320. Reduce the following argument, consisting of three disjunctive propositions, to the form of an ordinary categorical syllogism: Everything is either M or P, Everything is either not S or not M, therefore, Everything is either P or not S. [K.]
321. Discuss the logical conclusiveness of fatalistic reasoning like this:—If I am fated to be drowned now, there is no use in my struggling; if not, there is no need of it. But either I am fated to be drowned now or I am not; so that it is either useless or needless for me to struggle against it. [B.]
CHAPTER VII.
IRREGULAR AND COMPOUND SYLLOGISMS.
322. The Enthymeme.—By the enthymeme, Aristotle meant what has been called the “rhetorical syllogism” as opposed to the apodeictic, demonstrative, theoretical syllogism. The following is from Mansel’s notes to Aldrich (pp. 209 to 211): “The enthymeme is defined by Aristotle, συλλογισμὸς ἐξ εἰκότων ἤ σημείων. The εἰκὸς and σημεῖων themselves are propositions; the former stating a general probability, the latter a fact, which is known to be an indication, more or less certain, of the truth of some further statement, whether of a single fact or of a general belief. The former is a proposition nearly, though not quite, universal ; as ‘Most men who envy hate’: the latter is a singular proposition, which however is not regarded as a sign, except relatively to some other proposition, which it is supposed may be inferred from it. The εἰκός, when employed in an enthymeme, will form the major premiss of a syllogism such as the following:
| Most men who envy hate, | |
| This man envies, | |
| therefore, | This man (probably) hates. |
“The reasoning is logically faulty; for, the major premiss not being absolutely universal, the middle term is not distributed.
“The σημεῖων will form one premiss of a syllogism which may be in any of the three figures, as in the following examples: