CHAPTER VIII. 



THE RULE OF SUCCESSION 1 . 



1. IN the last chapter we discussed at some length the 

 nature of the kinds of inference in Probability which corre 

 spond to those termed, in Logic, immediate and mediate infer 

 ences. We ascertained what was the meaning of saying, for 

 example, that the chance of any given man A. B. dying 

 in a year is 1, when concluded from the general proposition 

 that one man out of three in his circumstances dies. We 

 also discussed the nature and evidence of rules of a more 

 completely inferential character. But to stop at this point 

 would be to take a very imperfect view of the subject. If 

 Probability is a science of real inference about things, it 

 must surely lead up to something more than such merely 

 formal conclusions ; we must be able, if not by means of it, at 

 any rate by some means, to step beyond the limits of what 

 has been actually observed, and to draw conclusions about 

 what is as yet unobserved. This leads at once to the ques 

 tion, What is the connection of Probability with Induction ? 

 This is a question into which it will be necessary to enter 

 now with some minuteness. 



That there is a close connection between Probability and 

 Induction, must have been observed by almost every one 



1 A word of apology may be offered one of Induction. But such a title I 



here for the introduction of a new cannot admit, for reasons which will 



name. The only other alternative be almost immediately explained, 

 would have been to entitle the rule 



