Scott Edgar
Saint Mary's University
In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and infinitesimals do not entail the paradoxes of the infinitesimal and continuum. Essential to that defense is an interpretation, developed in the paper, of Cohen's positions in the PIM as deeply rationalist. The interest in developing this interpretation is not just that it reveals how Cohen's views in the PIM avoid the paradoxes of the infinitesimal and continuum. It also reveals some of what is at stake, both historically and philosophically, in Russell's criticism of Cohen.
Keywords Hermann Cohen  Neo-Kantianism  Bertrand Russell
Categories (categorize this paper)
DOI 10.1086/710180
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
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

Hermann Cohen on the Role of History in Critical Philosophy.Scott Edgar - 2022 - European Journal of Philosophy 30 (1):148-168.

Add more citations

Similar books and articles

Hermann Cohen on the Concept of History: An Invention of Prophetism?Myriam Bienenstock - 2012 - Journal of Jewish Thought and Philosophy 20 (1):55-70.
Hermann Cohen.Scott Edgar - 2010 - Stanford Encyclopedia of Philosophy.
Cassirer’s Revision of Cohen. Ira - 2019 - Proceedings of the 4th International Conference on Contemporary Education, Social Sciences and Humanities (ICCESSH 2019).
Hermann Cohen's Concept of the Transcendental Method.Vladimir Zeman - 1997 - In Tom Rockmore & Vladimir Zeman (eds.), Transcendental Philosophy and Everyday Experience. Humanities Press. pp. 111-124.
Hermann Cohen, Maimonides, and the Jewish Virtue of Humility.Robert Erlewine - 2010 - Journal of Jewish Thought and Philosophy 18 (1):27-47.
Hermann Cohen's Critical Idealism (Review).Sebastian Luft - 2007 - Journal of the History of Philosophy 45 (4):668-670.


Added to PP index

Total views
420 ( #23,195 of 2,505,142 )

Recent downloads (6 months)
77 ( #10,254 of 2,505,142 )

How can I increase my downloads?


My notes