Immanuel Kant’s Philosophy of Mathematics in Terms of His Theory of Space and Time

Yıl 2012, Sayı: 18 - Kaygı (18) 2012, 45 - 70, 15.04.2012

Hülya Yaldır , Necdet Guner

Öz

At the beginning of the modern age, mathematics had a great importance for the study of Nature. Galileo claimed that ‘the book of nature was written in a kind of mathematical code, and that if we could only crack that code, we could uncover her ultimate secrets’. But, how can mathematics, consisting of necessary tautological truths that are infallible and non-informative, be regarded as the language of natural sciences, while the knowledge of natural sciences is informative, empirical and fallible? Or, is there another alternative: as Hume claimed, modern sciences only depend on empirical data deriving from our perceptions, rather than having the necessity of mathematics. Many philosophers have tried to find an adequate answer for the problem of the relationship between mathematical necessity and contingent perceptions, but the difficulty remained unsolved until Kant’s construction of his original philosophy of the nature as well as the limits of human reason. The main purpose of this study is to show how Kant overcomes this difficulty by making use of the examples of Euclidean geometry and of arithmetic: there are synthetic a priori (a priori, universal, necessary, but at the same time informative) judgments, and indeed mathematical propositions are of this kind.

Anahtar Kelimeler

a priori, a posteriori, analytic, synthetic, synthetic a priori, mathematics, geometry, arithmetic, space, time, imagination

Kaynakça

• Kant, Critique of Pure Reason, trans. N. Kemp Smith, New York: St Martin’s, 1965.
• John Cottingham, Robert Stoothoff, and Dugald Murdoch (eds. and trans.), The Philosophical Writings of Descartes, vols: I & II, Cambridge: Cambridge University Press, 1985.
• John Cottingham, Robert Stoothoff, Dugald Murdoch, and Anthony Kenny (eds. and trans.), vol. III, Cambridge: Cambridge University Press, 1991.
• Corry, L. (2008) ‘The Development of the Idea of Proof’, in The Princeton Companion to Mathematics, ed. Timothy Gowers, Princeton and Oxford: Princeton University Press.
• Cottingham, J. (1984) Rationalism, Granada Publishing.
• Cottingham, J. (1988) The Rationalists, Oxford: Oxford University Press.
• Dummett, M. (1998) ‘The Philosophy of Mathematics’, in Philosophy 2, Further Through the Subject, ed. A. C. Grayling, Oxford: Oxford University Press.
• Euclid, (1956) The Thirteen Books of Euclid’s Elements Translated from the Text of Heiberg, 3 vols. New York: Dover Publications, With introduction and commentary by T. L. Heath.
• Friedman, M. (1985) ‘Kant’ Theory of Geometry’, The Philosophical Review, Vol. 94, No.4, Oct., 461-462.
• Gowers, T. (ed.), (2008) The Princeton Companion to Mathematics, Princeton University Press.
• Hanna, R. (2002) ‘Mathematics for Humans: Kant’s Philosophy of Arithmetic Revisited’, European Journal of Philosophy, 10, 328-352.
• Hanna, R. (2001) Kant and the Foundations of Analytic Philosophy, Oxford: Clarendon/Oxford University Press.
• Hume, D. (2007) An Enquiry concerning Human Understanding, ed. Peter Millican, Oxford: Oxford University Press.
• Leibniz, G. W. (2010) The Monadology, trans. Robert Latta, eBooks@Adelaide, http://ebooks.adelaide.edu.au/l/leibniz/gottfried/l525m/
• Locke, J. (1975) An Essay concerning Human Understanding, ed. P. H. Nidditch, Oxford: Oxford University Press.
• Martin, R. M. (2003) The Philosopher’s Dictionary, Broadview Press.
• Restall, G. (2009) ‘A Priori Truths’, in Central Issues of Philosophy, ed. John Shand, Wiley-Blackwell.
• Sedgwick, P. (2001) Descartes to Derrida, Blackwell.
• Shabel, L. (2003a) Mathematics in Kant’s Critical Philosophy, Routledge.
• Ward, A. (2006) Kant: Three Critiques, Cambridge: Polity Press.