Abstract
In the Grundlagen, Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive.
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References
Armstrong D.M.: Truth and Truthmakers. Cambridge University Press, Cambridge (2004)
Armstrong D.M.: A World of States of Affairs. Cambridge University Press, Cambridge (1997)
Bostock David: ‘Empiricism in the Philosophy of Mathematics’. In: Irvine, A.D. (eds) Philosophy of Mathematics, pp. 157–229. Elsevier/North Holland, Amsterdam (2009)
Boyer Carl B., Uta C. Merzbach: A History of Mathematics, 2nd edn. John Wiley & Sons, New York (1991)
Britton, Karl, ‘The Nature of Arithmetic: a Reconsideration of Mill’s Views’, Proceedings of the Aristotelian Society, 48 (1947-48), II, 1–12.
Burge Tyler: ‘A Theory of Aggregates’. Nous 2, 97–117 (1977)
Burgess John: Fixing Frege. Princeton University Press, Princeton (2005)
Dummett Michael: Frege: Philosophy of Mathematics. Harvard University Press, Cambridge, Mass (1991)
Franklin James: ‘Aristotelian Realism’. In: Irvine, A.D. (eds) Philosophy of Mathematics, pp. 103–155. Elsevier/North Holland, Amsterdam (2009)
Frege, Gottlob, Die Grundlagen der Arithmatik (1884), trans. by J. L. Austin as The Foundations of Arithmetic, 2nd rev. edn, Oxford: Blackwell, 1980.
Geach Peter: ‘Frege’s Grundlagen’. Philosophical Review 60, 535–544 (1951)
Johnson W.E.: Logic: Part I. Cambridge University Press, Cambridge (1921)
Kessler Glenn: ‘Frege, Mill, and the Foundations of Arithmetic’. Journal of Philosophy 77, 65–79 (1980)
Kitcher, Philip, ‘Arithmetic for the Millian’, Philosophical Studies 37 (1980), 215–36.
Kitcher Philip: ‘Mill, Mathematics and the Naturalist Tradition’. In: Skorupski, J. (eds) The Cambridge Companion to Mill, pp. 57–111. Cambridge University Press, Cambridge (1998)
Lewis David: Parts of Classes. Blackwell, Oxford (1991)
McClure, Alexander K., Lincoln’s Yarns and Stories, Chicago and Philadelphia: The John C. Winston Company, 1900.
Mill, John Stuart, A System of Logic: Ratiocinative and Inductive (1843), Collected Works of John Stuart Mill, vols 7 & 8, Toronto: University of Toronto Press, 1973.
Quine, W.V., Word and Object, Cambridge, Mass.: MIT Press, 1960.
Resnik, Michael D., Frege and the Philosophy of Mathematics, Ithaca, NY: Cornell University Press, 1980, pp. 137–60.
Russell Bertrand: Introduction to Mathematical Philosophy. George Allen and Unwin Ltd, London (1919)
Van Inwagen Peter: Ontology Identity, and Modality: Essays in Metaphysics. Cambridge University Press, Cambridge (2001)
Weiner Joan: Frege in Perspective. Cornell University Press, Ithaca, NY (1990)
Wright Crispin: Frege’s Conception of Numbers as Objects. Aberdeen University Press, Aberdeen (1983)
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Irvine, A.D. Frege on Number Properties. Stud Logica 96, 239–260 (2010). https://doi.org/10.1007/s11225-010-9285-z
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DOI: https://doi.org/10.1007/s11225-010-9285-z