Infinitesimals and Other Idealizing Completions in Neo-Kantian Philosophy of Mathematics

Abstract
We seek to elucidate the philosophical context in which the so-called revolution of rigor in inifinitesimal calculus and mathematical analysis took place. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at that time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our main thesis is that Marburg Neo-Kantian philosophy formulated a sophisticated position towards the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals, nor whiggishly subscribed to the new orthodoxy of the "great triumvirate" of Cantor, Dedekind, and Weierstrass. Expressed in terms of modern mathematics, the Marburg philosophers saw the introduction of both infinitesimals and limits as completions whose prototype was Dedekind's of the rational number system resulting in the real numbers. At least partially,, this idea of "completions" can be captured in terms of a category-theoretical description of the conceptual development of modern mathematics. The feasibility of such a modern reformuation may be taken as evidence that the philosophical resources of Marburg neo-Kantianism may be of interest even for contemporary philosophy of mathematics.
Keywords Infinitesimals  Limits  Philosophy of mathematics  Neo-Kantianism  Hermann Cohen  Natorp  Cassirer  Cantor  Robinson
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Translate to english
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,621
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

No citations found.

Add more citations

Similar books and articles
Ernst Cassirer's Neo-Kantian Philosophy of Geometry.Jeremy Heis - 2011 - British Journal for the History of Philosophy 19 (4):759 - 794.
Hermann Cohen.Scott Edgar - 2010 - Stanford Encyclopedia of Philosophy.
Ernst Cassirer. Ausgewählter Wissenschaftlicher Briefwechsel (Review).Thora Ilin Bayer - 2010 - Journal of the History of Philosophy 48 (3):403-404.
What Does (the Young) Heidegger Mean by the Seinsfrage?Carleton B. Christensen - 1999 - Inquiry : An Interdisciplinary Journal of Philosophy 42 (3 & 4):411 – 437.
Idealization in Cassirer's Philosophy of Mathematics.Thomas Mormann - 2007 - Philosophia Mathematica 16 (2):151 - 181.
Is Cassirer a Neo-Kantian Methodologically Speaking?Massimo Ferrari - 2009 - In Rudolf A. Makkreel & Sebastian Luft (eds.), Neo-Kantianism in Contemporary Philosophy. Indiana University Press.

Monthly downloads

Added to index

2011-11-13

Total downloads

91 ( #56,771 of 2,168,962 )

Recent downloads (6 months)

1 ( #346,364 of 2,168,962 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums