On the Dialectical Foundations of Mathematics

41 Pages Posted: 21 Dec 2011

See all articles by D.F. Damsma

D.F. Damsma

Amsterdam School of Economics

Date Written: January 1, 2011

Abstract

This paper tracks the systematic dialectical determination of mathematical concepts in Hegel’s Encyclopädie der philosophischen Wissenschaften (1830,1817) and investigates the insights that can be gained from such a perspective on the mathematical. To begin with, the determination of Numbers and arithmetical operations from Being shows that the One and the successor function have a qualitative base and need not be presupposed. It is also shown that even for infinite Intensive Magnitudes (cardinals) there exists an Extensive Magnitude through which they gain meaning. This makes the ‘bad’ in Hegel’s ‘bad infinity’ a trifle problematic. Finally, if ‘Dasein’ is interpreted as the whole of perception in the present, Place can be viewed as the spatial Now, Motion as the passage from Place to Now and Matter as the actual (as opposed to observed) Presence of the natural realm.

Keywords: Systematic dialectics, Hegel, Mathematics, Philosophy

JEL Classification: B00, C00

Suggested Citation

Damsma, D.F., On the Dialectical Foundations of Mathematics (January 1, 2011). Available at SSRN: https://ssrn.com/abstract=1975242 or http://dx.doi.org/10.2139/ssrn.1975242

D.F. Damsma (Contact Author)

Amsterdam School of Economics ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

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