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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


Reals by Abstraction

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:
10.1093/0198236395.003.0016
Subject:
Philosophy, Logic/Philosophy of Mathematics

The neo‐Fregean argues that principles having a certain `abstractive’ form can play a distinctive foundational role in the philosophy of mathematics––the paradigm being the reduction of elementary ... 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


Introduction

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:
10.1093/0198236395.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

The introduction to The Reason's Proper Study outlines how the essays collected in this volume fit into the broader neo‐Fregean philosophical programme. The notion of an ’abstraction principle’ is ... 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


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


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


The mathematical practice of definitions by abstraction from Euclid to Frege (and beyond)

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/9780198746829.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, History of Philosophy

The first chapter is devoted to showing that, contrary to what Frege intimates in the Grundlagender Arithmetik, abstraction principles were quite widespread in the mathematical practice that preceded ... More


Carving Content at the Joints

Stephen Yablo

in Things: Papers on Objects, Events, and Properties

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199266487
eISBN:
9780191594274
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199266487.003.0011
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

Frege's content carving approach to mathematical ontology overgenerates; for all manner of objects come into view when we recarve, the vast majority with nothing whatsoever to recommend them. This ... More


Hale and Wright on the Metaontology of Neo-Fregeanism

Matti Eklund

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/9780199645268.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

A number of authors—for example Fraser MacBride, Ted Sider, Katherine Hawley, and myself—have recently discussed the issue of the metaontology of the neo-Fregeanism of Bob Hale and Crispin Wright. ... More


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