Authors
Jeremy Heis
University of California, Irvine
Abstract
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 and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant.
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DOI 10.1080/09608788.2011.583421
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References found in this work BETA

Critique of Pure Reason.Immanuel Kant - 1991 - In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford University Press.
Critique of Pure Reason.Wolfgang Schwarz - 1966 - Philosophy and Phenomenological Research 26 (3):449-451.
Reconsidering Logical Positivism.Michael Friedman - 1999 - Cambridge University Press.

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Citations of this work BETA

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.
The Epistemological Question of the Applicability of Mathematics.Paola Cantù - 2018 - Journal for the History of Analytical Philosophy 6 (3).
Articulating Space in Terms of Transformation Groups: Helmholtz and Cassirer.Francesca Biagioli - 2018 - Journal for the History of Analytical Philosophy 6 (3).
Realism, Functions, and the a Priori: Ernst Cassirer's Philosophy of Science.Jeremy Heis - 2014 - Studies in History and Philosophy of Science Part A 48:10-19.
Dedekind and Cassirer on Mathematical Concept Formation†.Audrey Yap - 2017 - Philosophia Mathematica 25 (3):369-389.

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Idealization in Cassirer's Philosophy of Mathematics.Thomas Mormann - 2008 - Philosophia Mathematica 16 (2):151 - 181.
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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.
Ernst Cassirer. Ausgewählter Wissenschaftlicher Briefwechsel (Review).Thora Ilin Bayer - 2010 - Journal of the History of Philosophy 48 (3):403-404.

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