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

Year 2012, Issue: 18 - Kaygı (18) 2012, 45 - 70, 15.04.2012

Hülya Yaldır , Necdet Guner

Abstract

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.

Keywords

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

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