Destructive dilemma is the name of a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either Q is false or S is false, then either P or R must be false. In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents has to be false. Destructive dilemma is the disjunctive version of modus tollens. The disjunctive version of modus ponens is the constructive dilemma. The rule can be stated:
where the rule is that wherever instances of "", "", and "" appear on lines of a proof, "" can be placed on a subsequent line.
Read more about Destructive Dilemma: Formal Notation, Natural Language Example, Proof, Example Proof
Famous quotes containing the words destructive and/or dilemma:
“The result of civilization, at the Sandwich Islands and elsewhere, is found productive to the civilizers, destructive to the civilizees. It is said to be compensation—a very philosophical word; but it appears to be very much on the principle of the old game, “You lose, I win”: good philosophy for the winner.”
—Herman Melville (1819–1891)
“Books of natural history aim commonly to be hasty schedules, or inventories of God’s property, by some clerk. They do not in the least teach the divine view of nature, but the popular view, or rather the popular method of studying nature, and make haste to conduct the persevering pupil only into that dilemma where the professors always dwell.”
—Henry David Thoreau (1817–1862)