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