338 PROF. W. STANLEY JEVONS ON 



which implies that there is a certain indefinite number of 

 men who are not aged. 



Develope A and B in (i) by the law of duality, and we 

 have 



(AB) + {Ab) = (AB) + (aB) - w. 



Subtract (AB) from both sides, and insert for {Ab) its value 

 in (2), and we have 



{aB)=tv + w' (3) 



which proves that there are some aged persons in the house 

 who are not men, and assigns their quantity, so far as it 

 can be assigned. The number of such persons we learn is 

 at least equal to the number of men who are not aged, and 

 exceeds it by w — that is, the excess of the number of aged 

 persons over the men, if such excess exists, which the pre- 

 mises do not determine. 



Adding {ab) to both sides of (3) we get 



(^a)=w-]-w' -{- {ab) ; 



but this expression contains two unknown quantities, 

 namely, w and {ab). As no quantity can be intrinsically 

 negative, w' is the lowest limit of the number of persons 

 who are not men ; and the number is to be increased by tv, 

 4f it have value, and also by the number of persons, if such 

 there be, who are neither men nor aged. 



13. The most celebrated instance to which this method 

 can be applied is one also proposed by Professor De Mor- 

 gan^, and discussed by Boole f. It is as follows ; — 



Most B'sare A's (i) 



Most B's are C's (2) 



Therefore some C^s are A^s (3) 



Here, of course, most means more than half, and is one of 



^ Formal Logic, p. J63. 



t Trans, of tlie Cambridge Philosophical Society, vol. xi. part ii. p. i. 



