On finite Hume

Research output: Contribution to journalArticle

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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)150-159
Number of pages10
JournalPhilosophia Mathematica
Volume8
Issue number2
DOIs
Publication statusPublished - 1 Jun 2000