

 neither greater nor less. The process of inferring the par 

 ticular from the general is not accompanied by the slightest 

 diminution of certainty. If one of these immediate infer 

 ences is justified at all, it will be equally right in every 

 case. 



But it is by no means necessary that this characteristic 

 should exist in all cases. There is a class of immediate in 

 ferences, almost unrecognized indeed in logic, but constantly 

 drawn in practice, of which the characteristic is, that as they 

 increase in particularity they diminish in certainty. Let me 

 assume that I am told that some cows ruminate ; I cannot 

 infer logically from this that any particular cow does so, 

 though I should feel some way removed from absolute dis 

 belief, or even indifference to assent, upon the subject ; but 

 if I saw a herd of cows I should feel more sure that some of 

 them were ruminant than I did of the single cow, and my 

 assurance would increase with the numbers of the herd about 

 which I had to form an opinion. Here then we have a class 

 of things as to the individuals of which we feel quite in 

 uncertainty, whilst as we embrace larger numbers in our 

 assertions we attach greater weight to our inferences. It is 

 with such classes of things and such inferences that the 

 science of Probability is concerned. 



3. In the foregoing remarks, which are intended to 

 be purely preliminary, we have not been able altogether to 

 avoid some reference to a subjective element, viz. the degree 

 of our certainty or belief about the things which we are 

 supposed to contemplate. The reader may be aware that 

 by some writers this element is regarded as the subject- 

 matter of the science. Hence it will have to be discussed 

 in a future chapter. As however I do not agree with the 

 opinion of the writers just mentioned, at least as regards 



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