11 found
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  1.  23
    Interpreting the Infinitesimal Mathematics of Leibniz and Euler.Jacques Bair, Piotr Błaszczyk, Robert Ely, Valérie Henry, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, Patrick Reeder, David M. Schaps, David Sherry & Steven Shnider - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):195-238.
    We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...)
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  2.  7
    Leibniz Versus Ishiguro: Closing a Quarter Century of Syncategoremania.Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, David M. Schaps & David Sherry - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):117-147.
    Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...)
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  3.  23
    Almost Equal: The Method of Adequality From Diophantus to Fermat and Beyond.Mikhail G. Katz, David M. Schaps & Steven Shnider - 2013 - Perspectives on Science 21 (3):283-324.
    Adequality, or παρισóτης (parisotēs) in the original Greek of Diophantus 1 , is a crucial step in Fermat’s method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat’s collected works (1891, pp. 133–172). The first article, Methodus ad Disquirendam Maximam et Minimam 2 , opens with a summary of an algorithm for finding the maximum or minimum value of an (...)
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  4.  11
    Gregory’s Sixth Operation.Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Tahl Nowik, David M. Schaps & David Sherry - 2018 - Foundations of Science 23 (1):133-144.
    In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...)
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  5.  17
    Greek and Latin Riddles - Kwapisz, Petrain, Szymański the Muse at Play. Riddles and Wordplay in Greek and Latin Poetry. Pp. X + 420, Ills. Berlin and Boston: De Gruyter, 2013. Cased, €109.95, Us$154. Isbn: 978-3-11-027000-6. [REVIEW]David M. Schaps - 2014 - The Classical Review 64 (1):89-91.
  6.  9
    Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms.Tiziana Bascelli, Piotr Błaszczyk, Alexandre Borovik, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, David M. Schaps & David Sherry - 2018 - Foundations of Science 23 (2):267-296.
    Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.
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  7.  16
    Money and the Early Greek Mind. Homer, Philosophy, Tragedy. [REVIEW]David M. Schaps - 2007 - The Classical Review 57 (1):10-12.
  8. Socrates and the Socratics.David M. Schaps - 2003 - Classical World: A Quarterly Journal on Antiquity 96 (2).
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  9.  13
    For All That a Woman: Medea 1250, ΔϒΣTϒXHΣ Δ'EΓ&303A9; ΓϒNH.David M. Schaps - 2006 - Classical Quarterly 56 (2).
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  10.  7
    History (S.) Von Reden Money in Ptolemaic Egypt: From the Macedonian Conquest to the End of the Third Century BC. Cambridge: Cambridge University Press, 2007. Pp. Xxii + 354, Illus. £55. 9780521852647. [REVIEW]David M. Schaps - 2009 - Journal of Hellenic Studies 129:191-.
  11.  5
    For All That a Woman: Medea 1250.David M. Schaps - 2006 - Classical Quarterly 56 (02):590-.
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