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AbstractionismEssays in Philosophy of Mathematics$
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Philip A Ebert and Marcus Rossberg

Print publication date: 2016

Print ISBN-13: 9780199645268

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780199645268.001.0001

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Impredicativity in the Neo-Fregean Program

Impredicativity in the Neo-Fregean Program

Chapter:
12 (p.247) Impredicativity in the Neo-Fregean Program
Source:
Abstractionism
Author(s):

Øystein Linnebo

Philip A. Ebert

Marcus Rossberg

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199645268.003.0012

This article examines the role and legitimacy of impredicative reasoning in the neo-Fregean program. Two different forms of such reasoning are distinguished, the main arguments about their legitimacy are disentangled and analyzed, and relevant technical results are stated. It is suggested that certain mild predicativity restrictions may lead to fruitful theories of abstraction.

Keywords:   abstraction, Dummett, Frege, Hale, logicism, neo-logicism, predicativity, Wright

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