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Applying Pure Mathematics

Published online by Cambridge University Press:  01 April 2022

Anthony Peressini
Anthony Peressini*
Affiliation:
Marquette University
*
†Department of Philosophy, Marquette University, Milwaukee, WI 53201–1881; e-mail: [email protected]
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Abstract

Much of the current thought concerning mathematical ontology and epistemology follows Quine and Putnam in looking to the indispensable application of mathematics in science. A standard assumption of the indispensability approach is some version of confirmational holism, i.e., that only “sufficiently large” sets of beliefs “face the tribunal of experience.” In this paper I develop and defend a distinction between a pure mathematical theory and a mathematized scientific theory in which it is applied. This distinction allows for the possibility that pure mathematical theories are systematically insulated from such confirmation in virtue of their being distinct from the “sufficiently large” blocks of scientific theory that are empirically confirmed.

Type
Mathematics and Science
Information
Philosophy of Science , Volume 66 , Issue S3: Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers Sep., 1999 , 1999 , pp. S1 - S13
Copyright
Copyright © 1999 by the Philosophy of Science Association

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Footnotes

‡

I thank Mike Byrd, Malcolm Forster, Penelope Maddy, Michael Resnik, Elliott Sober, and Mark Steiner for comments and discussion.

References

Gladkii, Aleksei V. (1983), Elements of Mathematical Linguistics. New York: Mouton Publishers.CrossRefGoogle Scholar
Gross, Maurice (1972), Mathematical Models in Linguistics. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Guicciardini, Niccolo (1989), The Development of Newtonian Calculus in Britain, 1700–1800. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Maddy, Penelope (1992), “Indispensability and Practice”, Journal of Philosophy 89: 275–289.CrossRefGoogle Scholar
Morrison, Michael A. (1990), Understanding Quantum Physics: A User's Manual. Englewood Cliffs, NJ: Prentice Hall.Google Scholar
Partee, Barbara H., Meulen, Alice ter, and Wall, Robert E. (1990), Mathematical Methods in Linguistics. Boston: Kluwer Academic.Google Scholar
Peressini, Anthony F. (1997), “Troubles with Indispensability: Applying Pure Mathematics in Physical Theory”, Philosophia Mathematica 5: 901–918.CrossRefGoogle Scholar
Resnik, Michael (1990), “Between Mathematics and Physics”, in A. Fine, M. Forbes, and L. Wessels (eds.), PSA 1990, vol. 2. East Lansing, MI: Philosophy of Science Association, 369–378.Google Scholar
Resnik, Michael. (1992), “Applying Mathematics and the Indispensability Argument”, in Echeverria, Javier et al. (eds.), The Space of Mathematics. New York: Walter de Gruyter.Google Scholar
Shelton, Laverne (1980), “The Abstract and the Concrete: How Much Difference Does This Distinction Make?”, unpublished paper delivered at APA eastern division meetings.Google Scholar
Sober, Elliott (1993), “Mathematics and Indispensability”, Philosophical Review 102: 35–57.CrossRefGoogle Scholar
Steiner, Mark (1978), “Mathematics, Explanation, and Scientific Knowledge”, Noûs 12: 17–28.CrossRefGoogle Scholar
Steiner, Mark. (1989), “The Application of Mathematics to Natural Science”, Journal of Philosophy 86: 449–480.CrossRefGoogle Scholar
Steiner, Mark. (1992), “Mathematical Rigor in Physics” In Physics (ed.), Proof and Knowledge in Mathematics. New York: Routledge.Google Scholar
Steiner, Mark. (1995), “The Applicabilities of Mathematics”, Philosophia Mathematica (III) 3: 129–156.CrossRefGoogle Scholar
Sudberry, Anthony (1986), Quantum Mechanics and the Particles of Nature: An Outline for Mathematicians. Cambridge: Cambridge University Press.Google Scholar
Vineberg, Susan (1996), “Confirmation and the Indispensability of Mathematics to Science”, Philosophy of Science 63 (Proceedings): S256–S263.CrossRefGoogle Scholar
Wall, Robert E. (1972), Introduction to Mathematical Linguistics. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Weinberg, Steven (1986), “Mathematics: The Unifying Thread in Science”, Gina Kolata (ed.), Notices of the American Mathematical Society 33, 716–733.Google Scholar