-12 On Implicational and Equational Logic, 



denote a statement, as in my system, or else each letter must 

 in both forms denote a quality or thing, as in Prof. Jevons's 

 system. On the supposition that each letter denotes a state- 

 ment, my notation exhibits clearly the very remarkable fact 

 that in the syllogism (a : (3)(/3 : 7) : (« : 7), the very same 

 relation which connects a with /3, and B with 7, connects also 

 the combined premises (a : /3)(/3 : 7) with the conclusion a : 7. 

 On the assumption that each letter denotes a statement, Prof. 

 Jevons's notation (as I have shown) could only show this co- 

 incidence of relation in a very clumsy and roundabout manner; 

 while, on the assumption that each letter denotes a thing or 

 quality (as in his system), his notation could scarcely be used 

 in this extended way at all. 



The same remarks apply to many other useful and symme- 

 trical formulae, which, so far as I can see, are altogether unin- 

 terpretable on Prof. Jevons's hypothesis that each letter 

 should denote a thing or quality ; while on my hypothesis, 

 that each letter should denote a statement, every formula con- 

 veys a clear and precise meaning, which it is scarcely possible 

 to misunderstand. Take, for example, the formulae: — 



(1) (A:a)(B:5)(0:c)... : (ABC . . . : abc . . .); 



(2) (A : a)(B : 6)(0 : c) . . . : (A + B + C + ... : a + b + c + ...); 



(3) [x : a)(x : b)(x : c) . . . = (# : abc . . . ); 



(4) (a : x)(b : x)(c : x) . . . = (a + b + c + . . . : x); 



(5) (a : x) + (b : x) + {c : x) + . . . : (abc . . . : x), 



(6) (x : a) + (x :b) + (x: c) + ...: (x: a + b + c + ...). 



These formulae express logical laws of undoubted truth, which 

 Prof. Jevons could scarcely express in his notation without the 

 help of words. 



Prof. Jevons approves to some extent of my accent to ex- 

 press denial, and occasionally adopts this notation in his new 

 work ; but he finds it difficult, he says, to believe that there is 

 any advantage in my innovations in other respects, and he is 

 of opinion that " my proposals tend towards throwing Formal 

 Logic back into its ante-Boolian confusion/' To this general 

 condemnatory opinion it is difficult to make any definite reply; 

 I can only express my regret that Prof. Jevons has nowhere 

 throughout his book given a single example of this tendency in 

 my proposals " towards throwing Formal Logic back into its 

 ante-Boolian confusion." Abundant materials were at his 

 disposal for comparing my method with his own in the fairest 

 and most decisive way possible, namely in the actual solution 

 of problems. Out of the various problems of which I have 

 published solutions he might surely have found one with which 



