SECT. 9.] Credibility of Extraordinary Stories. 415 



comes to the same thing, in the case of the bag with black 

 and white balls, has been questioned or objected to 1 on the 

 ground that it is contrary to all experience to suppose that 

 the testimony of a moderately good witness could be so 

 enormously depreciated under such circumstances. I should 

 prefer to base the objection on the ground that experience 

 scarcely ever presents such circumstances as those supposed ; 

 but if we postulate their existence the given conclusion seems 

 correct enough. Assume that a man is merely required to 

 say yes or no ; assume also a group or succession of cases in 

 which no should rightly be said very much oftener than 

 yes. Then, assuming almost any general truthfulness of the 

 witness, we may easily suppose the (rightful occasions for 

 denial to be so much the more frequent that a majority of 

 his affirmative answers will actually occur as false noes 

 rather than as correct ayes. This of course lowers the 

 average value of his ayes/ and renders them comparatively 

 untrustworthy. 



Consider the following example. I have a gardener whom 

 I trust as to all ordinary matters of fact. If he were to 

 tell me some morning that my dog had run away I should 

 fully believe him. He tells me however that the dog has 

 gone mad. Surely I should accept the statement with much 

 hesitation, and on the grounds indicated above. It is not 

 that he is more likely to be wrong when the dog is mad ; 

 but that experience shows that there are other complaints 

 (e.g. fits) which are far more common than madness, and 

 that most of the assertions of madness are erroneous asser 

 tions referring to these. This seems a somewhat parallel 

 case to that in which we find that most of the assertions 

 that a white ball had been drawn are really false assertions 

 referring to the drawing of a black ball. Practically I do 



1 Todhunter s History, p. 400. Philosophical Magazine, July, 1864. 



