Author:
Dirk Damsma
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Brief Contents

Marx’s critique of Hegel relates not to Hegel’s dialectical method as such, but mainly to Hegel’s obsession with reconciling the realms of pure thought (Logic) and of nature in his theory of society. Hegel’s treatment of ideas as self-contained entities rather than entities contained in man, actually inspired Marx’s category of alienation. Alienation is one of the by-products of generalised exchange. When there is generalised exchange, the abstraction of value must materialise as money. As a result categories pertaining to capitalism are real and ideal at the same time. By implication, Marx’s own dialectical theory was to allow for unreconciled oppositions between ontologically quantitative abstractions-in-practice (Chapter 1).

Since mathematics is firmly rooted in the realm of pure thought (as far as Hegel is concerned) and its application requires qualitative mediation so as to allow for measures to be formed, Hegel’s obsession with reconciliation forbade him from applying mathematical techniques directly to the study of society (Chapter 2).

Marx was not hindered by such inhibitions, because part of the abstractions in society represents abstractions-in-practice and he did not believe in Hegel’s imperative of reconciliation. So, for Marx, there were no fundamental philosophical objections to the articulation of mathematical models alongside, and integrated with, his systematic-dialectical account. However, he never got round to presenting his models as part of his systematic dialectics in his forays into mathematical modelling, such as his schemes of reproduction (Chapter 3).

Hence some reconstructive work to improve these schemes is possible and warranted (Chapter 4).

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