On finite hume

Philosophia Mathematica 8 (2):150-159 (2000)
Fraser MacBride
University of Manchester
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.
Keywords Neo-Fregeanism  Hume's Principle  Finite Hume's Principle  arithmetic  Heck  Wright
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DOI 10.1093/philmat/8.2.150
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The Julio César Problem.Fraser MacBride - 2005 - Dialectica 59 (2):223–236.
The Julio César Problem.Fraser MacBride - 2005 - Dialectica 59 (2):223-236.

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