Editing False (logic) (section)

{{Short description|Possessing negative truth value}}
{{see also|False statement}}
In [[logic]], '''false''' (Its noun form is [[Truth|falsity]]) or '''untrue''' is the state of possessing negative [[truth value]] and is a [[nullary]] [[logical connective]]. In a [[truth function|truth-functional]] system of propositional logic, it is one of two postulated truth values, along with its [[negation]], [[logical truth|truth]].<ref>Jennifer Fisher, ''On the Philosophy of Logic'', Thomson Wadsworth, 2007, {{ISBN|0-495-00888-5}}, [https://books.google.com/books?id=k8L_YW-lEEQC&pg=PT27 p. 17.]</ref>  Usual notations of the false are [[0 (number)|0]] (especially in [[Boolean Logic|Boolean logic]] and [[computer science]]), O (in [[Polish notation|prefix notation]], O''pq''), and the [[up tack]] symbol&nbsp;<math>\bot</math>.<ref>[[Willard Van Orman Quine]], ''Methods of Logic'', 4th ed, Harvard University Press, 1982, {{ISBN|0-674-57176-2}}, [https://books.google.com/books?id=liHivlUYWcUC&pg=PA34 p. 34.]</ref><ref>{{Cite web|title=Truth-value {{!}} logic|url=https://www.britannica.com/topic/truth-value|access-date=2020-08-15|website=Encyclopedia Britannica|language=en}}</ref>

Another approach is used for several [[theory (mathematical logic)|formal theories]] (e.g., [[intuitionistic propositional calculus]]), where a propositional constant (i.e. a nullary connective),&nbsp;<math>\bot</math>, is introduced, the truth value of which being always false in the sense above.<ref>[[George Edward Hughes]] and D.E. Londey, ''The Elements of Formal Logic'', Methuen, 1965, [https://books.google.com/books?id=JbwOAAAAQAAJ&pg=PA151 p. 151.]</ref><ref>Leon Horsten and Richard Pettigrew, ''Continuum Companion to Philosophical Logic'', Continuum International Publishing Group, 2011, {{ISBN|1-4411-5423-X}}, [https://books.google.com/books?id=w_abLTXIFkcC&pg=PA199 p. 199.]</ref><ref>[[Graham Priest]], ''[[An Introduction to Non-Classical Logic|An Introduction to Non-Classical Logic: From If to Is]]'', 2nd ed, Cambridge University Press, 2008, {{ISBN|0-521-85433-4}}, [https://books.google.com/books?id=rMXVbmAw3YwC&pg=PA105 p. 105.]</ref> It can be treated as an absurd proposition, and is often called absurdity.