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 &or; &not;p).

 p  &not;p    (p &or; &not;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 &and; &not;p).

 p  &not;p    (p &and; &not;p) T    F       F F     T       F 