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HOW APPLIED MATHEMATICS BECAME PURE

Published online by Cambridge University Press:  01 June 2008

PENELOPE MADDY
PENELOPE MADDY*
Affiliation:
University of California, Irvine
*
*DEPARTMENT OF LOGIC AND PHILOSOPHY OF SCIENCE, UNIVERSITY OF CALIFORNIA AT IRVINE, IRVINE, CA 92697-5100, USA. E-mail: [email protected]
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Abstract

This paper traces the evolution of thinking on how mathematics relates to the world—from the ancients, through the beginnings of mathematized science in Galileo and Newton, to the rise of pure mathematics in the nineteenth century. The goal is to better understand the role of mathematics in contemporary science.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 1 , June 2008 , pp. 16 - 41
Copyright
Copyright © Association for Symbolic Logic 2008

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References

BIBLIOGRAPHY

Arfken, G. (1985). Mathematical Methods for Physicists (third edition). San Diego, CA: Academic Press.Google Scholar
Benacerraf, P. (1973). Mathematical truth. Reprinted in Benacerraf and Putnam [1983], pp. 403–420.CrossRefGoogle Scholar
Benacerraf, P., & Putnam, H., editors. (1983). Philosophy of Mathematics (second edition). Cambridge: Cambridge University Press.Google Scholar
Brown, T., LeMay, E., Bursten, B., & Murphy, C. (2006). Chemistry: The Central Science (tenth edition). Upper Saddle River, NJ: Pearson-Prentice Hall.Google Scholar
Calinger, R. (1975). Euler's “Letters to a Princess of Germany” as an expression of his mature scientific outlook. Archive for History of Exact Sciences, 15, 211–233.CrossRefGoogle Scholar
Carnap, R. (1932). The elimination of metaphysics through logical analysis of language. Reprinted in Ayer, A. J., editor, Logical Positivism. New York: Free Press [1959], pp. 60–81.Google Scholar
Carnap, R. (1950). Empiricism, ontology and semantics. Reprinted in Benacerraf and Putnam [1983], pp. 241–257.Google Scholar
Cohen, B., & Smith, G. (2002a). Introduction to Cohen and Smith [2002b]. In Cohen and Smith [2002b], pp. 1–32.CrossRefGoogle Scholar
Cohen, B., & Smith, G., editors. (2002b). Cambridge Companion to Newton. Cambridge: Cambridge University Press.Google Scholar
Duhem, P. (1906). The Aim and Structure of Physical Theory (Wiener, P., translator) Princeton, NJ: Princeton University Press, 1954.Google Scholar
Einstein, A. (1905). On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat. Reprinted in his Investigations of the Theory of Brownian Movement (Fürth, R., editor, Cowper, A. D., translator). Mineola, NY: Dover [1956], pp. 1–18.Google Scholar
Einstein, A. (1949). Autobiographical notes. In Schilpp, P. S., editor, Albert Einstein: Philosopher-Scientist. La Salle, IL: Open Court, pp. 1–105.Google Scholar
Emch, G. (1972). Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York: Wiley.Google Scholar
Emch, G., & Liu, C. (2002) The Logic of Thermo-Statistical Physics. Berlin: Springer.CrossRefGoogle Scholar
Engel, T., & Reid, P. (2006). Thermodynamics, Statistical Thermodynamics, and Kinetics. San Francisco, CA: Pearson-Benjamin-Cummings.Google Scholar
Feynman, R., Leighton, R., & Sands, M. (1964). The Feynman Lectures on Physics, vol. 2. Reading, MA: Addison-Wesley.Google Scholar
Fourier, J. (1822). The Analytical Theory of Heat (Freeman, A., translator). Mineola, NY: Dover, 1955.Google Scholar
Fraenkel, A., Bar-Hillel, Y., & Levy, A. (1973). Foundations of Set Theory (second edition). Amsterdam: North Holland.Google Scholar
Galileo, G. (1638). Two New Sciences. (second edition, Drake, S., editor and translator). Toronto: Wall & Emerson, 1974.Google Scholar
Gödel, K. (1964). What is Cantor's continuum problem? Reprinted in Benacerraf and Putnam [1983], pp. 470–485.Google Scholar
Guicciardini, N. (2002). Analysis and synthesis in Newton's mathematical work. In Cohen and Smith [2002b], pp. 308–328.Google Scholar
Hall, A. R. (2002). Newton versus Leibniz: From geometry to metaphysics. In Cohen and Smith [2002b], pp. 431–454.CrossRefGoogle Scholar
Halliday, D., Resnick, R., & Walker, J. (2005). Fundamentals of Physics. Hoboken, NJ: John Wiley & Sons.Google Scholar
Ihde, A. (1964). The Development of Modern Chemistry. New York: Dover, 1984.Google Scholar
Jech, T. (2003). Set Theory (third millennium edition, revised and expanded). Berlin: Springer.Google Scholar
Kanamori, A. (2003). The Higher Infinite (second edition). Berlin: Springer.Google Scholar
Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.Google Scholar
Machamer, P. (1998a). Galileo's machines, his mathematics, and his experiments. In Machamer [1998b], pp. 53–79.CrossRefGoogle Scholar
Machamer, P., editor (1998b). Cambridge Companion to Galileo. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Maddy, P. (1997). Naturalism in Mathematics. Oxford: Oxford University Press.Google Scholar
Maddy, P. (2007). Second Philosophy. Oxford: Oxford University Press.CrossRefGoogle Scholar
Malament, D. (1996). In defense of a dogma: why there cannot be a relativistic quantum mechanics of (localizable) particles. In Clifton, R., editor, Perspectives on Quantum Reality. Amsterdam: North Holland, pp. 1–10.Google Scholar
McQuarrie, D., & Simon, J. (1997). Physical Chemistry. Sausalito, CA: University Science Books.Google Scholar
Moore, G. H. (1982). Zermelo's Axiom of Choice. New York: Springer.CrossRefGoogle Scholar
Newton, I. (1687). The Principia: Mathematical Principles of Natural Philosophy (Cohen, B., and Whitman, A., translator). Berkeley, CA: University of California Press, 1999.CrossRefGoogle Scholar
Nye, M. J. (1972). Molecular Reality. London: MacDonald.Google Scholar
Pais, A., Jacob, M., Olive, D., & Atiyah, M. (1998). Paul Dirac: The Man and His Work (Goddard, P., editor). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Partington, J. R. (1957). A Short History of Chemistry (third edition). New York: Dover, 1989.Google Scholar
Perrin, J. (1913). Atoms (Hammick, D., translator). Woodbridge, CT: Ox Bow Press, 1990.Google Scholar
Resnik, M. (1997). Mathematics as a Science of Patterns. Oxford: Oxford University Press.Google Scholar
Rice, J. (2007). Mathematical Statistics and Data Analysis (third edition). Belmont, CA: Thomson.Google Scholar
Shapiro, A. (2002). Newton's optics and atomism. In Cohen and Smith [2002b], pp. 227–255.Google Scholar
Silverman, A. (2003). Plato's Middle Period Metaphysics and Epistemology. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy (Summer 2003 Edition). Available from: http://plato.stanford.edu/archives/sum2003/entries/plato-metaphysics/.Google Scholar
Slowik, E. (2005). Descartes's physics. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy (Fall 2005 Edition). Available from: http://plato.stanford.edu/archives/fall2005/entries/descartes-physics/.Google Scholar
Smith, C., & Wise, N. (1989). Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge: Cambridge University Press.Google Scholar
Smith, G. (2002). The methodology of the Principia. In Cohen and Smith [2002b], pp. 138–173.Google Scholar
Stein, H. (1990). On Locke, “the Great Huygenius, and the incomparable Mr. Newton”. In Bricker, P. & Hughes, R. I. G., editors, Philosophical Perspectives on Newtonian Science. Cambridge, MA: MIT Press, pp. 17–47.Google Scholar
Tritton, D. J. (1988). Physical Fluid Dynamics (second edition). Oxford: Oxford University Press.Google Scholar
Truesdell, C. (1960). The field viewpoint in classical physics. Reprinted in his [1984], pp. 21–40.Google Scholar
Truesdell, C. (1968). A program toward rediscovering the rational mechanics of the age of reason. In his Essays in the History of Mechanics. Berlin: Springer-Verlag, pp. 85–137.CrossRefGoogle Scholar
Truesdell, C. (1981). The role of mathematics in science as exemplified by the work of the Bernoullis and Euler. Reprinted in his [1984], pp. 97–132.Google Scholar
Truesdell, C. (1984). An Idiot's Fugitive Essays on Science (second edition). New York: Springer-Verlag.CrossRefGoogle Scholar
Uffink, J. (2007). Compendium of the foundations of classical statistical mechanics. In Butterfield, J. & Earman, J., editors, Handbook of Philosophy of Physics. Amsterdam: North Holland, pp. 923–1073.CrossRefGoogle Scholar
Urquhart, A. (1990). The logic of physical theory. In Irvine, A., editor, Physicalism in Mathematics. Dordrecht: Kluwer, pp. 145–154.CrossRefGoogle Scholar
van der Pol, B. & Bremmer, H. (1950). Operational Calculus. Cambridge: Cambridge University Press.Google Scholar
Wedberg, A. (1955). Plato's Philosophy of Mathematics. Westport, CT: Greenwood, 1977.Google Scholar
Wilson, M. (2006). Wandering Significance. Oxford: Oxford University Press.CrossRefGoogle Scholar
Wise, N. (1981). The flow analogy to electricity and magnetism. Archive for History of Exact Sciences, 25, 19–70.CrossRefGoogle Scholar
Witten, E. (1998). Magic, mystery, and matrix. Notices of the American Mathematical Society, 45, 1124–1129.Google Scholar
Zemanian, A. H. (1965). Distribution Theory and Transform Analysis. New York: Dover.Google Scholar