Kidd. — On Probability. lvii 



from data almost as simple, the profound philosopher Mill arrived at a resultant 

 probability widely different from the demonstrable conclusion. Allowing, as 

 all do, that the sequence of numerically expressed probabilities is a matter of 

 rigorous demonstration, we cannot consistently deny that Probability is some- 

 thing else than Belief. 



The relation of Probability to Belief is more correctly delineated in the 

 older writers than in the most recent. " Probability," says Hume (Essays), 

 " arises from a superiority of chances on any side ; and, according as this 

 superiority encreases and surpasses the opposite chances, the probability 

 receives a proportionate encrease, and begets a still higher degree of belief or 

 assent to that side in which we discover the superiority." The real relations 

 are here indicated : the "chances," i.e. alternatives, determine the probability ; 

 and this probability, so far as we " discover n it, " begets " a correspondent 

 belief. The definition of Probability given by the chief writer on the philo- 

 sophy of Induction, Mr. Mill, is also essentially correct. The " probability to 

 us," he observes (System of Logic, III. xviii. 1), " means the degree of 

 expectation which we are warranted in entertaining by our present evidence." 



The distinction between the actual belief and due belief, which is slurred 

 over by some writers who identify Probability with Belief, is fundamental ; 

 and the resultant diversity is great. To ascertain actual beliefs, we must 

 interrogate men's minds j to estimate the degrees of belief that are warranted, 

 we must look to the objective evidence of facts. As the eye does not cause or 

 constitute the rays of light, nor their abundance or paucity ; and as the ear 

 does not produce the acoustic vibrations of the atmosphere ; so neither does 

 the recipience of the mind create the evidence that is presented to it. And as 

 visibility, therefore, differs from seeing, and audibility from hearing, so 

 probability differs from belief. 



15. In concluding these remarks on the nature and basis of Probability, 

 permit me to summarize in a few words the principal results at which we have 

 arrived, in so far as they appear to be peculiar to this paper. 



First, Probability is a property of suppositions or propositions, and of 

 these only. 



Secondly, the most appropriate definition of Probability appears to be 

 simply this : The probability of a proposition is its claim to be accepted as 

 true ; and the value of the claim is determined by the relation of what is 

 predicated to the data. As Truth and Falsity, strictly so called, are properties 

 of propositions only, and Probability is the claim to be true, hence, as above 

 mentioned, it is only to propositions that Probability also belongs. 



Thirdly, when a numerical value is assigned to a probability, the denomina- 

 tor of the fraction represents some quantity, of whatsoever kind it may be, 

 which is assumed to be an object of thought, and to be divisible into pnnnl 



