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The Role of Magnitude in Kant's Critical Philosophy

Published online by Cambridge University Press:  01 January 2020

Daniel Sutherland
Daniel Sutherland*
Affiliation:
University of Illinois at Chicago, Chicago, IL60607-7114, USA
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Extract

In the Critique of Pure Reason, Kant argues for two principles that concern magnitudes. The first is the principle that ‘All intuitions are extensive magnitudes,’ which appears in the Axioms of Intuition (B202); the second is the principle that ‘In all appearances the real, which is an object of sensation, has an intensive magnitude, that is, a degree,’ which appears in the Anticipations of Perception (B207). A circle drawn in geometry and the space occupied by an object such as a book are paradigm examples of extensive magnitudes, while the intensity of a light is a paradigm example of an intensive magnitude. These principles justify and explain the possibility of applying mathematics to objects of experience. The Axioms principle also explains the possibility of any mathematical cognition at all.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 34 , Issue 3 , September 2004 , pp. 411 - 441
Copyright
Copyright © The Authors 2004

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References

Allison, H. 1983. Kant's Transcendental Idealism: An Interpretation and Defense. New Haven: Yale University Press.Google Scholar
Bennett, J. 1966. Kant's Analytic. London: Cambridge University Press.Google Scholar
Brittan, G. 1978. Kant's Theory of Science. Princeton, NJ: Princeton University Press.Google Scholar
Cassirer, E. 1954. Kant's First Critique: An Appraisal of the Permanent Significance of Kant's Critique of Pure Reason. New York: MacMillan.Google Scholar
Friedman, M. 1992. Kant and the Exact Sciences. Cambridge, MA: Harvard University Press.Google Scholar
Friedman, M. 2000. ‘Geometry, Construction and Intuition in Kant and His Successors,’ in Between Logic and Intuition: Essays in Honor of Charles Parsons, Sher, G. and Tieszen, R. eds. New York: Cambridge University Press.Google Scholar
Guyer, P. 1987. Kant and the Claims of Knowledge. New York: Cambridge University Press.CrossRefGoogle Scholar
Hintikka, J. 1969. ‘On Kant's Notion of Intuition (Anschauung),’ in The First Critique: Reflections on Kant's Critique of Pure Reason, Macintosh, J.J. and Penelhum, T. eds. Belmont, CA: Wadsworth Publishing Company.Google Scholar
Hintikka, J. 1974a. ‘Kant's “New Method of Thought” and His Theory of Mathematics,’ in Knowledge and the Known. Dordrecht: D.Reidel.CrossRefGoogle Scholar
Hintikka, J. 1974b. ‘Kant on the Mathematical Method,’ in Knowledge and the Known. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Kant, I. 1902. Kant's Gesammelte Schriften. 29 vols. Berlin: Reimer, G. subsequently Walter de Gruyter & Co.Google Scholar
Kant, I. 1992. Theoretical Philosophy, 1755 -1770. Walford, D. trans. and ed. The Cambridge edition of the works of Immanuel Kant. New York: Cambridge University PressGoogle Scholar
Kant, I. 1998. Critique of Pure Reason. P. Guyer and A.W. Wood, trans. The Cambridge edition Of the works of Immanuel Kant. New York: Cambridge University Press.Google Scholar
Kitcher, P. 1982. ‘How Kant Almost Wrote “Two Dogmas of Empiricism,’” in Essays on Kant's Critique of Pure Reason, Mohanty, J.N. and Shahan, R. W. eds. Norman: University of Oklahoma Press.Google Scholar
Krantz, David H. Lee, D. Suppes, P. Tversky, A. 1971. Foundations of Measurement, 2 vols. New York: Academic Press.Google Scholar
Longuenesse, B. 1998. Kant and the Capacity to Judge: Sensibility and Discursivity in the Transcendental Analytic of the Critique of Pure Reason. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Parsons, C. 1983a. ‘Infinity and Kant's Conception of the “Possibility of Experience,’” in Mathematics in Philosophy. Ithaca: Cornell University Press.Google Scholar
Parsons, C. 1983b. ‘Kant's Philosophy of Arithmetic.’ In Mathematics in Philosophy. Ithaca: Cornell University Press.Google Scholar
Parsons, C. 1984. ‘Arithmetic and the Categories.’ Topoi 3.CrossRefGoogle Scholar
Paton, H.J. 1965. Kant's Metaphysic of Experience: A Commentary on the First Half of the Kritik der reinen Vernunft. London, New York: Allen & Unwinn: Humanities Press.Google Scholar
Raymund, Schmidt. 1926. Kritik der reinenvernonft. Leipzig: F. Meiner.Google Scholar
Shabel, L. 1998. ‘Kant on the “Symbolic Construction” of Mathematical Concepts,’ Studies in the History and Philosophy of Science 29.CrossRefGoogle Scholar
Smith, N.K. 1965. The Critique of Pure Reason. New York: St. Martin's Press.Google Scholar
Smith, N.K. 1979. A Commentary to Kant's Critique of Pure Reason. 2nd ed. London: Macmillan.Google Scholar
Vaihinger, H. 1900. ‘Siebzig textkritische Randglossen zur Analytik,’ Kant-Studien 4.CrossRefGoogle Scholar
Walsh, W.H. 1975. Kant's Criticism of Metaphysics. Edinburgh: Edinburgh University Press.Google Scholar
Wilson, K.D. 1975. ‘Kant on Intuition.’ Philosophical Quarterly 25.CrossRefGoogle Scholar
Wolff, R.P. 1963. Kant's Theory of Mental Activity. Cambridge, MA: Harvard University Press.Google Scholar