Abstract
The success of empiricism in accounting for our knowledge of the tri-dimensionality of the physical world is intimately connected with its ability to refute Kant’s claim that the existence of such similar but incongruent counterparts as the left and right hands constitutes evidence for his transcendental a priori of space.1 Since the reasons for the untenability of this particular Kantian contention are not given even in Reichenbach’s definitive empiricist critique of the transcendental idealist theory of space2 and are not sufficiently known to the philosophical public, I shall give a brief statement of them.
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Notes
Kant: Werke, edited by E. Cassirer (Berlin: Bruno Cassirer Verlag; 1912), Vol. II, pp. 393–400 and Vol. IV, §13, pp. 34–36.
H. Reichenbach: “Kant und die Naturwissenschaft,” Die Naturwissenschaften, Vol. XXI (1933), pp. 601–606 and 624–26; Relativitätstheorie und Erkenntnis Apriori (Berlin: J. Springer; 1920), and PST, op. cit.
G. Lechalas: “L’Axiome de libre Mobilité,” Revue de Métaphysique et de Morale, Vol. VI (1898), p. 754. This property of reflections had already been pointed out by Mobius in his Der Barycentrische Calcul (Leipzig: Barth; 1827), p. 184.
Cf. F. Klein: Elementary Mathematics From An Advanced Standpoint, (New York: Dover Publications, Inc.; 1939), Vol. II, pp. 39–42; H. Weyl: Philosophy of Mathematics and Natural Science, op. cit., pp. 79–85. For a more elementary account, see O. Holder: Die Mathematische Methode, op. cit., pp. 387–89.
J. Hadamard: Lectures on Cauchys Problem in Linear Partial Differential Equations (New Haven: Yale University Press; 1923), pp. 53–54, 175–77, and 235–36.
A. Einstein: The Meaning of Relativity (Princeton: Princeton University Press; 1955), pp. 165–66
A. A. Fraenkel and Y. Bar-Hillel: Foundations of Set Theory (Amsterdam: North Holland Publishing Company; 1958), p. 200. Chapter iv of this work gives an admirably comprehensive and lucid survey of the respects in which neo-intuitionist restrictions involve mutilations of the system o£ classical mathematics.
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© 1973 D. Reidel Publishing Company, Dordrecht, Holland
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Grünbaum, A. (1973). Empiricism and the Three-Dimensionality of Space. In: Philosophical Problems of Space and Time. Boston Studies in the Philosophy of Science, vol 12. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2622-2_11
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DOI: https://doi.org/10.1007/978-94-010-2622-2_11
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