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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


Abstraction and Epistemic Entitlement: On the Epistemological Status of Hume’s Principle

Crispin Wright

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/9780199645268.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

The abstractionist program of foundations for classical mathematical theories is, like its traditional logicist ancestors, first and foremost an epistemological project. Its official aim is to ... 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


In good company? On Hume’s Principle and the assignment of numbers to infinite concepts

Paolo Mancosu

in Abstraction and Infinity

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198746829
eISBN:
9780191809095
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198746829.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics, History of Philosophy

In this chapter Mancosu generalizes some worries, raised by Richard Heck, emerging from the theory of numerosities (discussed in Chapter 3) to a line of thought resulting in what he calls a ‘good ... More


Field and Fregean Platonism

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:
10.1093/0198236395.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper starts by offering a brief reconstruction of the Neo‐Fregean approach as suggested in Frege's Conception of Numbers as Objects and distinguishes various challenges against the method of ... More


Abstraction and Infinity

Paolo Mancosu

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198746829
eISBN:
9780191809095
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198746829.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, History of Philosophy

The book provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. The notion of abstraction in question is that ... More


Relax? Don’t Do It! Why Moral Realism Won’t Come Cheap

Sarah McGrath

in Oxford Studies in Metaethics, Volume 9

Published in print:
2014
Published Online:
June 2014
ISBN:
9780198709299
eISBN:
9780191781056
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198709299.003.0008
Subject:
Philosophy, Moral Philosophy

Relaxed realists hold that there are deep differences between moral truths and the truths studied by the empirical sciences, but they deny that these differences raise troubling metaphysical or ... More


Caesar and Circularity

William Stirton

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/9780199645268.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

The purpose of the article is to discuss whether HP can be counted as a potential definition of the function taking a concept to its cardinality. Frege himself argued for a negative answer to this ... More


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