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Hegel’s ‘Bad Infinity’ as a Logical Problem

Published online by Cambridge University Press:  14 September 2016

Vojtěch Kolman
Vojtěch Kolman*
Affiliation:
Institute of Philosophy and Religious Studies, Charles University, Prague, Czech Republicvojtech.kolman@ff.cuni.cz
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Abstract

The paper analyses the concept of ‘bad infinity’ in connection with Hegel’s critique of infinitesimal calculus and with the belittling of Hegel’s mathematical notions by the representatives of modern logic and the foundations of mathematics. The main line of argument draws on the observation that Hegel’s difference is only derivatively a mathematical one and is primarily of a broadly logico-epistemological nature. Because of this, the concept of bad infinity can be fruitfully utilized, by way of inversion, in an analysis of the conceptual shortcomings of the most prominent foundational attempts at dealing with infinite quanta, such as Cantor’s set theory and Hilbert’s axiomatism. As such, the paper is an attempt at reconstructing Hegel’s philosophy of mathematics and its role in his philosophical system and, more importantly, as a contribution to logic in the more general and radical sense of the word.

Type
Articles
Information
Hegel Bulletin , Volume 37 , Issue 2 , October 2016 , pp. 258 - 280
Copyright
© The Hegel Society of Great Britain 2016 

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