A valid form of logical inference in propositional logic, which infers from two conditional and an disjunction a new disjunction as conclusion.
Formally, the constructive dilemma has three premises, it looks as follows:
Premise 1:A ⟶ B–if A, then B
Premise 2:C ⟶ D–if C, then D
Premise 3:A ∨ C–A or C [or both]
Conclusion:B ∨ D–B or D [or both]
A practical example could be the following:
If the sun shines tomorrow, [then] we will go to the beach.
If it rains tomorrow, [then] we will visit a museum.
Tomorrow the sun will shine, or it will rain [or both].
Therefore, tomorrow we will visit a museum, or go to the beach [or both].
The constructive dilemma can be seen as a combination of two Modus Ponens which are connected by a disjunction (“or”) statement.
The term “dilemma” in this context should be understood as a “decision” between two conditionals.
The relationships between the various statements in a constructive dilemma can best be explained by showing them as a diagram:
The form of the constructive dilemma is a variation of the Modus Ponens and thus is subject to the same fallacies, though they appear in slightly different ways.
A typical fallacious form would be the following:
Premise 1:A ⟶ B–if A, then B
Premise 2:C ⟶ D–if C, then D
Premise 3:B ∨ D–B or D [or both]
Conclusion:–A ∨ C
This is efectively a variation of the fallacy of affirming the consequent in that it reverses the direction of a disjunct statement. This could be visualized, in the diagram above by reversing the arrow in the middle to point up instead of down, indicating an (illicit) commutation of the third premise with the conclusion.