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Is Hume's Principle Analytic?

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:
10.1093/0198236395.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper is a reply to George Boolos's three papers (Boolos (1987a, 1987b, 1990a)) concerned with the status of Hume's Principle. Five independent worries of Boolos concerning the status of Hume's ... More


On the Philosophical Significance of Frege's Theorem

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:
10.1093/0198236395.003.0013
Subject:
Philosophy, Logic/Philosophy of Mathematics

Frege's theorem is the result that elementary arithmetic may be derived from the second‐ order sentence often referred to as ’Hume's Principle’ (HP). In this essay, Wright considers whether ... More


Implicit Definition and the a Priori

Bob Hale and 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:
10.1093/0198236395.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper discusses the idea, labelled as “the traditional connection” that implicit definitions aim to found a priori knowledge of logic and mathematics. In the first part, it discusses and rejects ... More


Postscript

Bob Hale and 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:
10.1093/0198236395.003.0017
Subject:
Philosophy, Logic/Philosophy of Mathematics

This postscript outlines 18 outstanding issues for the neo‐Fregean programme, which are divided into three categories. The first of these concerns the nature and philosophical significance of the ... More


Dummett's Critique of Wright's Attempt to Resuscitate Frege

Bob Hale

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:
10.1093/0198236395.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

In Frege: Philosophy of Mathematics (1991), Michael Dummett argues that the neo‐Fregean programme––championed by Crispin Wright––is destined to fail for four reasons: (i) no satisfactory solution has ... More


On the Harmless Impredicativity of N= (Hume's Principle )

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:
10.1093/0198236395.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

To play its intended role in the derivation of the axioms of arithmetic (Frege's Theorem), Hume's Principle has to be taken to be impredicative, i.e. the cardinality operator has to be applicable to ... More


Objections and Comparisons

Alan Weir

in Truth Through Proof: A Formalist Foundation for Mathematics

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199541492
eISBN:
9780191594915
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541492.003.0005
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

Relativism is distinguished from pluralism; mathematical theses which are true in some systems but not others are held to express different propositions which different truth values in each. ... More


Hume’s Principle and Entitlement: On the Epistemology of the Neo-Fregean Program

Nikolaj Jang Lee Pedersen

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/9780199645268.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

Hume’s Principle (HP) is the key principle in the neo-Fregean account of arithmetical knowledge. In discussing the epistemology of the neo-Fregean program, Crispin Wright has proposed that acceptance ... More


Critical Notice of Michael Dummett's Frege: Philosophy of Mathematics

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:
10.1093/0198236395.003.0010
Subject:
Philosophy, Logic/Philosophy of Mathematics

Though Michael Dummett's assessment of Frege's philosophy of mathematics in Frege: Philosophy of Mathematics (1991) is strikingly positive compared to the one given in Frege: Philosophy of Language ... More


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


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