238. Reduce the following arguments to ordinary syllogistic form:
(i) No M is S, Whatever is not M is P, therefore, All S is P ;
(ii) It cannot be that no not-S is P, for some M is P and no M is S ;
(iii) It is impossible for the three propositions, All M is P, Anything that is not M is not S, Some things that are not P are S, all to be true together;
(iv) Everything is M or P, Nothing is both S and M, therefore, All S is P. [K.]
239. Shew that the following syllogisms break directly or indirectly all the rules of the syllogism:
(1) All P is M, All S is M, therefore, Some S is not P ;
(2) All M is P, All M is S, therefore, No S is P. [K.]
[The so-called rules that every syllogism contains three and only three terms, and that every syllogism consists of three and only three propositions, are not here included under the rules of the syllogism.]
240. In a circular argument involving two valid syllogisms, Q and U are used as premisses to prove R, while R and V are used as premisses to prove Q ; shew that U and V must be a pair of complementary propositions, i.e., of the forms All M is N and All N is M respectively. [J.]
241. Shew that if two valid syllogisms have a common premiss while the other premisses are contradictories, both the conclusions must be particular. [K.]
242. Given the premisses of a valid syllogism, examine in what cases it is (a) possible, (b) impossible, to determine which is the minor term and which the major term. [J.]
CHAPTER II.
THE FIGURES AND MOODS OF THE SYLLOGISM.
243. Figure and Mood.—By the figure of a syllogism is meant the position of the terms in the premisses. Denoting the major, middle, and minor terms by the letters P, M, S respectively, and stating the major premiss first, we have four figures of the syllogism as shewn in the following table:—