CHANCE, AND ITS ELIMINATION. 373 



observed, that in proportion to the multiplication of instances pointing to A 

 as the antecedent, the characteristic uncertainty of the method diminishes, 

 and the existence of a law of connection 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 conception of what is meant by chance, and 

 how the phenomena which common language ascribes to that abstraction 

 are really produced. 



§ 2. Chance is usually spoken of in direct antithesis to law ; whatever, it 

 is supposed, can not be ascribed to any law is attributed to chance. It is, 

 however, certain that whatever happens 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 

 knowledge of the causes in existence, it would have been abstractedly pos- 

 sible to foretell the effect. 



An event occurring by chance may be better described as a coincidence 

 from which we have no ground to infer a uniformity — the occurrence of 

 a phenomenon in certain circumstances, 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 cir- 

 cumstances is not complete. Whatever the fact be, since it has occurred 

 once, we may be sure that if all the same circumstances were repeated it 

 would occur again ; and not only if all, but there is some particular portion 

 of those circumstances on which the phenomenon is invariably consequent. 

 With most of them, however, it is not connected in any permanent man- 

 ner; its conjunction 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 con- 

 nected 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 another 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 colloca- 

 tion of primeval causes. 



If the same casual coincidence never occurred a second time, we should 

 have an easy test for distinguishing 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 resulted, we could not distinguish it from a casual 

 one ; but if it occurred twice, we should know that the phenomena so con- 

 joined must be in some way connected through their causes. 



