Constructive dilemma
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A logical constructive dilemma is a formal logical argument that takes the form:
- 1a) P → Q.
- b) R → S.
- 2) Either P or R is true.
Therefore, either Q or S is true.
In logical operator notation
where 
represents the logical assertion.
In sum, this argument states that if one premise implies another, and another implies a third, and either the first premise or the second premise is true, then one of the conclusions is true, or the other is true. An example:
- If Ronald Reagan wins the election, he will be President.
- If Jimmy Carter wins the election, he will be President.
- Either Ronald Reagan wins the election or Jimmy Carter wins the election.
- Therefore, either Jimmy Carter will be President or Ronald Reagan will be President.
The Dilemma derives its name because of the transfer of disjunctive operants. Because one cannot have P&R, one cannot have both Q&S. In this example, the situation in which Ronald Reagan and Jimmy Carter are both presidents produces a logical contradiction.
