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Kant on the Acquisition of Geometrical Concepts

Published online by Cambridge University Press:  01 January 2020

John J. Callanan
John J. Callanan*
Affiliation:
King’s College London, London, UK
*
*Email: john.callanan@kcl.ac.uk
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Abstract

It is often maintained that one insight of Kant’s Critical philosophy is its recognition of the need to distinguish accounts of knowledge acquisition from knowledge justification. In particular, it is claimed that Kant held that the detailing of a concept’s acquisition conditions is insufficient to determine its legitimacy. I argue that this is not the case at least with regard to geometrical concepts. Considered in the light of his pre-Critical writings on the mathematical method, construction in the Critique can be seen to be a form of concept acquisition, one that is related to the modal phenomenology of geometrical judgement.

Keywords

Kantconceptsgeometryconstructionphenomenology
Type
Research Article
Information
Canadian Journal of Philosophy , Volume 44 , Issue 5-6: Special Issue: Mathematics in Kant’s Critical Philosophy , December 2014 , pp. 580 - 604
Copyright
Copyright © Canadian Journal of Philosophy 2014

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References

Anderson, R. Lanier. 2004. “It Adds Up After All: Kant’s Philosophy of Arithmetic in Light of the Traditional Logic.” Philosophy and Phenomenological Research LXIX (3): 501–540.CrossRefGoogle Scholar
Anderson, R. Lanier. 2005. “The Wolffian Paradigm and its Discontents: Kant’s Containment Definition of Analyticity in Historical Context.” Archiv fur Geschichte der Philosophie 87: 22–74.CrossRefGoogle Scholar
Ansarib, D., Chee, W. L., and Venkatramana, V.. 2005. “Neural Correlates of Symbolic and Non-Symbolic Arithmetic.” Neuropsychologia 43: 744–753.Google Scholar
Callanan, John J. 2011. “Normativity and the Acquisition of the Categories.” Bulletin of the Hegel Society of Great Britain(Special Issue on Kant and Hegel)63/64: 1–26.Google Scholar
Callanan, John J. 2014. “Mendelssohn and Kant on Mathematics and Metaphysics 2014.” Kant YearbookVol. 6 (1): 1–22.CrossRefGoogle Scholar
Callanan, John J. (submitted for publication). “Kant on Signs in Concreto in Geometry.”Google Scholar
Cassirer, Ernst. 1981. Kant’s Life and Thought. Translated by James Haden. New Haven, CT: Yale University Press.Google Scholar
de Jong, Willem R. 1995. “Kant’s Analytic Judgments and the Traditional Theory of Concepts.” Journal of the History of Philosophy 33: 613–641.Google Scholar
Dunlop, Katherine. 2013. “Mathematical Method and Newtonian Science in the Philosophy of Christian Wolff.” Studies in History and Philosophy of Science Part A 44: 457–469.CrossRefGoogle Scholar
Fias, W., and Verguts, T.. 2004. “Representation of Number in Animals and Humans: A Neural Model.” Journal of Cognitive Neuroscience 16 (9): 1493–1504.Google Scholar
Friedman, Michael. 1985. “Kant’s Theory of Geometry.” The Philosophical Review 94: 455–506.CrossRefGoogle Scholar
Friedman, Michael. 2012. “Kant on Geometry and Spatial Intuition.” Synthese 186: 231–255.CrossRefGoogle Scholar
Guyer, Paul. 1998. Kant and the Claims of Knowledge. Cambridge: Cambridge University Press.Google Scholar
Hintikka, Jaako. 1969. “On Kant’s Notion of Intuition (Anschauung).” In Kant’s First Critique, edited by Penelhum, T. and Macintosh, J. J., 38–53. Belmont, CA: Wadsworth.Google Scholar
Howell, Robert. 1973. “Intuition, Synthesis and Individuation in the Critique of Pure Reason.” Noûs 7 (3): 207–232.CrossRefGoogle Scholar
Kant, Immanuel. 1900–. Kants Gesammelte Schriften, edited by German Academy of Sciences. Berlin: De Gruyter.Google Scholar
Kant, Immanuel. 1992a. Lectures on Logic. Translated and edited by J. Michael Young. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kant, Immanuel. 1992b. Theoretical Philosophy 1755–1770. Translated and edited by R. Meerbote and D. Walford. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kant, Immanuel. 1997a. Lectures on Metaphysics. Translated and edited by K. Ameriks and S. Naragon. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kant, Immanuel. 1997b. Critique of Pure Reason. Translated by Paul Guyer and Allen Wood. Cambridge: Cambridge University Press.Google Scholar
Kant, Immanuel. 2002. Theoretical Philosophy After 1781. Translated and edited by Henry Allison and Peter Heath. Cambridge: Cambridge University Press.Google Scholar
Kitcher, Philip. 1980. “A Priori Knowledge.” The Philosophical Review 89: 3–23.CrossRefGoogle Scholar
Lachterman, D. R. 1989. The Ethics of Geometry. London: Routledge.Google Scholar
Leibniz, G. W. 1996. New Essays on Human Understanding. Translated by Peter Remnant and Jonathan Bennett. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lipton, Jennifer S., and Spelke, Elizabeth S.. 2005. “Preschool Children’s Mapping of Number Words to Nonsymbolic Numerosities.” Child Development 76 (5): 978–988.CrossRefGoogle ScholarPubMed
Longuenesse, Beatrice. 1998. Kant and the Capacity to Judge. Translated by C.T. Wolfe. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Manders, K. 2008. “Diagram-based Geometrical Practice.” In The Philosophy of Mathematical Practice, edited by Mancosu, P., 65–79. Oxford: Oxford University Press.CrossRefGoogle Scholar
Merritt, Melissa McBay. 2006. “Science and the Synthetic Method of the ‘Critique of Pure Reason’.” The Review of Metaphysics 59 (3): 517–539.Google Scholar
Owen, David. 1999. Hume’s Reason. Oxford: Oxford University Press.Google Scholar
Parsons, Charles. 1983. “Kant’s Philosophy of Arithmetic.” In Mathematics and Philosophy: Selected Essays, 110–149. Ithaca, NY: Cornell University Press.Google Scholar
Proops, Ian. 2005. “Kant’s Conception of Analytic Judgment.” Philosophy and Phenomenological Research LXX: 588–612.CrossRefGoogle Scholar
Shabel, Lisa. 2003. Mathematics in Kant’s Critical Philosophy. London: Routledge.Google Scholar
Shabel, Lisa. 2004. “Kant’s ‘Argument from Geometry’.” Journal of the History of Philosophy 42: 195–215.CrossRefGoogle Scholar
Shabel, Lisa. 2006. “Kant’s Philosophy of Mathematics.” In Cambridge Companion to Kant and Modern Philosophy, edited by Guyer, Paul, 94–128. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Shabel, Lisa. 2010. “The Transcendental Aesthetic.” In Cambridge Companion to Kant’s Critique of Pure Reason, edited by Guyer, Paul, 93–117. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Spelke, Elizabeth S. 2011. “Natural Number and Natural Geometry.” In Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought, edited by Brannon, E. and Dehaene, S.. Attention & Performance, XXIV, 287–317. Oxford: Oxford University Press.CrossRefGoogle Scholar
Sutherland, Daniel. 2010. “Philosophy, Geometry, and Logic in Leibniz, Wolff, and the Early Kant.” In Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science, edited by Dickson, M. and Domski, M., 155–192. Chicago, IL: Open Court.Google Scholar
Thompson, Manley. 1972. “Singular Terms and Intuitions in Kant’s Epistemology.” The Review of Metaphysics 26 (2): 314–343.Google Scholar
Tonelli, Giorgio. 1974. “Leibniz on Innate Ideas and the Early Reactions to the Publication of the Nouveaux Essais (1765).” Journal of the History of Philosophy 12 (4): 437–454.Google Scholar
Warren, Daniel. 1998. “Kant and the A Priority of Space.” The Philosophical Review 107: 179–224.CrossRefGoogle Scholar
Waxman, Wayne. 2005. Kant and the Esmpiricists: Understanding Understanding. Oxford: Oxford University Press.CrossRefGoogle Scholar
Young, J. Michael. 1982. “Kant on the Construction of Arithmetical Concepts.” Kant-Studien 73: 17–46.CrossRefGoogle Scholar