82 Modes of establishing the Groups or Series. [CHAP. IV. 



called the Principle of Sufficient Keason. It takes this 

 form; Here are four kinds of throws which may happen; 

 once admit that the separate elements of them, namely, H 

 and T, happen equally often, and it will follow that the above 

 combinations will also happen equally often, for no reason can 

 be given in favour of one of them that would not equally hold 

 in favour of the others. 



To a certain extent we must admit the validity of the 

 principle for the purpose. In the case of the throws given 

 above, it would be valid to prove the equal frequency of (1) 

 and (3) and also of (2) and (4) ; for there is no difference 

 existing between these pairs except what is introduced by our 

 own notation 1 . TH is the same as HT, except in the order 

 of the occurrence of the symbols H and T, which we do not 

 take into account. But either of the pair (1) and (3) is 

 different from either of the pair (2) and (4). Transpose the 

 notation, and there would still remain here a distinction which 

 the mind can recognize. A succession of the same thing 

 twice running is distinguished from the conjunction of two 

 different things, by a distinction which does not depenc 

 upon our arbitrary notation only, and would remain entirely 

 unaltered by a change in this notation. The principle there 

 fore of Sufficient Reason, if admitted, would only prove thai 

 doublets of the two kinds, for example (2) and (4), occur 

 equally often, but it would not prove that they must each 



1 I am endeavouring to treat this tween the terms of the series? The 



rule of Sufficient Eeason in a way succession seems then reduced to a 



that shall be legitimate in the opinion dull uniformity, a mere iteration of 



of those who accept it, but there the same thing many times ; the 



seem very great doubts whether a series we contemplated has disap- 



contradiction is not involved when peared. If the sides are not abso- 



we attempt to extract results from lutely alike, what becomes of the 



it. If the sides are absolutely alike, applicability of the rule ? 

 how can there be any difference be- 



