Truth Be Told

Sense, Quantity, and Extension

by John Justice (Author)
©2015 Monographs VIII, 79 Pages


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.

Table Of Contents

  • Cover
  • Title
  • Copyright
  • About the author(s)/editor(s)
  • About the book
  • This eBook can be cited
  • Table of Contents
  • Acknowledgments
  • Introduction
  • Chapter 1. Reflexive Senses
  • Frege’s Theory of Sense and Referent
  • Kripke’s Criticism of Frege
  • Kripke’s Mistake
  • Individuating Names
  • Kripke’s Puzzles about Names
  • Incorporating Deictic Terms
  • Chapter 2. Sense and Quantity
  • Frege’s Semantic Theory
  • Improving on Frege
  • Montague’s Semantic Theory
  • Workarounds for an Inherited Flaw
  • Root of the Difficulties
  • Chapter 3. Fixing Extensions
  • Local Noun-Phrase Extensions
  • Lexical Noun Phrases
  • Deictic and Possessive Determiners
  • Composing Truth-Values
  • Composing Verb-Phrase Extensions
  • Existential Import and the Empty Set
  • Chapter 4. Formal Semantics
  • The Individuation of Expressions
  • The Formal Representation of Semantic Structure
  • Formal Semantics
  • Applications
  • Chapter 5. Liar Paradoxes: The Irreflexivity of Extension Reports
  • Reference and Extension
  • Reporting Truth-Values
  • Avoiding Liar’s Revenge
  • Contingent Liars
  • Predicate Self-Evaluation
  • A Referential Paradox
  • Upshot
  • Bibliography
  • Index
  • Series index

| vii →


This book had its origin in Richard Mendelsohn’s 1994 NEH Summer Seminar at CUNY’s Graduate Center, Reference: Language and Reality. Professor Mendelsohn’s encouragement led ultimately to the publication of “On Sense and Reflexivity” (2001), which is an early version of the first chapter of this book.

Mitchell Green of the University of Connecticut has repeatedly advised me and encouraged me to continue on this project. Without him, it would not have reached publication.

Jim Scow has for the past several years been my most valuable reader and critic. At every stage of the process he has corrected my errors and improved my reasoning. He deserves much of the credit for the book.

| 1 →


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 truth-values and the sub- sentential contributions toward truth-values as the referents (Bedeutungen) of sentences and their constituents. Frege’s leading idea was that the truth or falsity of a sentence consisting of a singular-term subject and a verb phrase was a value, which he dubbed truth-value, that resulted when a function, the referent of the predicate (verb phrase), was applied to an individual, the referent of the singular-term subject (1891a). Because he had found in “On Sinn and Bedeutung” that singular terms must have both senses and referents, and because it appeared that a simple sentence’s truth-value depended on its subject’s referent rather than on its sense, Frege concluded that a sentence’s truth-value should be considered the sentence’s referent (1892a). Having come to think of truth-values as the referents of sentences, Frege was soon thinking of concepts, the functions that yield truth-values when supplied with individuals as arguments, as the referents of “concept words” (predicates) (1892b). For Frege, the truth-values of these simple sentences were the sentences’ referents, which were derived by the application of functions designated by predicates to individuals designated by singular-term subjects. The determination of a sentence’s truth-value (its referent) depended entirely on the referents of its constituents.


VIII, 79
ISBN (Hardcover)
Publication date
2015 (July)
Liar paradox Grelling paradox Formal semantics gottlob frege
New York, Bern, Berlin, Bruxelles, Frankfurt am Main, Oxford, Wien, 2015. VIII, 79 pp.

Biographical notes

John Justice (Author)

John Justice is the recipient of a PhD in philosophy from the University of Texas at Austin. Currently, Dr. Justice is Emeritus Professor of Philosophy at Randolph College, receiving the honor of Mary Frances Williams Professor. His publications include «On Sense and Reflexivity» in the Journal of Philosophy, «Mill-Frege Compatibilism» in the Journal of Philosophical Research, «The Semantics of Rigid Designation» in Ratio, and «Unified Semantics of Singular Terms» in The Philosophical Quarterly.


Title: Truth Be Told
book preview page numper 1
book preview page numper 2
book preview page numper 3
book preview page numper 4
book preview page numper 5
book preview page numper 6
book preview page numper 7
book preview page numper 8
book preview page numper 9
book preview page numper 10
book preview page numper 11
book preview page numper 12
book preview page numper 13
book preview page numper 14
book preview page numper 15
book preview page numper 16
book preview page numper 17
book preview page numper 18
90 pages