It being a combination of hypothetical and disjunctive propositions the dilemma is sometimes appropriately referred to as the “hypothetico-disjunctive” argument. Theorder of the premises is indifferent, yet it seems to be more natural to use the hypothetical first; thus the definition.
14. FOUR FORMS.
The four forms of the dilemma are the simple constructive, the simple destructive, the complex constructive, and the complex destructive. The following symbolizations illustrate these four kinds:
Simple Constructive Dilemma.
If A is B, W is X; and if C is D, W is X,
But either A is B or C is D,
Hence W is X.
This is termed a simple dilemma because there is but one consequent; namely, W is X. The conclusion being affirmative makes it constructive.
Simple Destructive Dilemma.
If A is B, W is X; and if A is B, Y is Z,