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Truth Be Told

Sense, Quantity, and Extension


John Justice

Truth Be Told explains how truth and falsity result from relations that sentences have to the contexts in which they occur and the circumstances at which they are evaluated. It offers a precise conception of truth and a clear diagnosis of the Liar and Grelling paradoxes. Currently, semantic theory employs generalized quantifiers as the extensions of noun phrases in explanations of the composition of truth-values. Generalized quantifiers are direct descendants of the second-level functions to truth-values that Gottlob Frege considered to be the referents of his unrestricted quantifiers. During the past fifty years, Frege’s original quantifier referents have been revised and generalized with the result that now every noun phrase, of any type, has a generalized quantifier as its extension. This evolution of noun-phrase extensions from Frege’s referents has retained two of the original theory’s flaws. First, generalized quantifiers inherit a troublesome intrusion of predicate extensions. Second, the senses of names and deictic terms are still not identified, with the result that their extensions are not sharply distinguished from their referents. Truth Be Told frees semantic theory from these Fregean flaws. Its theory of sense, quantity, and extension yields an intuitive composition of sentence truth-values and secures an accurate understanding of truth. Its final chapter applies the theory in a diagnosis of the Liar and Grelling paradoxes that is immune to the notorious revenge paradoxes.
Truth Be Told can be used for courses in philosophy of language, semantics, and the foundations of logic.
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This book explains how sentences get to be true or false, which is to say that it propounds a theory of semantics. The truth or falsity of a declarative sentence depends on the sentence, the circumstance with respect to which the sentence is evaluated, and sometimes the context in which the sentence occurs. Since speakers of natural languages are able to express and understand an unlimited number of sentences, it must be possible to figure out what a sentence means and whether it is true by, first, understanding how its constituent phrases are constructed from finite resources to have particular meanings and relations to a circumstance and, next, understanding how these constituent phrases combine to produce a sentence with its particular meaning and relation to the circumstance. The meaning and the truth-value of a sentence result from rule-governed combinations of its constituents’ meanings and relations to the circumstance at which the sentence is evaluated. There seems to be no other way to explain the limitless productivity of language’s finite and learnable resources.

Gottlob Frege established the point of departure for the subsequent efforts of philosophers and linguists to construct an accurate and complete account of how sentences’ meanings and truth-values derive from the meanings and truth-value contributions of their constituents. Today, semantic theorists ← 1 | 2 → generally call both the truth-values of sentences and the contributions to the determination of truth-values made by sentences’ constituents extensions. This is not how Frege spoke of them. He thought of...

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