Russell's paradox in consistent fragments of Frege's grundgesetze der arithmetik

In Godehard Link (ed.), One Hundred Years of Russell’s Paradox. de Gruyter (2004)

Abstract

We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.

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Kai Wehmeier
University of California, Irvine

References found in this work

Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
Saving Frege From Contradiction.George Boolos - 1987 - Proceedings of the Aristotelian Society 87:137--151.
On the Consistency of the First-Order Portion of Frege's Logical System.Terence Parsons - 1987 - Notre Dame Journal of Formal Logic 28 (1):161-168.

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Citations of this work

Materialism and Qualia: The Explanatory Gap.Joseph Levine - 1983 - Pacific Philosophical Quarterly 64 (October):354-61.
Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.

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