Flagstaff, AZ 86011, US'
author:
- Piotr Błaszczyk
- Vladimir Kanovei
- 'Karin U. Katz'
- 'Mikhail G. Katz'
- Taras Kudryk
- Thomas Mormann
- David Sherry
title: 'Is Leibnizian calculus embeddable in first order logic?'
---

Introduction
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Leibniz famously denied that infinite aggregates can be viewed as *wholes*, on the grounds that they would lead to a violation of the principle that the whole is greater than the part. Yet the infinitary idea is latent in Leibniz in the form of a distinction between *assignable* and *inassignable* quantities [@Ch p. 153], and explicit in his comments as to the violation of Definition V.4 of Euclid’s *Elements* [@Le95b p. 322]. This definition is closely related to what is known since [@Sto83] as the *Archimedean property*, and was translated by Barrow in 1660 as follows:

> *Those numbers are said to have a ratio betwixt them, which being multiplied may exceed one the other* [@Eu60].

Furthermore, Leibniz produced a number of results in infinitesimal calculus which, nowadays, are expressed most naturally by means of quantifiers that range over infinite aggregates. This tension leads us to examine a possible relationship between Leibnizian infinitesimal calculus and a modern logical system known 