Is Leibnizian Calculus Embeddable in First Order Logic?

Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann, David Sherry

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones.

Original languageEnglish (US)
Pages (from-to)717-731
Number of pages15
JournalFoundations of Science
Volume22
Issue number4
DOIs
StatePublished - Dec 1 2017

Keywords

  • Abraham Robinson
  • First order logic
  • Infinitesimal calculus
  • Leibniz
  • Ontology
  • Procedures
  • Weierstrass

ASJC Scopus subject areas

  • General
  • History and Philosophy of Science

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    Błaszczyk, P., Kanovei, V., Katz, K. U., Katz, M. G., Kudryk, T., Mormann, T., & Sherry, D. (2017). Is Leibnizian Calculus Embeddable in First Order Logic? Foundations of Science, 22(4), 717-731. https://doi.org/10.1007/s10699-016-9495-6