Abstract
Empiricism in the philosophy of mathematics has quite a long history, and the version of this approach which I will try to sketch in what follows is naturally based on a development of older views. It seems sensible therefore to start by considering some of these earlier versions of the position. I will not, however, attempt a complete history of empiricism in the philosophy of mathematics, but rather mention just those earlier ideas which I would like to incorporate, at least partially, in my own theory. My starting point is accordingly Mill’s philosophy of mathematics, which he expounded in A System of Logic (Mill 1843, Book II Chs. 5 and 6 and Book III Ch. 24).
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References
Aristotle, (1976). Metaphysics. Translated by J. Annas. Oxford: Oxford University Press.
Aristotle, (1941). “Physics.” In the Basic Works of Aristotle. (1941). R. McKeon. (Ed.). New York: Ranom House. 213–394.
Benacerraf, P. (1973). “Mathematical Truth.” Reprinted in (Benecerraf and Putnam 1973, 403–420).
Benacerraf, P. and H. Putnam. (Eds.). (1973). Philosophy of Mathematics Selected Readings. 2nd Edition. Cambridge: Cambridge University Press.
Chihara, C. S. (1982). “A Gödelian thesis regarding mathematical objects: Do they exist? And can we perceive them?” The Philosophical Review. Vol. 91: 211–27.
Chihara, C. S. (1990). Constructibility and Mathematical Existence. Oxford: Oxford University Press.
Church, A. (1940). “On the concept of a random sequence.” Bulletin of the American Mathematical Society. Vol. 46: 130–2.
Daston, L. (1988). Classical Probability in the Enlightenment. Princeton: Princeton University Press.
David, F. N. (1962). Games, Gods and Gambling. New York: Hafner Publishing Company.
Field, H. (1980). Science without Numbers. Princeton: Princeton University Press.
Frege, G. (1968). The Foundations of Arithmetic. A logico-mathematical enquiry into the concept of number. Translated by J. L. Austin. Oxford: Blackwell Publishers.
Gillies, D. A. (1973). An Objective Theory ofProbability. London: Methuen.
Gillies, D. A. (1982). Frege, Dedekind, and Peano on the Foundations ofArithmetic. Assen: Van Gorcum.
Gillies, D. A. (Ed.). (1992a). Revolutions in Mathematics. Oxford: Oxford University Press.
Gillies, D. A. (1992b). “Do We Need Mathematical Objects?” Review of (Chihara 1990). British Journalfor the Philosophy ofScience. Vol. 43: 263–78.
Gillies, D. A. (1993). Philosophy ofScience in the Twentieth Century: Four Central Themes. Oxford: Blackwell Publishers.
Gödel, K. (1947/63). “What is Cantor’s continuum problem?” Reprinted in (Benacerraf and Putnam 1983, 470–85).
Hacking, I. (1975). The Emergence ofProbability. Cambridge: Cambridge University Press.
Kant, I. (1959a). Critique ofPure Reason. Translated by N. K. Smith. London: MacMillan.
Kant, I. (1959b). Prolegomena to any Future Metaphysics that will be able to Present itself as Science. Translated by P. G. Lucas. Manchester: Manchester University Press.
Kant, I. (1970). Metaphysical Foundations of Natural Science. Translated by J. Ellington. The Library of Liberal Arts. Indianapolis and New York: Bobbs-Merrill.
Keynes, J. M. (1921). A Treatise on Probability. London: Macmillan.
Kitcher, P. S. (1980). “Arithmetic for the Millian.” Philosophical Studies. Vol. 37: 215–36.
Kitcher, P. S. (1983). The Nature ofMathematical Knowledge. Oxford: Oxford University Press.
Maddy, P. (1980). “Perception and Mathematical Intuition.” Philosophical Review. Vol. 89: 163–96.
Maddy, P. (1981). “Sets and Numbers.” Nous. Vol. 15: 495–511.
Maddy, P. (1990). Realism in Mathematics. Oxford: Oxford University Press.
Mill, J. S. (1843). A System of Logic Ratiocinative and Inductive being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation. 8th Edition. (1936). London: Longmans, Green and Company.
Mises, R. von. (1951). Probability, Statistics and Truth. 2nd revised English edition. London: Allen & Unwin.
Quine, W. V. O. (1951). “Two Dogmas of Empiricism.” Reprinted in (Quine, 1961, 20–46).
Quine, W. V. O. (1961). From a Logical Point of View. 2nd Rev. Ed. New York: Harper Torchbooks, New York and Evanston: Harper & Row.
Resnik, M.D. (1980). Frege and the Philosophy of Mathematics. Ithaca: Cornell University Press.
Wald, A. (1937). “Die Widerspruchsfreiheit des Kollektivbegriffes.” Ergebnisse eines Mathematischen Colloquiums. Vol. 8: 38–72.
Wittgenstein, L. (1966). Lectures and Conversations on Aesthetics, Psychology and Religious Belief. Edited by Cyril Barrett. Oxford: Blackwell Publishers.
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Gillies, D. (2000). An Empiricist Philosophy of Mathematics and Its Implications for the History of Mathematics. In: Grosholz, E., Breger, H. (eds) The Growth of Mathematical Knowledge. Synthese Library, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9558-2_3
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