358 Fallacies. [CHAP. xiv. 



to them represent the entire break-down of any such theory. 

 The error, of course, is obvious enough, and one which, with 

 the figures thus before him, hardly any one could fail to 

 avoid. But if one may judge from common conversation 

 and other such sources of information, it is found in practice 

 exceedingly difficult adequately to retain the conviction that 

 even though only one in 200 instances were favourable, 

 this would represent odds of about 20 to 1 in favour of the 

 theory. If hereditary transmission did not prevail, only one 

 in 4000 sons would thus rival their fathers; but we find 

 actually, let us say (we are of course taking imaginary pro 

 portions here), that one in 200 does. Hence, if the statistics 

 are large enough to be satisfactory, there has been some 

 influence at work which has improved the chances of mere 

 coincidence in the ratio of 20 to 1. We are in fact so little 

 able to realise the meaning of very large numbers, that is, 

 to retain the ratios in the mind, where large numbers are 

 concerned, that unless we repeatedly check ourselves by 

 arithmetical considerations we are too apt to treat and esti 

 mate all beyond certain limits as equally vast and vague. 



26. (VI.) In discussing the nature of the connexion 

 between Probability and Induction, we examined the claims 

 of a rule commonly given for inferring the probability that 

 an event which had been repeatedly observed would recur 

 again. I endeavoured to show that all attempts to obtain 

 and prove such a rule were necessarily futile ; if these reasons 

 were conclusive the employment of such a rule must of 

 course be regarded as fallacious. A few examples may con 

 veniently be added here, tending to show how instead of 

 there being merely a single rule of succession we might better 

 divide the possible forms into three classes. 



(1) In some cases when a thing has been observed to 

 happen several times it becomes in consequence more likely 



