CHANCE, AND ITS ELIMINATION. 



345 



have no common antecedent except 

 A, this does not prove that there is 

 any connection between a and A, since 

 a may have many causes, and may 

 have been produced, in these different 

 instances, not by anything which the 

 instances had in common, but by some 

 of those elements in them which were 

 different. We nevertheless observed, 

 that in proportion to the multipli- 

 cation of instances pointing to A as 

 the antecedent the characteristic un- 

 certainty of the method diminishes, 

 and the existence of a law of con- 

 nection between A and a more nearly 

 approaches to certainty. It is now 

 to be determined after what amount 

 of experience this certainty may be 

 deemed to be practically attained, and 

 the connection between A and a may 

 be received as an empirical law. 



This question may be otherwise 

 stated in more familiar terms : — After 

 how many and what sort of instances 

 may it be concluded that an observed 

 coincidence between two phenomena 

 is not the effect of chance ? 



It is of the utmost importance for 

 understanding the logic of induction 

 that we should form a distinct con- 

 ception of what is meant by chance, 

 and how the phenomena which com- 

 mon language ascribes to that abstrac- 

 tion are really produced. 



§ 2. Chance is usually spoken of in 

 direct antithesis to law ; whatever (it 

 is supposed) cannot be ascribed to any 

 law is attributed to chance. It is, 

 however, certain, that whatever hap- 

 pens is the result of some law ; is an 

 effect of causes, and could have been 

 predicted from a knowledge of the 

 existence of those causes, and from 

 their laws. If I turn up a particular 

 card, that is a consequence of its place 

 in the pack. Its place in the pack 

 was a consequence of the manner in 

 which the cards were shuffled, or of 

 the order in which they were played 

 in the last game ; which, again, were 

 effects of prior causes. At every stage, 

 if we had possessed an accurate know- 

 ledge of the causes in existence, it 



would have been abstractly possible to 

 foretell the effect. 



An event occurring by chance may 

 be better described as a coincidence 

 from which we have no ground to 

 infer an uniformity : the occurrence 

 of a phenomena, in certain circum- 

 stances, without our having reason on 

 that account to infer that it will 

 happen again in those circumstances. 

 This, however, when looked closely 

 into, implies that the enumeration of 

 the circumstances is not complete. 

 Whatever the fact be, since it has 

 occurred once, we may be sure that if 

 all the same circumstances were re- 

 peated, it would occur again ; and 

 not only if all, but there is some 

 particular portion of those circum- 

 stances on which the phenomenon is 

 invariably consequent. With most of 

 them, however, it is not connected in 

 any permanent manner : its conjunc- 

 tion with those is said to be the effect 

 of chance, to be merely casual. Facts 

 casually conjoined are separately the 

 effects of causes, and therefore of laws; 

 but of different causes, and causes not 

 connected by any law. 



It is incorrect, then, to say that any 

 phenomenon is produced by chance ; 

 but we may say that two or more 

 phenomena are conjoined by chance, 

 that they co-exist or succeed one an- 

 other only by chance ; meaning that 

 they are in no way related through 

 causation ; that they are neither cause 

 and effect, nor effects of the same 

 cause, nor effects of causes between 

 which there subsists any law of co- 

 existence, nor even effects of the same 

 collocation of primeval causes. 



If the same casual coincidence 

 never occurred a second time, we 

 should have an easy test for distin- 

 guishing such from the coincidences 

 which are the results of a law. As 

 long as the phenomena had been found 

 together only once, so long, unless we 

 knew some more general laws from 

 which the coincidence might have re- 

 sulted, we could not distinguish it 

 fn^m a casual one ; but if it occurred 

 twice, we should know that the phfe- 



