ILLUSTRATIONS OF THE LOGIC OF SCIENCE. 211 



for thousands of years, yet the inference that all swans were white was 

 " not a good induction," because it was not known that color was a 

 usual generic character (it, in fact, not being so by any means). But 

 it is mathematically demonstrable that an inductive inference may have 

 as high a degree of probability as you please independent of any ante- 

 cedent knowledge of the constancy of the character inferred. Before 

 it was known that color is not usually a character of genera, there was 

 certainly a considerable probability that all swans were white. But 

 the further study of the genera of animals led to the induction of their 

 non-uniformity in regard to color. A deductive application of this gen- 

 eral proposition would have gone far to overcome the probability of the 

 universal whiteness of swans before the black species was discovered. 

 When we do know anything in regard to the general constancy or in- 

 constancy of a character, the application of that general knowledge to 

 the particular class to which any induction relates, though it serves to 

 increase or diminish the force of the induction, is, like every application 

 of general knowledge to particular cases, deductive in its nature and 

 not inductive. 



In the third place, to say that inductions are true because similar 

 events happen in similar circumstances or, what is the same thing, 

 because objects similar in some respects are likely to be similar in oth- 

 ers is to overlook those conditions which really are essential to the 

 validity of inductions. When we take all the characters into account, 

 any pair of objects resemble one another in just as many particulars as 

 any other pair. If we limit ourselves to such characters as have for us 

 any importance, interest, or obviousness, then a synthetic conclusion 

 may be drawn, but only on condition that the specimens by which we 

 judge have been taken at random from the class in regard to which we 

 are to form a judgment, and not selected as belonging to any sub-class. 

 The induction onby has its full force when the character concerned has 

 been designated before examining the sample. These are the essentials 

 of induction, and they are not recognized in attributing the validity of 

 induction to the uniformity of Nature. The explanation of induction 

 by the doctrine of probabilities, given in the last of these papers, is not 

 a mere metaphysical formula, but is one from which all the rules of 

 synthetic reasoning can be deduced systematically and with mathemati- 

 cal cogency. But the account of the matter by a principle of Nature, 

 even if it were in other respects satisfactory, presents the fatal disad- 

 vantage of leaving us quite as much afloat as before in regard to the 

 proper method of induction. It does not surprise me, therefore, that 

 those who adopt this theory have given erroneous rules for the conduct 

 of reasoning, nor that the greater number of examples put forward by 

 Mr. Mill in his first edition, as models of what inductions should be, 

 proved in the light of further scientific progress so particularly unfor- 

 tunate that they had to be replaced by others in later editions. One 

 would have supposed that Mr. Mill might have based an induction on 



