SECT. 7.] The Rules of Inference in Probability. 175 



Probability without having properly mastered its principles, 

 we may go further. It would really not be asserting too 

 much to say that they seem to think themselves justified in 

 assuming that where we know nothing about the distribution 

 of the properties alluded to we must assume them to be dis 

 tributed as above described, and therefore apportion our 

 belief in the same ratio. This is called assuming the events 

 to be independent, the supposition being made that the rule 

 will certainly follow from this independence, and that we 

 have a right, if we know nothing to the contrary, to assume 

 that the events are independent. 



The validity of this last claim has already been discussed 

 in the first chapter ; it is only another of the attempts to 

 construct a priori the series which experience will present to 

 us, and one for which no such strong defence can be made as 

 for the equality of heads and tails in the throws of a penny. 

 But the meaning to be assigned to the independence of the 

 events in question demands a moment s consideration. 



The circumstances of the problem are these. There are 

 two different qualities, by the presence and absence respec 

 tively of each of which, amongst the individuals of a series, 

 two distinct pairs of classes of these individuals are pro 

 duced. For the establishment of the rule under discussion 

 it was found that one supposition was both necessary and 

 sufficient, namely, that the division into classes caused by 

 each of the above distinctions should subdivide each of the 

 classes created by the other distinction in the same ratio 

 in which it subdivides the whole. If the independence be 

 granted and so defined as to mean this, the rule of course 

 will stand, but, without especial attention being drawn to 

 the point, it does not seem that the word would naturally 

 be so understood. 



7. The above, then, being the fundamental rules of 



