# Infinitesimals as an Issue of Neo-Kantian Philosophy of Science

@article{Mormann2013InfinitesimalsAA, title={Infinitesimals as an Issue of Neo-Kantian Philosophy of Science}, author={Thomas Mormann and Mikhail G. Katz}, journal={HOPOS: The Journal of the International Society for the History of Philosophy of Science}, year={2013}, volume={3}, pages={236 - 280} }

We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely, the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others… Expand

#### 19 Citations

Namur Is mathematical history written by the victors ?

We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy… Expand

Ju n 20 13 IS MATHEMATICAL HISTORY WRITTEN BY THE VICTORS ?

- 2013

We examine prevailing philosophical and historical views about the origin of infinitesimal mathematics in light of modern infinitesimal theories, and show the works of Fermat, Leibniz, Euler, Cauchy… Expand

Hermann Cohen's Das Princip der Infinitesimal-Methode: The history of an unsuccessful book.

- Philosophy, Medicine
- Studies in history and philosophy of science
- 2016

The "puzzle of Cohen's Infinitesimalmethode" can be solved by looking beyond the scholarly results of the book, and instead focusing on the style of philosophy it exemplified, which is shown to be Marburg Neo-Kantianism. Expand

Hermann Cohen’s Principle of the Infinitesimal Method: A Defense

- HOPOS: The Journal of the International Society for the History of Philosophy of Science
- 2020

In Bertrand Russell’s 1903 The Principles of Mathematics, he offers an apparently devastating criticism of The Principle of the Infinitesimal Method and Its History (PIM) by the neo-Kantian Hermann… Expand

Leibniz's well-founded fictions and their interpretations

- Philosophy, Mathematics
- 2018

Leibniz used the term fiction in conjunction with infinitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that of… Expand

Procedures of Leibnizian infinitesimal calculus: an account in three modern frameworks

- Mathematics
- 2020

Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g.,… Expand

Cohen’s Logik der reinen Erkenntnis and Cassirer’s Substanzbegriff und Funktionsbegriff

- 2020

Abstract This paper compares Cohen’s Logic of Pure Knowledge and Cassirer’s Substance and Function in order to evaluate how in these works Cohen and Cassirer go beyond the limits established by… Expand

Proofs and Retributions, Or: Why Sarah Can’t Take Limits

- Philosophy
- 2015

The small, the tiny, and the infinitesimal (to quote Paramedic) have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that… Expand

Is mathematical history written by the victors

- Mathematics
- 2013

The ABCs of the History of Infinitesimal Mathematics The ABCs of the history of infinitesimal mathematics are in need of clarification. To what extent does the famous dictum “history is always… Expand

Is Leibnizian Calculus Embeddable in First Order Logic?

- Computer Science, Mathematics
- 2016

If, as it is argued here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal calculus, then modern infiniteimal frameworks are more appropriate to interpreting LeibNizianInfinity calculus than modern Weierstrassian ones. Expand

#### References

SHOWING 1-10 OF 84 REFERENCES

Ernst Cassirer's Neo-Kantian Philosophy of Geometry

- Philosophy
- 2011

One of the most important philosophical topics in the early twentieth century – and a topic that was seminal in the emergence of analytic philosophy – was the relationship between Kantian philosophy… Expand

Hermann Cohen's Das Prinzip der Infinitesimalmethode, Ernst Cassirer, and the Politics of Science in Wilhelmine Germany

- Philosophy
- Perspectives on Science
- 2003

Few texts summarize and at the same time compound the challenges of their author's philosophy so sharply as Hermann Cohen's Das Prinzip der Infinitesimalmethode und seine Geschichte (1883). The… Expand

Critical philosophy begins at the very point where logistic leaves off: Cassirer's Response to Frege and Russell

- Philosophy
- Perspectives on Science
- 2010

This paper concerns the reception of the new logic and logicism of Frege and Russell among the German Neo-Kantian philosophers of the Marburg school. Paul Natorp and Ernst Cassirer both object to… Expand

Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond

- Philosophy, Mathematics
- 2013

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s… Expand

Mathematical Metaphors in Natorp’s Neo-Kantian Epistemology and Philosophy of Science

- Philosophy
- 2005

A basic thesis of Neokantian epistemology and philosophy of science contends that the knowing subject and the object to be known are only abstractions. What really exists, is the relation between… Expand

Cassirer, Reader, Publisher, and Interpreter of Leibniz’s Philosophy

- Philosophy
- 2012

As early as 1894, Cassirer began an in-depth study of the writings of Kant, Leibniz, and Descartes, and of Hermann Cohen as well. But it wasn’t until the spring of 1896 that he began to attend… Expand

Infinitesimals, Imaginaries, Ideals, and Fictions

- Philosophy, Mathematics
- 2012

Leibniz entertained various conceptions of infinitesimals, considering them sometimes as ideal things and other times as fictions. But in both cases, he compares infinitesimals favorably to imaginary… Expand

Debates about infinity in mathematics around 1890: The Cantor-Veronese controversy, its origins and its outcome

- Philosophy, Mathematics
- 1998

This article was found among the papers left by Prof. Laugwitz (May 5, 1932–April 17, 2000). The following abstract is extracted from a lecture he gave at the Fourth Austrain Symposion on the History… Expand

Leibniz, Gottfried Wilhelm

- Philosophy
- 2013

Gottfried Wilhelm Leibniz (1646–1716) was a German philosopher, mathematician, physicist, scientist, politician, diplomat, historian and librarian. He is known as the last universal genius and as one… Expand

Idealization in Cassirer's Philosophy of Mathematics†

- Philosophy
- 2007

The notion of idealization has received considerable attention in contemporary philosophy of science but less in philosophy of mathematics. An exception was the ‘critical idealism’ of the neo-Kantian… Expand