A valid form of logical inference in propositional logic, which infers from two conditional and a negativedisjunct statement a new negative disjunct statement.
Formally, the destructive 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: ⌐B ∨ ⌐D – not Bor not D [or neither] Conclusion: ⌐A ∨ ⌐C – not Aor not C [or neither]
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 go to the museum.
Tomorrow we will either not got to the museum or not go to the beach [or neither]. Therefore it will either not rain or the sun will not shine [or neither].
Description
The destructive dilemma can be seen as a combination of two Modus Tollens, which are connected by a disjunct 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:
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