Leibniz’s Contested Infinitesimals: Further Depictions

By : Mikhail G. Katz, Karl Kuhlemann

Page No: 77-112

Abstract
We contribute to the lively debate in current scholarship on the Leibnizian calculus. In a recent text, Arthur and Rabouin argue that non-Archimedean continua are incompatible with Leibniz’s concepts of number, quantity and magnitude. They allege that Leibniz viewed infinitesimals as contradictory, and claim to deduce such a conclusion from an analysis of the Leibnizian definition of quantity. However, their argument is marred by numerous errors, deliberate omissions, and misrepresentations, stemming in a number of cases from flawed analyses in their earlier publications. We defend the thesis, traceable to the classic study by Henk Bos, that Leibniz used genuine infinitesimals, which he viewed as fictional mathematical entities (and not merely shorthand for talk about more ordinary quantities) on par with negatives and imaginaries. 2020 Mathematics Subject Classification. Primary 01A45, 01A61 Secondary 01A85, 01A90, 26E35.

Authors
Mikhail G. Katz : Department of Mathematics, Bar Ilan University, Ramat Gan 5290002 Israel.
Karl Kuhlemann : Gottfried Wilhelm Leibniz University Hannover, D-30167 Hannover, Germany.
 

DOI: https://doi.org/10.32381/GB.2023.45.1.4