Although Hegel is generally not known as a philosopher of mathematics, he maintained a deep interest in the history of mathematics, especially in its transformations between antiquity and the modern age. Charles S. Peirce, who was the son of a distinguished mathematician and was involved in developments in mathematics in the second half of the nineteenth century, was critical of what he perceived as Hegel’s lack of mathematical acumen. Nevertheless, he recognized in Hegel’s Science of Logic structural features of his (...) own mathematically informed philosophy. In this article, I look to Hegel’s discussion of magnitude in The Science of Logic, and especially to his conception of the relation between continuous and discrete magnitudes, in order to articulate a solution he might have offered to difficulties encountered by Peirce in his opposition to Cantor’s set-theoretical analysis of the continuum. It is argued that Hegel’s interest in the ancient Platonic/Pythagorean tradition in mathematics provided him with crucial resources in this regard. (shrink)

The fragmentary nature ofGSmakes it difficult to read as it stands, and for this reason, I have rearranged the material slightly so that it falls into four primary, reasonably coherent, parts. Their titles are: ‘The nature of mathematical objects’, ‘Thirteen propositions of Euclid 1’, ‘The philosophy of parallel lines’ and ‘On the algebra of geometrical figures’.GSactually starts with ‘Thirteen propositions of Euclid 1’. The justification for the reversal of order in the translation is to have Hegel's philosophical basis for geometry (...) available first, to provide a context for his detailed discussion of geometrical propositions. The reader can easily reconstruct the original order ofGSas follows. Interchange the first and second parts and also the third and fourth parts. Next, move the passages marked a …. a', b …. b',c….c'to the places in the text markeda-a',b-b'andc-c'. For the reader wishing to locate the original German passages inDok., the page and paragraph for each of these passages are given at the start of that passage.In addition, subtitles for sections in these parts have been added which do not appear in the original. They are included in the translation to help orient the reader. I have inserted in some places words not in the original in order to clarify the meaning of the text. These insertions as well as my comments on the text are also enclosed within square brackets. Further clarifications can be found in the appended endnotes. (shrink)