But if A is B, C is D; But if E is F, G is H;
(A is B): (E is F):
.'. C is D. .'. G is H.

.'. Either C is D or G is H.

A Dilemma, then, is a compound Conditional Syllogism, having for its
Major Premise two Hypothetical Propositions, and for its Minor Premise a
Disjunctive Proposition, whose alternative terms either affirm the
Antecedents or deny the Consequents of the two Hypothetical Propositions
forming the Major Premise.

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.

2. The Complex Constructive--

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--

If A is B, C is D; and if A is B, E is F:
But either C is not D, or E is not F:
.'. A is not B.

If table-rappers are to be trusted, the departed are spirits;
and they also exert mechanical energy:

But either the departed are not spirits, or they do not
exert mechanical energy:

.'. Table-rappers are not to be trusted.

4. Complex Destructive--

If A i