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  1. Gottfried Wilhelm Leibniz.Brandon C. Look - 2008 - Stanford Encyclopedia of Philosophy.
    Gottfried Wilhelm Leibniz (1646–1716) was one of the great thinkers of the seventeenth and eighteenth centuries and is known as the last “universal genius”. He made deep and important contributions to the fields of metaphysics, epistemology, logic, philosophy of religion, as well as mathematics, physics, geology, jurisprudence, and history. Even the eighteenth century French atheist and materialist Denis Diderot, whose views could not have stood in greater opposition to those of Leibniz, could not help being awed by his achievement, writing (...)
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  • Polemics in Public: Poncelet, Gergonne, Plücker, and the Duality Controversy.Jemma Lorenat - 2015 - Science in Context 28 (4):545-585.
    ArgumentA plagiarism charge in 1827 sparked a public controversy centered between Jean-Victor Poncelet (1788–1867) and Joseph-Diez Gergonne (1771–1859) over the origin and applications of the principle of duality in geometry. Over the next three years and through the pages of various journals, monographs, letters, reviews, reports, and footnotes, vitriol between the antagonists increased as their potential publicity grew. While the historical literature offers valuable resources toward understanding the development, content, and applications of geometric duality, the hostile nature of the exchange (...)
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  • Maimon’s Theory of Differentials As The Elements of Intuitions.Simon Duffy - 2014 - International Journal of Philosophical Studies 22 (2):1-20.
    Maimon’s theory of the differential has proved to be a rather enigmatic aspect of his philosophy. By drawing upon mathematical developments that had occurred earlier in the century and that, by virtue of the arguments presented in the Essay and comments elsewhere in his writing, I suggest Maimon would have been aware of, what I propose to offer in this paper is a study of the differential and the role that it plays in the Essay on Transcendental Philosophy (1790). In (...)
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  • Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics.Vladimir Kanovei, Mikhail G. Katz & Thomas Mormann - 2013 - Foundations of Science 18 (2):259-296.
    We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...)
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  • Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond. [REVIEW]Mikhail G. Katz & David Sherry - 2013 - Erkenntnis 78 (3):571-625.
    Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...)
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  • 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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  • Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of the differential calculus.David Rabouin & Richard T. W. Arthur - 2020 - Archive for History of Exact Sciences 74 (5):401-443.
    In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...)
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  • What Does God Know but can’t Say? Leibniz on Infinity, Fictitious Infinitesimals and a Possible Solution of the Labyrinth of Freedom.Elad Lison - 2020 - Philosophia 48 (1):261-288.
    Despite his commitment to freedom, Leibniz’ philosophy is also founded on pre-established harmony. Understanding the life of the individual as a spiritual automaton led Leibniz to refer to the puzzle of the way out of determinism as the Labyrinth of Freedom. Leibniz claimed that infinite complexity is the reason why it is impossible to prove a contingent truth. But by means of Leibniz’ calculus, it actually can be shown in a finite number of steps how to calculate a summation of (...)
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  • Labyrinth of Continua.Patrick Reeder - 2018 - Philosophia Mathematica 26 (1):1-39.
    This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...)
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  • Presupposition, Aggregation, and Leibniz’s Argument for a Plurality of Substances.Richard T. W. Arthur - 2011 - The Leibniz Review 21:91-115.
    This paper consists in a study of Leibniz’s argument for the infinite plurality of substances, versions of which recur throughout his mature corpus. It goes roughly as follows: since every body is actually divided into further bodies, it is therefore not a unity but an infinite aggregate; the reality of an aggregate, however, reduces to the reality of the unities it presupposes; the reality of body, therefore, entails an actual infinity of constituent unities everywhere in it. I argue that this (...)
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  • Leibniz on Bodies and Infinities: Rerum Natura and Mathematical Fictions.Mikhail G. Katz, Karl Kuhlemann, David Sherry & Monica Ugaglia - 2024 - Review of Symbolic Logic 17 (1):36-66.
    The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility innature, rather than inmathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are logical fictions, contradictory in (...)
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  • The Jesuits and the Method of Indivisibles.David Sherry - 2018 - Foundations of Science 23 (2):367-392.
    Alexander’s "Infinitesimal. How a dangerous mathematical theory shaped the modern world"(London: Oneworld Publications, 2015) is right to argue that the Jesuits had a chilling effect on Italian mathematics, but I question his account of the Jesuit motivations for suppressing indivisibles. Alexander alleges that the Jesuits’ intransigent commitment to Aristotle and Euclid explains their opposition to the method of indivisibles. A different hypothesis, which Alexander doesn’t pursue, is a conflict between the method of indivisibles and the Catholic doctrine of the Eucharist. (...)
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