7 1 4 THE POPULAR SCIENCE MONTHLY. 



of the third ball being white would be the same whatever the first 

 two were. But, by inspecting the table, the reader can see that in 

 each group all orders of the balls occur with equal frequency, so that 

 it makes no difference whether they are drawn out in the order they 

 were put in or not. Hence the colors of the balls already drawn have 

 no influence on the probability of any other being white or black. 



Now, if there be any way of enumerating the possibilities of 

 Nature so as to make them equally probable, it is clearly one which 

 should make one arrangement or combination of the elements of Na- 

 ture as probable as another, that is, a distribution like that we have 

 supposed, and it, therefore, appears that the assumption that any such 

 thing can be done, leads simply to the conclusion that reasoning from 

 past to future experience is absolutely worthless. In fact, the moment 

 that you assume that the chances in favor of that of which we are to- 

 tally ignorant are even, the problem about the tides does not differ, 

 in any arithmetical particular, from the case in which a penny (known 

 to be equally likely to come up heads and tails) should turn up heads 

 m times successively. In short, it would be to assume that Nature is 

 a pure chaos, or chance combination of independent elements, in which 

 reasoning from one fact to another would be impossible ; and since, as 

 we shall hereafter see, there is no- judgment of pure observation with- 

 out reasoning, it would be to suppose all human cognition illusory and 

 no real knowledge possible. It would be to suppose that if we have 

 found the order of Nature more or less regular in the past, this has 

 been by a pure run of luck which we may expect is now at an end. 

 Now, it may be we have no scintilla of proof to the contrary, but 

 reason is unnecessary in reference to that belief which is of all the 

 most settled, which nobody doubts or can doubt, and which he who 

 should deny would stultify himself in so doing. 



The relative probability of this or that arrangement of Nature is 

 something which we should have a right to talk about if universes 

 were as plenty as blackberries, if we could put a quantity of them in 

 a bag, shake them well up, draw out a sample, and examine them to 

 see what proportion of them had one arrangement and what propor- 

 tion another. But, even in that case, a higher universe would contain 

 us, in regard to whose arrangements the conception of probability 

 could have no applicability. 



IV. 



We have examined the problem proposed by the conceptualists, 

 which, translated into clear language, is this : Given a synthetic con- 

 clusion ; required to know out of all possible states of things how many 

 will accord, to any assigned extent, with this conclusion ; and we have 

 found that it is only an absurd attempt to reduce synthetic to analytic 

 reason, and that no definite solution is possible. 



But there is another problem in connection with this subject. It 



