Abstract
This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the ∃-instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual.
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REFERENCES
Beck, L.: 1965, Studies in the Philosophy of Kant, Bobbs Merrill Company, Indianapolis.
Beth, E.W.: 1965, The Foundations of Mathematics, North Holland Publishing Co., Amsterdam.
Brittan, G.: 1978, Kant's Theory of Science, Princeton University Press, Princeton.
Broad, C. D.: 1941–42, ‘Kant's Theory of Mathematical and Philosophical Reasoning', Proceedings of the Aristotelian Society 42, 1–24.
Friedman, M.: 1992, Kant and the Exact Sciences, Harvard University Press, Cambridge.
Heath, T., ed.: 1956, The Thirteen Books of Euclid 's Elements, Vol.1, Dover Publications, New York.
Hempel, C.: 1947, ‘On the Nature of Mathematical Truth', in H. Feigl and W. Sellars (eds.), Readings in Philosophical Analysis, Appleton Century Crotts, New York, pp. 222–237.
Hempei, C.: 1947, ‘Geometry and Empirical Science', in H. Feigl and W. Sellars (eds.), Readings in Philosophical Analysis, Appleton Century Crotts, New York, pp. 238–249.
Hilbert, D.: 1902, The Foundations of Geometry, Open Court Publishing Company, Chicago.
Hintikka, J.: 1967, ‘Kant on the Mathematical Method', Monist 51, 352–375.
Hintikka, J.: 1969, ‘On Kant's Notion of Intuition (Anschauung)', in T. Penelhum and J. J. MacIntosh (eds.), The First Critique, Wadsworth Publishing Company, Belmont, pp. 38–53.
Hintikka, J.: 1972, ‘Kantian Intuition', Inquiry 15, 341–345.
Hintikka, J.: 1973, Logic, Language Games and Information, Clarendon Press, Oxford.
Hintikka, J.: 1980, ‘C. S Peirce's ‘First Real Discovery’ and its Contemporary Relevance', Monist 63,304–315.
Hopkins, J.: 1973, ‘Visual Geometry', Philosophical Review 82, 3–34.
Kant, I.: 1929, Critique of Pure Reason (trans. by K. N. Smith), Macmillan Press, London.
Kant, I.: 1951, Prolegomena to Any Future Metaphysics (trans. by L. W. Beck), Bobbs Merrill Company, Indianapolis.
Kitcher, P.: 1975, ‘Kant and the Foundations of Mathematics', Philosophical Review 84, 23–50.
Martin, G.: 1955, Kant's Metaphysics and Theory of Science (trans. by P. G. Lucas), Manchester University Press, Manchester.
Parsons, C.: 1992, ‘Kant's Philosophy of Arithmetic’ and ‘Postscript’, in C. Posy (ed.), Kant's Philosophy of Mathematics, Kluwer Academic Publishers, Dordrecht, pp. 43–79.
Peirce, C. S.:.1931–58, in C. Hartshorne and P. Weiss (eds., Collected Papers of Charles Sanders Peirce, Vols. 2–4, Harvard University Press, Cambridge. (Reference to these volumes is by volume and page no., e.g. 2.267 = volume 2, paragraph 267.)
Peirce, C. S.: 1976, in C. Eisele (ed.), The New Elements of Mathematics, Vol. 4, Mouton, The Hague.
Russell, B.: 1903, The Principles of Mathematics, Cambridge University Press, Cambridge.
Russell, B.: 1920, Introduction to Mathematical Philosophy, Simon and Schuster, New York.
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Shin, Sj. Kant's Syntheticity Revisited by Peirce. Synthese 113, 1–41 (1997). https://doi.org/10.1023/A:1005068218051
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DOI: https://doi.org/10.1023/A:1005068218051