CHANCE, AND ITS ELIMINATION. 313 



limits ; after wliat quantity of experience a generalization which rests 

 solely upon the Method of Agreement, can be considered sufficiently 

 established, even as an empirical law. In a former chapter, when 

 treating of the Methods of Direct Induction, we expressly reserved this 

 question,* and the time is now come for endeavoring to solve it. 



We found that the Method of Agreement has the defect of not 

 proving causation, and can therefore only be employed for the ascer- 

 tainment of empirical laws. But we found, moreover, that besides this 

 deficiency, it labors under a characteristic imperfection, tending to 

 render uncertain even such conclusions as it is in itself adapted to 

 prove. This imperfection arises from Plurality of Causes. Although 

 two or more cases in which the phenomenon a has been met with, may 

 have no common antecedent except A, this does not prove that there 

 is any connexion 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 propor- 

 tion to the multiplication of instances pointing to A as the antecedent, 

 the characteristic uncertainty of the method diminishes, and the exist- 

 ence of a law of connexion between A and a more nearly approaches 

 to certainty. It is now to be determined, after what amount of expe- 

 rience 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 phenomena is not the effect of 

 chance ? 



It is of the utmost importance for understanding the logic of induc- 

 tion, that we should form a distinct conception of what is meant by 

 chance, and how the phenomena which common language asciibes tx> 

 that abstraction are really produced. 



§ 2. Chance is usually spoken of in direct antithesis to law ; what- 

 ever (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 the effects of prior causes. 

 At every stage, if we had possessed an accurate knowledge of tlie 

 causes in existence, it would have been abstractedly possible to foretell 

 the effect. 



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

 from which we have no ground to infer an 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 circum- 

 stances. 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 cir- 



* Supra, p. 252. 



