340 Fallacies. [CHAP, xiv, 



could be established (if sound) on this ground alone. That 

 is, if it really could be shown that experience in the long run 

 confirmed the preponderance of successes on one side or the 

 other according to the relative frequency of the sun-spots, 

 we should have to accept the fact that the two classes of 

 events were not really independent. One of the two, which 

 ever it may be, must be suspected of causing or influencing 

 the other; or both must be caused or influenced by some 

 common circumstances. 



10. (III.) The fallacy described at the commencement 

 of this chapter arose from determining to judge of an ob 

 served or reported event by the rules of Probability, but 

 employing a wrong set of statistics in the process of judging. 

 Another fallacy, closely connected with this, arises from the 

 practice of taking some only of the characteristics of such an 

 event, and arbitrarily confining to these the appeal to Pro 

 bability. Suppose I toss up twelve pence, and find that eleven 

 of them give heads. Many persons on witnessing such an occur 

 rence would experience a feeling which they would express by 

 the remark, How near that was to getting all heads ! And if 

 any thing very important were staked on the throw they 

 would be much excited at the occurrence. But in what 

 sense were we near to twelve ? There is a not uncommon 

 error, I apprehend, which consists in unconsciously regarding 

 the eleven heads as a thing which is already somehow 

 secured, so that one might as it were keep them, and then 

 take our chance for securing the remaining one. The eleven 

 are mentally set aside, looked upon as certain (for they have 

 already happened), and we then introduce the notion of 

 chance merely for the twelfth. But this twelfth, having 

 also happened, has no better claim to such a distinction than 

 any of the others. If we will introduce the notion of chance 

 in the case of the one that gave tail we must do the same in 



