Introduction to Philosophy/Logic/Tautologies and Contradictions

Introduction to Philosophy > Logic > Tautologies and Contradictions Tautologies A truth table column which consists entirely of T's indicates a situation where the proposition is true no matter whether the individual propositions of which it is composed are true or false. The most simple example would be (p ∨ ¬p). p   ¬p   (p ∨ ¬p) T   F       T F   T       T A proposition which is true independently of the truth or falsity of the atomic propositions from which it is composed is known as a tautology. Contradictions Similarly, a proposition which is false independently of the truth or falsity of the atomic propositions from which it is composed is known as a contradiction. The simplest example of this would be (p ∧ ¬p). p   ¬p   (p ∧ ¬p) T   F       F F   T       F