The hypothetical propositions in the major premise, may have all four terms distinct (as in the above example); and then the conclusion is a disjunctive proposition, and the Dilemma is said to be Complex. Or the two hypothetical propositions may have a common antecedent or a common consequent; and then the conclusion is a categorical proposition, and the Dilemma is said to be Simple.
Again, the alternatives of the disjunctive minor premise may be affirmative or negative: if affirmative, the Dilemma is called Constructive; and if negative, Destructive.
Using, then, only affirmative hypothetical propositions in the major premise, there are four Moods:
1. The Simple Constructive—
If A is B, C is D; and if E is F, C is D:
But either A is B, or E is F:
∴ C is D.
If the Tories win the election, the Government will avoid innovation; and if the Whigs win, the House of Lords will prevent them innovating:
But either the Tories or the Whigs will win:
∴ There will be no innovation.
If A is B, C is D; and if E is F, G is H:
But either A is B, or E is F:
∴ Either C is D or G is H.
If appearance is all that exists, reality is a delusion; and if there is a substance beyond consciousness, knowledge of reality is impossible:
But either appearance is all, or there is a substance beyond consciousness:
∴ Either reality is a delusion, or a knowledge of it is impossible.
3. Simple Destructive—