Linked bibliography for the SEP article "Indispensability Arguments in the Philosophy of Mathematics" by Mark Colyvan |
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Although the indispensability argument is to be found in many places in Quine's writings (including 1976; 1980a; 1980b; 1981a; 1981c), the locus classicus is Putnam's short monograph Philosophy of Logic (included as a chapter of the second edition of the third volume of his collected papers (Putnam, 1979b)). See also Putnam (1979a) and the introduction of Field (1989) which has an excellent outline of the argument. Colyvan (2001) is a sustained defence of the argument.
See Chihara (1973), and Field (1980; 1989) for attacks on the second premise and Colyvan (1999b; 2001), Lyon and Colyvan (2008), Maddy (1990), Malament (1982), Resnik (1985), Shapiro (1983) and Urquhart (1990) for criticisms of Field's program. For a fairly comprehensive look at nominalist strategies in the philosophy of mathematics (including a good discussion of Field's program), see Burgess and Rosen (1997), while Feferman (1993) questions the amount of mathematics required for empirical science. See Azzouni (1997; 2004), Balaguer (1996b; 1998), Leng (2002; 2010), Maddy (1992; 1995; 1997), Melia (2000; 2002), Peressini (1997), Pincock (2004), Sober (1993), Vineberg (1996) and Yablo (1998; 2005) for attacks on the first premise. Baker (2001; 2005), Colyvan (1998; 1999a; 2001; 2002; 2007; 2010), Hellman (1999) and Resnik (1995a; 1997) reply to some of these objections.
For variants of the Quinean indispensability argument see Maddy (1992) and Resnik (1995a).
- Azzouni, J., 1997, “Applied Mathematics, Existential Commitment and the Quine-Putnam Indispensability Thesis”, Philosophia Mathematica, 5(3): 193–209. (Scholar)
- Azzouni, J., 2004, Deflating Existential Consequence, New York: Oxford University Press. (Scholar)
- Baker, A., 2001, “Mathematics, Indispensability and Scientific Progress”, Erkenntnis, 55(1): 85–116. (Scholar)
- Baker, A., 2005, “Are There Genuine Mathematical Explanations of Physical Phenomena?”, Mind, 114(454): 223–238. (Scholar)
- Balaguer, M., 1996a, “Towards a Nominalization of Quantum Mechanics”, Mind, 105(418): 209–226. (Scholar)
- Balaguer, M., 1996b, “A Fictionalist Account of the Indispensable Applications of Mathematics”, Philosophical Studies, 83(3): 291–314. (Scholar)
- Balaguer, M., 1998, Platonism and Anti-Platonism in Mathematics, New York: Oxford University Press. (Scholar)
- Benacerraf, P., 1983a, “What Numbers Could Not Be”, reprinted in Benacerraf and Putnam (1983), pp. 272–294. (Scholar)
- Benacerraf, P., 1983b, “Mathematical Truth”, reprinted in Benacerraf and Putnam (1983), pp. 403–420 and in Hart (1996), pp. 14–30. (Scholar)
- Benacerraf, P. and Putnam, H. (eds.), 1983, Philosophy of Mathematics: Selected Readings, 2nd edition, Cambridge: Cambridge University Press. (Scholar)
- Bueno, O., 2003, “Is it Possible to Nominalize Quantum Mechanics?”, Philosophy of Science, 70(5): 1424–1436. (Scholar)
- Burgess, J., 1983, “Why I Am Not a Nominalist”, Notre Dame Journal of Formal Logic, 24(1): 93–105. (Scholar)
- Burgess, J. and Rosen, G., 1997, A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics, Oxford: Clarendon. (Scholar)
- Chihara, C., 1973, Ontology and the Vicious Circle Principle, Ithaca, NY: Cornell University Press. (Scholar)
- Colyvan, M., 1998, “In Defence of Indispensability”, Philosophia Mathematica, 6(1): 39–62. (Scholar)
- Colyvan, M., 1999a, “Contrastive Empiricism and Indispensability”, Erkenntnis, 51(2–3): 323–332. (Scholar)
- Colyvan, M., 1999b, “Confirmation Theory and Indispensability”, Philosophical Studies, 96(1): 1–19. (Scholar)
- Colyvan, M., 2001, The Indispensability of Mathematics, New York: Oxford University Press. (Scholar)
- Colyvan, M., 2002, “Mathematics and Aesthetic Considerations in Science”, Mind, 111(441): 69–74. (Scholar)
- Colyvan, M., 2007, “Mathematical Recreation Versus Mathematical Knowledge”, in M. Leng, A. Paseau, and M. Potter (eds.), Mathematical Knowledge, Oxford: Oxford University Press, pp. 109–122. (Scholar)
- Colyvan, M., 2010, “There is No Easy Road to Nominalism”, Mind, 119(474): 285–306. (Scholar)
- Feferman, S., 1993, “Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics”, Proceedings of the Philosophy of Science Association, 2: 442–455. (Scholar)
- Field, H.H., 1980, Science Without Numbers: A Defence of Nominalism, Oxford: Blackwell. (Scholar)
- Field, H.H., 1989, Realism, Mathematics and Modality, Oxford: Blackwell. (Scholar)
- Hart, W.D. (ed.), 1996, The Philosophy of Mathematics, Oxford: Oxford University Press. (Scholar)
- Hellman, G., 1999, “Some Ins and Outs of Indispensability: A Modal-Structural Perspective”, in A. Cantini, E. Casari and P. Minari (eds.), Logic and Foundations of Mathematics, Dordrecht: Kluwer, pp. 25–39. (Scholar)
- Irvine, A.D. (ed.), 1990, Physicalism in Mathematics, Dordrecht: Kluwer. (Scholar)
- Kitcher, P., 1984, The Nature of Mathematical Knowledge, New York: Oxford University Press. (Scholar)
- Leng, M., 2002, “What's Wrong with Indispensability? (Or, The Case for Recreational Mathematics)”, Synthese, 131(3): 395–417. (Scholar)
- Leng, M., 2010, Mathematics and Reality, Oxford: Oxford University Press. (Scholar)
- Lyon, A. and Colyvan, M., 2008, “The Explanatory Power of Phase Spaces”, Philosophia Mathematica, 16(2): 227–243. (Scholar)
- Maddy, P., 1990, “Physicalistic Platonism”, in A.D. Irvine (ed.), Physicalism in Mathematics, Dordrecht: Kluwer, pp. 259–289. (Scholar)
- Maddy, P., 1992, “Indispensability and Practice”, Journal of Philosophy, 89(6): 275–289. (Scholar)
- Maddy, P., 1995, “Naturalism and Ontology”, Philosophia Mathematica, 3(3): 248–270. (Scholar)
- Maddy, P., 1997, Naturalism in Mathematics, Oxford: Clarendon Press. (Scholar)
- Maddy, P., 1998, “How to be a Naturalist about Mathematics”, in H.G. Dales and G. Oliveri (eds.), Truth in Mathematics, Oxford: Clarendon, pp. 161–180. (Scholar)
- Malament, D., 1982, “Review of Field's Science Without Numbers”, Journal of Philosophy, 79(9): 523–534 and reprinted in Resnik (1995b), pp. 75–86. (Scholar)
- Melia, J., 2000, “Weaseling Away the Indispensability Argument”, Mind, 109(435): 455–479 (Scholar)
- Melia, J., 2002, “Response to Colyvan”, Mind, 111(441): 75–80. (Scholar)
- Parsons, C., 1980, “Mathematical Intuition”, Proceedings of the Aristotelian Society, 80: 145–168; reprinted in Resnik (1995b), pp. 589–612 and in Hart (1996), pp. 95–113. (Scholar)
- Parsons, C., 1983, “Quine on the Philosophy of Mathematics”, in Mathematics in Philosophy: Selected Essays, Ithaca, NY: Cornell University Press, pp. 176–205. (Scholar)
- Peressini, A., 1997, “Troubles with Indispensability: Applying Pure Mathematics in Physical Theory”, Philosophia Mathematica, 5(3): 210–227. (Scholar)
- Pincock, C., 2004, “A Revealing Flaw in Colyvan's Indispensability Argument”, Philosophy of Science, 71(1): 61–79. (Scholar)
- Putnam, H., 1979a, “What is Mathematical Truth”, in Mathematics Matter and Method: Philosophical Papers, Volume 1, 2nd edition, Cambridge: Cambridge University Press, pp. 60–78. (Scholar)
- Putnam, H., 1979b, “Philosophy of Logic”, reprinted in Mathematics Matter and Method: Philosophical Papers, Volume 1, 2nd edition, Cambridge: Cambridge University Press, pp. 323–357. (Scholar)
- Quine, W.V., 1960, Word and Object, Cambridge, MA: MIT Press. (Scholar)
- Quine, W.V., 1976, “Carnap and Logical Truth” reprinted in The Ways of Paradox and Other Essays, revised edition, Cambridge, MA: Harvard University Press, pp. 107–132 and in Benacerraf and Putnam (1983), pp. 355–376. (Scholar)
- Quine, W.V., 1980a, “On What There Is”, reprinted in From a Logical Point of View, 2nd edition, Cambridge, MA: Harvard University Press, pp. 1–19. (Scholar)
- Quine, W.V., 1980b, “Two Dogmas of Empiricism”, reprinted in From a Logical Point of View, 2nd edition, Cambridge, MA: Harvard University Press, pp. 20–46; reprinted in Hart (1996), pp. 31–51 (Page references are to the first reprinting). (Scholar)
- Quine, W.V., 1981a, “Things and Their Place in Theories”, in Theories and Things, Cambridge, MA: Harvard University Press, pp. 1–23. (Scholar)
- Quine, W.V., 1981b, “Five Milestones of Empiricism”, in Theories and Things, Cambridge, MA: Harvard University Press, pp. 67–72. (Scholar)
- Quine, W.V., 1981c, “Success and Limits of Mathematization”, in Theories and Things, Cambridge, MA: Harvard University Press, pp. 148–155. (Scholar)
- Quine, W.V., 1984, “Review of Parsons', Mathematics in Philosophy,” Journal of Philosophy, 81(12): 783–794. (Scholar)
- Quine, W.V., 1986, “Reply to Charles Parsons”, in L. Hahn and P. Schilpp (eds.), The Philosophy of W.V. Quine, La Salle, ILL: Open Court, pp. 396–403. (Scholar)
- Resnik, M.D., 1985, “How Nominalist is Hartry Field's Nominalism”, Philosophical Studies, 47: 163–181. (Scholar)
- Resnik, M.D., 1995a, “Scientific Vs Mathematical Realism: The Indispensability Argument”, Philosophia Mathematica, 3(2): 166–174. (Scholar)
- Resnik, M.D. (ed.), 1995b, Mathematical Objects and Mathematical Knowledge, Aldershot (UK): Dartmouth. (Scholar)
- Resnik, M.D., 1997, Mathematics as a Science of Patterns, Oxford: Clarendon Press. (Scholar)
- Shapiro, S., 1983, “Conservativeness and Incompleteness”, Journal of Philosophy, 80(9): 521–531; reprinted in Resnik (1995b), pp. 87–97 and in Hart (1996), pp. 225–234 (Scholar)
- Sober, E., 1993, “Mathematics and Indispensability”, Philosophical Review, 102(1): 35–57. (Scholar)
- Urquhart, A., 1990, “The Logic of Physical Theory”, in A.D. Irvine (ed.), Physicalism in Mathematics, Dordrecht: Kluwer, pp. 145–154. (Scholar)
- Vineberg, S., 1996, “Confirmation and the Indispensability of Mathematics to Science”, PSA 1996 (Philosophy of Science, supplement to vol. 63), pp. 256–263. (Scholar)
- Yablo, S., 1998, “Does Ontology Rest on a Mistake?”, Aristotelian Society (Supplementary Volume), 72: 229–261. (Scholar)
- Yablo, S., 2005, “The Myth of the Seven”, in M.E. Kalderon (ed.), Fictionalism in Metaphysics, Oxford: Oxford University Press, pp. 90–115. (Scholar)
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