Logic Tautology: Logical formula which is true in every possible interpretation
In propositional logic, a tautology (from the Greek word ταυτολογία) is a propositional formula that is always true, and is sometimes denoted by the symbol ⊤ (a symbol also reserved for the truth value 'true').
- A tautology can also be a figure of speech
In other words, a tautology cannot be wrong. For example, formulae in maths are tautological, because they always hold true for any values. The philosopher Ludwig Wittgenstein first applied the term to propositional logic in 1921.
A statement in logic is considered contingent if it is neither a tautology nor false.
Some examples of tautologies in natural language include:
- "I know that this is Wikipedia because I know that this is Wiki Simple English."
- "I am president of this club because I am the president of this club."
- "The first rule of the tautology club is the first rule of the tautology club."
These tautologies are sentences of the following form:
- A is true because A is true
Indeed, if A is not true, then A is not true, so the tautology is still true.
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