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

Peter Hylton

Published in print:
2005
Published Online:
May 2010
ISBN:
9780199286355
eISBN:
9780191713309
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199286355.001.0001
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

The work of Bertrand Russell had a decisive influence on the emergence of analytic philosophy, and on its subsequent development. The essays collected in this volume, by one of the authorities on ... More


Conclusion

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/9780199541492.003.0010
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter summaries the key thesis of the book: that, given the Sense/Circumstance/World framework in the philosophy of language, we can show that mathematics expresses objective truths, but not ... More


Frege’s Conception of Logic

Patricia A. Blanchette

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199891610
eISBN:
9780199933211
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199891610.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Frege’s Coneption of Logic explores the relationship between Frege’s understanding of conceptual analysis and his understanding of logic. It is argued that the fruitfulness of Frege’s ... More


Introduction

Patricia A. Blanchette

in Frege’s Conception of Logic

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199891610
eISBN:
9780199933211
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199891610.003.0000
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter lays out the central theme of the book, the interaction between Frege’s understanding of conceptual analysis and his understanding of logic. It also sketches the contents of the ... More


Some Historical Preliminaries

Denis McManus

in The Enchantment of Words: Wittgenstein's “Tractatus Logico-Philosophicus”

Published in print:
2006
Published Online:
January 2007
ISBN:
9780199288021
eISBN:
9780191713446
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199288021.003.0002
Subject:
Philosophy, History of Philosophy

Frege and Russell were particularly important influences on the early Wittgenstein, and this chapter presents a brief sketch of some themes in their work. Two themes in particular are emphasized: (1) ... More


Grundlagen

Michael Potter

in Reason's Nearest Kin: Philosophies of Arithmetic from Kant to Carnap

Published in print:
2002
Published Online:
May 2007
ISBN:
9780199252619
eISBN:
9780191712647
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199252619.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

If our ability to count depends on the structure of space and time, this may explain its applicability to the things we intuit in space and time, but it will also limit its applicability to just ... More


Logicism in the Twenty‐first Century

Bob Hale and Crispin Wright

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:
10.1093/0195148770.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

According to Gottlob Frege, his logicism died when it was discovered that the underlying theory of extensions is inconsistent. The neo-logicist attempts to found mathematics on other abstraction ... More


Logicism Reconsidered

Agustín Rayo

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:
10.1093/0195148770.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

Roughly, logicism is the view that mathematics is logic. This chapter identifies several distinct logicist theses, and shows that their truth-values can be established on minimal assumptions. There ... More


Finding a problem

Michael Potter

in Wittgenstein's Notes on Logic

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199215836
eISBN:
9780191721243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215836.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter addresses the question of what led Wittgenstein to study philosophy with Russell in Cambridge. Since the narrative of Wittgenstein's life before 1911 is well summarized in available ... More


Analytic Philosophy in America: And Other Historical and Contemporary Essays

Scott Soames

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160726
eISBN:
9781400850464
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160726.001.0001
Subject:
Philosophy, American Philosophy

This collection of recent and unpublished essays traces milestones in the field of analytic philosophy from its beginnings in Britain and Germany in the late nineteenth and early twentieth centuries, ... More


The Contradiction (i): The Problem

David Bostock

in Russell's Logical Atomism

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199651443
eISBN:
9780191741197
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199651443.003.0002
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

The chapter gives some background on the mathematical achievements of Cantor and Dedekind, and describes how Russell aimed to show that all mathematics can be derived from a purely logical starting ... 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


Logic in Russell's Logicism

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/9780199286355.003.0004
Subject:
Philosophy, History of Philosophy, Logic/Philosophy of Mathematics

This chapter articulates a major theme in Russell's thought: his conception of logic and of the philosophy of logic. It begins by raising the question of the philosophical significance that logicism, ... More


Abstract Objects: A Case Study

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/9780199266487.003.0009
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

Numbers have many puzzling features. Their properties are mostly essential to them, but they exist in all possible worlds. Number theory seems a priori, yet it makes existence claims and existence ... More


The Oxford Handbook of Philosophy of Mathematics and Logic

Stewart Shapiro (ed.)

Published in print:
2005
Published Online:
July 2005
ISBN:
9780195148770
eISBN:
9780199835560
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0195148770.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. After an introduction, the book begins with a historical section, ... More


Logicism and Conceptual Analysis

Patricia A. Blanchette

in Frege’s Conception of Logic

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199891610
eISBN:
9780199933211
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199891610.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter explains the role of conceptual analysis in Frege’s logicist project. It is explained that Frege employs conceptual analyses in order to reduce arithmetical truths to complexes of ... More


 Philosophy of Mathematics and Its Logic:: Introduction

Stewart Shapiro

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:
10.1093/0195148770.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter provides a broad overview of the philosophy of mathematics and the philosophy of logic. It gives brief coverage to the various issues and positions, such as platonism or realism, ... More


THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL

William Demopoulos and Peter Clark

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:
10.1093/0195148770.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

The common thread running through the logicism of Frege, Dedekind, and Russell is their opposition to the Kantian thesis that our knowledge of arithmetic rests on spatio-temporal intuition. Our ... More


Naturalism Reconsidered

Alan Weir

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:
10.1093/0195148770.003.0014
Subject:
Philosophy, Logic/Philosophy of Mathematics

Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian ... 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


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