THE DIAGRAMMATIC REPRESENTATION OF SYLLOGISMS.
288. The application of the Eulerian diagrams to syllogistic reasonings.—In shewing the application of the Eulerian diagrams to syllogistic reasonings we may begin with a syllogism in Barbara:
| All M is P, | |
| All S is M, | |
| therefore, | All S is P. |
The premisses must first be represented separately by means of the diagrams. Each yields two cases; thus,—
To obtain the conclusion, each of the cases yielded by the major premiss must now be combined with each of those yielded by the minor. This gives four combinations,[373] and whatever is true of S in terms of P in all of them is the conclusion required.
[373] These combinations afford a complete solution of the problem as to what class-relations between S, M, and P are compatible with the premisses; and similarly in other cases. The syllogistic conclusion is obtained by the elimination of M.
In each case S either coincides with P or is included within P ; hence all S is P may be inferred from the given premisses.