Leibniz's Laws of Continuity and Homogeneity

TL;DR

This paper reexamines Leibniz's differential calculus, arguing that his methods were more coherent and logically consistent than critics have claimed, based on detailed textual analysis.

Contribution

It provides a detailed textual analysis showing Leibniz's calculus was free of contradictions, challenging previous criticisms of its foundations.

Findings

Leibniz's methods are more coherent than previously thought

The foundations of Leibniz's calculus are logically consistent

Criticisms of Leibniz's infinitesimal calculus are addressed

Abstract

We explore Leibniz's understanding of the differential calculus, and argue that his methods were more coherent than is generally recognized. The foundations of the historical infinitesimal calculus of Newton and Leibniz have been a target of numerous criticisms. Some of the critics believed to have found logical fallacies in its foundations. We present a detailed textual analysis of Leibniz's seminal text Cum Prodiisset, and argue that Leibniz's system for differential calculus was free of contradictions.