1880.] representation of logical propositions. 55 



the expenditure of further time and thought. As a whole, it 

 seems to me distinctly inferior to the scheme of Euler. 



Hamilton's own system of notation is pretty well known. It is 

 given in his Logic (end of Vol. n.) with a table, and is described 

 in his Discussions. Some account of it will also be found in 

 Dr Thomson's Laws of Thought. It has been described (by himself) 

 as "easy, simple, compendious, all-sufficient, consistent, manifest, 

 precise, complete ; " the corresponding antithetic adjectives being 

 freely expeuded in the description of the schemes of those who had 

 gone before him. To my thinking it does not deserve to rank 

 as a diagrammatic scheme at all, though he does class it with 

 the others as " geometric " : but is purely symbolical. What 

 was aimed at in the methods above described was something that 

 should explain itself at once, as in the circles of Euler, or need but 

 a hint of explanation, as in the lines of Lambert. But there 

 is clearly nothing in the two ends of a wedge to suggest subjects 

 and predicates, or in a colon and comma to suggest distribution 

 and non-distribution. 



So far we have considered merely the case of categorical pro- 

 positions ; it still remains to say a few words as to the attempts 

 made thus to represent other kinds of proposition. The Hypo- 

 thetical may be dismissed at once, probably no logician having 

 supposed that these could be exhibited in diagrams so as to come 

 out in any way distinct from categoricals. Of course when we 

 consider the hypothetical form as an optional rendering which 

 only differs verbally from the categorical, we may regard our 

 diagrams as representing either form indifferently. But this 

 course, which I regard as the sound one, belongs essentially to 

 the modern or class view of the import of propositions. Those 

 who adopt the judgment interpretation can hardly in consistency 

 come to any other conclusion than that hypothetical are distinct 

 from categoricals, and do not as such admit of diagrammatic 

 representation. 



The Disjunctive stands on a rather different footing, and some 

 attention has been directed to its representation from the very 

 first. Lambert, for instance, has represented what we must regard 

 as a particular case of disjunction, in the subordination of a plu- 

 rality of species to a genus, after this fashion : — 



This of course indicates the fact that the three classes A", Y, Z, 

 together make up the extent of A. 



