Abstract
I argue on the basis of an example, Fourier theory applied to the problem of vibration, that Field's program for nominalizing science is unlikely to succeed generally, since no nominalistic variant will provide us with the kind of physical insight into the phenomena that the standard theory supplies. Consideration of the same example also shows, I argue, that some of the motivation for mathematical fictionalism, particularly the alleged problem of cognitive access, is more apparent than real.
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References
Benacerraf, P.: 1973, ‘Mathematical Truth’,Journal of Philosophy 70, 661–79.
Chihara, C.: 1990,Constructibility and Mathematical Existence, Clarendon Press, Oxford.
Dettman, J.: 1969,Mathematical Methods in Physics and Engineering, McGraw-Hill, New York.
Field, H.: 1980,Science Without Numbers, Princeton University Press, Princeton.
Field, H.: 1989,Realism, Mathematics and Modality, Basil Blackwell, Oxford.
Grattan-Guinness, I.: 1970,The Development of the Foundations of Analysis from Euler to Riemann, MIT Press, Cambridge, Massachusetts.
Hellman, G.: 1989,Mathematics without Numbers: Towards Modal Structural Interpretation, Oxford University Press, Oxford.
Kline, M.: 1972,Mathematical Thought from Ancient to Modern Times, Oxford University Press, Oxford.
Lay-Yong, L.: 1986, ‘The Conceptual Origins of our Numeral System and the Symbolic Form of Algebra’,Archive for the History of Exact Sciences 36, 183–95.
Liston, M.: forthcoming, ‘How Abstract Objects Strike Us’,Dialectica.
Maddy, P.: 1990,Realism in Mathematics, Clarendon Press, Oxford.
Malament, D.: 1982, Review of Field (1980),Journal of Philosophy 79, 523–34.
Pipes, L.: 1958,Applied Mathematics for Engineers and Physicists, McGraw-Hill, New York.
Putnam, H.: 1975, ‘What is Mathematical Truth?’,Mathematics, Matter and Method, Cambridge University Press, Cambridge, pp. 60–78.
Resnik, M.: 1981, ‘Mathematics as a Science of Patterns: Ontology and Reference’,Noûs 15, 529–50.
Resnik, M.: 1983, Review of Field (1980),Noûs 27, 514–19.
Robinson, B.: 1953, ‘Concerning the Frequencies Resulting from Distortion’,American Journal of Physics 21, 391.
Schwartz, R.: 1986, ‘I'm Going to Make You a Star’,Midwest Studies in Philosophy 11, 427–39.
Shapiro, S.: 1983a, ‘Conservativeness and Completeness’,Journal of Philosophy 81, 521–31.
Shapiro, S.: 1983b, ‘Mathematics and Reality’,Philosophy of Science 50, 523–48.
Slater, J. and N. Frank: 1947,Mechanics, McGraw-Hill, New York.
Smail, L.: 1925,History and Synopsis of the Theory of Summable Infinite Processes, University of Oregon Press, Eugene, Oregon.
Steiner, M.: 1978, ‘Mathematics, Explanation, and Scientific Knowledge’,Noûs 12, 17–28.
Wilson, M.: 1993, ‘Honorable Intensions’, Steven J. Wagner and Richard Warner (eds.),Naturalism: A Critical Appraisal, University of Notre Dame Press, Notre Dame, Indiana.
Wood, A.: 1966,Acoustics, Dover Publications, New York.
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I would like to thank Mark Wilson, who first suggested that I look at the literature on applied Fourier theory, and whose paper ‘Honorable Intensions’ (1993) helped me understand it better. I would also like to acknowledge gratefully support from a UWM Graduate School Research Committee Award.
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Liston, M. Taking mathematical fictions seriously. Synthese 95, 433–458 (1993). https://doi.org/10.1007/BF01063881
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DOI: https://doi.org/10.1007/BF01063881