TRILEMMA.
If A is B, C is D; and if E is F, G is H; and if K is L, M is N.
Either A is B or E is F or K is L.
.'. Either C is D or G is H or K is L.
§ 788. Having seen what the true dilemma is, we shall now examine some forms of reasoning which resemble dilemmas without being so.
§ 789. This, for instance, is not a dilemma—
If A is B or if E is F, C is D.
But A is B and E is F.
.'. C is D.
If he observes the sabbath or if he refuses to eat pork, he is a
Jew.
But he both observes the sabbath and refuses to eat pork.
.'. He is a Jew.
What we have here is a combination of two partly conjunctive syllogisms with the same conclusion, which would have been established by either of them singly. The proof is redundant.
§ 790. Neither is the following a dilemma—
If A is B, C is D and E is F.
Neither C is D nor E is F.
.'. A is not B.
If this triangle is equilateral, its sides and its angles will be
equal.
But neither its sides nor its angles are equal.
.'. It is not equilateral.