tauto

Tauto, often used as shorthand for tautology, is a term encountered in logic and mathematics to denote a statement whose truth is guaranteed by its form rather than by any particular content. The element taútos derives from Greek, meaning “the same” or “identical,” and the term is used in English to refer to statements that are true in every possible interpretation.

In propositional logic, a tautology is a formula that evaluates to true under every possible assignment of truth values to its atomic propositions. Such formulas are true by virtue of their logical form alone and are sometimes called logically valid. Examples include P ∨ ¬P, the law of the excluded middle, and P → P. A truth table for a tautology contains only true entries for the formula, regardless of the truth values of the components.

In rhetoric, tautology describes a pleonastic or redundant expression—expressions that repeat the same idea—such as “free gift” or “true facts.” This sense is distinct from the logical notion, though both originate from the same root.

Ta fferences and related concepts: A tautology is the opposite of a contradiction, which is always false, and it is distinct from contingent statements, which can be true or false depending on circumstances. In formal contexts, tautologies are central to discussions of logical validity and proof, serving as the foundational truth on which valid arguments can be built.