360 Fallacies. [CHAP. xiv. 



That it does so belong will be easily seen if we bear in mind 

 the fundamental conception of the science. We are there 

 introduced to a series, for purposes of inference an indefi 

 nitely extended series, of terms, about the details of which, 

 information, except on certain points, is not given ; our know 

 ledge being confined to the statistical fact, that, say, one in 

 ten of them has some attribute which we will call X. Sup 

 pose now that five of these terms in succession have been X, 

 what hint does this give about the sixth being also an XI 

 Clearly none at all ; this past fact tells us nothing ; the for 

 mula for our inference is still precisely what it was before, 

 that one in ten being X it is one to nine that the next term 

 is X. And however many terms in succession had been of 

 one kind, precisely the same formula would still be given. 



28. The way in which events will justify the answer 

 given by this formula is often misunderstood. For the 

 benefit therefore of those unacquainted with some of the 

 conceptions familiar to mathematicians, a few words of ex 

 planation may be added. Suppose then that we have had 

 X twelve times in succession. This is clearly an anomalous 

 state of things. To suppose anything like this continuing 

 to occur would be obviously in opposition to the statistics, 

 which assert that in the long run only one in ten is X. 

 But how is this anomaly got over? In other words, how 

 do we obviate the conclusion that JT s must occur more 

 frequently than once in ten times, after such a long succes 

 sion of them as we have now had ? Many people seem to 

 believe that there must be a diminution of X s afterwards 

 to counterbalance their past preponderance. This however 

 would be quite a mistake ; the proportion in which they 

 occur in future must remain the same throughout ; it cannot 

 be altered if we are to adhere to our statistical formula. 

 The fact is that the rectification of the exceptional disturb- 



