Truth value

In logic, a truth value is a value indicating the extent to which a statement is true. In classical bivalent logic there are only two truth values, usually we denote true and false (and sometimes represented by pairs as (1,0) or (V,F), etc.). However polyvalent logic the set of truth values includes other possibilities, and even in modal logic the description of the truth value requires the most complex notion of possible worlds. In fuzzy logic the truth value is any real number in the closed interval [0,1].

The set of truth values of a given type of logic is the range of a logical interpretation over the set of all possible propositions

Introduction

The truth value of the proposition «it rains and it doesn't rain» is a contradiction and will always be false, regardless of the value that we consider V or F of “it rains” (p) and of “it doesn't rain” (¬p). The truth function "not" is defined by a truth table. Algebraically, the set {true, false}, or logical function, forms a simple (subdirectly irreducible) Boolean algebra. Other Boolean algebras can be used as sets of truth values in multi-valued logic, while intuitionistic logic generalizes Boolean algebras to Heyting algebras.

In mole theory, the subobject classifier of moles takes the place of the set of truth values.

This nomenclature is perhaps more in keeping with prevailing usages in mathematics than with those in philosophy.