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

Foundations of Science 22 (1):125-140 (2017)

Authors
David Sherry
Northern Arizona University
Abstract
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 between generalization, rigor, and intuition. He further argues that our attempt to show that Cauchy is part of a long infinitesimalist tradition confuses text with context and thereby misunderstands the significance of Cauchy’s use of infinitesimals. Here we defend our original analysis of various misconceptions and misinterpretations concerning the history of infinitesimals and, in particular, the role of infinitesimals in Cauchy’s mathematics. We show that Schubring misinterprets Proclus, Leibniz, and Klein on non-Archimedean issues, ignores the Jesuit context of Moigno’s flawed critique of infinitesimals, and misrepresents, to the point of caricature, the pioneering Cauchy scholarship of D. Laugwitz.
Keywords Archimedean axiom  Cauchy  Felix Klein  Horn-angle  Infinitesimal  Leibniz  Ontology  Procedure
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s10699-015-9473-4
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,223
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

View all 20 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

A Cauchy-Dirac Delta Function.Mikhail G. Katz & David Tall - 2013 - Foundations of Science 18 (1):107-123.
On the Cauchy Completeness of the Constructive Cauchy Reals.Robert S. Lubarsky - 2007 - Mathematical Logic Quarterly 53 (4‐5):396-414.
Cauchy's Continuum.Karin U. Katz & Mikhail G. Katz - 2011 - Perspectives on Science 19 (4):426-452.
Infinitesimals as an Issue of Neo-Kantian Philosophy of Science.Thomas Mormann & Mikhail Katz - 2013 - Hopos: The Journal of the International Society for the History of Philosophy of Science (2):236-280.
Complex Analysis in Subsystems of Second Order Arithmetic.Keita Yokoyama - 2007 - Archive for Mathematical Logic 46 (1):15-35.

Analytics

Added to PP index
2015-12-25

Total views
17 ( #532,097 of 2,285,770 )

Recent downloads (6 months)
8 ( #128,563 of 2,285,770 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature