Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T21:51:23.394Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical Idealization

Published online by Cambridge University Press:  01 January 2022

Christopher Pincock
Get access Rights & Permissions [Opens in a new window]

Abstract

Mathematical idealizations are scientific representations that result from assumptions that are believed to be false, and where mathematics plays a crucial role. I propose a two stage account of how to rank mathematical idealizations that is largely inspired by the semantic view of scientific theories. The paper concludes by considering how this approach to idealization allows for a limited form of scientific realism.

Type
Philosophy of Mathematics and Physics
Information
Philosophy of Science , Volume 74 , Issue 5: Proceedings of the 2006 Biennial Meeting of the Philosophy of Science Association. Part I: Contributed Papers. Edited by Cristina Bicchieri and Jason Alexander , December 2007 , pp. 957 - 967
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

I would like to thank Robert Batterman, Gabriele Contessa, Eric Hiddleston, Nicholaos Jones, and Susan Vineberg for helpful discussions and encouragement.

References

Batterman, Robert (2002a), “Asymptotics and the Role of Minimal Models”, Asymptotics and the Role of Minimal Models 53:21–38.Google Scholar
Batterman, Robert (2002b), The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence. New York: Oxford University Press.Google Scholar
Batterman, Robert (2007), “On the Specialness of Special Functions (the Nonrandom Effusions of the Divine Mathematician)”, On the Specialness of Special Functions (the Nonrandom Effusions of the Divine Mathematician) 58:263–286.Google Scholar
Cartwright, Nancy (1983), How the Laws of Physics Lie. New York: Oxford University Press.CrossRefGoogle Scholar
Cartwright, Nancy (1989), Nature’s Capacities and Their Measurement. New York: Oxford University Press.Google Scholar
Cartwright, Nancy (1999), The Dappled World: A Study of the Boundaries of Science. New York: Cambridge University Press.CrossRefGoogle Scholar
Chakravartty, Anjan (2001), “The Semantic or Model-Theoretic View of Theories and Scientific Realism”, The Semantic or Model-Theoretic View of Theories and Scientific Realism 127:325–345.Google Scholar
Contessa, Gabriele (2007), “Scientific Representation, Interpretation, and Surrogative Reasoning”, Scientific Representation, Interpretation, and Surrogative Reasoning 74:48–68.Google Scholar
da Costa, Newton, and French, Steven (2003), Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning. New York: Oxford University Press.CrossRefGoogle Scholar
Demopoulos, William (2003), “On the Rational Reconstruction of Our Theoretical Knowledge”, On the Rational Reconstruction of Our Theoretical Knowledge 54:371–403.Google Scholar
Fine, Arthur (1984), “The Natural Ontological Attitude”, in Leplin, J. (ed.), Scientific Realism. Berkeley: University of California Press, 83–107.Google Scholar
Jones, Martin R. (2005), “Idealization and Abstraction: A Framework”, in Jones, Martin R. and Cartwright, Nancy (eds.), Idealization XII: Correcting the Model; Idealization and Abstraction in the Sciences. Amsterdam: Rodopi, 173–217.CrossRefGoogle Scholar
Laymon, Ronald (1995), “Experimentation and the Legitimacy of Idealization”, Experimentation and the Legitimacy of Idealization 77:353–375.Google Scholar
McMullin, Ernan (1985), “Galilean Idealization”, Galilean Idealization 16:247–273.Google Scholar
Morrison, Margaret (2000), Unifying Scientific Theories: Physical Concepts and Mathematical Structures. New York: Cambridge University Press.CrossRefGoogle Scholar
Morrison, Margaret (2005), “Approximating the Real: The Role of Idealization in Physical Theory”, in Jones, Martin R. and Cartwright, Nancy (eds.), Idealization XII: Correcting the Model; Idealization and Abstraction in the Sciences. Amsterdam: Rodopi, 145–172.Google Scholar
Steiner, Mark (2005), “Mathematics—Application and Applicability”, in Shapiro, S. (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic. New York: Oxford University Press, 625–650.CrossRefGoogle Scholar
Suárez, Mauricio (2003), “Scientific Representation: Against Similarity and Isomorphism”, Scientific Representation: Against Similarity and Isomorphism 17:225–244.Google Scholar
Suárez, Mauricio (2004), “An Inferential Conception of Scientific Representation”, An Inferential Conception of Scientific Representation 71:767–779.Google Scholar
Thomson-Jones, Martin (2006), “Models and the Semantic View”, Models and the Semantic View 73:524–535.Google Scholar
van Fraassen, Bas (1991), Quantum Mechanics: An Empiricist View. New York: Oxford University Press.CrossRefGoogle Scholar
Wilson, Mark (2006), Wandering Significance: An Essay on Conceptual Behaviour. New York: Oxford University Press.CrossRefGoogle Scholar