PP-2007-24: Formalizability and Knowledge Ascriptions in Mathematical Practice

PP-2007-24: Wilhelmus, Eva (2007) Formalizability and Knowledge Ascriptions in Mathematical Practice. [Report]

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Abstract

We investigate the truth conditions of knowledge ascriptions for the case of mathematical knowledge. The availability of a formalizable mathematical proof appears to be a natural criterion: (*) X knows that p iff X has available a formalizable proof of p. Yet, formalizability plays no major role in actual mathematical practice. We present results of an empirical study, which suggest that certain readings of formalizability criteria like (*) are not necessarily applied by mathematicians when ascribing knowledge. Further, we argue that the concept of mathematical knowledge underlying the actual use of 'to know' in mathematical practice is compatible with certain philosophical intuitions, but seems to differ from philosophical knowledge conceptions underlying (*).

Item Type: Report
Report Nr: PP-2007-24
Series Name: Prepublication (PP) Series
Year: 2007
Uncontrolled Keywords: philosophy of mathematics; epistemology; mathematical knowledge
Subjects: Philosophy
Depositing User: Benedikt
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/258

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