50 INDUCTION. 



is any connexion between a and A, since a may have many 

 causes, and may have been produced, in these different in- 

 stances, 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 cha- 

 racteristic uncertainty of the method diminishes, and the 

 existence of a law of connexion 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 connexion 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 pheno- 

 mena 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 pro- 

 duced. 



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 

 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 an uni- 

 formity : the occurrence of a phenomenon in certain circum- 



