NUMERICALLY DEFINITE REASONING. 333 



means that A is identical with B, which differs from D_, it 

 does not follow that 



(A) = (B)~(D). 



Two classes of objects may differ in qualities, and yet they 

 may agree in number. This is a point which strongly 

 confirms me in the opinion I have already expressed, that 

 all inference really depends upon equations, not differ- 

 ences'^ ; and I shall therefore employ throughout this 

 paper only equations which may be almost indifferently 

 used in the qualitative or quantitative meaning. 



6. I shall employ, as in logic, a joint term, such as A B 

 (or ABC), to mean the class possessing all the qualities 

 of A and B (or of A and B and C) . To every positive 

 term there corresponds a negative term, denoted by the 

 corresponding small italic letter. Thus the negative of A 

 is «, of B 5, and so on. If, then, A means man, a means 

 simply not man. Hence a b will mean the combination 

 of qualities of not being A and not being B. 



7. The sign -I- is used to stand for the disjunctive con- 

 junction or, but in an unexclusive sense. Thus 



A = BIC 



means that whatever has the qualities of A, must have 

 either the qualities of B or of C; but it may have the qualities 

 of both. This unexclusive character of the terms and signs 

 of logic, which creates a profound difference between my 

 system and that of Prof. Boole, prevents me from convert- 

 ing alternatives into numbers as they stand. It does not 

 follow from the statement that A is either B or C, that 

 the number of A's is equal to the number of B^s added to 

 the number of C^s; for some objects, or possibly all, 

 may have been counted twice in this addition. Thus, if 

 we say An elector is either an elector for a borough, or for 

 a county, or for a university, it does not follow that the 



* Substitution of Similars, pp. i6, 17. 



