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Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units

Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units

Oscar M. Esquisabel and Federico Raffo Quintana, “Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1319–42, DOI 10.17990/RPF/2017_73_3_1319.

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Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units

Type Journal Article
Author Oscar M. Esquisabel
Author Federico Raffo Quintana
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1319-1342
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1319
Language English
Abstract In this paper, we analyze the arguments that Leibniz develops against the concept of infinite number in his first Parisian text on the mathematics of the infinite, the Accessio ad arithmeticam infinitorum. With this goal, we approach this problem from two angles. The first, rather philosophical or axiomatic, argues against the number of all numbers appealing to a reductio ad absurdum, showing that the acceptance of the infinite number goes against the principle of the whole and the part, which is analytically demonstrated. So, discussing the ideas of Galileo, Leibniz concludes that the infinite number equals 0. Moreover, Leibniz seems to arrive at the same conclusion through his rule for adding the infinite series resulting from the harmonic triangle. Although he acknowledges the conjectural character of this conclusion, he seems to consider it to be a reinforcement of his first argument. Moreover, in reconstructing the justification of the given rule, we try to show that Leibniz does not appeal to the application of infinitesimal quantities, but rather to a treatment of the infinite series in terms of totalities.
Date Added 17/01/2018, 17:50:51
Modified 18/01/2018, 10:30:11

Tags:

  • Galileo,
  • infinite number,
  • infinite series,
  • infinitesimal calculus,
  • Leibniz,
  • mathematical conjecture
  • mathematics,

Notes:

  • Carlos Solis Santos. “El atomismo inane de Galileo.” Theoria 59 (2007): 213-231.
    David Rabouin. “The Difficulty of Being Simple: On Some Interactions Between Mathematics and Philosophy in Leibniz’s Analysis of Notions”. In G. W. Leibniz, interrelations between Mathematics and Philosophy, edited by Norma Goethe, Philip Beeley and David Rabouin, 49-72. Dordrecht; Heidelberg; New York; London: Springer, 2015.
    Eberhard Knobloch. “Galileo and Leibniz: Different Approaches to Infinity.” Archive for History of Exact Sciences, 54 (1999): 87-99.
    Elad Lison. “The Philosophical Assumptions Underlying Leibniz’s Use of the Diagonal Paradox in 1672.” Studia Leibnitiana 38 (2006): 197-208.
    Gottfried W. Leibniz. Sämtliche Schriften und Briefe. Edited by the Deutsche Akademie der Wissenschaften. Darmstadt, Leipzig, Berlin: Akademie-Verlag, 1923 et sq. [Quoted as A, followed by series (in Roman numerals), volume (in Arabic numerals) and page number. Ex.: A VII 6, 600]. 
    Gottfried W. Leibniz. Quadrature arithmétique du cercle, de l’ellipse et de l’hyperbole et la trigonométrie sans tables trigonométriques qui en est le corollaire. Introduction, translation and notes by Marc Parmentier, latin text edited by Eberhard Knobloch. Vrin: Paris, 2004.
    Gregory of Saint Vincent. Opus geometricum quadraturae circuli et sectionum coni. Anvers, 1647.
    Joseph E. Hofmann. Leibniz in Paris, 1672-1676. His growth to mathematical maturity. Cambridge & New York: Cambridge University Press, 1974.
    Manuel Sellés García. “La paradoja de Galileo.” Asclepio. Revista de Historia de la Medicina y de la Ciencia, 58, 1 (2006): 113-148.
    Michel Serfati. “Order in Descartes, Harmony in Leibniz: Two Regulative Principles of Mathematical Analysis.” Studia Leibnitiana 45, 1 (2013): 59-96.
    Michel Serfati. “‘On the Sum of All Differences’ and the Origin of Mathematics According to Leibniz: Mathematical and Philosophical Aspects.” In Perspectives on Theory of Controversies and the Ethics of Communication, edited by Dana Riesenfeld and Giovanni Scarafile, 69-79. Dordrecht; Heidelberg; New York; London: Springer, 2014.
    Oscar M. Esquisabel. “Leibniz: las bases semióticas de la characteristica universalis.” Representaciones, 8, 1 (2012): 5-32.
    Philip Beeley. “Approaching Infinity. Philosophical Consequences of Leibniz’s Mathematical Investigations in Paris and Thereafter.” In The Philosophy of the Young Leibniz, edited by Mark Kulstad, Mogens Laerke, and David Snyder, David (Studia Leibnitiana Sonderheft 35), 29-48. Franz Steiner Verlag: Stuttgart, 2009.
    René Descartes. Oeuvres de Descartes. Edited by Charles Adam and Paul Tannery. Vrin: Paris, 1897-1910. [Quoted as AT, followed by the volume in Roman numbers].
    Richard T. Arthur. “Actual Infinitesimals in Leibniz’s Early Thought.” In The Philosophy of the Young Leibniz, edited by Mark Kulstad, Mogens Laerke, and David Snyder, David (Studia Leibnitiana Sonderheft 35), 11-28. Franz Steiner Verlag: Stuttgart, 2009.
    Samuel Levey. “Leibniz on Mathematics and the Actually Infinite Division of Matter.” The Philosophical Review 107, 1 (1998): 49-96.
    Samuel Levey. “Comparability of Infinities and Infinite Multitude.” In G. W. Leibniz, interrelations between Mathematics and Philosophy, edited by Norma Goethe, Philip Beeley and David Rabouin, 157-187. Dordrecht; Heidelberg; New York; London: Springer, 2015.
    Thomas Hobbes. The English Works of Thomas Hobbes. Edited by William Molesworth, London: Bohn, 1839, vol. 1.
    Ursula Goldenbaum. “Indivisibila Vera – How Leibniz Came to Love Mathematics Appendix: Leibniz’s Marginalia in Hobbes’ Opera Philosophica and De Corpore.” In Infinitesimal Differences: Controversies between Leibniz and his Contemporaries, edited by Ursula Goldenbaum and David Jesseph, 67-76. Berlin and New York: Walter de Gruyter, 2008.

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