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  1.  17
    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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  2.  18
    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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    Galileo’s Quanti: Understanding Infinitesimal Magnitudes.Tiziana Bascelli - 2014 - Archive for History of Exact Sciences 68 (2):121-136.
    In On Local Motion in the Two New Sciences, Galileo distinguishes between ‘time’ and ‘quanto time’ to justify why a variation in speed has the same properties as an interval of time. In this essay, I trace the occurrences of the word quanto to define its role and specific meaning. The analysis shows that quanto is essential to Galileo’s mathematical study of infinitesimal quantities and that it is technically defined. In the light of this interpretation of the word quanto, Evangelista (...)
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  4.  17
    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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