Book contents
- Quine, New Foundations, and the Philosophy of Set Theory
- Quine, New Foundations, and the Philosophy of Set Theory
- Copyright page
- Dedication
- Contents
- Preface
- Introduction
- Part I Set Theory’s Beginnings
- Part II Quine, Set Theory, and Philosophy
- Part III New Foundations and the Philosophy of Set Theory
- Bibliography
- Index
- References
Bibliography
Published online by Cambridge University Press: 13 December 2018
Book contents
- Quine, New Foundations, and the Philosophy of Set Theory
- Quine, New Foundations, and the Philosophy of Set Theory
- Copyright page
- Dedication
- Contents
- Preface
- Introduction
- Part I Set Theory’s Beginnings
- Part II Quine, Set Theory, and Philosophy
- Part III New Foundations and the Philosophy of Set Theory
- Bibliography
- Index
- References
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- Quine, New Foundations, and the Philosophy of Set Theory , pp. 195 - 206Publisher: Cambridge University PressPrint publication year: 2018
References
Banach, Stefan and Tarski, Alfred. “Sur la Décomposition des ensembles de points en parties respectivement congruents” (1924). In Tarski, , Collected Papers, pp. 121–54.Google Scholar
Barrett, Robert B. and Gibson, Roger, eds. Perspectives on Quine (Cambridge: Basil Blackwell, 1990).Google Scholar
Barwise, Jon and Etchemendy, John. The Liar: An Essay on Truth and Circularity (New York, NY: Oxford University Press, 1987).Google Scholar
Benacerraf, Paul and Putnam, Hilary, eds. Philosophy of Mathematics: Selected Readings. 2nd edn (New York, NY: Cambridge University Press, 1983).Google Scholar
Boolos, George. Logic, Logic, and Logic. Ed. Jeffrey, Richard, with Introductions and Afterward by Burgess, John P. (Cambridge, MA: Harvard University Press, 1998).Google Scholar
Boolos, George. “On Second-Order Logic” (1975). In Logic, Logic, and Logic, pp. 37–53.Google Scholar
Boolos, George. “The Iterative Conception of Set” (1971). In Logic, Logic, and Logic, pp. 13–29.Google Scholar
Burali-Forti, Cesare. “A Question on Transfinite Numbers” (1897). In van Heijenoort, , From Frege to Gödel, pp. 104–11.Google Scholar
Burali-Forti, Cesare. “On Well-Ordered Classes” (1897). In van Heijenoort, , From Frege to Gödel, pp. 111–12.Google Scholar
Cantor, Georg. Contributions to the Founding of the Theory of Transfinite Numbers (1895, 1897), trans. Jourdain, Philip E. B. (New York, NY: Dover, 1955).Google Scholar
Cantor, Georg. Gesammelte Abhandlungen: Mathematische und Philosophischen Inhalts. Ed. Zermelo, Ernst (Hildesheim: Georg Olms Verlagsbuchhandlung, 1962).Google Scholar
Cantor, Georg. “Mitteilungen zur Lehre vom Transfiniten” (1887, 1888). In Gesammelte, pp. 378–439.Google Scholar
Cantor, Georg. “On a Property of the Totality of All Real Algebraic Numbers” (1874). In Ewald, , From Kant to Hilbert, pp. 839–43.Google Scholar
Cantor, Georg. “On an Elementary Question in the Theory of Manifolds” (1891). In Ewald, , From Kant to Hilbert, pp. 920–2.Google Scholar
Cantor, Georg. “Foundations of a General Theory of Manifolds: A Mathematico-Philosophical Investigation into the Theory of the Infinite” (1883). In Ewald, William, ed., From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol. II (Oxford: Clarendon Press, 1996), pp. 381–408.Google Scholar
Cantor, Georg, Dedekind, Richard, and Hilbert, David. “Cantor’s Late Correspondence with Dedekind and Hilbert.” In Ewald, , From Kant to Hilbert, pp. 923–40.Google Scholar
Carlson, Matthew. “Logic and the Structure of the Web of Belief.” Journal for the History of Analytical Philosophy 3:5 (2015): https://jhaponline.org/jhap/article/view/28.Google Scholar
Carnap, Rudolf. Foundations of Logic and Mathematics (Chicago, IL: University of Chicago Press, 1939).Google Scholar
Carnap, Rudolf. Meaning and Necessity: A Study in Semantics and Modal Logic, 2nd enlarged edn (Chicago, IL: University of Chicago Press, 1956).Google Scholar
Carnap, Rudolf. “Empiricism, Semantics, and Ontology.” In Meaning and Necessity, pp. 205–21.Google Scholar
Carnap, Rudolf. Logical Syntax of Language, trans. Smeaton, Amethe (Paterson, NJ: Littlefield, Adams, and Company, 1959).Google Scholar
Carnap, Rudolf. Logical Foundations of Probability, 2nd edn (Chicago, IL: University of Chicago Press, 1962).Google Scholar
Carnap, Rudolf. “Intellectual Autobiography.” In Schilpp, P. A. The Philosophy of Rudolf Carnap (La Salle, IL: Open Court, 1963), pp. 3–84.Google Scholar
Carnap, Rudolf. Philosophy and Logical Syntax (London: Thoemmes Press, 1996) [originally published 1935].Google Scholar
Church, Alonzo. “Comparison of Russell’s Resolution of the Semantical Antinomies with That of Tarski.” Journal of Symbolic Logic 41: 4 (December 1976), pp. 747–60.CrossRefGoogle Scholar
Clark, Peter, Hallett, Michael, and DeVidi, David, eds. Vintage Enthusiasms: Essays in Honour of J. L. Bell (Glasgow ePrints Service: http://eprints.gla.ac.uk/3810, 2008). Accessed 8 September 2018.Google Scholar
Dauben, Joseph Warren. Georg Cantor: His Mathematics and Philosophy of the Infinite (Princeton, NJ: Princeton University Press, 1979).Google Scholar
Devlin, Keith. The Joy of Sets: Fundamentals of Contemporary Set Theory. 2nd edn (New York, NY: Springer, 1993).CrossRefGoogle Scholar
Ebbinghaus, Heinz-Dieter. Ernst Zermelo: An Approach to His Life and Work (New York, NY: Springer, 2007).Google Scholar
Ewald, William, ed. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, vol. II (Oxford: Clarendon Press, 1996).Google Scholar
Feferman, Solomon. “Arithmetization of Meta-Mathematics in a General Setting.” Fundamenta Mathematicae 69 (1960), pp. 35–92.Google Scholar
Ferreirós, José. Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics (Boston, MA: Birkhäuser, 1999).CrossRefGoogle Scholar
Floyd, Juliet and Shieh, Sanford, eds. Future Pasts: The Analytic Tradition in Twentieth-Century Philosophy (New York, NY: Oxford University Press, 2001).CrossRefGoogle Scholar
Forster, Thomas. “The Status of the Axiom of Choice in Set Theory with a Universal Set.” Journal of Symbolic Logic 50:3 (1985), pp. 701–7.Google Scholar
Forster, Thomas. Set Theory with a Universal Set: Exploring an Untyped Universe (Oxford: Clarendon Press, 1992).Google Scholar
Forster, Thomas. “The Iterative Conception of Set.” Review of Symbolic Logic 1:1 (2008), pp. 97–110.Google Scholar
Fraenkel, A. A., Bar-Hillel, Y., and Levy, A.. Foundations of Set Theory, 2nd rev. edn (Amsterdam: North-Holland, 1973).Google Scholar
Frege, Gottlob. The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, trans. Austin, J. L., 2nd rev. edn (Evanston, IL: Northwestern University Press, 1968 [1884]).Google Scholar
Frege, Gottlob. Grundgesetze der Arithemetik I/II (New York, NY: Georg Olms, 1998 [1893, 1903]).Google Scholar
Frege, Gottlob. “Letter to Russell” (1902). In van Heijenoort, , From Frege to Gödel, pp. 127–8.Google Scholar
Garciadiego, Alejandro. Bertrand Russell and the Origins of the Set-Theoretic “Paradoxes” (Boston, MA: Birkhäuser, 1992).CrossRefGoogle Scholar
Gentzen, Gerhard. The Collected Papers of Gerhard Gentzen. Ed. Szabo, M. E. (Amsterdam: North-Holland, 1969).Google Scholar
Gentzen, Gerhard. “The Consistency of Elementary Number Theory.” In Collected Papers, pp. 132–213.Google Scholar
Gentzen, Gerhard. “The Consistency of the Simple Theory of Types.” In Collected Papers, pp. 214–22.Google Scholar
Gibson, Roger. The Philosophy of W. V. Quine: An Expository Essay (Tampa, FL: University of South Florida Press, 1982).Google Scholar
Gibson, Roger. Enlightened Empiricism: An Examination of W. V. Quine’s Theory of Knowledge (Tampa, FL: University of South Florida Press, 1992).Google Scholar
Gödel, Kurt. Kurt Godel: Collected Works, 2 vols., Eds. Feferman, Solomon, Dawson, John W. Jr., Kleene, Stephen C., Moore, Gregory H., Solovay, Robert M. and van Heijenoort, Jean (New York, NY: Oxford University Press, 1986, 1990).Google Scholar
Gödel, Kurt. “On Formally Undecidable Propositions of Principia Mathematica and Related Systems I.” In Kurt Gödel: Collected Works, vol. I, pp. 145–95.Google Scholar
Gödel, Kurt. “Russell’s Mathematical Logic.” In Schilpp, , The Philosophy of Bertrand Russell, pp. 123–53.Google Scholar
Gödel, Kurt. “The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory.” In Kurt Gödel: Collected Works, vol. II, pp. 33–101.Google Scholar
Gödel, Kurt. “What Is Cantor’s Continuum Problem?” In Benacerraf, and Putnam, , Philosophy of Mathematics, pp. 470–85.Google Scholar
Griffin, Nicholas. Russell’s Idealist Apprenticeship (Oxford: Clarendon Press, 1991).CrossRefGoogle Scholar
Gustaffson, Martin. “Quine’s Conception of Explication – And Why It Isn’t Carnap’s.” In Harman, Gilbert and Lepore, Ernie, eds, A Companion to W.V.O. Quine (Malden, MA: Wiley-Blackwell, 2014), pp. 508–25.Google Scholar
Hager, Paul. “Russell’s Method of Analysis.” In Griffin, Nicholas, eds, The Cambridge Companion to Bertrand Russell (New York, NY: Cambridge University Press, 2003), pp. 310–31.Google Scholar
Hahn, Edwin and Schilpp, Paul A., eds. The Philosophy of W. V. Quine, expanded edn (Chicago, IL: Open Court, 1998).Google Scholar
Hallett, Michael. Cantorian Set Theory and Limitation of Size (Oxford: Clarendon Press, 1984).Google Scholar
Hilbert, David and Bernays, Paul. Grundlagen der Mathematik, 2 vols., 2nd edn (New York, NY: Springer, 1968/1970).CrossRefGoogle Scholar
Hintikka, Jaakko, ed. Essays on the Development of the Foundations of Mathematics (Dordrecht: Kluwer Academic Publishers, 1995).Google Scholar
Holmes, Randall. “The Set-Theoretical Program of Quine Succeeded, but Nobody Noticed.” Modern Logic 4 (1994), pp. 1–47.Google Scholar
Holmes, Randall. Elementary Set Theory with a Universal Set. Cahiers du Centre de Logique, vol. 10 (Louvain-la-Neuve: Academia, 1998).Google Scholar
Hrbacek, Karel and Jech, Thomas. Introduction to Set Theory, 3rd rev. and expanded edn (New York, NY: Marcel Dekker, 1999).Google Scholar
Hylton, Peter. “Analyticity and the Indeterminacy of Translation.” Synthese 52:2 (1982), pp. 173–5.CrossRefGoogle Scholar
Hylton, Peter. Russell, Idealism, and the Emergence of Analytic Philosophy (Oxford: Clarendon Press, 1990).Google Scholar
Hylton, Peter. “Quine on Reference and Ontology.” In The Cambridge Companion to Quine, ed. Gibson, Roger (New York, NY: Cambridge University Press, 2004), pp. 115–50.Google Scholar
Hylton, Peter. Propositions, Functions, and Analysis: Selected Essays on Russell’s Philosophy (Oxford: Clarendon Press, 2005).CrossRefGoogle Scholar
Hylton, Peter. “Beginning with Analysis.” In Propositions, Functions, and Analysis, pp. 30–48.Google Scholar
Hylton, Peter. “Frege and Russell.” In Propositions, Functions, and Analysis, pp. 153–84.Google Scholar
Hylton, Peter. “Logic in Russell’s Logicism.” In Propositions, Functions, and Analysis, pp. 49–82.Google Scholar
Hylton, Peter. “Russell’s Substitutional Theory.” In Propositions, Functions, and Analysis, pp. 83–107.Google Scholar
Hylton, Peter. “The Nature of the Proposition and the Revolt Against Idealism.” In Propositions, Functions, and Analysis, pp. 9–29.Google Scholar
Hylton, Peter. “The Theory of Descriptions.” In Propositions, Functions, and Analysis, pp. 189–94.Google Scholar
Hylton, Peter. “The Vicious Circle Principle.” In Propositions, Functions, and Analysis, pp. 108–14.Google Scholar
Hylton, Peter. “Quine’s Naturalism Revisited.” In Harman, Gilbert and Lepore, Ernie, eds. A Companion to W.V.O. Quine (Malden, MA: Wiley-Blackwell, 2014), pp. 148–62.Google Scholar
Jech, Thomas, ed. Axiomatic Set Theory, vol. II (Providence, RI: American Mathematical Society, 1974).Google Scholar
Jech, Thomas. “About the Axiom of Choice.” In Barwise, , Handbook of Mathematical Logic, pp. 345–70.Google Scholar
Jensen, Ronald. “On the Consistency of a Slight (?) Modification of Quine’s NF,” Synthese 19 (1969), pp. 250–63.Google Scholar
Kanamori, Akahiro. “The Mathematical Development of Set Theory from Cantor to Cohen.” The Bulletin of Symbolic Logic 2:1 (March 1996), pp. 1–71.CrossRefGoogle Scholar
Kleinberg, Eugene M. Infinitary Combinatorics and the Axiom of Determinateness. Lecture Notes in Mathematics 612 (New York, NY: Springer).Google Scholar
Kline, Morris, Mathematical Thought from Ancient to Modern Times (New York, NY: Oxford University Press, 1972).Google Scholar
Kreisel, George. “On the Mathematical Significance of Consistency Proofs.” Journal of Symbolic Logic 23:2 (1958), pp. 155–82.Google Scholar
Kunen, Kenneth. Set Theory: An Introduction to Independence Proofs (New York, NY: North-Holland, 1980).Google Scholar
Lindenbaum, Adolf and Tarski, Alfred. “Communication sur les Recherches de la Théorie des Ensembles” (1926). In Tarski, Collected Papers, pp. 171–204.Google Scholar
Linnebo, Øystein. “Sets, Properties, and Unrestricted Quantification.” In Rayo, and Uzquiano, , Absolute Generality, pp. 149–78.Google Scholar
MacClane, Saunders. “Locally Small Categories and the Foundations of Set Theory.” In Infinitistic Methods: Proceedings of the Symposium on Foundations of Mathematics (New York, NY: Pergamon Press, 1961), pp. 25–43.Google Scholar
MacLane, Saunders. “Categorical Algebra and Set-Theoretic Foundations.” Proceedings of Symposia in Pure Mathematics XIII:pt. I (1971), pp. 231–40.CrossRefGoogle Scholar
Maddy, Penelope. Defending the Axioms: On the Philosophical Foundations of Set Theory (New York, NY: Oxford University Press, 2011).CrossRefGoogle Scholar
Martin, Donald A. “Review of Set Theory and Its Logic.” Journal of Philosophy 67:4 (1970), pp. 111–14.CrossRefGoogle Scholar
Mendelson, Elliott. Introduction to Mathematical Logic (Boca Raton, FL: CRC Press, 1997).Google Scholar
Mirimanoff, Dimitri. “Les Antinomies de Russell et de Burali-Forti et le Problème Fondamental de la Théorie des Ensembles.” L’Enseignement Mathématique 19 (1917), pp. 37–52.Google Scholar
Mirimanoff, Dimitri. “Remarques sur la Théorie des Ensembles.” L’Enseignement Mathématique 19 (1917), pp. 208–17.Google Scholar
Moore, G. E. G. E. Moore: The Early Essays. Ed. Regan, Tom (Philadelphia, PA: Temple University Press, 1986), pp. 59–80.Google Scholar
Moore, Gregory H. “The Origins of Zermelo’s Axiomatization of Set Theory.” Journal of Philosophical Logic 7 (1978), pp. 307–29.CrossRefGoogle Scholar
Moore, Gregory H. Zermelo’s Axiom of Choice: Its Origins, Development, and Influence (New York, NY: Springer, 1982).CrossRefGoogle Scholar
Moore, Gregory H. “The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number.” In Hintikka, Jaakko, eds, Essays on the Development of the Foundations of Mathematics (Dordrecht: Kluwer Academic Publishers, 1995), pp. 215–39.Google Scholar
Moore, Gregory H. and Garciadiego, Alejandro. “Burali-Forti’s Paradox: A Reappraisal of Its Origins.” Historia Mathematica 8 (1981), pp. 319–50.Google Scholar
Morris, Sean. “Quine, Russell, and Naturalism: From a Logical Point of View.” Journal of the History of Philosophy 53:1 (2015), pp. 133–55.CrossRefGoogle Scholar
Morris, Sean. “The Significance of Quine’s New Foundations for the Philosophy of Set Theory.” The Monist 100:2 (2017), 167–79.Google Scholar
Moschovakis, Yiannis. Descriptive Set Theory (New York, NY: North-Holland, 1980), Ch. 6.Google Scholar
Mycielski, Jan and Stanislaw, Swierczkowski, “On the Lebesgue Measureability and the Axiom of Determinateness.” Fundamenta Mathematicae 54 (1964), pp. 67–71.CrossRefGoogle Scholar
Parsons, Charles. “What Is the Iterative Conception of Set?” In Benacerraf, and Putnam, , Philosophy of Mathematics, pp. 503–29.Google Scholar
Peirce, Charles. Collected Papers. Vol. II (Cambridge, MA: Harvard University Press, 1932.Google Scholar
Potter, Michael. “Iterative Set Theory.” The Philosophical Quarterly 43:171 (1993), pp. 178–93.CrossRefGoogle Scholar
Potter, Michael. Set Theory and Its Philosophy (New York, NY: Oxford University Press, 2004).CrossRefGoogle Scholar
Quine, W. V. “New Foundations for Mathematical Logic,” American Mathematical Monthly 44:2 (1937), pp. 70–80.CrossRefGoogle Scholar
Quine, W. V. “On Cantor’s Theorem.” Journal of Symbolic Logic 2:3 (September 1937), pp. 120–4.Google Scholar
Quine, W. V. “Unification of Universes in Set Theory.” Journal of Symbolic Logic 21:3 (1956), pp. 267–79.Google Scholar
Quine, W. V. Ontological Relativity and Other Essays (New York, NY: Columbia University Press, 1969).CrossRefGoogle Scholar
Quine, W. V. “Epistemology Naturalized.” In Ontological Relativity and Other Essays, pp. 69–90.Google Scholar
Quine, W. V. Set Theory and Its Logic, rev. edn (Cambridge, MA: Harvard University Press, 1969).Google Scholar
Quine, W. V. Methods of Logic, 3rd edn (Chicago, IL: Holt Rinehart, and Winston, 1972).Google Scholar
Quine, W. V. The Ways of Paradox and Other Essays, rev. and enlarged ed. (Cambridge, MA: Harvard University Press, 1976).Google Scholar
Quine, W. V. “Foundations of Mathematics” (1965). In The Ways of Paradox and Other Essays, pp. 22–32.Google Scholar
Quine, W. V. “Mr. Strawson on Logical Theory” (1953). In The Ways of Paradox and Other Essays, pp. 137–57.Google Scholar
Quine, W. V. “Necessary Truth” (1963). In The Ways of Paradox and Other Essays, pp. 68–76.Google Scholar
Quine, W. V. “Posits and Reality” (1955). In The Ways of Paradox and Other Essays, pp. 246–54.Google Scholar
Quine, W. V. From a Logical Point of View: Nine Logico-Philosophical Essays, 2nd rev. edn (Cambridge, MA: Harvard University Press, 1980).CrossRefGoogle Scholar
Quine, W. V. “New Foundations for Mathematical Logic” with supplementary remarks. In From a Logical Point of View, pp. 80–101.Google Scholar
Quine, W. V. “Two Dogmas of Empiricism” (1951). In From a Logical Point of View, pp. 20–46.Google Scholar
Quine, W. V. “On the Individuation of Attributes” (1975). In Theories and Things, pp. 100–12.Google Scholar
Quine, W. V. Methods of Logic, 4th edn (Cambridge, MA: Harvard University Press, 1982).Google Scholar
Quine, W. V. The Logic of Sequences: A Generalization of Principia Mathematica (1932) (New York, NY: Garland, 1990).Google Scholar
Quine, W. V. Selected Logic Papers, enlarged edn (Cambridge, MA: Harvard University Press, 1995).Google Scholar
Quine, W. V. “A Bibliography of the Publications of W. V. Quine.” In Hahn, and Schilpp, , Philosophy of W. V. Quine, pp. 743–64.Google Scholar
Quine, W. V. “Autobiography of W. V. Quine.” In Hahn, and Schilpp, , Philosophy of W. V. Quine, pp. 1–46, 729–41.Google Scholar
Quine, W. V. “Confessions of a Confirmed Extensionalist.” In Floyd, and Shieh, , Future Pasts, pp. 215–21.Google Scholar
Quine, W. V. “Set-Theoretic Foundations for Logic” (1936). In Selected Logic Papers, pp. 83–99.Google Scholar
Quine, W. V. “The Inception of New Foundations” (1987). In Selected Logic Papers, pp. 286–9.Google Scholar
Quine, W. V. “Whitehead and the Rise of Modern Logic” (1941). In Selected Logic Papers, pp. 3–36.Google Scholar
Quine, W. V. “Carnap and Logical Truth,” Reprinted in , W. V. , Quine, The Ways of Paradox and Other Essays, rev. and enlarged edn (Cambridge, MA: Harvard University Press, 1976), pp. 107–32.Google Scholar
Quine, W. V. “Concepts of Negative Degree.” In Proceedings of the National Academy of Sciences of the United States of America 22:1 (1936), pp. 40–5.Google ScholarPubMed
Quine, W. V. From Stimulus to Science (Cambridge, MA: Harvard University Press, 1995).CrossRefGoogle Scholar
Quine, W. V. “On the Theory of Types,” Journal of Symbolic Logic 3:4 (1938), pp. 125–39.Google Scholar
Quine, W. V. “A Theory of Classes Presupposing No Canons of Type.” In Proceedings of the National Academy of Sciences 22 (1936), 320–26.Google Scholar
Quine, W. V. “Truth by Convention.” In The Ways of Paradox and Other Essays, rev. and enlarged edn (Cambridge, MA: Harvard University Press, 1976), pp. 77–106.Google Scholar
Quine, W. V. “Ontological Relativity.” In Ontological Relativity and Other Essays, pp. 26–48.Google Scholar
Quine, W. V. “Set-Theoretic Foundations for Logic,” Journal of Symbolic Logic 1 (1936), pp. 45–57.CrossRefGoogle Scholar
Quine, W. V. “The Ways of Paradox” (1962). In The Ways of Paradox and Other Essays, pp. 1–18.Google Scholar
Quine, W. V. “Two Dogmas in Retrospect.” Reprinted in Quine, W. V., Confessions of a Confirmed Extensionalist and Other Essays. Eds. Føllesdal, Dagfinn and Quine, Douglas B. (Cambridge, MA: Harvard University Press, 2008), pp. 390–401.Google Scholar
Quine, W. V. Philosophy of Logic, 2nd edn (Cambridge, MA: Harvard University Press, 1986).Google Scholar
Quine, W. V. “The Scope and Language of Science.” Reprinted in Quine, W. V., The Ways of Paradox and Other Essays, rev. and enlarged edn (Cambridge, MA: Harvard University Press, 1976), pp. 228–45.Google Scholar
Quine, W. V. “Things and Their Place in Theories.” In Quine, W. V., Theories and Things (Cambridge, MA: Harvard University Press, 1981), pp. 1–23.Google Scholar
Quine, W. V. Pursuit of Truth, rev. ed. (Cambridge, MA: Harvard University Press, 1992).Google Scholar
Quine, W. V. “Reply to Jules Vuillemen.” In Hahn, and Schilpp, , The Philosophy of W. V. Quine, pp. 619–20.Google Scholar
Quine, W. V. and Ullian, Joseph. The Web of Belief, 2nd edn (New York, NY: Random House, 1978).Google Scholar
Ramsey, F. P. “The Foundations of Mathematics.” Proceedings of the London Mathematical Society, s2–25:1 (1926), pp. 338–84.Google Scholar
Ramsey, F. P. The Foundations of Mathematics and Other Logical Essays. Ed. Braithewaite, R. B. (New York, NY: Humanities Press, 1950).Google Scholar
Ramsey, F. P. “The Foundations of Mathematics” (1925). In The Foundations of Mathematics, pp. 1–61.Google Scholar
Rang, B. and Thomas, W., “Zermelo’s Discovery of the ‘Russell Paradox.’” Historia Mathematica 8 (1981), pp. 15–22.CrossRefGoogle Scholar
Rayo, Agustin and Uzquiano, Gabriel, eds. Absolute Generality (New York, NY: Oxford University Press, 2006).CrossRefGoogle Scholar
Reck, Erich. “Carnapian Explication: A Case Study and a Critique.” In Wagner, Pierre, ed., Carnap’s Ideal of Explication and Naturalism (New York, NY: Palgrave-Macmillan, 2012), pp. 96–116.CrossRefGoogle Scholar
Resnick, Michael D. “On the Philosophical Significance of Consistency Proofs.” Journal of Philosophical Logic 3:1/2 (1974), pp. 133–47.Google Scholar
Robinson, Abraham. “Non-Standard Analysis.” Selected Papers, vol. 2. Eds, Keisler, H. J. et al. (New Haven, CT: Yale University Press, 1979), pp. 3–11.Google Scholar
Ricketts, Thomas. “Languages and Calculi.” In Hardcastle, Gary L. and Richardson, Alan W., eds, Logical Empiricism in North America (Minneapolis, MN: University of Minnesota Press, 2003), pp. 257–80.Google Scholar
Rieger, Adam. “An Argument for Finsler-Aczel Set Theory.” Mind 109:434 (2000), pp. 241–53.CrossRefGoogle Scholar
Rieger, Adam. “Paradox, ZF, and the Axiom of Foundation.” In Clark, Hallett, and DeVidi, , Vintage Enthusiasms, pp. 1–22.Google Scholar
Rieger, Adam. “Paradox, ZF, and the axiom of foundation.” In Clark, Peter, Hallett, Michael, and DeVidi, David, eds, Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell. Springer (2011), pp. 171–187. ISBN 9789400702134 (doi:10.1007/978-94-007-0214-1_9).CrossRefGoogle Scholar
Rosser, J. Barkley. “On the Consistency of Quine’s New Foundations for Mathematical Logic.” Journal of Symbolic Logic 4:1 (1939), pp. 15–24.CrossRefGoogle Scholar
Rosser, J. Barkley. “Review of Specker’s ‘The Axiom of Choice in Quine’s New Foundations for Mathematical Logic.’” Journal of Symbolic Logic 19:2 (1954), pp. 127–8.Google Scholar
Rosser, J. Barkley. Logic for Mathematicians, 2nd edn with additional appendices (Mineola, NY: Dover Publications, 1978).Google Scholar
Russell, Bertrand. Introduction to Mathematical Philosophy (London: George Allen and Unwin, 1919).Google Scholar
Russell, Bertrand. Our Knowledge of the External World (New York, NY: W. W. Norton, 1929).Google Scholar
Russell, Bertrand. Principles of Mathematics, 2nd edn (London: George Allen and Unwin, 1937 [first edition 1903]).Google Scholar
Russell, Bertrand. Logic and Knowledge: Essays 1901–1950. Ed. Marsh, Robert C. (London: George Allen and Unwin, 1956).Google Scholar
Russell, Bertrand. Essays in Analysis. Ed. Lackey, Douglas (London: George Allen and Unwin, 1973).Google Scholar
Russell, Bertrand. “On Some Difficulties in the Theory of Transfinite Ordinals and Order Types” (1905). In Essays in Analysis, pp. 135–64.Google Scholar
Russell, Bertrand. “The Regressive Method of Discovering the Premises of Mathematics.” In Essays in Analysis, pp. 272–83.Google Scholar
Russell, Bertrand. The Collected Papers of Bertrand Russell, vol. 2. Eds. Griffin, Nicholas and Lewis, Albert C. (New York, NY: Routledge, 1990).Google Scholar
Russell, Bertrand. My Philosophical Development (New York, NY: Routledge, 1993 [1958]).Google Scholar
Russell, Bertrand. “Mathematical Logic as Based on the Theory of Types” (1908). In van Heijenoort, , From Frege to Gödel, pp. 150–82.Google Scholar
Russell, Bertrand. The Collected Papers of Bertrand Russell, vol. 3. Ed. Moore, Gregory H. (New York, NY: Routledge, 1993).Google Scholar
Russell, Bertrand. “On Some Difficulties of Continuous Quantity” (1896). In The Collected Papers, pp. 44–58.Google Scholar
Russell, Bertrand. “Review of Essai critique sur la hypothèse des atomes dans la science contemporaine” (1896). In The Collected Papers, pp. 35–43.Google Scholar
Schilpp, Paul Arthur, ed. The Philosophy of Bertrand Russell (La Salle, IL: Open Court Press, 1971).Google Scholar
Scott, Dana. “Axiomatizing Set Theory.” In Jech, , Axiomatic Set Theory, vol. II, pp. 207–14.Google Scholar
Shoenfield, Joseph. “Axioms of Set Theory.” In Barwise, , Handbook of Mathematical Logic, pp. 321–44.Google Scholar
Sierpinski, Waclaw. “L’hypothèse généralisée du continu et l’axiom du choix.” Fundamenta Mathematica 34 (1947), pp. 1–5.CrossRefGoogle Scholar
Specker, Ernst P. “The Axiom of Choice in Quine’s New Foundations for Mathematical Logic.” Proceedings of the National Academy of Sciences 39:9 (September 1953), pp. 972–5.Google Scholar
Szabo, M. E., ed. The Collected Papers of Gerhard Gentzen (Amsterdam: North-Holland, 1969).Google Scholar
Tait, William. “Frege Versus Cantor and Dedekind: On the Concept of Number.” In The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History (New York, NY: Oxford University Press, 2005), pp. 212–51.Google Scholar
Tait, William. The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History (New York, NY: Oxford University Press, 2005).CrossRefGoogle Scholar
Tarski, Alfred. Collected Papers, vol. I, 1921–34. Eds Givant, Steven and McKenzie, Ralph N. (Boston, MA: Birkhäuser, 1986).Google Scholar
Ullian, Joseph. “Quine and the Field of Mathematical Logic.” In Hahn, and Schilpp, , Philosophy of W. V. Quine, pp. 569–89.Google Scholar
van Heijenoort, Jean, ed. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (Cambridge, MA: Harvard University Press, 1967).Google Scholar
von Neumann, John. “An Axiomatization of Set Theory” (1925). In van Heijenoort, , From Frege to Gödel, pp. 393–413.Google Scholar
von Neumann, John. John von Neumann: Collected Works, vol. I. Ed. Taub, Abraham H. (New York, NY: Pergamon Press, 1961).Google Scholar
von Neumann, John. “Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre” (1929). In Collected Works, pp. 494–508.Google Scholar
Wang, Hao. “The Concept of Set.” In Benacerraf, and Putnam, , eds., Philosophy of Mathematics, pp. 530–70.Google Scholar
Weir, Alan. “Is It Too Much to Ask, to Ask for Everything?” In Rayo, and Uzquiano, , Absolute Generality, pp. 333–68.Google Scholar
Whitehead, Alfred North and Russell, Bertrand. Principia Mathematica, 3 vols. 2nd edn (Cambridge: Cambridge University Press, 1925, 1927 [first edn 1910, 1912, 1913]).Google Scholar
Wittgenstein, Ludwig. Tractatus Logico-Philosophicus (New York, NY: Routledge, 1990 [1922]).Google Scholar
Wittgenstein, Ludwig. Cambridge Letters: Correspondence with Russell, Keynes, Moore, Ramsey, and Sraffa. eds. McGuinnes, Brian and von Wright, Georg Henrik (Malden, MA: Blackwell Publishers, 1997).Google Scholar
Zermelo, Ernst. “A New Proof of the Possibility of a Well-Ordering” (1908). In van Heijenoort, , From Frege to Gödel, pp. 183–98.Google Scholar
Zermelo, Ernst. “Investigations into the Foundations of Set Theory I” (1908). In van Heijenoort, , From Frege to Gödel, pp. 199–215.Google Scholar
Zermelo, Ernst. “On Boundary Numbers and Domains of Sets: New Investigations in the Foundations of Set Theory” (1930). In Ewald, , From Kant to Hilbert, pp. 1219–33.Google Scholar
Zermelo, Ernst. “Proof That Every Set Can Be Well-Ordered” (1904). In van Heijenoort, , From Frege to Gödel, pp. 139–41.Google Scholar