NUMERICALLY DEFINITE REASONING. 337 



Thus 



53 = 45 +(^C), 

 whence 



(iC) = 8, 



which is the first qusesitum. 



To obtain the second^ the number of Abe's, we have 



(A) = (ABC) + (ABc) + (A^C) + (Abe) 

 100= 45 + + 8 + {Abe) 

 Hence 



{Abe)= 47. 



I now proceed to exemplify the use of the method by 

 applying it to examples drawn chiefly from previous 

 writers. 



12. Professor De Morgan suggests the following as an 

 argument which cannot be put into any ordinary form of 

 the syllogism"^. 



" For every man in the house there is a person who is 

 aged; some of the men are not aged. It follows, that 

 some persons in the house are not men." 



This argument proceeds, as I conceive, not by any form 

 of syllogism, but by a pair of simple equations. Taking 



A=man, 



B= aged person, 



and putting w, w' for unknown and indefinite numbers, 

 the first premise gives the equation 



(A) = (B)-«; . (I) 



meaning that the number of aged persons equals or exceeds 

 the number of men. The second statement may be put 

 in this form, 



(Ab)=w' (2) 



* Syllabus of a proposed System of Logic, i860, p. 29. 

 SER. III. VOL. IV. Z 



