USE OF A SYMBOLICAL LAXGUAGE. 245 



plausible as it sounded, would lead to iuconsistency of 

 notation. For, since a:- : ^ is equivalent to z' : x', con- 

 sistency of notation required that {x : z) should denote 

 the same chance as {z' : x')c; and, as I had interpreted the 

 symbols, this would not be the case. The chance that z is 

 true, on the assumption that x is true, is not generally 

 equal to the chance that x is false on the assumption that 

 z is false. I was thus forced to the conclusion that I had 

 put a wrong interpretation on the symbols {x :z)c and 

 {z':a!')c, which must be equivalent, and that neither of 

 them, therefore, was the proper symbol for the chance 

 which I wished to express. It became necessary, therefore, 

 since there did not appear to be sufficient data for logi- 

 cally inferring a correct expression for this chance, to 

 invent a new and arbitrary symbol for it ; and then the 

 important question presented itself as to what that symbol 

 should be. It must, if possible, be brief and easily 

 formed ; it must be formed, at least partly, of the symbols 

 X and z ; and yet it must be some unambiguous combination 

 of those symbols — that is to say, a combination which 

 should convey no other meaning either by definition or by 

 implication. Out of several symbols that oflfered them- 

 selves as candidates for the important post to be filled, I 

 at last selected the symbol z^ as the one most likely to 

 perform efiectively the duties required of it. 



The symbol z^. being thus fairly installed, I was struck 

 by the resemblance between it in some respects and the 

 symbol Zc. Both expressed the chance of the truth of z, 

 though on generally different assumptions ; and, what was 

 more remarkable, some of the formulae which I had ob- 

 tained involving the constant suffix c, as 



(a + /3)e=«o + /3..-(«i3)<., 



were also true when for c I substituted the variable suffix 



