362 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



Irishmen are quick-tempered is false, then the finding of a 

 single additional case does increase the probability of the 

 law. Under such conditions the probability of the law is 

 increased by the mere number of cases, without regard to 

 the element of variety which these cases contribute. 



Still another approach to the problem of the operational 

 derivation of scientific laws, closely associated with the 

 work of Keynes and Nicod, is the attempt to determine 

 probabilities on the basis of frequencies. Techniques of 

 this kind become especially applicable when the correlation 

 is known not to hold universally. The problem then centers 

 about the attempt to determine the proportion of favorable 

 cases as measured against the totality of cases, favorable 

 and unfavorable, in order to determine the probability that 

 the correlation will occur in any given case. The probability 

 of any given case is then determined by the limiting value 

 of the ratio of the number of favorable cases to the total 

 number of cases, when the total number becomes very 

 large. The probability of throwing a two on a die is J since 

 in the long run a two will be thrown once in every six throws. 

 A law derived in this way is called a statistical law since it 

 has meaning only if applied to large numbers. If it were 

 known, for example, that there are Irishmen who are not 

 quick-tempered, the probability of any given Irishman pos- 

 sessing this quality would be determined by counting the 

 cases of Irishmen who exhibit this feature and then dividing 

 by the total ascertained number of Irishmen, i.e., those 

 possessing the property and those not possessing it. 



It is well to be as clear as a brief discussion of this kind 

 permits concerning the distinction between probabilities of 

 the kind sought by Keynes and Nicod, and those which are 

 based on frequencies. The former are universal laws which 

 are only probably true, while the latter are statements of 

 frequencies. In the former the evidence is only affirmative, 

 in the latter it is both affirmative and negative. Both state 

 only probabilities with reference to any individual case, 

 but the former forbid certainty because the universality of 



