Hegel and Mathematics

1931 text: Hegel's merit in correctly recognising the subject matter
of mathematics deserves to stand high in our estimation, particularly
in view of the fact that even today this question causes the greatest
difficulties in the most varied idealistic and eclectic philosophical
trends because they reflect material reality in a distorted way. Thus
the intuitionists (Weyl, Brouwer), following Kant, take the view that
pure a priori intuition forms the subject matter of mathematics, while
the logicists, who since Leibnitz take mathematics to be part of
logic, see in axioms and theorems the laws of reason. The formalists,
like Hilbert, deny the existence of a particular subject matter of
mathematics at all, holding the latter to be a mere collection of
rules that permit us to form various combinations and transformations.
The mechanistic empiricists who classify mathematics as part of
physics deny its specific nature, think that its subject matter is
physical space and physical time. Others, like Mach, seek its subject
matter in psychology, etc. However, all these definitions lead to
difficulties that none of these philosophical systems is able to
overcome..... http://www.marxists.org/reference/subject/philosophy/works/ru/kolman.htm

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