[171] It is important to give both these schemes as it will be found that neither one of them will by itself suffice when this method is used for illustrating the syllogism. For obvious reasons the E diagram is the same in both schemes.
It must be understood that the two diagrams given above in the cases of A, I, and O are alternative in the sense that we may select which we please to represent our proposition; but either represents it completely.
We shall find later on that for the purpose of illustrating the syllogistic moods, Lambert’s method is a good deal less cumbrous than Euler’s.[172] An adaptation of Lambert’s diagrams in which the contradictories of S and P are introduced as well 166 as S and P themselves will be given in section [131]. This more elaborated scheme will be found useful for illustrating the various processes of immediate inference.
[172] Dr Venn (Symbolic Logic, p. 432) remarks, “As a whole Lambert’s scheme seems to me distinctly inferior to the scheme of Euler, and has in consequence been very little employed by other logicians.” The criticism offered in support of this statement is directed chiefly against Lambert’s own representation of the particular affirmative proposition, namely,
This diagram certainly seems as appropriate to O as it does to I; but the modification introduced in the text, and indeed suggested by Dr Venn himself, is not open to a similar objection.
128. Dr Venn’s Diagrams.—In the diagrammatic scheme employed by Dr Venn (Symbolic Logic, chapter 5) the diagram
does not itself represent any proposition, but the framework into which propositions may be fitted. Denoting not-S by Sʹ and what is both S and P by SP, &c., it is clear that everything must be contained in one or other of the four classes SP, SPʹ, SʹP, SʹPʹ ; and the above diagram shews four compartments (one being that which lies outside both the circles) corresponding to these four classes. Every universal proposition denies the existence of one or more of such classes, and it may therefore be diagrammatically represented by shading out the corresponding compartment or compartments. Thus, All S is P, which denies the existence of SPʹ, is represented by