Since it is a distinguishing characteristic of the dilemma that the minor should be alternative, it follows that the hypotheticals into which the major premiss of a constructive dilemma may be resolved must contain at least two distinct antecedents. They may, however, have a common consequent. The conclusion of the dilemma will then categorically affirm this consequent, and will correspond with it in form.[396] The dilemma itself is in this case called simple. If, on the other hand, the major premiss contains more than one consequent, the conclusion will necessarily be alternative, and the dilemma is called complex.
[396] It will usually be a simple categorical; but see the following [note].
364 Similarly, in a destructive dilemma the hypotheticals into which the major can be resolved must have more than one consequent, but they may or may not have a common antecedent; and the dilemma will be simple or complex accordingly.
We have then four forms of dilemma as follows:
(i) The simple constructive dilemma.
If A is B, E is F ; and if C is D, E is F ;
but Either A is B or C is D ;
therefore, E is F.
(ii) The complex constructive dilemma.
If A is B, E is F ; and if C is D, G is H ;
but Either A is B or C is D ;
therefore, Either E is F or G is H.[397]
(iii) The simple destructive dilemma.
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 ;
therefore, A is not B.
(iv) The complex destructive dilemma.