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, Opq), and the up tack symbol $\bot$ .^[2]^[3]

Another approach is used for several formal theories (e.g., intuitionistic propositional calculus), where a propositional constant (i.e. a nullary connective), $\bot$ , is introduced, the truth value of which being always false in the sense above.^[4]^[5]^[6] It can be treated as an absurd proposition, and is often called absurdity.

^ 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.

[1] Jennifer Fisher, On the Philosophy of Logic, Thomson Wadsworth, 2007, ISBN 0-495-00888-5, p. 17.

[2] Willard Van Orman Quine, Methods of Logic, 4th ed, Harvard University Press, 1982, ISBN 0-674-57176-2, p. 34.

[3] "Truth-value | logic". Encyclopedia Britannica. Retrieved 2020-08-15.

[4] George Edward Hughes and D.E. Londey, The Elements of Formal Logic, Methuen, 1965, p. 151.

[5] Leon Horsten and Richard Pettigrew, Continuum Companion to Philosophical Logic, Continuum International Publishing Group, 2011, ISBN 1-4411-5423-X, p. 199.

[6] 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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