tautology
Sign in to savelogical formula which is true in every possible interpretation
In the Vinony graph
Within Vinony's link graph, tautology is referenced by 557 other articles, and connects out to first-order logic, recursive set and semantic theory of truth.
It sits within the topics Classical logic, Logical expressions and Logical truth.
Its subject is documented across 39 Wikipedia language editions.
Wikidata facts
- Subclass of
- proposition
Show 5 more facts
- notation
- double turnstile
- opposite of
- logical contradiction
- different from
- tautology
- maintained by WikiProject
- WikiProject Mathematics
- discoverer or inventor
- Ludwig Wittgenstein
via Wikidata · CC0
~21 min read
Encyclopedic overview
In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. It is a logical truth. For example, a formula that states "the ball is green or the ball is not green" is always true, regardless of what a ball is and regardless of its colour. Tautology is usually, though not always, used to refer to valid formulas of propositional logic.
The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement. In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false.
Excerpted from Wikipedia’s “tautology” article, available under the CC BY-SA 4.0 licence.