Is Leibnizian calculus embeddable in first order logic?
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
Keywords
Cite
@article{arxiv.1605.03501,
title = {Is Leibnizian calculus embeddable in first order logic?},
author = {Piotr Blaszczyk and Vladimir Kanovei and Karin U. Katz and Mikhail G. Katz and Taras Kudryk and Thomas Mormann and David Sherry},
journal= {arXiv preprint arXiv:1605.03501},
year = {2016}
}
Comments
22 pages, to appear in Foundations of Science