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Reliability in Mathematical Physics

Published online by Cambridge University Press:  01 April 2022

Michael Liston
Michael Liston*
Affiliation:
Department of Philosophy, University of Wisconsin—Milwaukee
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Abstract

In this paper I argue three things: (1) that the interactionist view underlying Benacerraf's (1973) challenge to mathematical beliefs renders inexplicable the reliability of most of our beliefs in physics; (2) that examples from mathematical physics suggest that we should view reliability differently; and (3) that abstract mathematical considerations are indispensable to explanations of the reliability of our beliefs.

Type
Research Article
Information
Philosophy of Science , Volume 60 , Issue 1 , March 1993 , pp. 1 - 21
Copyright
Copyright © Philosophy of Science Association 1993

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Footnotes

†

I am indebted to many for help with this paper: to Yvon Gauthier, Henri Lauener, and Ruth Marcus for criticisms of a distant relative at the World Congress in Philosophy, Brighton, England, 1988; to ACLS for a travel grant; to my colleagues, Mark Kaplan, John Koethe, Bob Schwartz, and Julius Sensat; to Jeff King; to an anonymous referee for comments on a related paper; and especially to Mark Wilson for many suggestions.

‡

Send reprint requests to the author, Department of Philosophy, University of Wisconsin at Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA.

References

Benacerraf, P. (1973), “Mathematical Truth”, Journal of Philosophy 70: 661–679.CrossRefGoogle Scholar
Boyd, R. (1973), “Realism, Underdetermination, and a Causal Theory of Evidence”, Noûs 7: 1–12.CrossRefGoogle Scholar
Chihara, C. (1990), Constructibility and Mathematical Existence. Oxford: Clarendon Press.Google Scholar
Duhem, P. (1954), The Aim and Structure of Physical Theory. Translated by P. Wiener. New York: Atheneum Press.CrossRefGoogle Scholar
Field, H. (1980), Science Without Numbers. Princeton: Princeton University Press.Google Scholar
Fodor, J. (1987), Psychosemantics. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Kline, M. (1972), Mathematical Thought from Ancient to Modern Times. Oxford: Oxford University Press.Google Scholar
Landau, E. D. and Lifshitz, E. M. (1969), Mechanics. Oxford: Pergamon Press.Google Scholar
Liston, M. (forthcoming), “Taking Mathematical Fictions Seriously”, Synthese.Google Scholar
Maddy, P. (1990), Realism in Mathematics. Oxford: Clarendon Press.Google Scholar
Malament, D. (1982), Review of Science Without Numbers, by Hartry Field. Journal of Philosophy 79: 523–534.Google Scholar
McGinn, C. (1981), “Modal Reality”, in Healey, R. (ed.), Reduction, Time and Reality. Cambridge, England: Cambridge University Press, pp. 143–187.Google Scholar
Miller, R. (1987), Fact and Method. Princeton: University of Princeton Press.Google Scholar
Putnam, H. (1975), “What is Mathematical Truth?” in Mathematics, Matter and Method. Cambridge, England: Cambridge University Press, pp. 60–78.Google Scholar
Shapiro, S. (1983), “Mathematics and Reality”, Philosophy of Science 50: 523–548.CrossRefGoogle Scholar
Truesdell, C. (1968), Essays in the History of Mechanics. New York: Springer-Verlag.CrossRefGoogle Scholar
van Fraassen, B. (1975), “Critical Notice: Hilary Putnam's Philosophy of Logic”, Philosophy of Logic 4: 731–743.Google Scholar
van Fraassen, B. (1980), The Scientific Image. Oxford: Clarendon Press.CrossRefGoogle Scholar
Wilson, M. (1985), “What is This Thing Called ‘Pain‘?” Pacific Philosophical Quarterly 66: 227–267.CrossRefGoogle Scholar