Tautology (logic)

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A tautology can also be a figure of speech

In propositional logic, a tautology (from the Greek word ταυτολογία) is a propositional formula that is always true. 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 correct if it is neither a tautology nor false.

Examples of a tautology:

  • "I know that this is wikipedia because I know that this is wikipedia."
  • "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."

In other words, a tautology is:

  • A is true because A is true

And if A is not true, then A is not true, so the tautology is still true.