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SSRN Electronic Journal
Article . 2011 . Peer-reviewed
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On the Dialectical Foundations of Mathematics

Authors: Damsma, D.;

On the Dialectical Foundations of Mathematics

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
bronze