In logic, a tautology is a formula

Well-formed formula

In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word which is part of a formal language...

 which is true in every possible interpretation

Interpretation (logic)

An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...

. Philosopher Ludwig Wittgenstein

Ludwig Wittgenstein

Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...

 first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies

Tautology (rhetoric)

Tautology is an unnecessary or unessential repetition of meaning, using different and dissimilar words that effectively say the same thing...

, and continues to be used in that alternate sense today.

A formula is satisfiable

Satisfiability and validity

In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation that makes the formula true. A formula is valid if all interpretations make the formula true...

 if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable.