380 INDUCTION. 



conceived by Laplace and by mathematicians generally, has not the funda- 

 mental fallacy which I had ascribed to it. 



We must remember that the probability of an event is not a quality of 

 the event itself, but a mere name for the degree of ground which we, or 

 some one else, have for expecting it. The probability of an event to one 

 person is a different thing from the probability of the same event to an- 

 other, or to the same pei'son after he has acquired additional evidence. The 

 probability to me, that an individual of whom I know nothing but his name 

 will die within the year, is totally altered by my being told the next minute 

 that he is in the last stage of a consumption. Yet this makes no difference 

 in the event itself, nor in any of the causes on which it depends. Every 

 event is in itself certain, not probable ; if we knew all, we should either 

 know positively that it will happen, or positively that it will not. But its 

 probability to us means the degree of expectation of its occurrence, which 

 we are warranted in entertaining by our present evidence. 



Bearing this in mind, I think it must be admitted, that even when we 

 have no knowledge whatever to guide our expectations, except the knowl- 

 edge that what happens must be some one of a certain number of possibili- 

 ties, we may still reasonably judge, that one supposition is more probable 

 to us than another supposition ; and if we have any interest at stake, we 

 shall best provide for it by acting conformably to that judgment. 



§ 2. Suppose that we are required to take a ball from a box, of which 

 we only know that it contains balls both black and white, and none of any 

 other color. We know that the ball we select will be either a black or a 

 white ball ; but we have no ground for expecting black rather than white, 

 or white rather than black. In that case, if we are obliged to make a choice, 

 and to stake something on one or the other supposition, it will, as a question 

 of prudence, be perfectly indifferent which ; and we shall act precisely as 

 we should have acted if we had known beforehand that the box contained 

 an equal number of black and white balls. But though our conduct would 

 be the same, it would not be founded on any surmise that the balls were in 

 fact thus equally divided ; for we might, on the contrary, know by au- 

 thentic information that the box contained ninety-nine balls of one color, 

 and only one of the other ; still, if we are not told which color has only one, 

 and which has ninety-nine, the drawing of a white and of a black ball will 

 be equally probable to us. We shall have no reason for staking any thing 

 on the one event rather than on the other ; the option between the two will 

 be a matter of indifference ; in other words, it will be an even chance. 



But let it now be supposed that instead of two there are three colors — 

 white, black, and red ; and that we are entirely ignorant of the proportion 

 in which they are mingled. We should then have no reason for expecting 

 one more than 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 color, as, for instance, white ? 

 Surely not. From the very fact that black and red are each of them sep- 

 arately 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 Avhite, or more black balls than white and red, and iu such case 



