A new Symbolic Treatment of the Old Logic. 203 



of B being true ; or, in simpler language, that if, or when, 

 A is true, B is true also.* 



Before going any further, we have to consider the 

 question, which is important as one of procedure though it 

 is not one of fact or law, whether we assert the existence of 

 whatever we make the subject of a proposition. In common 

 discourse we usually do so, unless we guard our meaning ; but 

 anything corresponding to parenthetical clauses for such a 

 purpose would be unmanageable in logic ; and the implica- 

 tion that existence is generally asserted of every term would 

 lead to false results. The following instance, though not 

 in this precise form, is mentioned in Mill's Logic : — " A 

 dragon is a serpent ; a dragon breathes flame : therefore 

 some serpents breathe flame." This is in form exactly similar 

 to the following, which is a valid syllogism according to the 

 usual rules : — " Butterflies are insects ; butterflies have 

 wings : therefore some insects have wings." 



Here are two syllogisms where the conclusion of one is 

 true and that of the other false, for a reason which does not 

 appear in the premises, viz. : that the subject of the premises 

 is in the one case existent and in the other non-existent. 

 The best way is to make no implication at all as to the 

 existence of our subjects ; and, in such propositions as the 

 above, to substitute for the word " some," such an expression 

 as " an undetermined quantity of," and, to represent it in 



notation by the algebraic expression -, which Boole some- 

 times uses in this sense. With this convention, the conclusion 

 about the dragon is seen to be right, though without signi- 

 ficance ; a portion of the class serpents, undetermined by the 

 premises of the syllogism^ breathes flame ; but in fact this 

 portion is without extent, so that the proposition is neither 

 true nor false. If the necessity for such a convention is 



* This is the meaning constantly assigned to the symbols in MacColl's 

 " Calculus of Equivalent Statements." 



