Richard T. W. Arthur
McMaster University
In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests, I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1007/s00407-013-0119-z
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,683
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Leibniz Versus Ishiguro: Closing a Quarter Century of Syncategoremania.Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, David M. Schaps & David Sherry - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):117-147.
Actual and Ideal Infinitesimals in Leibniz’s Specimen Dynamicum.Tzuchien Tho - 2016 - Journal of Early Modern Studies 5 (1):115-142.


Added to PP index

Total views
1 ( #1,516,202 of 2,462,378 )

Recent downloads (6 months)
1 ( #449,313 of 2,462,378 )

How can I increase my downloads?


Sorry, there are not enough data points to plot this chart.

My notes