64- INDUCTION. 



another, and if obliged to bet, should venture our stake on 

 red, white, or black, with equal indifference. But should we 

 be indifferent whether we betted for or against some one 

 colour, as, for instance, white ? Surely not. From the very 

 fact that black and red are each of them separately equally 

 probable to us with white, the two together must be twice as 

 probable. We should in this case expect not-white rather 

 than white, and so much rather, that we would lay two to one 

 upon it. It is true, there might for aught we knew be more 

 white balls than black and red together ; and if so, our bet 

 would, if we knew more, be seen to be a disadvantageous one. 

 But so also, for aught we knew, might there be more red balls 

 than black and white, or more black balls than white and red, 

 and in such case the effect of additional knowledge would be 

 to prove to us that our bet was more advantageous than we 

 had supposed it to be. There is in the existing state of our 

 knowledge a rational probability of two to one against white ; 

 a probability fit to be made a basis of conduct. No reasonable 

 person would lay an even wager in favour of white, against 

 black and red ; though against black alone, or red alone, he 

 might do so without imprudence. 



The common theory, therefore, of the calculation of chances, 

 appears to be tenable. Even when we know nothing except 

 the number of the possible and mutually excluding contin 

 gencies, and are entirely ignorant of their comparative fre 

 quency, we may have grounds, and grounds numerically 

 appreciable, for acting on one supposition rather than on 

 another ; and this is the meaning of Probability. 



3. The principle, however, on which the reasoning 

 proceeds, is sufficiently evident. It is the obvious one, that 

 when the cases which exist are shared among several kinds, 

 it is impossible that each of those kinds should be a majority 

 of the whole: on the contrary, there must be a majority 

 against each kind, except one at most ; and if any kind has 

 more than its share in proportion to the total number, the 

 others collectively must have less. Granting this axiom, and 

 assuming that we have no ground for selecting any one kind 



