Synthese 199 (1-2):1409-1434 (2020)

Abstract
Additional theorizing about mathematical practice is needed in order to ground appeals to truly useful notions of the virtues in mathematics. This paper aims to contribute to this theorizing, first, by characterizing mathematical practice as being epistemic and “objectual” in the sense of Knorr Cetina The practice turn in contemporary theory, Routledge, London, 2001). Then, it elaborates a MacIntyrean framework for extracting conceptions of the virtues related to mathematical practice so understood. Finally, it makes the case that Wittgenstein’s methodology for examining mathematics and its practice is the most appropriate one to use for the actual investigation of mathematical practice within this MacIntyrean framework. At each stage of thinking through mathematical practice by these means, places where new virtue-theoretic questions are opened up for investigation are noted and briefly explored.
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DOI 10.1007/s11229-020-02802-0
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References found in this work BETA

Philosophical Investigations.Ludwig Josef Johann Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell.
After Virtue: A Study in Moral Theory.Alasdair C. MacIntyre - 1983 - University of Notre Dame Press.
Philosophy and Real Politics.Raymond Geuss - 2008 - Princeton University Press.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.

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