Is Leibnizian Calculus Embeddable in First Order Logic?

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

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.

Keywords

First order logic Infinitesimal calculus Ontology Procedures Leibniz Weierstrass Abraham Robinson 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Piotr Błaszczyk
    • 1
  • Vladimir Kanovei
    • 2
    • 3
  • Karin U. Katz
    • 4
  • Mikhail G. Katz
    • 4
  • Taras Kudryk
    • 5
  • Thomas Mormann
    • 6
  • David Sherry
    • 7
  1. 1.Institute of MathematicsPedagogical University of CracowCracowPoland
  2. 2.IPPIMoscowRussia
  3. 3.MIITMoscowRussia
  4. 4.Department of MathematicsBar Ilan UniversityRamat GanIsrael
  5. 5.Department of MathematicsLviv National UniversityLvivUkraine
  6. 6.Department of Logic and Philosophy of ScienceUniversity of the Basque Country UPV/EHUDonostia San SebastianSpain
  7. 7.Department of PhilosophyNorthern Arizona UniversityFlagstaffUSA

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