Introduction to Philosophy/Logic/Tautologies and Contradictions
Introduction to Philosophy > Logic > Tautologies and Contradictions
Tautologies
editA 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
editSimilarly, 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