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,
But either W is not X or Y is not Z,
Hence A is not B.
This is simple because there is but one antecedent, A is B, and destructive because the conclusion is negative.
Complex Constructive Dilemma.
If A is B, W is X; and if C is D, Y is Z,
But either A is B or C is D,
Hence either W is X or Y is Z.
This is complex because there are two antecedents andtwo consequents; constructive, inasmuch as the conclusion is affirmative.
Complex Destructive Dilemma.
If A is B, W is X; and if C is D, Y is Z,
But either W is not X or Y is not Z,
Hence either A is not B or C is not D.
This is complex because there are two antecedents as well as two consequents, and destructive because the conclusion is negative. Briefly: (1) A simple dilemma is one where either the antecedent or consequent is repeated; whereas if neither is repeated the dilemma is complex. (2) A constructive dilemma contains an affirmative conclusion; while a destructive dilemma uses a negative conclusion. (3) A simple dilemma has as its conclusion a categorical proposition; whereas the conclusion of a complex dilemma is always disjunctive.
If the number of antecedents and consequents be increased, a trilemma, tetralemma, etc., may result.
ILLUSTRATION—Trilemma.
If A is B, W is X; and if C is D, Y is Z; and if E is F, U is V,
But either A is B, or C is D, or E is F,
Hence either W is X, or Y is Z, or U is V.
Some authorities define a dilemma as a syllogism in which the “major-hypothetical” has more than one antecedent while the “minor” must be disjunctive. This viewpoint necessarily excludes the second form or the simple destructive dilemma. The weight of authority, however, appears to favor the classification here recommended.