360 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



Keynes insists that the problem of induction is intimately 

 connected with two problems, both of which are important 

 in the determination of the probability of a generalization. 

 On the one hand is the likeness which holds between the 

 several cases; this is called Analogy. On the other hand is 

 the number of cases; this is called Pure Induction. But 

 Keynes insists that "an increase in the number of experi- 

 ments is only valuable in so far as, by increasing, or possibly 

 increasing, the variety found amongst the non-essential 

 characteristics of the instances, it strengthens the Negative 

 Analogy." x By Negative Analogy Keynes means the dis- 

 similarity in non-essential characteristics of the instances. 

 Hence in the supposition, say, that metals conduct elec- 

 tricity, the probability of the law is increased by finding 

 more and more cases in which it holds ; but the effect of these 

 instances is not in their number but rather in the fact that 

 by increasing the variety of the cases one is able to narrow 

 the scope of the generalization. By this method the known 

 negative analogy is increased. But the positive analogy must 

 also be increased. This can be done both by decreasing the 

 determinateness of the predicate-term and by increasing the 

 determinateness of the subject-term of the law. By this 

 method the cases which do not properly come under the 

 law are excluded, and possible exceptions are thus avoided. 

 Symbolically stated, a law of the form "all A is XY ' is less 

 probable than one of the form "all A is X" and this, in 

 turn, is less probable than one of the form "all AB is X." 

 For example, that all Irishmen are red-headed and quick- 

 tempered is less probable than that all Irishmen are quick- 

 tempered; and this, in turn, is less probable than that all 

 Irishmen from Cork are quick-tempered. Hence probability 

 can be increased by defining less narrowly the known re- 

 semblances as expressed in the predicate-term, and by de- 

 fining more narrowly the known resemblances as expressed 

 in the subject-term. 



Nicod agrees with the greater part of this analysis, but 



1 Op. cit., p. 219. 



