260 PROCEEDINGS OF THE AMERICAN ACADEMY 



difficulties. "When the probability of such a function is required, he 

 can only obtain it by a departure from the strictness of his system. 

 And on account of the absence of that symbol, he is led to declare 

 that, -without adopting the principle that simple, unconditioned events 

 whose probabilities are given are independent, a calculus of logic 

 applicable to probabilities would be impossible. 



The question as to the adoption of this principle is certainly not one 

 of words merely. The manner in which it is answered, however, 

 partly determines the sense in which the term " probability " is taken. 



In the propriety of language, the probability of a fact either is, or 

 solely depends upon, the strength of the argument in its favor, sup- 

 posing all relevant relations of all known facts to constitute that argu- 

 ment. Now, the strength of an argument is only the frequency with 

 which such an argument will yield a true conclusion when its premises 

 are true. Hence probability depends solely upon the relative fre- 

 quency of a specific event (namely, that a certain kind of argument 

 yields a true conclusion from true premises) to a generic event 

 (namely, that that kind of argument occurs with true premises). 

 Thus, when an ordinary man says that it is highly probable that it 

 will rain, he has reference to certain indications of rain, — that is, to 

 a certain kind of argument that it will rain, — and means to say that 

 there is an argument that it will rain, which is of a kind of which but a 

 small proportion fail. " Probability," in the untechnical sense, is there- 

 fore a vague word, inasmuch as it does not indicate what one, of the 

 numerous subordinated and co-ordinated genera to which every argu- 

 ment belongs, is the one the relative frequency of the truth of which 

 is expressed. It is usually the case, that there is a tacit understand- 

 ing upon this point, based perhaps on the notion of an infima species 

 of argument. But an infima species is a mere fiction in logic. And 

 very often the reference is to a very wide genus. 



The sense in which the term should be made a technical one is 

 that which will best subserve the purposes of the calculus in question. 

 Now, the only possible use of a calculation of a probability is security 

 in the long run. But there can be no question that an insurance 

 company, for example, which assumed that events were independent 

 without any reason to think that they really were so, would be sub- 

 jected to great hazard. Suppose, says Mr. Venn, that an insurance 

 company knew that nine tenths of the Englishmen who go to Madeira 

 die, and that nine tenths of the consumptives who go there get well. 



