352 Fallacies. [CHAP. xiv. 



are unwilling to resort to mathematical valuation of chances, 

 they must be regarded as merely a special form of the modal 

 difficulties discussed in the last chapter, and need not there 

 fore be reconsidered here ; but a word or two may be added 

 concerning the views of some who have looked at the matter 

 from the mathematician s point of view. 



The principal of these is perhaps Buffon. He has ar 

 rived at the estimate (Arithmetique Morale vm.) that this 

 practical zero is equivalent to a chance of yo&quot;,t&amp;gt;w. ^ke 

 grounds for selecting this fraction are found in the fact that, 

 according to the tables of mortality accessible to him, it 

 represents the chance of a man of 56 dying in the course of 

 the next day. But since no man under common circum 

 stances takes the chance into the slightest consideration, it 

 follows that it is practically estimated as having no value. 



It is obvious that this result is almost entirely arbitrary, 

 and in fact his reasons cannot be regarded as anything more 

 than a slender justification from experience for adopting a 

 conveniently simple fraction ; a justification however which 

 would apparently have been equally available in the case of 

 any other fractions lying within wide limits of the one 

 selected 1 . 



21. There is one particular form of this error, which, 

 from the importance occasionally attached to it, deserves 

 perhaps more special examination. As stated above, there 

 can be no doubt that, however unlikely an event may be, if 

 we (loosely speaking) vary the circumstances sufficiently, or 



1 This theoretical or absolute neg- tion will be found described in Mr 

 lect of what is very rare must not be Merriman s Least Squares (p. 166). 

 confused with the practical neglect But this rests on the understanding 

 sometimes recommended by astro- that a smaller balance of error would 

 nomical and other observers. A thus result in the long run. The 

 criterion, known as Chauvenet s, for very rare event is deliberately re- 

 indicating the limits of such rejec- jected, not overlooked. 



