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Response to Dummett

Crispin Wright

in The Reason's Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics

Published in print:
2001
Published Online:
November 2003
ISBN:
9780198236399
eISBN:
9780191597565
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198236395.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics

Crispin Wright's neo‐Fregean approach to arithmetic––centred around Hume's Principle (N=)––involves two claims to the effect that (i) being informed that Hume's Principle is analytic of the ... More


Conservativeness, Cardinality, and Bad Company

Roy T. Cook, Philip A. Ebert, and Marcus Rossberg

in Abstractionism: Essays in Philosophy of Mathematics

Published in print:
2016
Published Online:
January 2017
ISBN:
9780199645268
eISBN:
9780191755330
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199645268.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper argues that abstraction principles must be conservative in a number of distinct senses if they are to be acceptable, and uses this insight to present a solution to the Bad Company Problem. ... More


Introduction to Abstractionism

Philip A. Ebert and Marcus Rossberg

in Abstractionism: Essays in Philosophy of Mathematics

Published in print:
2016
Published Online:
January 2017
ISBN:
9780199645268
eISBN:
9780191755330
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199645268.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

We offer a general introduction to Abstractionism by outlining its history and by presenting the core philosophical and mathematical tenets of the abstractionist projects. We then locate the 16 ... More


Ineffability within the Limits of Abstraction Alone

Stewart Shapiro and Gabriel Uzquiano

in Abstractionism: Essays in Philosophy of Mathematics

Published in print:
2016
Published Online:
January 2017
ISBN:
9780199645268
eISBN:
9780191755330
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199645268.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics

The purpose of this article is to assess the prospects for a Scottish neo-logicist foundation for a set theory. We show how to reformulate a key aspect of our set theory as a neo-logicist abstraction ... More


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