# Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond

@article{Katz2013LeibnizsIT, title={Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond}, author={Mikhail G. Katz and David Sherry}, journal={Erkenntnis}, year={2013}, volume={78}, pages={571-625} }

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others…

## 67 Citations

EQUIVOCATION IN THE FOUNDATIONS OF LEIBNIZ’S INFINITESIMAL FICTIONS

- Philosophy
- 2012

In this article, I address two different kinds of equivocations in reading Leibniz’s fictional infinite and infinitesimal. These equivocations form the background of a reductive reading of infinite…

Leibniz�s well-founded fictions and their interpetations

- PhilosophyMatematychni Studii
- 2018

Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that of…

Namur Is mathematical history written by the victors ?

- Mathematics

We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy…

Procedures of Leibnizian infinitesimal calculus: an account in three modern frameworks

- PhilosophyBritish Journal for the History of Mathematics
- 2021

Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g. Ishiguro,…

LEIBNIZ ON BODIES AND INFINITIES: RERUM NATURA AND MATHEMATICAL FICTIONS

- PhilosophyThe Review of Symbolic Logic
- 2021

The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often…

Leibniz versus Ishiguro: Closing a Quarter Century of Syncategoremania

- PhilosophyHOPOS: The Journal of the International Society for the History of Philosophy of Science
- 2016

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter…

Infinitesimals as an Issue of Neo-Kantian Philosophy of Science

- PhilosophyHOPOS: The Journal of the International Society for the History of Philosophy of Science
- 2013

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely, the so-called revolution in rigor in…

Ju n 20 13 IS MATHEMATICAL HISTORY WRITTEN BY THE VICTORS ?

- Mathematics
- 2013

We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy…

Interpreting the Infinitesimal Mathematics of Leibniz and Euler

- Philosophy
- 2016

Abstract
We apply Benacerraf’s distinction between mathematical ontology and mathematical practice (or the structures mathematicians use in practice) to examine contrasting interpretations of…

Controversies in the Foundations of Analysis: Comments on Schubring’s Conflicts

- Philosophy
- 2016

Foundations of Science recently published a rebuttal to a portion of our essay it published 2 years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his 2005 book, Conflicts…

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