Abstract
How do Kant’s views on the nature of mathematics compare with some modern views? Now Kant’s position on mathematics, indeed his position in history, may advantageously be seen in relation to the threads left lying loose by philosophers preceding him. I can best move into the topic of this essay by listing briefly three of these threads left by Descartes. These Cartesian threads are the following:
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1.
Descartes’ failure fully to develop the philosophical aspect of the mathematical language; Descartes had shown by means of his doctrine of matter with its primary qualities that mathematics applied to extension (matter) but not how, (to meet this need, Kant elaborated a metaphysics of experience to replace Descartes’ dualism);
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2.
his failure to show that the mathematical language referred to the non-geometrical aspects of nature (Newton’s physics, developing the concept of mass, rendered this demand insistant);
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3.
his failure to develop an adequate doctrine of value (Kant sought to satisfy this requirement with the last two Critiques and his writings on ethics).
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Notes
“Les axiomes géométriques ne sont donc ni des judgments synthétiques a priori ni des faits expérimentaux. “Ce sont des conventions; notre choix, parmi toutes les conventions possibles, est guidé par des faits expérimentaux; mais il reste libre et n’est limité que par le nécessité d’éviter toute contradiction.” H. Poincaré, La Science et l’Hypothèse (Paris: Flammarion, 1943), p.66.
Einsteins Reletivitätstheorie und ihre Stellung im System der Gesamterfahrung (Dresden, 1921).
Cf. The Elements of Non-Euclidean Geometry, D.M.Y. Sommerville (New York: Dover, 1958), p.64.
Substance and Function in Einstein’s Theory of Relativity (New York: Dover, 1953), p.417f.
See his Modern Philosophy of Science (New York: Humanities Press, 1959), p.28f.
It is interesting that Leibniz interpreted the expression 0/0 as equal to 1. Leibniz, Philosophical Papers and Letters, ed. and trans, by L.E. Loemker (Chicago: University of Chicago Press, 1956), vol.ii, p.886f.
In other epochs of our history, perhaps the experience of space, and consequently the geometry of experience, could have been different. Cf. my Principles of Interpretation (Athens: Ohio University Press, 1983) chap. II. See also Patrick Heelan, Space-Perception and the Philosophy of Science, (Berkeley: University of California Press, 1983), especially chapter 2.
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© 1989 Kluwer Academic Publishers
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Ballard, E.G. (1989). On Kants Philosophic Grammar of Mathematics. In: Philosophy and the Liberal Arts. Contributions To Phenomenology, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2368-3_11
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