Is Leibnizian calculus embeddable in first order logic?

TL;DR

This paper investigates whether Leibnizian infinitesimal calculus can be represented within first-order logic by focusing on procedural aspects rather than ontological issues, suggesting modern infinitesimal frameworks may be more suitable for interpretation.

Contribution

It demonstrates that first-order logic can potentially embed Leibnizian calculus procedures, favoring modern infinitesimal frameworks over traditional Weierstrassian approaches.

Findings

First-order logic can develop proxies for Leibnizian inferential moves.

Modern infinitesimal frameworks are more suitable for Leibnizian calculus.

Ontological issues are set aside to focus on procedural embedding.

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