NDLI: UvA-DARE ( Digital Academic Repository ) On the dialectical foundations of mathematics

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UvA-DARE ( Digital Academic Repository ) On the dialectical foundations of mathematics

Content Provider	Semantic Scholar
Author	Damsma, D. F. Link
Copyright Year	2008
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. 1 I am grateful to Christopher Arthur, Gerard Alberts, Marcel Boumans and Patrick Murray for their interest in the research that led to this paper and their valuable suggestions for reading. I also want to thank Wouter Krasser, Tijmen Daniels and Marcel Boumans for help with some of the mathematical points. Despite his illness Louk Fleischhacker read my paper thoroughly before he deceased. His comments have been very helpful and I will remember him with great gratitude. Furthermore, I am indebted to David Gray Carlson for his valuable comments on an earlier version of this paper, his enthusiastic support and his readiness to explain some of the puzzling passages in Hegel’s Wissenschaft der Logik (1812, 1813, 1816) whenever I asked. Last, but not least I want to extend my gratitude to Geert Reuten for his continual support and his valuable comments on earlier versions of this paper. All remaining mistakes are my own.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://pure.uva.nl/ws/files/1314370/96369_286fulltext.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article

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