Ernst Cassirer's Neo-Kantian Philosophy of Geometry

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
Immanuel Kant (1991). Critique of Pure Reason. In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell. pp. 449-451.
Immanuel Kant (1992). Lectures on Logic. Cambridge University Press.

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Citations of this work BETA
Erich H. Reck (2013). Frege, Dedekind, and the Origins of Logicism. History and Philosophy of Logic 34 (3):242-265.
Jonathan Everett (2015). The Constitutive a Priori and the Distinction Between Mathematical and Physical Possibility. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52:139-152.
Alison Laywine (2014). Kant on Conic Sections. Canadian Journal of Philosophy 44 (5-6):719-758.

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K. Sundaram (1972). Kant or Cassirer: A Study in Complementarity. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 3 (1):40-48.

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