Math by Pure Thinking: R First and the Divergence of Measures in Hegel's Philosophy of Mathematics

European Journal of Philosophy 25 (4):985-1020 (2017)
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We attribute three major insights to Hegel: first, an understanding of the real numbers as the paradigmatic kind of number ; second, a recognition that a quantitative relation has three elements, which is embedded in his conception of measure; and third, a recognition of the phenomenon of divergence of measures such as in second-order or continuous phase transitions in which correlation length diverges. For ease of exposition, we will refer to these three insights as the R First Theory, Tripartite Relations, and Divergence of Measures. Given the constraints of space, we emphasize the first and the third in this paper.
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