208 Induction. [CHAP. ix. 



out of ten die in their first four years. It belongs to Induc 

 tion to say whether we are justified in generalizing our obser 

 vation into the assertion, All infants die in that proportion. 

 When such a proposition is obtained, whatever may be the 

 value to be assigned to it, we recognize in it a series of a 

 familiar kind, and it is at once claimed by Probability. 



In this latter case the division into two parts, the induc 

 tive and the ratiocinative, seems decidedly more than one of 

 convenience ; it is indeed imperatively necessary for clearness 

 of thought and cogency of treatment. It is true that in 

 almost every example that can be selected we shall find 

 both of the above elements existing together and combining 

 to determine the degree of our conviction, but when we come 

 to examine them closely it appears to me that the grounds 

 of their cogency, the kind of conviction they produce, and 

 consequently the rules which they give rise to, are so en 

 tirely distinct that they cannot possibly be harmonized into 

 a single consistent system. 



The opinion therefore according to which certain In 

 ductive formulae are regarded as composing a portion of 

 Probability, and which finds utterance in the Rule of Suc 

 cession criticised in our last chapter, cannot, I think, be 

 maintained. It would be more correct to say, as stated 

 above, that Induction is quite distinct from Probability, yet 

 co-operates in almost all its inferences. By Induction we 

 determine, for example, whether, and how far, we can safely 

 generalize the proposition that four men in ten live to be 

 fifty-six ; supposing such a proposition to be safely generalized, 

 we hand it over to Probability to say what sort of inferences 

 can be deduced from it. 



7. So much then for the opinion which tends to regard 

 pure Induction as a subdivision of Probability. By the 

 majority of philosophical and logical writers a widely different 



