38 



Mr Venn, On the various notations adopted fur [Dec. 6, 



111. 



Implication 

 (non-convertible) 



IV. 



Common Form 

 (convertible) 



fll. 

 12. 

 13. 

 14. 



| 15. 

 L 



rie. 



17. 



18 



V. Notional 



VI. Nondescript, and 

 Arbitrary 



21. 



22. 



23. 



+ S-P 

 Si'P 

 S : P' 

 S'—< P 



1 s 



S.P 



S)(P 



S>P 



19. tS II tP 



20. S 



L-ScoP 

 S = P 



in n 



24. Sx= - P 



25. nS-P 



26. mS-P 



Darjes. 

 Grassmann. 

 Maccoll. 

 Peirce. 



Frege. 



De Morgan. 

 Wundt. 

 Ploucquet. 

 Bentham. 

 P Hamilton. 



Leibnitz. 

 Lambert. 



Lambert. 



Maimon. 



Ploucquet. 



Chase. 



As most of these forms are marked off from each other by 

 more or less distinct specific differences, it will be well to go a little 

 into detail in describing them. 



1. This would need but little explanation to any logical reader. 

 It simply indicates the destruction of the class SP, or the emptiness 

 of the corresponding compartment. I prefer it myself as a primary 

 statement of such a proposition. 



2. The characteristic of Mr Macfarlane's notation here lies in 

 the attempt to mark the limits of the ' universe.' He considers 

 that the subject of the proposition marks the limits of the implied 

 universe. " Every general proposition refers to a definite universe ; 

 which is the subject of the judgment, and, it may be, of a series of 

 judgments. For example, ' all men are mortal ' refers to the 

 universe 'men.' 'No men are perfect' refers to the same uni- 

 verse" (Algebra of Logic, p. 29). Hence his symbolic form is read 

 off, " Within the universe of & there is no such thing as a P." 



3 — 6. These four forms are to all intents and purposes identical. 

 The only distinction between them is that (3) introduces an ar- 

 bitrary sign (v) to express the indeterminateness of the selection to 

 be made from not-P; that (4) employs a well-known mathematical 

 symbol to express the same idea; whilst (6) disguises this inde- 



