Linked bibliography for the SEP article "Fictionalism in the Philosophy of Mathematics" by Mark Balaguer |
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- Armour-Garb, B., forthcoming, “Understanding Mathematical Fictionalism,” Philosophia Mathematica. (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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- Maddy, P., 1990, Realism in Mathematics, Oxford: Oxford University Press. (Scholar)
- Malament, D., 1982, Review of Field, Science Without Numbers, Journal of Philosophy, 79: 523–34. (Scholar)
- Melia, J., 2000, “Weaseling Away the Indispensability Argument,” Mind, 109: 455–79. (Scholar)
- –––, 2002, “Response to Colyvan,” Mind, 111: 75–79. (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)
- Priest, G., 2003, “Meinongianism and the Philosophy of Mathematics,” Philosophia Mathematica, 11: 3–15. (Scholar)
- –––, 2005, Towards Non-Being, Oxford: Oxford University Press. (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, 2nd ed., New York: Harper and Row. (Scholar)
- Resnik, M., 1985, “How Nominalist is Hartry Field's Nominalism?” Philosophical Studies, 47: 163–181. (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)
- Routley, R., 1980, Exploring Meinong's Jungle and Beyond, Canberra: RSSS, Australian National University. (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)
- Stanley, J., 2002, “Hermeneutic Fictionalism,” Midwest Studies in Philosophy, 25: 36–71. (Scholar)
- Steiner, M., 1975, Mathematical Knowledge, Ithaca, NY: Cornell University Press. (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)
- 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)
- Zalta, E., 1988, Intensional Logic and the Metaphysics of Intentionality, Cambridge, MA: Bradford/MIT Press. (Scholar)
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