LAW, CAUSE 361 



feels that Keynes has neglected the effect on the probability 

 of a law due to the mere increase in the number of cases. 

 Nicod is responsible for the introduction of the convenient 

 terms "confirmation' and "infirmation." 1 A law "all 

 A is B r is confirmed by any case in which A and B occur 

 together, and infirmed by any case in which A occurs in the 

 absence of B. It is generally recognized that infirmation 

 definitely decreases probability but not that confirmation 

 increases probability. Nicod, however, insists upon the 

 fact that mere multiplication of instances does increase the 

 probability of a law, entirely apart from the fact to which 

 Keynes referred that such multiplication increases the nega- 

 tive analogy. Such a contention, however, rests upon two 

 assumptions which Nicod states explicitly. "It is at first 

 necessary that the law possess, from the very start, a prob- 

 ability that is not null no matter how small it may be." 

 And 'it is necessary, besides, that on the hypothesis that 

 the law is false, its successive verification in an infinite 

 number of cases is infinitely improbable; or in more precise 

 terms, that its improbability exceeds any limit for a suffi- 

 ciently large number of cases." 2 According to Nicod 's 

 thesis, therefore, if one grants that a single instance of an 

 association contributes a finite probability to the law (or 

 possesses a minimum of empirical necessity, in the termi- 

 nology employed earlier in the chapter), and if one grants 

 that the multiplication of such instances to infinity would 

 be infinitely improbable if the law were false, then each new 

 instance even though it introduces no differing factor does 

 increase the probability of the law. For example, the illus- 

 tration of the Irishmen may be formulated, somewhat in- 

 accurately, in the following terms: If the existence of a 

 single Irishman who is quick-tempered makes it at least 

 slightly probable that all Irishmen should be so character- 

 ized, and if it is highly improbable that one should continue 

 to find Irishmen possessing this feature if the law that all 



1 These words have already been introduced, though in a slightly different sense. 

 See above, Chapter XI, p. 222. 



2 Op. cit., p. 274. 



