USE OF A SYMBOLICAL LANGUAGE. 243 



the ordinary logic, and especially towards the syllogism. 

 The only book on logic that I possessed was Prof. Bain's 

 work ; and to this I turned. The resemblance which my 

 method bore to Boole's, as therein described, of course 

 struck me at once ; but Boole's treatment of the syllogism 

 was more likely to put me on the wrong track than to 

 help me. As my most elementary symbols denoted state- 

 ments, not necessarily connected with quantity at all, I 

 could not see how the syllogism, with its ever recurring 

 all, some, none, could be brought within the reach of my 

 method. The Cartesian system of analytical geometry at 

 last supplied the desiderated hint as to the proper mode of 

 procedure. In this system, as every mathematician 

 knows, one single point is spoken of in every equation, but 

 with the understanding that it is a representative point, 

 and that the equational statement made respecting it is 

 also true respecting every other point in the locus ex- 

 pressed by this equational statement. 



The symbol : , which I had already begun to use as an 

 occasionally convenient abbreviation for the word ^^ im- 

 plies," now became almost imperative. Syllogistic rea- 

 soning is strictly restricted to classification. The state- 

 ment " All X is Y " is equivalent to the conditional state- 

 ment '' If any thing belongs to the class X, it must also 

 belong to the class Y." Speaking then of something 

 originally unclassed, if x denote the statement " It belongs 

 to the class X," and if y denote the statement '^ It belongs 

 to the class Y," then the implicational statement x : y 

 (or X implies y) will be equivalent to the syllogistic state- 

 ment '' All X is Y." 



It was evident after this that x : j/ would be the proper 

 symbolical expression for " No X is Y ;" but, strange to 

 say, the discovery of the suitable symbolic expressions for 

 " Some X is Y " and " some X is not Y" caused me no 



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