David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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British Journal for the History of Philosophy 19 (4):759 - 794 (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 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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References found in this work BETA
Immanuel Kant (2007/1991). Critique of Pure Reason. In Elizabeth Schmidt Radcliffe, Richard McCarty, Fritz Allhoff & Anand Vaidya (eds.), Philosophy and Phenomenological Research. Blackwell Pub. Ltd. 449-451.
Michael Friedman (1999). Reconsidering Logical Positivism. Cambridge University Press.
Philip Kitcher (1983). The Nature of Mathematical Knowledge. Oxford University Press.
Paul Guyer (2006). Kant. Routledge.
Citations of this work BETA
Jeremy Heis (2014). Realism, Functions, and the a Priori: Ernst Cassirer's Philosophy of Science. Studies in History and Philosophy of Science Part A 48:10-19.
Jonathan Everett (forthcoming). 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.
Erich H. Reck (2013). Frege, Dedekind, and the Origins of Logicism. History and Philosophy of Logic 34 (3):242-265.
Rossella Lupacchini (2014). Hilbert's Axiomatics as ‘Symbolic Form’? Perspectives on Science 22 (1):1-34.
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