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Kant on conic sections

Published online by Cambridge University Press:  01 January 2020

Alison Laywine
Alison Laywine*
Affiliation:
Department of Philosophy, McGill University, Montreal, Canada
*
*Email: [email protected]
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Abstract

This paper tries to make sense of Kant’s scattered remarks about conic sections to see what light they shed on his philosophy of mathematics. It proceeds by confronting his remarks with the source that seems to have informed his thinking about conic sections: the Conica of Apollonius. The paper raises questions about Kant’s attitude towards mathematics and the way he understood the cognitive resources available to us to do mathematics.

Keywords

KantApolloniusconic sections
Type
Research Article
Information
Canadian Journal of Philosophy , Volume 44 , Issue 5-6: Special Issue: Mathematics in Kant’s Critical Philosophy , December 2014 , pp. 719 - 758
Copyright
Copyright © Canadian Journal of Philosophy 2014

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References

Apollonius. 2008. Apollonius de Perge: Les Coniques, tome 1.1: Livre I. Commentaire historique et mathématique, édition et traduction du texte arabe par Roshdi Rashed. Berlin: Walter de Gruyter.Google Scholar
Apollonius. 2010. Apollonius de Perge: Les Coniques, tome 2.1: Livres II et III. Commentaire historique et mathématique, édition et traduction du texte arabe par Roshdi Rashed. Berlin: Walter de Gruyter.Google Scholar
Brittan, Gordon. 1992. “Algebra and Intuition.” In Chap. 12 in Kant’s Philosophy of Mathematics: Modern Essays, edited by Posy, Carl, 325–339. Dordrecht: Kluwer.Google Scholar
Dijksterhuis, E. J. 1987. Archimedes. Translated by C. Dikshoorn. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Eberhard, Johann. August. 1789. Philosophisches Magazin. Halle: Gebauer.Google Scholar
Fried, Michael, and Unguru, Sabetai. 2001. Apollonius of Perga’s Conica: Text, Context, Subtext. Leiden: Brill.CrossRefGoogle Scholar
Friedman, Michael. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press.Google Scholar
Friedman, Michael. 2013. Kant’s Construction of Nature. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Heath, Thomas. 1981. A History of Greek Mathematics. 2 vols. New York: Dover.Google Scholar
Heiberg, J. L., ed. 1891. Apollonii Pergaei Quae Exstant Cum Commentariis Antiquis. 2 vols. Leipzig: Teubner.Google Scholar
Heis, Jeremy. 2011. “Ernst Cassirer’s Neo-Kantian Philosophy of Geometry.” British Journal for the History of Philosophy 19 (4): 759–794. 10.1080/09608788.2011.583421.CrossRefGoogle Scholar
Kant, Immanuel. 1902. Kant’s gesammelte Schriften Herausgegeben von der Königlich Preußischen Akademie der Wissenschaften.Google Scholar
Kant, Immanuel. 1916. Kritik der reinen Vernunft, edited by Erdmann, Benno. 6th ed.Berlin: Walter de Gruyter.Google Scholar
Knorr, Wilbur. 1986. The Ancient Tradition of Geometric Problems. New York: Dover.Google Scholar
de la Hire, Philippe. 1685. Sectiones Conicae. Paris: Etienne Michallet.Google Scholar
Laywine, Alison. 1998. “Problems and Postulates: Kant on Reason and Understanding.” Journal of the History of Philosophy 36 (2): 279–311.CrossRefGoogle Scholar
Laywine, Alison. 2003. “Kant on Sensibility and the Understanding in the 1770s.” Canadian Journal of Philosophy 33 (4): 443–483.CrossRefGoogle Scholar
Newton, Isaac. 1972. Philosophiae Naturalis Principia Mathematica, edited by Koyré, Alexandre and Cohen, I. Bernard. 3rd ed.Cambridge, MA: Harvard University Press.Google Scholar
Pappus. 1876–1878. Collectionis Quae Supersunt, edited by Hultsch, F.. 3 vols. Berlin: Weidmann.Google Scholar
Pascal, Blaise. 1964. Oeuvres Complètes, edited by Mesnard, Jean. 2nd vol. Paris: Desclée de Brouwer.Google Scholar
Plato. 1992. Opera, edited by Burnet, . 4th vol. Oxford: Clarendon Press.Google Scholar
Rashed, Roshdi. 2005. “Les premières classifications des courbes.” Physis XLII (1): 1–64.Google Scholar
Saito, Ken. 2004. “Book II of Euclid’s Elements in Light of the Theory of Conic Sections.” In Chap. 7 in Classics in the History of Greek Mathematics, edited by Christianidis, Jean, 136–169. Dordrecht: Springer Verlag.Google Scholar
Schlosser, J. G. 1795. Plato’s Briefe, Nebst Einer Historischen Einleitung und Anmerkungen. Königsberg: Friedrich Nikolovius.Google Scholar
Steiner, Jakob. 1881. Gesammelte Werke, edited by Weierstrass, Karl. Vol. 1 of the Gesammelte Werke. Berlin: G. Reimer.Google Scholar
Sutherland, Daniel. 2006. “Kant on Arithmetic, Algebra and the Theory of Proportions.” Journal of the History of Philosophy 44 (4): 533–558.CrossRefGoogle Scholar
Zeuthen, H. G. 1966. Die Lehre von den Kegelschnitten im Altertum. Hildesheim: Georg Olms.Google Scholar