Linked bibliography for the SEP article "Fictionalism in the Philosophy of Mathematics" by Mark Balaguer

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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.

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Armour-Garb, B., 2011, “Understanding Mathematical Fictionalism,” Philosophia Mathematica, 19: 335–44. (Scholar)
Arnzenius, F. and C. Dorr, 2012, “Calculus as Geometry,” in Space, Time, and Stuff, F. Arntzenius, Oxford: Oxford University Press, pp. 213–78. (Scholar)
Azzouni, J., 1994, Metaphysical Myths, Mathematical Practice, Cambridge: Cambridge University Press. (Scholar)
–––, 2004, Deflating Existential Consequence: A Case for Nominalism, Oxford: Oxford University Press. (Scholar)
–––, 2010, Talking About Nothing: Numbers, Hallucinations, and Fictions, Oxford: Oxford University Press. (Scholar)
Baker, A., 2005, “Are There Genuine Mathematical Explanations of Physical Phenomena?,” Mind, 114: 223–38. (Scholar)
–––, 2009, “Mathematical Explanation in Science,” British Journal for the Philosophy of Science, 60: 611–633. (Scholar)
Balaguer, M., 1995, “A Platonist Epistemology,” Synthese, 103: 303–25. (Scholar)
–––, 1996a, “A Fictionalist Account of the Indispensable Applications of Mathematics,” Philosophical Studies, 83: 291–314. (Scholar)
–––, 1996b, “Towards a Nominalization of Quantum Mechanics,” Mind, 105: 209–26. (Scholar)
–––, 1998a, Platonism and Anti-Platonism in Mathematics, Oxford: Oxford University Press. (Scholar)
–––, 1998b, “Attitudes Without Propositions,” Philosophy and Phenomenological Research, 58: 805–26. (Scholar)
–––, 2001, “A Theory of Mathematical Correctness and Mathematical Truth,” Pacific Philosophical Quarterly, 82: 87–114. (Scholar)
–––, 2009, “Fictionalism, Theft, and the Story of Mathematics,” Philosophia Mathematica, 17: 131–62. (Scholar)
Bangu, S., 2008, “Inference to the Best Explanation and Mathematical Realism,” Synthese, 160: 13–20. (Scholar)
Benacerraf, P., 1965, “What Numbers Could Not Be,” reprinted in Benacerraf and Putnam (1983), pp. 272–94. (Scholar)
–––, 1973, “Mathematical Truth,” Journal of Philosophy, 70: 661–79. (Scholar)
Benacerraf, P. and Putnam, H. (eds.), 1983, Philosophy of Mathematics, Cambridge: Cambridge University Press. (Scholar)
Berto, F. and M. Plebani, 2015, Ontology and Metaontology: A Contemporary Guide, London: Bloomsbury Academic. (Scholar)
Brouwer, L.E.J., 1912, “Intuitionism and Formalism,” reprinted in Benacerraf and Putnam (1983), 77–89. (Scholar)
–––, 1948, “Consciousness, Philosophy, and Mathematics,” reprinted in Benacerraf and Putnam (1983), 90–96. (Scholar)
Bueno, O., 2003, “Is It Possible to Nominalize Quantum Mechanics?,” Philosophy of Science, 70: 1424–36. (Scholar)
–––, 2005, “Dirac and the Dispensability of Mathematics,” Studies in History and Philosophy of Modern Physics, 36: 465–90. (Scholar)
–––, 2009, “Mathematical Fictionalism,” in New Waves in Philosophy of Mathematics, O. Bueno and Ø. Linnebo (eds.), Hampshire: Palgrave Macmillan, pp. 59–79. (Scholar)
Burgess, J., 1983, “Why I am Not a Nominalist,” Notre Dame Journal of Formal Logic, 24: 93–105. (Scholar)
–––, 2004, “Mathematics and Bleak House,” Philosophia Mathematica, 12: 18–36. (Scholar)
Burgess, J. and G. Rosen, 1997, A Subject With No Object, New York: Oxford University Press. (Scholar)
Chihara, C., 1990, Constructibility and Mathematical Existence, Oxford: Oxford University Press. (Scholar)
–––, 2004, A Structuralist Account of Mathematics, Oxford: Oxford University Press. (Scholar)
–––, 2010, “New Directions for Nominalist Philosophers of Mathematics,” Synthese, 176: 153–75. (Scholar)
Cole, J., 2009, “Creativity, Freedom, and Authority: A New Perspective on the Metaphysics of Mathematics,” Australasian Journal of Philosophy, 87: 589–608. (Scholar)
Colyvan, M., 2001, The Indispensability of Mathematics, New York: Oxford University Press. (Scholar)
–––, 2002, “Mathematics and Aesthetic Considerations in Science,” Mind, 111: 69–74. (Scholar)
–––, 2010, “There is No Easy Road to Nominalism,” Mind, 119: 285–306. (Scholar)
Contessa, G., 2016, “It Ain’t Easy: Fictionalism, Deflationism, and Easy Arguments in Ontology,” Mind, 125: 1057–73. (Scholar)
Corkum, P., 2012, “Aristotle on Mathematical Truth,” British Journal for the History of Philosophy, 20: 763–76. (Scholar)
Curry, H.B., 1951, Outlines of a Formalist Philosophy of Mathematics, Amsterdam: North-Holland. (Scholar)
Daly, C., 2006, “Mathematical Fictionalism—No Comedy of Errors,” Analysis, 66: 208–16. (Scholar)
–––, 2008, “Fictionalism and the Attitudes,” Philosophical Studies, 139: 423–40. (Scholar)
Daly, C. and S. Langford, 2009, “Mathematical Explanation and Indispensability Arguments,” Philosophical Quarterly, 59: 641–58. (Scholar)
Dorr, C., 2008, “There are No Abstract Objects,” in Contemporary Debates in Metaphysics, T. Sider, J. Hawthorne, and D. Zimmerman (eds.), Oxford: Blackwell Publishing, pp. 12–64. (Scholar)
Field, H., 1980, Science Without Numbers, Princeton, NJ: Princeton University Press. (Scholar)
–––, 1989, Realism, Mathematics, and Modality, New York: Basil Blackwell. (Scholar)
–––, 1998, “Mathematical Objectivity and Mathematical Objects,” in Contemporary Readings in the Foundations of Metaphysics, C. MacDonald and S. Laurence (eds.), Oxford: Basil Blackwell, pp. 387–403. (Scholar)
–––, 2016, Science Without Numbers,, Second Edition, Oxford: Oxford University Press. (Scholar)
Frege, G., 1884, Der Grundlagen die Arithmetik. Translated by J.L. Austin as The Foundations of Arithmetic, Oxford: Basil Blackwell, 1953. (Scholar)
–––, 1893–1903, Grundgesetze der Arithmetik. Translated (in part) by M. Furth as The Basic Laws of Arithmetic, Berkeley, CA: University of California Press, 1964. (Scholar)
–––, 1919, “The Thought: A Logical Inquiry,” reprinted in Essays on Frege, E.D. Klemke (ed.), Urbana, IL: University of Illinois Press, 1968, 507–35. (Scholar)
Gödel, K., 1964, “What is Cantor’s Continuum Problem?,” reprinted in Benacerraf and Putnam (1983), 470–85. (Scholar)
Hale, R., 1987, Abstract Objects, Oxford: Basil Blackwell. (Scholar)
Hellman, G., 1989, Mathematics Without Numbers, Oxford: Clarendon Press. (Scholar)
–––, 1998, “Maoist Mathematics?,” Philosophia Mathematica, 6: 334–45. (Scholar)
Heyting, A., 1956, Intuitionism, Amsterdam: North-Holland. (Scholar)
Hilbert, D., 1899, Grundlagen der Geometrie. Translated by E. Townsend as Foundations of Geometry, La Salle, IL: Open Court, 1959. (Scholar)
Hoffman, S., 2004, “Kitcher, Ideal Agents, and Fictionalism,” Philosophia Mathematica, 12: 3–17. (Scholar)
Hofweber, T., 2005, “Number Determiners, Numbers, and Arithmetic,” The Philosophical Review, 114: 179–225. (Scholar)
Horgan, T., 1984, “Science Nominalized,” Philosophy of Science, 51: 529–49. (Scholar)
Horwich, P., 1991, “On the Nature and Norms of Theoretical Commitment,” Philosophy of Science, 58: 1–14. (Scholar)
Husserl, E., 1891, Philosophie der Arithmetik, Leipzig: C.E.M. Pfeffer. (Scholar)
Katz, J., 1981, Language and Other Abstract Objects. Totowa, NJ: Rowman & Littlefield, and Oxford: Blackwell. (Scholar)
–––, 1998, Realistic Rationalism, Cambridge, MA: MIT Press. (Scholar)
Kitcher, P., 1984, The Nature of Mathematical Knowledge, Oxford: Oxford University Press. (Scholar)
Lear, J., 1982, “Aristotle’s Philosophy of Mathematics,” The Philosophical Review, 91: 161–92. (Scholar)
Leng, M., 2005a, “Revolutionary Fictionalism: A Call to Arms,” Philosophia Mathematica, 13: 277–93. (Scholar)
–––, 2005b, “Mathematical Explanation,” in Mathematical Reasoning and Heuristics, C. Cellucci and D. Gillies (eds.), London: King’s College Publications, pp. 167–89. (Scholar)
–––, 2010, Mathematics and Reality, Oxford: Oxford University Press. (Scholar)
Liggins, D., 2010, “The Autism Objection to Pretence Theory,” Philosophical Quarterly, 60: 764–82. (Scholar)
Linnebo, Ø., 2006, “Epistemological Challenges to Mathematical Platonism,” Philosophical Studies, 129: 545–74. (Scholar)
Linsky, B. and E. Zalta, “Naturalized Platonism and Platonized Naturalism,” Journal of Philosophy, 92: 525–55. (Scholar)
Liston, M., 2003–04, “Thin- and Full-Blooded Platonism,” The Review of Modern Logic, 9: 129–61. (Scholar)
Maddy, P., 1990, Realism in Mathematics, Oxford: Oxford University Press. (Scholar)
–––, 1995, “Naturalism and Ontology,” Philosophia Mathematica, 3: 248–70. (Scholar)
–––, 1997, Naturalism in Mathematics, Oxford: Clarendon Press. (Scholar)
Malament, D., 1982, Review of Field, Science Without Numbers, Journal of Philosophy, 79: 523–34. (Scholar)
Marcus, R., 2015, Autonomy Platonism and the Indispensability Argument, Lanham, MD: Rowman and Littlefield. (Scholar)
McEvoy, M., 2012, “Platonism and the ‘Epistemic Role Puzzle’,” Philosophia Mathematica, 20: 289–304. (Scholar)
Melia, J., 2000, “Weaseling Away the Indispensability Argument,” Mind, 109: 455–79. (Scholar)
–––, 2002, “Response to Colyvan,” Mind, 111: 75–79. (Scholar)
Moltmann, F., 2013, “Reference to Numbers in Natural Language,” Philosophical Studies, 162: 499–536. (Scholar)
Mortensen, C., 1998, “On the Possibility of Science Without Numbers,” Australasian Journal of Philosophy, 76: 182–97. (Scholar)
O’Leary-Hawthorne, J., 1994, “What Does van Fraassen’s Critique of Scientific Realism Show?,” The Monist, 77: 128–45. (Scholar)
Parsons, C., 1971, “Ontology and Mathematics,” Philosophical Review, 80: 151–76. (Scholar)
–––, 1990, “The Structuralist View of Mathematical Objects,” Synthese, 84: 303–46. (Scholar)
Plebani, M., 2018, “Fictionalism Versus Deflationism: A New Look,” Philosophical Studies, 175: 301–16. (Scholar)
Putnam, H., 1967a, “Mathematics Without Foundations,” reprinted in Benacerraf and Putnam (1983), 295–311. (Scholar)
–––, 1967b, “The Thesis that Mathematics is Logic,” in Bertrand Russell, Philosopher of the Century, R. Schoenman (ed.), London: Allen and Unwin. (Scholar)
–––, 1971, Philosophy of Logic, New York: Harper and Row. (Scholar)
Quine, W.V.O., 1948, “On What There Is,” reprinted in Quine (1961), 1–19. (Scholar)
–––, 1951, “Two Dogmas of Empiricism,” reprinted in Quine (1961), 20–46. (Scholar)
–––, 1961, From a Logical Point of View, 2^nd ed., New York: Harper and Row. (Scholar)
Rayo, A., 2008, “On Specifying Truth Conditions,” Philosophical Studies, 47: 163–181. (Scholar)
–––, 2013, The Construction of Logical Space, Oxford: Oxford University Press. (Scholar)
Resnik, M., 1985, “How Nominalist is Hartry Field’s Nominalism?” The Philosophical Review, 117: 385–443. (Scholar)
–––, 1997, Mathematics as a Science of Patterns, Oxford: Oxford University Press. (Scholar)
Rosen, G., 1990, “Modal Fictionalism,” Mind, 99: 327–54. (Scholar)
–––, 2001, “Nominalism, Naturalism, Epistemic Relativism,” in Philosophical Topics, 15: 60–91. (Scholar)
Russell, B., 1912, The Problems of Philosophy. Reprinted 1959, Oxford: Oxford University Press. (Scholar)
Shapiro, S., 1983, “Conservativeness and Incompleteness,” Journal of Philosophy, 80: 521–31. (Scholar)
–––, 1997, Philosophy of Mathematics: Structure and Ontology, New York: Oxford University Press. (Scholar)
Sober, E., 1993, “Mathematics and Indispensability,” The Philosophical Review, 102: 35–57. (Scholar)
Stanley, J., 2001, “Hermeneutic Fictionalism,” Midwest Studies in Philosophy, 25(1): 36–71. (Scholar)
Steiner, M., 1975, Mathematical Knowledge, Ithaca, NY: Cornell University Press. (Scholar)
Szabo, Z., 2001, “Fictionalism and Moore’s Paradox,” Canadian Journal of Philosophy, 31: 293–307. (Scholar)
Thomas, R., 2000, “Mathematics and Fiction I: Identification,” Logique et Analyse, 43: 301–40. (Scholar)
–––, 2002, “Mathematics and Fiction II: Analogy,” Logique et Analyse, 45: 185–228. (Scholar)
Thomasson, A., 1999, Fiction and Metaphysics, Cambridge: Cambridge University Press. (Scholar)
–––, 2013, “Fictionalism Versus Deflationism,” Mind, 122: 1023–51. (Scholar)
van Fraassen, B., 1980, The Scientific Image, Oxford: Clarendon Press. (Scholar)
Walton, K., 1990, Mimesis as Make-Believe, Cambridge, MA: Harvard University Press. (Scholar)
Wittgenstein, L., 1956, Remarks on the Foundations of Mathematics, Oxford: Basil Blackwell. (Scholar)
Wright, C., 1983, Frege’s Conception of Numbers as Objects, Aberdeen, Scotland: Aberdeen University Press. (Scholar)
Yablo, S., 2002a, “Go Figure: A Path Through Fictionalism,” Midwest Studies in Philosophy, 25: 72–102. (Scholar)
–––, 2002b, “Abstract Objects: A Case Study,” Noûs, 36 (Supplementary Volume 1): 220–240. (Scholar)
–––, 2005, “The Myth of the Seven,” in Fictionalism in Metaphysics, M. Kalderon (ed.), New York: Oxford University Press, pp. 88–115. (Scholar)
–––, 2012, “Explanation, Extrapolation, and Existence,” Mind, 121: 1007–29. (Scholar)
–––, 2017, “If-Thenism,” Australasian Philosophical Review, 1: 115–33. (Scholar)
Yi, B., 2002, Understanding the Many, New York and London: Routledge. (Scholar)
Zalta, E., 1988, Intensional Logic and the Metaphysics of Intentionality, Cambridge, MA: Bradford/MIT Press. (Scholar)

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