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

Research output: Contribution to journalArticle

Abstract

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 interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions.

Original languageEnglish (US)
Pages (from-to)117-147
Number of pages31
JournalHOPOS
Volume6
Issue number1
DOIs
StatePublished - Mar 1 2016

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Gottfried Wilhelm Leibniz
Fiction
Logic
Euclid's Elements
Calculi
Infinity
Shorthand
Historical Evidence

ASJC Scopus subject areas

  • History and Philosophy of Science

Cite this

Bascelli, T., Błaszczyk, P., Kanovei, V., Katz, K. U., Katz, M. G., Schaps, D. M., & Sherry, D. (2016). Leibniz versus Ishiguro: Closing a quarter century of syncategoremania. HOPOS, 6(1), 117-147. https://doi.org/10.1086/685645

Leibniz versus Ishiguro : Closing a quarter century of syncategoremania. / Bascelli, Tiziana; Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Karin U.; Katz, Mikhail G.; Schaps, David M.; Sherry, David.

In: HOPOS, Vol. 6, No. 1, 01.03.2016, p. 117-147.

Research output: Contribution to journalArticle

Bascelli, T, Błaszczyk, P, Kanovei, V, Katz, KU, Katz, MG, Schaps, DM & Sherry, D 2016, 'Leibniz versus Ishiguro: Closing a quarter century of syncategoremania', HOPOS, vol. 6, no. 1, pp. 117-147. https://doi.org/10.1086/685645
Bascelli T, Błaszczyk P, Kanovei V, Katz KU, Katz MG, Schaps DM et al. Leibniz versus Ishiguro: Closing a quarter century of syncategoremania. HOPOS. 2016 Mar 1;6(1):117-147. https://doi.org/10.1086/685645
Bascelli, Tiziana ; Błaszczyk, Piotr ; Kanovei, Vladimir ; Katz, Karin U. ; Katz, Mikhail G. ; Schaps, David M. ; Sherry, David. / Leibniz versus Ishiguro : Closing a quarter century of syncategoremania. In: HOPOS. 2016 ; Vol. 6, No. 1. pp. 117-147.
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