DESCRIPTION OF A NOTATION FOR THE LodJC Of RELAT1M-. ■ 1 



latter enables us always to bring the exponent of the exponent of 6~" down to the 

 line, and make it a factor. By the former principle, objects not French violin 

 consist of objects not Frenchmen, together with object! DOl violinist*; b\ the lattei 

 individuals not servants of all women are the same as DCn-setrants of some women. 

 Another singular property of 6 — is that, 



(169.) if|>]>' e-z=\. 



" Case of the existence of — ," and ■ &ue f (he mm <*'«'< > > of — ." 



That which first led me to seek for the present extension of Boole*! logical Dotal -n 

 was the consideration that as he left his alg bra, neither h pothetieal propositions no. 



particular propositions could be properly exprc led. It is true thai I l«- was abl< » 



express hypothetical propositions in a way which answered sum. pnrpc> s perft tlj 



He could, for example, express the proposition. "Either the ran will shim .r the 



terprise will be postponed," by letting x denote -the truth of the pro, ition tha 

 the sun will shine," and y "the truth of the proposition that the enterprise Will be 



postponed " ; and writing, 



or, with the invertible addition, 



x + (l-x),y=l. 



But if he had given four letters denoting the four tern* "sun," "what ..abort t.. 

 shine," - the enterprise," and ■ what is about to be postponed," be could make 

 of these to express his disjunctive proposition, but would be obliged to as-mne otbe. 

 The imperfection of the algebra here was obvious. As for pabular proportion. 

 Boole could not accurately express them at all. He did undertake to ,*,.« then, 



and wrote 



v,x ; 



Some Y's are X's : v O T 



Some Y's are not X's : v,y = v,( 1 



The letter v is here used, says Boole, for an "indefinite class symbol" WjW J 

 a radical misapprehension of the nature of a F-^J* £ £ 'T L 

 Y's are X's, is not the same as saying that a logical . c 

 logical species need not be the name of *!*•«—► » 'J, „ , f fact 



scription of things fully expressed by a »« — ^ ^ .J ex tence from 



letber such a thing realty exist. - -»- ; log 



definition, but that argument has long been exploded If, ^ 



species 



general, there is not necessarily any such thing, and the 



(juatio 



