1880.] expressing the common propositions of Logic. 41 



extent shall be greater than those of S and P together, and Ave 

 may regard this as finite, and therefore suitable to logical treatment. 

 When our negative predicate, not-P, is thus brought down to finite 

 extent in the form of X— P, we can venture to refer 8 to it. We 

 imply, in fact, that S is a portion of not-P ; and we write it not by 

 an equation formula, but by an inclusion formula, as S<X — P. 



10. This is of considerable interest historically, since Segner's 

 Specimen Logicce (1740), is the first systematic attempt, so far as I 

 have seen, to construct a symbolic Logic. (He had nothing before 

 him of this kind to appeal to beyond a few ingenious suggestions 

 by Leibnitz.) The sign < is used in the same sense as by Dro- 

 bisch, A < B marking that the extent of B is inclusive of that 

 of A. But in one respect he seems to me distinctly in advance 

 of Drobiscb, and very much in advance of his time. This is in his 

 free use of negative terms in their full extent (he preserves the 

 old name of 'infinite' for them), for the representation of which 

 he uses the negative sign. Thus if A stands for man, — A stands 

 for not-man. It may be added that he had fully realized the fact 

 that it is symbolically indifferent whether we apply A to a positive 

 or to its contradictory, provided we preserve the antithesis between 

 + and — . Thus if A stands for non-triangulum, — A will stand for 

 triangulum, and so forth. Hence his expression S < — P marks 

 quite correctly that S is extensively a portion of not-P. 



This notation of course is very crude, being not of much value 

 even within the limits of the syllogism. The various syllogistic 

 moods are however worked through with its aid, but with certain 

 departures from the common view which need not here be de- 

 scribed. It may interest the historical student of this part of the 

 subject to say that Segner not only describes the symbolic pro- 

 cedure by which from two such premises as A < B, C <D, we can 

 infer AG < BD\ but also expressly calls attention to the "law of 

 duality" as it is sometimes termed, viz. that AA =A ; that is, he 

 points out that when A and G are the same no change is pro- 

 duced : — "subjecti enim idea, cum se ipsa composita, novam ideam 

 producere nequit." There are many other interesting points about 

 the work which must be passed over here. 



We now come to a group of forms which I have thrown to- 

 gether as adopting somewhat of an implication arrangement : some 

 of them indeed expressly describe themselves as indicating an 

 implication. Thus, 



11. This is best put into words as, " posit S, and we sublate P." 

 It turns entirely upon the representation of contradictories by + 

 and — , a representation which, as in the closely analogous case 

 just discussed, will do fairly well up to a certain point. If wo 



