Truth Values
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T ruth V alues First published Tue Mar 30, 2010; substantive rev ision We d Jun 4, 2014 Truth values have been put to quite different uses in philosophy and logic, being characterized, for example, as: • primitive abstract objects denoted by sentences in natural and formal languages, • abstract entities hypostatized as the equivalence classes of sentences, • what is aimed at in judgements, • values indicating the degree of truth of sentences, • entities that can be used to explain the vagueness of concepts, • values that are preserved in valid inferences, • values that convey information concerning a given proposition. Depending on their particular use, truth values have been treated as unanalyzed, as defined, as unstructured, or as structured entities. The notion of a truth value has been explicitly introduced into logic and philosophy by ottlob !rege"for the first time in !rege #$%#, and most notably in his seminal paper &!rege #$%'(. !rege conceived this notion as a natural component of his language analysis where sentences, being saturated expressions, are interpreted as a special )ind of names, which refer to &denote, designate, signify( a special )ind of objects: truth values. *oreover, there are, according to !rege, only two such objects: the True &das +ahre( and the False &das !alsche(: sentence proper is a proper name, and its -edeutung, if it has one, is a truth value: the True or the !alse &-eaney #%%/, '%/(. This new and revolutionary idea has had a far reaching and manifold impact on the development of modern logic. 0t provides the means to uniformly complete the formal apparatus of a functional analysis of language by generalizing the concept of a function and introducing a special )ind of functions, namely propositional functions, or truth value functions, whose range of values consists of the set of truth values. mong the most typical representatives of propositional functions one finds predicate expressions and logical connectives. s a result, one obtains a powerful tool for a conclusive implementation of the extensionality principle &also called the principle of compositionality(, according to which the
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