297. Shew diagrammatically that no conclusion can be obtained from IA in figure 1, from AA in figure 2, from AE in figure 3, from AO in figure 4. [K.]
298. Determine, by the aid of Euler’s diagrammatic scheme, all the relations that are à priori possible between three classes S, M, P. [K.]
299. Test the following argument (i) by Dr Venn’s diagrammatic scheme, (ii) by ordinary syllogistic methods:
“All brave persons are well-disciplined; no patriots are mercenary; but some mercenary persons have been found to be brave, and not all patriots can be considered well-disciplined; it follows that some brave and well-disciplined persons have been both mercenary and unpatriotic, while others that have been patriotic and unmercenary were but ill-disciplined cowards.” [C.]
300. Given All X is Y or Z, All Y is Z or X, All Z is X or Y, All YZ is X, All ZX is Y, All XY is Z, prove (a) by the aid of Dr Venn’s diagrammatic scheme, (b) without the aid of diagrams, that X, Y, Z are coextensive. [RR.]
CHAPTER V.
CONDITIONAL AND HYPOTHETICAL SYLLOGISMS.
301. The Conditional Syllogism, the Hypothetical Syllogism, and the Hypothetico-Categorical Syllogism.—The forms of reasoning in which conditional or hypothetical conclusions are inferred from two conditional or two hypothetical premisses are apparently overlooked by some logicians; at any rate, they frequently receive no distinct recognition, the term “hypothetical syllogism” being limited to the case in which one premiss only is hypothetical.
The following definitions may be given:
(1) A conditional syllogism is a reasoning consisting of two conditional premisses and a conditional conclusion;[376]
| e.g., | If any A is C, it is D, |
| If any A is B, it is C, | |
| therefore, | If any A is B, it is D. |