Abstract
For many philosophers not automatically inclined to Platonism, the indispensability argument for the existence of mathematical objectshas provided the best (and perhaps only) evidence for mathematicalrealism. Recently, however, this argument has been subject to attack, most notably by Penelope Maddy (1992, 1997),on the grounds that its conclusions do not sit well with mathematical practice. I offer a diagnosis of what has gone wrong with the indispensability argument (I claim that mathematics is indispensable in the wrong way), and, taking my cue from Mark Colyvan's (1998) attempt to provide a Quinean account of unapplied mathematics as `recreational', suggest that, if one approaches the problem from a Quinean naturalist starting point, one must conclude that all mathematics is recreational in this way.
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REFERENCES
Colyvan, M.: 1998, 'In Defence of Indispensability', Philosophia Mathematica 6, 39–62.
Field, H.: 1980, Science without Numbers, Princeton University Press, Princeton, NJ.
Maddy, P.: 1990, Realism in Mathematics, Oxford University Press, Oxford.
Maddy, P.: 1992, 'Indispensability and Practice', The Journal of Philosophy 89, 275–289.
Maddy, P.: 1997, Naturalism in Mathematics, Clarendon Press, Oxford.
Musgrave, A.: 1986, 'Arithmetical Platonism – Is Wright Wrong or Must Field Yield?', in M. Fricke (ed.), Essays in Honour of Bob Durant, Otago University Philosophy Department, Dunedin.
Putnam, H.: 1971, 'Philosophy of Logic', first published by Harper and Row, 1971; reprinted in his Mathematics, Matter and Method: Philosophical Papers, Vol. 1, Cambridge University Press, Cambridge, pp. 323–357.
Quine, W. V.: 1951, 'Two Dogmas of Empiricism', first published in Philosophical Review, Vol. 60, reprinted in W. V. Quine, From a Logical Point of View, Harvard University Press, Cambridge, MA, pp. 20–46.
Quine, W. V.: 1960, Word and Object, MIT Press, Cambridge, MA.
Resnik, M. D.: 1995, 'Scientific vs. Mathematical Realism: The Indispensability Argument', Philosophia Mathematica 3, 166–174.
Sober, E.: 1993, 'Mathematics and Indispensability', Philosophical Review 102, 35–57.
Sussmann, H. J. and R. S. Zahler: 1978, 'Catastrophe Theory as Applied to the Sociological and Biological Sciences: A Critique', Synthese 37, 117–216.
Tennant, N.: 2000, 'What is Naturalism in Mathematics, Really?', Philosophia Mathematica 8, 316–338.
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Leng, M. What's Wrong With Indispensability?. Synthese 131, 395–417 (2002). https://doi.org/10.1023/A:1016141509719
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DOI: https://doi.org/10.1023/A:1016141509719