Hostname: page-component-cb9f654ff-h4f6x Total loading time: 0 Render date: 2025-08-21T10:14:12.265Z Has data issue: false hasContentIssue false
  • English
  • Français

Infinity and givenness: Kant on the intuitive origin of spatial representation

Published online by Cambridge University Press:  01 January 2020

Daniel Smyth
Daniel Smyth*
Affiliation:
Department of Philosophy, University of Chicago, Chicago, IL, USA
*
*Email: dsmyth@uchicago.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

I advance a novel interpretation of Kant’s argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition.

Keywords

Kantintuitionsensibilityspaceinfinitycontinuumsingular representation

Information

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 44 , Issue 5-6: Special Issue: Mathematics in Kant’s Critical Philosophy , December 2014 , pp. 551 - 579
Copyright
Copyright © Canadian Journal of Philosophy 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Allison, Henry. 1983. Kant’s Transcendental Idealism – An Interpretation and Defense. New Haven, CT: Yale University Press.Google Scholar
Allison, Henry. 2004. Kant’s Transcendental Idealism – An Interpretation and Defense. Revised and Enlarged Edition. New Haven, CT: Yale University Press.CrossRefGoogle Scholar
Anderson, R. Lanier. 2004. “It Adds Up After All: Kant’s Philosophy of Arithmetic in Light of the Traditional Logic.” Philosophy and Phenomenological Research 69 (3): 501–540.CrossRefGoogle Scholar
Anderson, R. Lanier. Forthcoming. The Poverty of Conceptual Truth: Kant’s Analytic/Synthetic Distinction and the Limits of Metaphysics. Oxford: Oxford University Press.Google Scholar
Buroker, Jill Vance. 2006. Kant’s ‘Critique of Pure Reason’. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Carson, Emily. 1997. “Kant on Intuition in Geometry.” Canadian Journal of Philosophy 57 (4): 489–512.CrossRefGoogle Scholar
Descartes, René. 1964–1974. Oeuvres de Descartes, edited by Adam, Charles and Tannery, Paul. 12 vols., Revised Edition. Paris: J. Vrin [AT].Google Scholar
Domski, Mary. 2008. “Kant’s Argument for the Infinity of Space.” In Recht und Frieden in der Philosophie Kants – Akten des X. internationalen Kant-Kongresses, edited by Rohden, Valerio, Rerra, Ricardo, de Almeida, Guido, and Ruffing, Margit. 2 vols, 149–159. New York: De Gruyter.CrossRefGoogle Scholar
Engstrom, Stephen. 2006. “Understanding and Sensibility.” Inquiry 49 (1): 2–25.CrossRefGoogle Scholar
Euclid, . 1908. The Thirteen Books of Euclid’s ‘Elements’. Translated and edited by T.L. Heath.3 vols. Cambridge: Cambridge University Press.Google Scholar
Euler, Leonhard. 1911. “Vollständige Anleitungzur Algebra.” In Opera Omnia, edited by Ferdinand, Rudio, Krazer, Aldof, and Stäckel, Paul, series 1, 1 vols. Tübingen: Lipsiae & Berolini.Google Scholar
Ewing, A. C. 1950. A Short Commentary on Kant’s ‘Critique of Pure Reason’. 2nd ed.London: Metheun.Google Scholar
Falkenstein, Lorne. 1995. Kant’s Intuitionism. Toronto: University of Toronto Press.Google Scholar
Friedman, Michael. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press.Google Scholar
Gardner, Sebastian. 1999. Kant and the ‘Critique of Pure Reason’. New York: Routledge.Google Scholar
Grünbaum, Adolf. 1952. “A Consistent Conception of the Extended Linear Continuum as an Aggregate of Unextended Elements.” Philosophy of Science 19 (4): 288–306.CrossRefGoogle Scholar
Guyer, Paul. 1987. Kant and the Claims of Knowledge. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hollis, Martin. 1967. “Times and Spaces.” Mind 76 (304): 524–536.CrossRefGoogle Scholar
Kant, Immanuel. 1900. Gesammelte Schriften, edited by der Wissenschaften, Deutsche Akademie. Berlin: de Gruyter.Google Scholar
Kant, Immanuel. 1992. Theoretical Philosophy 1755–1770. translated and edited by David Walford, and Ralf Meerbote. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kästner, Abraham Gotthelf. 1758. Anfängsgründe der Arithmetik, Geometrie, ebenen und sphärischen Trigonometrie und Perspektiv. Göttingen: Vandenhoek and Ruprecht.Google Scholar
Kemp Smith, Norman. 1923. A Commentary to Kant’s ‘Critique of Pure Reason’. 2nd ed.London: MacMillan.Google Scholar
Leibniz, Gottfried Wilhelm. 1923. Sämtliche Schriften und Briefe. Series 6: Philosophische Schriften, edited by the Deutsche Akademie der Wissenschaften. Darmstadt: Akademie-Verlag [A].Google Scholar
Leibniz, Gottfried Wilhelm. 1978. Die philosophischen Schriften von Gottfried Wilhelm Leibniz, edited by Gerhardt, C. I.. 7 vols. Hildesheim: Georg Olms [G].Google Scholar
Leibniz, GottfriedWilhelm. 1981. New Essays on Human Understanding. Translated and edited by Peter Remnant and Jonathan Bennett.Cambridge: Cambridge University Press.Google Scholar
Levey, Samuel. 1998. “Leibniz on Mathematics and the Actually Infinite Division of Matter.” The Philosophical Review 107 (1): 49–96.CrossRefGoogle Scholar
Locke, John. 1959. Essay Concerning Human Understanding, edited by Campbell Fraser, Alexander. 2 vols. New York: Dover.Google Scholar
Longuenesse, Béatrice. 1998. Kant and the Capacity to Judge: Sensibility and Discursivity in the Analytic of the Critique of Pure Reason. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Meier, George Friedrich. 1752. Auszug aus der Vernunftlehre. Halle: Gebauer.Google Scholar
Melnick, Arthur. 1973. Kant’s Analogies of Experience. Chicago, IL: University of Chicago Press.Google Scholar
Messina, James. Forthcoming. “Conceptual Analysis and the Essence of Space: Kant’s Metaphysical Exposition Revisited.” Archiv für Geschichte der Philosopie.Google Scholar
Parsons, Charles. 1992. “The Transcendental Aesthetic.” In The Cambridge Companion to Kant, edited by Guyer, Paul, 62–100. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Parsons, Charles. 1998. “Infinity and Kant’s Conception of the ‘Possibility of Experience’.” In Kant’s ‘Critique of Pure Reason’ – Critical Essays, edited by Kitcher, Patricia, 45–58. Lanham: Rowman & Littlefield.Google Scholar
Parsons, Charles. 2012. “Arithmetic and the Categories.” In From Kant to Husserl: Selected Essays, 109–121. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
Paton, H. J. 1936. Kant’s Metaphysic of Experience. 2 vols. New York: MacMillan.Google Scholar
Pippin, Robert. 1982. Kant’s Theory of Form. New Haven, CT: Yale University Press.Google Scholar
Quentin, Anthony. 1962. “Times and Spaces.” Philosophy 37 (140): 130–174.CrossRefGoogle Scholar
Rosenberg, Jay F. 2005. Accessing Kant. Oxford: Oxford University Press.CrossRefGoogle Scholar
Rosenkoetter, Timothy, 2012. “Which Logic is Home to the (So-Called) ‘Table of Judgments’: An Unconsidered Alternative.” Unpublished manuscript.Google Scholar
Schechtman, Anat. 2014. “Descartes’ Argument for the Existence of the Idea of an Infinite Being.” Journal of the History of Philosophy 52 (3): 487–517.CrossRefGoogle Scholar
Shabel, Lisa. 2010. “The Transcendental Aesthetic.” In The Cambridge Companion to the ‘Critique of Pure Reason’, edited by Guyer, Paul, 93–117. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Smyth, Daniel. n.d. “Infinity and Givenness: Kant’s Critical Theory of Sensibility.” PhD diss., University of Chicago.Google Scholar
Strawson, P. F. 1966. The Bounds of Sense. London: Methuen.Google Scholar
Sutherland, Daniel. 2004. “Kant’s Philosophy of Mathematics and the Greek Mathematical Tradition.” The Philosophical Review 113 (2): 157–201.CrossRefGoogle Scholar
Vaihinger, Hans. 1892. Commentar zu Kants Kritik der reinen Vernunft. Vol. 2. Stuttgart: Union Deutsche Verlagsgesellschaft.Google Scholar
Wilson, Kirk Dallas. 1975. “Kant on Intuition.” Philosophical Quarterly 25 (100): 247–265.CrossRefGoogle Scholar