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  1. added 2019-06-19
    Hegel on Calculus.Christopher Yeomans & Ralph Kaufmann - 2017 - History of Philosophy Quarterly 34 (4):371-390.
    It is fair to say that Georg Wilhelm Friedrich Hegel's philosophy of mathematics and his interpretation of the calculus in particular have not been popular topics of conversation since the early part of the twentieth century. Changes in mathematics in the late nineteenth century, the new set-theoretical approach to understanding its foundations, and the rise of a sympathetic philosophical logic have all conspired to give prior philosophies of mathematics (including Hegel's) the untimely appearance of naïveté. The common view was expressed (...)
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  2. added 2019-06-17
    Math by Pure Thinking: R First and the Divergence of Measures in Hegel's Philosophy of Mathematics.Ralph M. Kaufmann & Christopher Yeomans - 2017 - European Journal of Philosophy 25 (4):985-1020.
    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, (...)
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  3. added 2019-06-06
    Hegel’s Misunderstood Treatment of Gauss in the Science of Logic: Its Implications for His Philosophy of Mathematics.Edward Beach - 2006 - Idealistic Studies 36 (3):191-218.
    This essay explores Hegel’s treatment of Carl Friedrich Gauss’s mathematical discoveries as examples of “Analytic Cognition.” Unfortunately, Hegel’s main point has been virtually lost due to an editorial blunder tracing back almost a century, an error that has been perpetuated in many subsequent editions and translations.The paper accordingly has three sections. In the first, I expose the mistake and trace its pervasive influence in multiple languages and editions of the Wissenschaft der Logik. In the second section, I undertake to explain (...)
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  4. added 2014-09-23
    Does Hegel Have Anything to Say to Modern Mathematical Philosophy?Alan L. T. Paterson - 2002 - Idealistic Studies 32 (2):143-158.
    This paper argues that Hegel has much to say to modern mathematical philosophy, although the Hegelian perspective needs to be substantially developed to incorporate within it the extensive advances in post-Hegelian mathematics and its logic. Key to that perspective is the self-referential character of the fundamental concepts of philosophy. The Hegelian approach provides a framework for answering the philosophical problems, discussed by Kurt Gödel in his paper on Bertrand Russell, which arise out of the existence in mathematics of self-referential, non-constructive (...)
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  5. added 2014-09-23
    The Successor Function and Induction Principle in a Hegelian Philosophy of Mathematics.Alan L. T. Paterson - 2000 - Idealistic Studies 30 (1):25-60.
  6. added 2014-09-23
    The Mathematical Infinite in Hegel.Alain Lacroix - 2000 - Philosophical Forum 31 (3&4):298-327.
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  7. added 2014-09-23
    Towards a Hegelian Philosophy of Mathematics.Alan L. T. Paterson - 1997 - Idealistic Studies 27 (1/2):1-10.
    There is at present no intelligible account of what the statements of pure mathematics are about. The philosophy of mathematics is in a mess! Marvin J. Greenberg.
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