Hegel’s ‘Bad Infinity’ as a Logical Problem

Paper shared without authorization.


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.

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