CHAPTER VII. 



THE RULES OF INFERENCE IN PROBABILITY. 



1. IN the previous chapter, an investigation was made into 

 what may be called, from the analogy of Logic, Immediate 

 Inferences. Given that nine men out of ten, of any assigned 

 age, live to forty, what could be inferred about the prospect 

 of life of any particular man ? It was shown that, although 

 this step was very far from being so simple as it is frequently 

 supposed to be, and as the corresponding step really is in 

 Logic, there was nevertheless an intelligible sense in which 

 we might speak of the amount of our belief in any one of 

 these proportional propositions, as they may succinctly be 

 termed, and justify that amount. We must now proceed to 

 the consideration of inferences more properly so called, I 

 mean inferences of the kind analogous to those which form the 

 staple of ordinary logical treatises. In other words, having 

 ascertained in what manner particular propositions could be 

 inferred from the general propositions which included them, 

 we must now examine in what cases one general proposition 

 can be inferred from another. By a general proposition here 

 is meant, of course, a general proposition of the statistical 

 kind contemplated in Probability. The rules of such infer 

 ence being very few and simple, their consideration will not 

 detain us long. From the data now in our possession we are 



