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What's wrong with indispensability?

Synthese 131 (3):395 - 417 (2002)

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  1. Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
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  • Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
    Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
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  • (4 other versions)Two Dogmas of Empiricism.W. V. O. Quine - 2011 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 202-220.
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  • Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
    Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...)
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  • Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
    Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
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  • Philosophy of Logic.Hilary Putnam - 1971 - New York, NY, USA: Routledge. Edited by Stephen Laurence & Cynthia Macdonald.
    First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.
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  • Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
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  • Mathematics and indispensability.Elliott Sober - 1993 - Philosophical Review 102 (1):35-57.
    Realists persuaded by indispensability arguments af- firm the existence of numbers, genes, and quarks. Van Fraassen's empiricism remains agnostic with respect to all three. The point of agreement is that the posits of mathematics and the posits of biology and physics stand orfall together. The mathematical Platonist can take heart from this consensus; even if the existence of num- bers is still problematic, it seems no more problematic than the existence of genes or quarks. If the two positions just described (...)
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  • Scientific vs. mathematical realism: The indispensability argument.Michael Resnik - 1995 - Philosophia Mathematica 3 (2):166-174.
    Penelope Maddy and Elliott Sober recently attacked the confirmational indispensability argument for mathematical realism. We cannot count on science to provide evidence for the truth of mathematics, they say, because either scientific testing fails to confirm mathematics (Sober) or too much mathematics occurs in false scientific theories (Maddy). I present a pragmatic indispensability argument immune to these objections, and show that this argument supports mathematical realism independently of scientific realism. Mathematical realism, it turns out, may be even more firmly established (...)
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  • In defence of indispensability.Mark Colyvan - 1998 - Philosophia Mathematica 6 (1):39-62.
    Indispensability arguments for realism about mathematical entities have come under serious attack in recent years. To my mind the most profound attack has come from Penelope Maddy, who argues that scientific/mathematical practice doesn't support the key premise of the indispensability argument, that is, that we ought to have ontological commitment to those entities that are indispensable to our best scientific theories. In this paper I defend the Quine/Putnam indispensability argument against Maddy's objections.
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  • Catastrophe theory as applied to the social and biological sciences: A critique.Héctor J. Sussmann & Raphael S. Zahler - 1978 - Synthese 37 (2):117 - 216.
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  • What is naturalism in mathematics, really?: A critical study of P. Maddy, Naturalism in Mathematics[REVIEW]Neil Tennant - 2000 - Philosophia Mathematica 8 (3):316-338.
    Review of PENELOPE MADDY. Naturalism in Mathematics. Oxford: Clarendon Press, 1997.
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