On finite Hume

MacBride, F. (2000) On finite Hume. Philosophia Mathematica, 8(2), pp. 150-159. (doi: 10.1093/philmat/8.2.150)

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Publisher's URL: http://dx.doi.org/10.1093/philmat/8.2.150

Abstract

Neo-Fregeanism contends that knowledge of arithmetic may be acquired by second-order logical reflection upon Hume's principle. Heck argues that Hume's principle doesn't inform ordinary arithmetical reasoning and so knowledge derived from it cannot be genuinely arithmetical. To suppose otherwise, Heck claims, is to fail to comprehend the magnitude of Cantor's conceptual contribution to mathematics. Heck recommends that finite Hume's principle be employed instead to generate arithmetical knowledge. But a better understanding of Cantor's contribution is achieved if it is supposed that Hume's principle really does inform arithmetical practice. More generally, Heck's arguments misconceive the epistemological character of neo-Fregeanism.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Macbride, Professor Fraser
Authors: MacBride, F.
College/School:College of Arts > School of Humanities > Philosophy
Journal Name:Philosophia Mathematica
Publisher:Oxford University Press
ISSN:0031-8019
ISSN (Online):1744-6406

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