Is Leibnizian calculus embeddable in first order logic?

Foundations of Science 22 (4):73 - 88 (2017)

Authors
Thomas Mormann
University of the Basque Country
David Sherry
Northern Arizona University
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 pro- cedural 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  Leibniz  Weierstrass  Abraham Robinson
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Reprint years 2017
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DOI 10.1007/s10699-016-9495-6
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Ontological Relativity.W. V. Quine - 1968 - Journal of Philosophy 65 (7):185-212.

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