Linked bibliography for the SEP article "Platonism in the Philosophy of Mathematics" by Øystein Linnebo

This is an automatically generated and experimental page

If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

This experiment has been authorized by the editors of the Stanford Encyclopedia of Philosophy. The original article and bibliography can be found here.

Azzouni, Jody, 2004, Deflating Existential Consequence: A Case for Nominalism, Oxford: Oxford University Press. (Scholar)
Balaguer, Mark, 1998, Platonism and Anti-Platonism in Mathematics, Oxford: Oxford University Press. (Scholar)
–––, 2001, “A theory of mathematical correctness and mathematical truth”, Pacific Philosophical Quarterly, 82: 87–114.
Benacerraf, Paul, 1965, “What numbers could not be”, Philosophical Review, 74: 47–73. (Scholar)
–––, 1973, “Mathematical Truth”, Journal of Philosophy, 70(19): 661–679. (Scholar)
–––, 1996, “What mathematical truth could not be, i”, in Benacerraf and His Critics, A. Morton and S. Stich, eds., Oxford: Blackwell. (Scholar)
Benacerraf, Paul and Putnam, Hilary (eds.), 1983, Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press. Second edition. (Scholar)
Bernays, Paul, 1935, “On Platonism in Mathematics”, Reprinted in Benacerraf and Putnam (1983). (Scholar)
Bigelow, John, 1988, The Reality of Numbers: A Physicalist’s Philosophy of Mathematics, Oxford: Clarendon. (Scholar)
Burgess, John P., 1999, “Review of Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology”, Notre Dame Journal of Formal Logic, 40(2): 283–91. (Scholar)
–––, 2004, “Review of Jody Azzouni, Deflating Existential Consequence: A Case for Nominalism”, Bulletin of Symbolic Logic, 10(4): 573–577. (Scholar)
Burgess, John P. and Rosen, Gideon, 1997, A Subject with No Object, Oxford: Oxford University Press. (Scholar)
Clarke-Doane, Justin, 2017, “What is the Benacerraf Problem?”, in New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity (Volume 28: Logic, Epistemology, and Unity of Science), F. Pataut (ed.), Cham: Springer, 17–43. (Scholar)
Cole, Julian C., 2013, “Towards an Institutional Account of the Objectivity, Necessity, and Atemporality of Mathematics”, Philosophia Mathematica, 21(1): 9–36. (Scholar)
Colyvan, Mark and Zalta, Edward N., 1999, “Mathematics: Truth and Fiction?”, Philosophia Mathematica, 7(3): 336–349. (Scholar)
Donaldson, Thomas, 2017, “The (metaphysical) foundations of arithmetic?”, Noûs, 51(4): 775–801. (Scholar)
Dummett, Michael, 1978a, “The philosophical basis of intuitionistic logic”, in Truth and Other Enigmas, Cambridge, MA: Harvard University Press, 215–247; reprinted in Benacerraf and Putnam (1983). (Scholar)
–––, 1978b, Truth and Other Enigmas, Cambridge, MA: Harvard University Press. (Scholar)
–––, 1981, Frege: Philosophy of Language, Cambridge, MA: Harvard University Press, second ed. (Scholar)
–––, 1991a, Frege: Philosophy of Mathematics, Cambridge, MA: Harvard University Press. (Scholar)
–––, 1991b, The Logical Basis of Metaphysics, Cambridge, MA: Harvard University Press. (Scholar)
Ebert, Philip and Rossberg, Marcus, 2007, “What is the purpose of neo-logicism?”, Travaux de Logique, 18: 33–61. (Scholar)
Feferman, Solomon, 2009, “Conceptions of the continuum”, Intellectica, 51: 169–89. (Scholar)
Field, Hartry, 1982, “Realism and Anti-Realism about Mathematics”, Philosophical Topics, 13(1): 45–69. (Scholar)
–––, 1989, Realism, Mathematics, and Modality, Oxford: Blackwell. (Scholar)
Fine, Kit, 1994, “Ontological Dependence”, Proceedings of the Aristotelian Society, 95: 269–290. (Scholar)
Frege, Gottlob, 1953, Foundations of Arithmetic, Oxford: Blackwell. Transl. by J.L. Austin. (Scholar)
Gaifman, Haim, 1975, “Ontology and Conceptual Frameworks, Part I”, Erkenntnis, 9: 329–353. (Scholar)
Gödel, Kurt, 1944, “Russell’s Mathematical Logic”, In Benacerraf and Putnam (1983). (Scholar)
–––, 1964, “What is Cantor’s Continuum Hypothesis?”, In Benacerraf and Putnam (1983). (Scholar)
–––, 1995, “Some basic theorems on the foundations of mathematics and their implications”, in Collected Words, S. Feferman et al, ed., Oxford: Oxford University Press, vol. III, 304–323. (Scholar)
Goodman, Nelson, 1956, “A World of Individuals”, reprinted. in P. Benacerraf and H. Putnam, eds., Philosophy of Mathematics: Selected Readings, 1st ed., Prentice-Hall. (Scholar)
Hale, Bob, 1987, Abstract Objects, Oxford: Blackwell. (Scholar)
Hale, Bob and Wright, Crispin, 2000, “Implicit Definition and the A Priori”, in New Essays on the A Priori, Paul Boghossian and Christopher Peacocke, eds., Oxford: Oxford University Press. Reprinted in Hale and Wright (2001). (Scholar)
–––, 2001, Reason’s Proper Study, Oxford: Clarendon. (Scholar)
Hellman, Geoffrey, 1989, Mathematics without Numbers, Oxford: Clarendon. (Scholar)
–––, 2001, “Three Varieties of Mathematical Structuralism”, Philosophia Mathematica, 9(3): 184–211. (Scholar)
Hamkins, Joel David, 2012, “The Set-Theoretic Multiverse”, Review of Symbolic Logic, 5(3): 416–449. (Scholar)
Hersh, Reuben, 1997, What is Mathematics, Really?, Oxford: Oxford University Press. (Scholar)
Hilbert, David, 1996, “Mathematical problems”, in From Kant to Hilbert, William Ewald, ed., Oxford: Oxford University Press, vol. 2, 1096–1105. (Scholar)
Hofweber, Thomas, 2000, “Quantification and non-existent objects”, in Empty Names, Fiction and the Puzzle of Non-Existence, Anthony Everett and Thomas Hofweber, eds., Stanford, CA: CSLI Publications, 249–73. (Scholar)
–––, 2005, “Number determiners, numbers, and arithmetic”, Philosophical Review, 114(2): 179–225. (Scholar)
–––, 2016, Ontology and The Ambitions of Metaphysics, Oxford: Oxford University Press. (Scholar)
Isaacson, Daniel, 1994, “Mathematical intuition and objectivity”, in Mathematics and Mind, Alexander George, ed., Oxford: Oxford University Press, chap. 5. (Scholar)
Jané, Ignasi, 2010, “Idealist and realist elements in Cantor’s approach to set theory”, Philosophia Mathematica, 18(2): 193–226. (Scholar)
Kitcher, Philip, 1978, “The plight of the platonist”, Noûs, 12: 119–136. (Scholar)
Kreisel, Georg, 1958, “Review of Wittgenstein’s remarks on the foundations of mathematics”, British Journal for the Philosophy of Science, 9: 135–158. (Scholar)
Lear, Jonathan, 1980, “Aristotelian infinity”, Proceedings of the Aristotelian Society, 80: 187–210. (Scholar)
Leng, Mary, 2010, Mathematics and Reality, Oxford: Oxford University Press. (Scholar)
Lewis, David, 1991, Parts of Classes, Oxford: Blackwell. (Scholar)
Linnebo, Øystein, 2006, “Epistemological challenges to mathematical platonism”, Philosophical Studies, 129(3): 545–574. (Scholar)
–––, 2008, “Structuralism and the notion of dependence”, Philosophical Quarterly, 58: 59–79. (Scholar)
–––, 2012, “Reference by abstraction”, Proceedings of the Aristotelian Society, 112: 45–71. (Scholar)
–––, 2013, “The potential hierarchy of sets”, Review of Symbolic Logic, 6(2): 205–228. (Scholar)
–––, 2017, Philosophy Of Mathematics, Princeton: Princeton University Press. (Scholar)
–––, 2018, Thin Objects: An Abstractionist Account, Oxford: Oxford University Press. (Scholar)
Linnebo, Øystein and Shapiro, Stewart, 2019, “Actual and Potential Infinity”, Noûs, 53(1): 160–191. (Scholar)
Linsky, Bernard and Zalta, Edward N., 1995, “Naturalized platonism versus platonized naturalism”, Journal of Philosophy, 92(10): 525–555. (Scholar)
Linsky, Bernard and Zalta, Edward N., 2006, “What is neologicism?”, Bulletin of Symbolic Logic, 12(1): 60–99. (Scholar)
MacBride, Fraser, 2005, “Structuralism Reconsidered”, in Oxford Handbook of Philosophy of Mathematics and Logic, Stewart Shapiro, ed., Oxford: Clarendon, 563–589. (Scholar)
Maddy, Penelope, 1990, Realism in Mathematics, Oxford: Clarendon. (Scholar)
–––, 1997, Naturalism in Mathematics, Oxford: Clarendon. (Scholar)
Martin, Donald A., 2001, “Multiple universes of sets and indeterminate truth values”, Topoi, 20(1): 5–16. (Scholar)
Moltmann, Friederike, 2013, “Reference to numbers in natural language”, Philosophical Studies, 162: 499–536. (Scholar)
Nutting, Eileen, 2020, “Benacerraf, Field, and the Agreement of Mathematicians”, Synthese, 197(5): 2095–2110. (Scholar)
Parsons, Charles, 1977, “What is the Iterative Conception of Set?” in Logic, Foundations of Mathematics, and Computability Theory (The University of Western Ontario Series in Philosophy of Science: Volume 9), R.E. Butts and J. Hintikka (eds.), Dortrecht: Springer, 335–367. (Scholar)
–––, 1980, “Mathematical Intuition”, Proceedings of the Aristotelian Society, 80: 145–68. (Scholar)
–––, 1983, Mathematics in Philosophy, Ithaca, NY: Cornell University Press. (Scholar)
–––, 1990, “The Structuralist View of Mathematical Objects”, Synthese, 84: 303–346. (Scholar)
–––, 1995, “Platonism and mathematical intuition in Kurt Gödel’s thought”, Bulletin of Symbolic Logic, 1(1): 44–74. (Scholar)
Quine, W.V., 1969, “Existence and quantification”, in Ontological Relativity and Other Essays, New York: Columbia University Press, 91–113. (Scholar)
Rayo, Agustín, 2008, “On specifying truth-conditions”, Philosophical Review, 117(3): 385–443. (Scholar)
–––, 2013, The Construction of Logical Space, Oxford: Oxford University Press. (Scholar)
Rees, D.A., 1967, “Platonism and the platonic tradition”, in The Encyclopedia of Philosophy, Paul Edwards, ed., New York: Macmillan, vol. 5, 333–341. (Scholar)
Resnik, Michael, 1980, Frege and the Philosophy of Mathematics, Ithaca, NY: Cornell University Press. (Scholar)
–––, 1997, Mathematics as a Science of Patterns, Oxford: Oxford University Press. (Scholar)
Restall, Greg, 2003, “Just what Is full-blooded platonism?”, Philosophia Mathematica, 11(1): 82–91. (Scholar)
Rosen, Gideon, 2011, “The reality of mathematical objects”, in Meaning in Mathematics, J. Polkinghorne (ed.), Oxford: Oxford University Press, 113–132. (Scholar)
Schiemer, Georg and Wigglesworth, John, 2019, “The Structuralist Thesis Reconsidered”, British Journal for the Philosophy of Science, 70(4): 1201–1226. (Scholar)
Schwartzkopff, Robert, 2011, “Numbers as Ontologically Dependent Entities: Hume’s Principle Revisited”, Grazer Philosophische Studien, 82(1): 353–373. (Scholar)
Shapiro, Stewart, 1997, Philosophy of Mathematics: Structure and Ontology, Oxford: Oxford University Press. (Scholar)
Snyder, Eric, 2017, “Numbers and Cardinalities: What’s Really Wrong with the Easy Argument for Numbers?”, Linguistics and Philosophy, 40(4): 373–400. (Scholar)
Studd, James, 2013, “The Iterative Conception of Set: a (Bi-)Modal Axiomatisation”, Journal of Philosophical Logic, 42(5): 1–29. (Scholar)
Wright, Crispin, 1983, Frege’s Conception of Numbers as Objects, Aberdeen: Aberdeen University Press. (Scholar)
–––, 1992, Truth and Objectivity, Cambridge, MA: Harvard University Press. (Scholar)
–––, 2000, Neo-Fregean Foundations for Analysis: Some Reflections, Notre Dame Journal of Formal Logic, 41(4): 317–334. (Scholar)
Yablo, Stephen, 2005, “The Myth of the Seven”, in Fictionalism in Metaphysics, M. Kalderon (ed.), Oxford: Oxford University Press, 88–115. (Scholar)

Generated Mon Mar 17 04:52:16 2025

Applied ethics	Epistemology	History of Western Philosophy	Meta-ethics	Metaphysics	Normative ethics
Philosophy of biology	Philosophy of language	Philosophy of mind	Philosophy of religion	Science Logic and Mathematics	More ...