1880.] representation of logical propositions. 53 



so as to coincide with BE. This seems to me to constitute the 

 essential characteristic of his scheme, which is worked out m a 

 variety of figures of a more or less complicated kind. It is de- 

 cidedly cumbrous, and not entirely effective as regards this its main 

 aim, but it deserves recognition as an attempt to remedy a real 

 defect in the ordinary scheme. 



Hamilton who, as we know, never could succeed in grasping the 

 nature of a triangle, entirely misconceived all this ; and seeing 

 that Maass began by talking of an angle he concluded that angles 

 were being employed as the representative of class relations. 

 Hence his judgment, hurled in a blast of wrathful and contemp- 

 tuous epithets, that this is " the only attempt made to illustrate 

 Logic, not by the relations of geometrical quantities, but by the 

 relations of geometrical relations, — angles " [Logic, II. 463). 



The above schemes aim at representing the relative extent of 

 class terms by the really analogous case of the relative extent of 

 closed figures, which therefore tell their tale somewhat directly. 

 A departure from this plan was made, shortly after the date of 

 Euler's letters, by Lambert, who introduced a more indirect scheme 

 of diagrammatic notation. He indicates the extent of a class 

 term by a straight line ; the inclusion of one term in another being- 

 represented by drawing a shorter line under the other, the ex- 

 clusion of two by one another by drawing them side by side, whilst 

 the corresponding case to the intersecting circles is presented by 

 drawing one line partially under the other, as follows — — 

 Thus Celarent might be represented : 



B A No B is A, 



C All C is B, 



.-.No GisA. 



So far the scheme is of essentially the same kind as that of 

 Euler* the only important difference being that the common part 



* The analogy which Lambert actually had in view seems however to have 

 been different. He evidently was influenced, like Alsted, by the technical expres- 

 sion, "thinking objects as under such and such a concept," which to modern cats 

 would sound as little more than a play on words. Thus be draws a line to repre- 

 sent the general concept and puts a row of dots underneath to represent the 

 individuals which stand under that concept. And again, " Ferner fordert der 

 Ansdruck, dass alle A untcr H gehoren, von Wort zu Wort gcnoiiunen, class man 

 die Linie A unter B setzen miisse." (Dian. § 181.) 



