44 Mr Venn, On the various notations adopted for [Dec. C, 



symmetrical and unsymnietrical forms clearly in view. His nota- 

 tion here is that which he adopted in his Formal Logic ; he changed 

 it subsequently in his papers in the Gamb. Phil. Transactions. 



As regards Ploucquet's expression, this is mainly employed in 

 the more symbolical parts of his logical treatises (e.g. his Method us 

 Galculandi). He there uses only two signs; one, an arbitrary and 

 somewhat misleading sign for negation, (>); and one for affirma- 

 tion (juxtaposition of the letters). The predicate is always distri- 

 buted, the whole and part of it being indicated by large and small 

 letters respectively. Thus 'AM A is B' stands, Ab, viz. 'All A is 

 some B.' ' No A is G ' stands A > G, viz. ' No A is any 67 _ The 

 processes of reasoning are then resolved into substitution of iden- 

 tities and recognition of non-identities. It may be remarked that 

 had Ploucquet broken sufficiently with the past to make a free use 

 of negative, or infinite predicates, he might have adopted another 

 form for these negative propositions. It is true that he does occa- 

 sionally employ such predicates, but not sufficiently often to have 

 devoted a special symbol to them. Had he written, for instance, 

 P for 'all not-P,' and p for 'some not-P', his expression for 'No S 

 is P' might have been Sp, viz. 'All S is some not-P,' in better 

 accordance with the familiar symbolic view at the present time, 

 and as illustrated in group (II). 



19, 20. These two must be regarded as precisely equivalent, 

 with one exception to be presently noticed. They are both 

 founded upon the doctrine of the Quantification of the Predicate, 

 and are meant to call attention to that characteristic. They may 

 be translated as saying ' the whole of S is distinct from the whole 

 of P.' Mr Bentham's t means totality, just like Hamilton's (:), 

 and the parallel lines of the one bear the same signification as the 

 wedge of the other, viz. ' distinct from,' or as Hamilton sometimes 

 puts it, ' not congruent with.' The differential characteristic of 

 Hamilton's symbol lies in the distinction between the thick and 

 thin ends of the wedge, which is meant to mark whether the pro- 

 position is read in extension or in intension. This attempt to 

 compress both these interpretations into one form is now, I pre- 

 sume, generally regarded as a mistake. (See Hamilton's Logic, n. 

 p. 47*3; Bentham's Logic, p. 134.) 



We now turn to a group the interpretation of which is neces- 

 sarily one of intension, that is, in which the letters stand for 

 notions or attributes and not for classes. 



21. Leibnitz's formula is given in his Specimen demonstrandi 

 (Erdmann, p. 96). It is not definitely assigned as a symbolic 

 expression of the proposition; and like some other of the logical 

 speculations in his shorter works seems indeed to have been 



