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  1. The senses of functions in the logic of sense and denotation.Kevin C. Klement - 2010 - Bulletin of Symbolic Logic 16 (2):153-188.
    This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...)
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  • The Consistency of predicative fragments of frege’s grundgesetze der arithmetik.Richard G. Heck - 1996 - History and Philosophy of Logic 17 (1-2):209-220.
    As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...
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  • Introduction to Montague Semantics.David R. Dowty, Robert Eugene Wall & Stanley Peters - 1981 - Springer.
    INTRODUCTION Linguists who work within the tradition of transformational generative grammar tend to regard semantics as an intractable, perhaps ultimately ...
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  • Frege: Philosophy of Language.Michael Dummett - 1973 - London: Duckworth.
    This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...
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  • Logic, Logic, and Logic.George Boolos - 1998 - Cambridge, Mass: Harvard University Press. Edited by Richard C. Jeffrey.
    This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; ...
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  • Semantics in generative grammar.Irene Heim & Angelika Kratzer - 1998 - Malden, MA: Blackwell. Edited by Angelika Kratzer.
    Written by two of the leading figures in the field, this is a lucid and systematic introduction to semantics as applied to transformational grammars of the ...
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  • The seas of language.Michael Dummett - 1993 - New York: Oxford University Press.
    Michael Dummett is a leading contemporary philosopher whose work on the logic and metaphysics of language has had a lasting influence on how these subjects are conceived and discussed. This volume contains some of the most provocative and widely discussed essays published in the last fifteen years, together with a number of unpublished or inaccessible writings. Essays included are: "What is a Theory of Meaning?," "What do I Know When I Know a Language?," "What Does the Appeal to Use Do (...)
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  • Frege.Michael Dummett - 1981 - Cambridge: Harvard University Press.
    In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...
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  • The Foundations of Frege’s Logic.Pavel Tichý - 1988 - New York: de Gruyter.
    Chapter One: Constructions. Entities, constructions, and functions When one travels from Los Angeles to New York, going, say, by way of St. Louis, Chicago, ...
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  • Mathematics in philosophy: selected essays.Charles Parsons - 1983 - Ithaca, N.Y.: Cornell University Press.
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
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  • Quality and concept.George Bealer - 1982 - New York: Oxford University Press.
    This study provides a unified theory of properties, relations, and propositions (PRPs). Two conceptions of PRPs have emerged in the history of philosophy. The author explores both of these traditional conceptions and shows how they can be captured by a single theory.
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  • Russell-Myhill paradox.Kevin C. Klement - 2003 - Internet Encyclopedia of Philosophy.
    The Russell-Myhill Antinomy, also known as the Principles of Mathematics Appendix B Paradox, is a contradiction that arises in the logical treatment of classes and "propositions", where "propositions" are understood as mind-independent and language-independent logical objects. If propositions are treated as objectively existing objects, then they can be members of classes. But propositions can also be about classes, including classes of propositions. Indeed, for each class of propositions, there is a proposition stating that all propositions in that class are true. (...)
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  • The number of senses.Kevin C. Klement - 2003 - Erkenntnis 58 (3):303 - 323.
    Many philosophers still countenance senses or meanings in the broadly Fregean vein. However, it is difficult to posit the existence of senses without positing quite a lot of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are also (...)
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  • (2 other versions)Notes on existence and necessity.Willard V. Quine - 1943 - Journal of Philosophy 40 (5):113-127.
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  • How to Russell a Frege-Church.David Kaplan - 1975 - Journal of Philosophy 72 (19):716-729.
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  • On the consistency of the Δ11-CA fragment of Frege's grundgesetze.Fernando Ferreira & Kai F. Wehmeier - 2002 - Journal of Philosophical Logic 31 (4):301-311.
    It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension (...)
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  • Systems of predicative analysis.Solomon Feferman - 1964 - Journal of Symbolic Logic 29 (1):1-30.
    This paper is divided into two parts. Part I provides a resumé of the evolution of the notion of predicativity. Part II describes our own work on the subject.Part I§1. Conceptions of sets.Statements about sets lie at the heart of most modern attempts to systematize all (or, at least, all known) mathematics. Technical and philosophical discussions concerning such systematizations and the underlying conceptions have thus occupied a considerable portion of the literature on the foundations of mathematics.
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  • (1 other version)The iterative conception of set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
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  • Some difficulties concerning Russellian intensional logic.C. Anthony Anderson - 1986 - Noûs 20 (1):35-43.
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  • Propositions and Attitude Ascriptions: A Fregean Account.David J. Chalmers - 2011 - Noûs 45 (4):595-639.
    When I say ‘Hesperus is Phosphorus’, I seem to express a proposition. And when I say ‘Joan believes that Hesperus is Phosphorus’, I seem to ascribe to Joan an attitude to the same proposition. But what are propositions? And what is involved in ascribing propositional attitudes?
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  • Admissible sets and structures: an approach to definability theory.Jon Barwise - 1975 - New York: Springer Verlag.
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  • Grundgesetze der arithmetik.Gottlob Frege - 1893 - Jena,: H. Pohle.
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  • (3 other versions)Principles of mathematics.Bertrand Russell - 1931 - New York,: W.W. Norton & Company.
    Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...)
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  • Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.
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  • (1 other version)Logic, Logic and Logic.George Boolos & Richard C. Jeffrey - 1998 - Studia Logica 66 (3):428-432.
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  • (2 other versions)Truth and Other Enigmas.Michael Dummett - 1978 - British Journal for the Philosophy of Science 32 (4):419-425.
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  • The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
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  • Basic Laws of Arithmetic.Philip A. Ebert & Marcus Rossberg (eds.) - 1964 - Berkeley,: Oxford University Press UK.
    This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework.
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  • Frege and the Logic of Sense and Reference.Kevin C. Klement - 2001 - New York: Routledge.
    This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and others (...)
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  • Russell's Theory of Identity of Propositions.Alonzo Church - 1984 - Philosophia Naturalis 21 (2/4):513-522.
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  • (1 other version)Basic Laws of Arithmetic.Gottlob Frege - 1893 - Oxford, U.K.: Oxford University Press. Edited by Philip A. Ebert, Marcus Rossberg & Crispin Wright.
    The first complete English translation of a groundbreaking work. An ambitious account of the relation of mathematics to logic. Includes a foreword by Crispin Wright, translators' Introduction, and an appendix on Frege's logic by Roy T. Cook. The German philosopher and mathematician Gottlob Frege (1848-1925) was the father of analytic philosophy and to all intents and purposes the inventor of modern logic. Basic Laws of Arithmetic, originally published in German in two volumes (1893, 1903), is Freges magnum opus. It was (...)
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  • (1 other version)The Philosophical Significance of Gödel's Theorem.Michael Dummett - 1963 - In Michael Dummett & Philip Tartaglia (eds.), Ratio. Duckworth. pp. 186--214.
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  • On the consistency of the first-order portion of Frege's logical system.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.
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  • Carnap and logical truth.Willard van Orman Quine - 1954 - Synthese 12 (4):350--74.
    Kant's question 'How are synthetic judgments a priori possible?' pre- cipitated the Critique of Pure Reason. Question and answer notwith- standing, Mill and others persisted in doubting that such judgments were possible at all. At length some of Kant's own clearest purported.
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  • A revised formulation of the logic of sense and denotation. Alternative (1).Alonzo Church - 1993 - Noûs 27 (2):141-157.
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  • Alonzo Church’s Contributions to Philosophy and Intensional Logic.C. Anthony Anderson - 1998 - Bulletin of Symbolic Logic 4 (2):129-171.
    §0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical (...)
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  • (2 other versions)The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
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  • (1 other version)Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
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  • (2 other versions)Michael Dummett, Frege: Philosophy of Language. [REVIEW]Hidé Ishiguro - 1974 - Philosophy 49 (190):438-442.
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  • (2 other versions)Notes on Existence and Necessity.Willard V. Quine - 1943 - Journal of Symbolic Logic 8 (1):45-47.
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  • Quality and Concept by George Bealer. [REVIEW]Ernest Sosa - 1985 - Journal of Philosophy 82 (7):382-387.
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  • (1 other version)Frege: Philosophy of Mathematics. [REVIEW]William Demopoulos - 1993 - Canadian Journal of Philosophy 23 (3):477-497.
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  • Frege, hilbert, and the conceptual structure of model theory.William Demopoulos - 1994 - History and Philosophy of Logic 15 (2):211-225.
    This paper attempts to confine the preconceptions that prevented Frege from appreciating Hilbert?s Grundlagen der Geometrie to two: (i) Frege?s reliance on what, following Wilfrid Hodges, I call a Frege?Peano language, and (ii) Frege?s view that the sense of an expression wholly determines its reference.I argue that these two preconceptions prevented Frege from achieving the conceptual structure of model theory, whereas Hilbert, at least in his practice, was quite close to the model?theoretic point of view.Moreover, the issues that divided Frege (...)
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  • On some difficulties in the theory of transfinite numbers and order types.Bertrand Russell - 1905 - Proceedings of the London Mathematical Society 4 (14):29-53.
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  • On Mental Entities.Willard V. Quine - 1976 - In Willard Van Orman Quine (ed.), The ways of paradox, and other essays. Cambridge: Harvard University Press.
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  • Higher recursion theory.Gerald E. Sacks - 1990 - New York, NY, USA: Cambridge University Press.
    This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
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  • (1 other version)Reviews. Willard V. Quine. Notes on existence and necessity. The journal of philosophy, vol. 40 , pp. 113–127.Alonzo Church - 1943 - Journal of Symbolic Logic 8 (2):45-47.
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  • (1 other version)Mathematics in Philosophy by Charles Parsons. [REVIEW]W. V. Quine - 1984 - Journal of Philosophy 81 (12):783-794.
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  • Problems arising in the formalization of intensional logic.John Myhill - 1958 - Logique Et Analyse 1 (1):78-83.
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  • All Things Indefinitely Extensible.Stewart Shapiro & Crispin Wright - 2006 - In Stewart Shapiro & Crispin Wright (eds.), All Things Indefinitely Extensible. pp. 255--304.
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