52 INDUCTION. 



recurrence, does not prove that it is an instance of any law ; 

 does not prove that it is not casual, or, in common language, 

 the effect of chance. 



And yet, when a coincidence cannot be deduced from known 

 laws, nor proved by experiment to be itself a case of causation, 

 the frequency of its occurrence is the only evidence from 

 which we can infer that it is the result of a law. Not, how- 

 ever, its absolute frequency. The question is not whether the 

 coincidence occurs often or seldom, in the ordinary sense of 

 those terms ; but whether it occurs more often than chance 

 will account for; more often than might rationally be ex- 

 pected if the coincidence were casual. We have to decide, 

 therefore, what degree of frequency in a coincidence, chance 

 will account for. And to this there can be no general answer. 

 We can only state the principle by which the answer must 

 be determined : the answer itself will be different in every 

 different case. 



Suppose that one of the phenomena, A, exists always, and 

 the other phenomenon, B, only occasionally : it follows that 

 every instance of B will be an instance of its coincidence with 

 A, and yet the coincidence will be merely casual, not the result 

 of any connexion between them. The fixed stars have been 

 constantly in existence since the beginning of human expe- 

 rience, and all phenomena that have come under human obser- 

 vation have, in every single instance, coexisted with them ; 

 yet this coincidence, though equally invariable with that 

 which exists between any of those phenomena and its own 

 cause, does not prove that the stars are its cause, nor that 

 they are in anywise connected with it. As strong a case 

 of coincidence, therefore, as can possibly exist, and a much 

 stronger one in point of mere frequency than most of those 

 which prove laws, does not here prove a law : why ? because, 

 since the stars exist always, they must coexist with every 

 other phenomenon, whether connected with them by causa- 

 tion or not. The uniformity, great though it be, is no 

 greater than would occur on the supposition that no such 

 connexion exists. 



On the other hand, suppose that we were inquiring whether 



