(3) that if only the antecedent be more than one, the conclusion will be a simple proposition; but if both antecedent and consequent be more than one, the conclusion will itself be disjunctive.
§ 781. The dilemma, it will be seen, differs from the partly conjunctive syllogism chiefly in the fact of having a disjunctive affirmation of the antecedent or denial of the consequent in the minor, instead of a simple one. It is this which constitutes the essence of the dilemma, and which determines its possible varieties. For if only the antecedent or only the consequent be more than one, we must, in order to obtain a disjunctive minor, affirm the antecedent or deny the consequent respectively; whereas, if there be more than one of both, it is open to us to take either course. This gives us four types of dilemma.
§ 782.
(1). Simple Constructive.
If A is B or C is D, E is F.
Either A is B or C is D.
.'. E is F.
(2). Simple Destructive.
If A is B, C is D and E is F.
Either C is not D or E is not F.
.'. A is not B.
(3). Complex Constructive.
If A is B, C is D; and if E is F, G is H.
Either A is B or E is F.
.'. Either C is D or G is H.
(4). Complex Destructive.