274 THE SCIENCE OF LOGIC 



unknown alteration in those influences would upset our calcula 

 tions. For example, were the uniform shape of a die, or the 

 uniform density of its texture, to alter imperceptibly, the equality 

 of alternatives which is essential to the calculation of probability 

 would be destroyed. It is, in fact, by determining experimentally 

 whether some one alternative occurs more frequently than it 

 should occur if the chances were equal, that we detect the exist 

 ence of a &quot; bias &quot; which may lead to the discovery of some causal 

 connexion or law (267). l In throwing dice, for instance, the five 

 may be found to turn up 97 times out of 600 trials, and 1003 

 times out of 6000 ; from which it is concluded a posteriori that 

 the probability in favour of the turning of five lies between ^V^ 

 and !$ or is about . The experiment so far as it goes, 

 for it cannot be carried on indefinitely verifies the supposition 

 that the sum-total of the influences at work was indifferent, and 

 hence made as often for any one as for any other alternative. 

 It is only, therefore, when we have the agencies under our own 

 control, and can experiment with them, that we can secure with 

 absolute certainty the constant prevalence of the same set of con 

 ditions. This is secured in all ordinary &quot; games of pure chance &quot;. 

 Before inquiring how far it can be assumed to prevail in natural 

 phenomena (268), we will examine the application of the calculus 

 of probability to data that are assumed to fulfil the two conditions 

 just set forth. We may observe here, however, that when the 

 requisite conditions are present, the estimate can be made for past 

 events as well as for future ones. The theory applies independently 

 of time. No doubt, its usual application is to games of chance, 

 dealing with a future event. But when some one, we do not 

 know which, out of a certain definite number of equally possible 

 alternatives has happened, we can apply the theory to determine 

 what degree of probability there is that such a definite alternative 

 has happened. 



&quot;Thus, for example, it is extremely improbable that a hand at whist 

 should consist entirely of trumps. Yet the probability of this is no less than 

 that of any other one definite hand. It is its interesting character which draws 

 special attention to it, and causes us to recognize how enormous are the odds 

 against it. This we do not recognize in the case of other hands. If, then, a 

 person told us he had held a hand of thirteen trumps the previous evening we 

 should probably feel more hesitation in believing him than if he told us he had 

 held a hand consisting of certain definitely named cards. Yet the antecedent 

 improbability would be no greater in the one case than in the other. Were 



1 Cf. JOYCE, op. cit., p. 372 ; VENN, Logic of Chance, pp. 78-82. 



