TEE THEOR Y OF PROBABILITIES. 7 



induction may vary, while this number remains unchanged. 

 This consideration appears almost to amount to a reductio ad 

 absurdum. 



13. If, on m occasions, a certain event has been observed, 

 there is a presumption that it will recur on the next occa- 

 sion. This presumption the theory of probabilities estimates at 



. But here two questions arise ; What shall constitute a 

 in ~r ^ 



" next occasion" ? What degree of similarity in the new event 

 to those which have preceded it, entitles it to be considered a 

 recurrence of the same event ? 



Let me take an example given by a late writer : 



Ten vessels sail up a river. All have flags. The presumption 



that the next vessel will have a flag is . Let us suppose the 



ten vessels to be Indiamen. Is the passing up of any vessel 

 whatever, from a wherry to a man of war, to be considered as 

 constituting a " next occasion" ? or will an Indiaman only satisfy 

 the conditions of the question ? 



It is clear that in the latter case, the presumption that the 

 next Indiaman would have a flag is much stronger, than that, 

 as in the former case, the next vessel of any kind would have 



one. Yet the theory gives as the presumption in both cases. 

 If right in one, it cannot be right in the other. Again, let all the 



flags be red. Is it - - that the next vessel will have a red flag, 

 12 



or a flag at all? If the same value be given to the presumption 

 in both cases, a flag of any other colour must be an impossibility. 

 It is to be noticed, that I only refer to the visible differences 

 among different kinds of vessels, and not to any knowledge we 

 may have about them from previous acquaintance. 



14. I turn to a more celebrated application of the theory. 

 All the movements of the planetary system, known as yet, 



are from west to east. This undoubtedly affords a strong pre- 

 sumption in favour of some common cause producing motion in 

 that direction. But this presumption depends not merely upon 

 the number of observed movements, but also on the natural 



