340 PROF. W. STANLEY JEVONS ON 



It is evident that tlie number of ABC's is indeterminate^ 

 because there is no condition to determine {Abe). But 

 reducing this to its minimum^ zero, we learn that the lower 

 limit of (ABC) is the excess of the sum of B's and C's 

 over A's. As no result can be negative, avc also learn 

 that if {Abe) =0, then (A) cannot exceed (B) + (C). 



15. This method gives us a clear view of the conditions 

 of any logical argument. Take a syllogism in Barbara, 

 thus : — 



Every A is B : in symbols A=: AB. 



Every B is C „ „ B = BC. 



.-.Every A is C „ ,, A = AC. 



What additional information do we require in order to 

 determine the number of all the classes of objects con- 

 cerned ? 



There are altogether eight conceivable combinations of 

 A, B, C, and their negatives, «, b, c, according to the laws 

 of thought ; but of these, four combinations are rendered 

 impossible by the premises, so that we have four quantities 

 assigned — 



(ABc)=o, [Abc)=o, 



{AbC)=o, (aBc)=o. 



There remain, then, four unknown quantities ; and unless 

 we have these assigned directly or indirectly, we do not 

 really know the relative numbers of the classes. But the 

 numbers of any four existing classes may, by a proper ar- 

 rangement of equations, be made to yield the number 

 of any other existing class. Thus, if 



(A) =93 (C) = i90 



(aBC)= 5 {abc)= 4, 



we may di^aw the following conclusions : — 



(abC) = (C) - (A) - («BC) = 190 - 93 - 5 = 92 ; 

 (B) = (ABC)-f(«BC)=93 + 5 = 98. 



