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Syntactic Restriction Strategies

Jonathan L. Kvanvig

in The Knowability Paradox

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter examines approaches to the paradox that wish to save anti-realism from the paradox by denying that the knowability assumption is a commitment of anti-realism. Such approaches contend ... More


Review of Dummett's Origins of Analytical Philosophy

Peter Hylton

in Propositions, Functions, and Analysis: Selected Essays on Russell's Philosophy

Published in print:
2005
Published Online:
May 2010
ISBN:
9780199286355
eISBN:
9780191713309
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199286355.003.0007
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

This chapter presents an extended review of Michael Dummett's book The Origins of Analytical Philosophy. It includes a group of essays relating to Russell's logic because the chief ground on which ... More


Intuitionism and Philosophy

Carl Posy*

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print:
2005
Published Online:
July 2005
ISBN:
9780195148770
eISBN:
9780199835560
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195148770.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

After sketching the essentials of L. E. J. Brouwer’s intuitionistic mathematics—separable mathematics, choice sequences, the uniform continuity theorem, and the intuitionistic continuum—this chapter ... More


Long Live the Manifestation Argument

Neil Tennant

in The Taming of the True

Published in print:
2002
Published Online:
October 2011
ISBN:
9780199251605
eISBN:
9780191698057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199251605.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This chapter aims to remedy the deficiencies exposed in philosopher Michael Dummett's manifestation argument as directed against the principle of bivalence. It evaluates the application of the ... More


Logical Necessity *

Ian Rumfitt

in Modality: Metaphysics, Logic, and Epistemology

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199565818
eISBN:
9780191722004
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199565818.003.0003
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

This chapter explains the notion of broadly logical necessity via the principle that ‘It is logically necessary that A’ is equivalent to ‘It is logically contradictory that not A’. The relevant ... More


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

Bob Hale and Crispin Wright

Published in print:
2001
Published Online:
November 2003
ISBN:
9780198236399
eISBN:
9780191597565
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198236395.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This volume collects together 15 papers in which Hale and Wright develop their neo‐Fregean approach to the philosophy of mathematics. Two key aspects of Frege's philosophy are drawn out and defended: ... More


Practice: Construction, Modality, Logic

Stewart Shapiro

in Philosophy of Mathematics: Structure and Ontology

Published in print:
2000
Published Online:
November 2003
ISBN:
9780195139303
eISBN:
9780199833658
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195139305.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter concerns a gap between the practice of mathematics and its current philosophical and semantic foundations. Mathematicians sometimes speak as if they perform constructions and dynamic ... More


The Search for the Diodorean Modal System

Arthur Prior

in Past, Present and Future

Published in print:
1967
Published Online:
October 2011
ISBN:
9780198243113
eISBN:
9780191680632
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198243113.003.0002
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

This chapter covers the following topics: the tense-logical basis of Diodorean modal logic, a matrix for Diodorean modality, modal systems between S4 and S5, Kripke's ‘branching time’ matrix, and ... More


Singular Terms (1)

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:
10.1093/0198236395.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

Inspired by remarks in Gottlob Frege's Grundlagen, Neo‐Fregeans claim that questions about the referentiality of an expression are to be determined through consideration of the expression's ... More


Singular Terms (2) 1

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:
10.1093/0198236395.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

This essay is the sequel to ’Singular Terms (1)’ (also in this volume). After reviewing the criterion for singular termhood proposed in the earlier paper, Hale moves on to considering objections to ... More


Why Frege Does not Deserve His Grain of Salt: A Note on the Paradox of ‘The Concept Horse’ and the Ascription of Bedeutungen to Predicates

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:
10.1093/0198236395.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper offers a new solution to the concept horse paradox, which arises within a Fregean semantics. First, an explication of the well‐known paradox is given and five constraints on a satisfactory ... More


Grundlagen §64

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:
10.1093/0198236395.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

In Section 64 of the Grundlagen, Frege claims that ’the direction of line a = the direction of line b’ and ’lines a and b are parallel’ share the same content, ’carved up’ in different ways. This ... 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


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


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


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


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


To Bury Caesar . . .

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:
10.1093/0198236395.003.0015
Subject:
Philosophy, Logic/Philosophy of Mathematics

In this paper, Bob Hale and Crispin Wright discuss the Caesar Problem, which raises the worry that abstraction principles––like the Direction Equivalence and Hume's Principle ––are subject to an ... More


Logic, Language, and Mathematics: Themes from the Philosophy of Crispin Wright

Alexander Miller (ed.)

Published in print:
2020
Published Online:
August 2020
ISBN:
9780199278343
eISBN:
9780191881442
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199278343.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This Festschrift volume contains a series of specially commissioned papers by leading philosophers on themes from the philosophy of Crispin Wright and a previously unpublished paper by George Boolos, ... More


Foreword

Crispin Wright

in Logic, Language, and Mathematics: Themes from the Philosophy of Crispin Wright

Published in print:
2020
Published Online:
August 2020
ISBN:
9780199278343
eISBN:
9780191881442
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199278343.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter is divided into four parts, corresponding to the partitioning of the essays in the volume. Part I, on neo-Fregeanism in the philosophy of mathematics develops replies to Demopolous, ... More


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