210 THE POPULAR SCIENCE MONTHLY. 



than might be supposed. As we shall be sure to examine any sample 

 with reference to these characters, they may be regarded not exactly as 

 predesignated, but as predetermined (which amounts to the same thing) ; 

 and we may infer that the sample represents the class in all these re- 

 spects if we please, remembering only that this is not so secure an 

 inference as if the particular quality to be looked for had been fixed 

 upon beforehand. 



The demonstration of this theory of induction rests upon principles 

 and follows methods which are accepted by all those Avho display in 

 other matters the particular knowledge and force of mind which qualify 

 them to judge of this. The theory itself, however, quite unaccount- 

 ably seems never to have occurred to any of the writers who have un- 

 dertaken to explain synthetic reasoning. The most widely-spread opin- 

 ion in the matter is one which was much promoted by Mr. John Stuart 

 Mill namely, that induction depends for its validity upon the uni- 

 formity of Nature that is, on the principle that what happens once 

 will, under a sufficient degree of similarity of circumstances, happen 

 again as often as the same circumstances recur. The application is 

 this : The fact that different things belong to the same class constitutes 

 the similarity of circumstances, and the induction is good, provided this 

 similarity is " sufficient." What happens once is, that a number of 

 these things are found to have a certain character ; what may be ex- 

 pected, then, to happen again as often as the circumstances recur con- 

 sists in this, that all things belonging to the same class should have the 

 same character. 



This analysis of induction has, I venture to think, various imperfec- 

 tions, to some of which it may be useful to call attention. In the first 

 place, when I put my hand in a bag and draw out a handful of beans, 

 and, finding three-quarters of them black, infer that about three-quar- 

 ters of all in the bag are black, my inference is obviously of the same 

 kind as if I had found any larger proportion, or the whole, of the sam- 

 ple black, and had assumed that it represented in that respect the rest 

 of the contents of the bag. But the analysis in question hardly seems 

 adapted to the explanation of this proportionate induction, where the 

 conclusion, instead of being that a certain event uniformly happens un- 

 der certain circumstances, is precisely that it does not uniformly occur, 

 but only happens in a certain proportion of cases. It is true that the 

 whole sample may be regarded as a single object, and the inference 

 may be brought under the formula proposed by considering the conclu- 

 sion to be that any similar sample will show a similar proportion among 

 its constituents. But this is to treat the induction as if it rested on a 

 single instance, which gives a very false idea of its probability. 



In the second place, if the uniformity of Nature were the sole war- 

 rant of induction, we should have no right to draw one in regard to a 

 character whose constancy we knew nothing about. Accordingly, Mr. 

 Mill says that, though none but white swans were known to Europeans 



