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False ❍｜Definition｜1st｜20251119205401-00-⌔
False (logic)
In logic, false (Its noun form is falsity) or untrue is the state of possessing negative truth value and is a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth.1 Usual notations of the false are 0 (especially in Boolean logic and computer science), O (in prefix notation, O pq), and the up tack symbol .23
Another approach is used for several formal theories (e.g., intuitionistic propositional calculus), where a propositional constant (i.e. a nullary connective), , is introduced, the truth value of which being always false in the sense above.456 It can be treated as an absurd proposition, and is often called absurdity.
Printed 2026-06-28.
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Link to original Footnotes
Jennifer Fisher, On the Philosophy of Logic, Thomson Wadsworth, 2007, ISBN 0-495-00888-5, p. 17. ↩
Willard Van Orman Quine, Methods of Logic, 4th ed, Harvard University Press, 1982, ISBN 0-674-57176-2, p. 34. ↩
“Truth-value | logic”. Encyclopedia Britannica. Retrieved 2020-08-15. ↩
George Edward Hughes and D.E. Londey, The Elements of Formal Logic, Methuen, 1965, p. 151. ↩
Leon Horsten and Richard Pettigrew, Continuum Companion to Philosophical Logic, Continuum International Publishing Group, 2011, ISBN 1-4411-5423-X, p. 199. ↩
Graham Priest, An Introduction to Non-Classical Logic: From If to Is, 2nd ed, Cambridge University Press, 2008, ISBN 0-521-85433-4, p. 105. ↩
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