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Talking About Nothing: Numbers, Hallucinations and Fictions

Jody Azzouni

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199738946
eISBN:
9780199866175
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199738946.001.0001
Subject:
Philosophy, General

Ordinary language and scientific language enable us to speak about, in a singular way (with demonstratives and names), what we recognize not to exist: fictions, the contents of our hallucinations, ... More


Constructibility and Mathematical Existence

Charles S. Chihara

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ... More


The Indispensability of Mathematics

Mark Colyvan

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195137545
eISBN:
9780199833139
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019513754X.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical ... More


Deflating Existential Consequence: A Case for Nominalism

Jody Azzouni

Published in print:
2004
Published Online:
January 2005
ISBN:
9780195159882
eISBN:
9780199834990
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0195159888.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

What in our theoretical pronouncements commits us to objects? The Quinean standard for ontological commitment involves (nearly enough) commitments when we utter “there is” or “there are” statements ... More


Mathematics and Reality

Mary Leng

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199280797
eISBN:
9780191723452
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199280797.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This book offers a defence of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical ... More


Introduction

Mary Leng

in Mathematics and Reality

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199280797
eISBN:
9780191723452
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199280797.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter introduces the indispensability argument for the existence of mathematical objects, presenting it as relying on three premises: (P1) Naturalism, (P2) Confirmational Holism, and (P3) ... More


The Indispensability of Mathematics

Mary Leng

in Mathematics and Reality

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199280797
eISBN:
9780191723452
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199280797.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter discusses Hartry Field's attempt to respond to the indispensability argument by showing how to dispense with mathematics in formulating our best scientific theories. It is pointed out ... More


Conclusion

Mary Leng

in Mathematics and Reality

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199280797
eISBN:
9780191723452
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199280797.003.0010
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

This chapter sums up the argument of the book, and ties up a few loose ends. In particular, it considers Michael Resnik's alternative ‘pragmatic’ version of the indispensability argument, and shows ... More


Pragmatism and Moral Objectivity

Hilary Putnam

in Women, Culture, and Development: A Study of Human Capabilities

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198289647
eISBN:
9780191596698
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198289642.003.0008
Subject:
Economics and Finance, Development, Growth, and Environmental

Putnam engages with moral objectivity and the question of ethical truth in this paper, in which he combats the idea that there is no intellectual structure worth taking seriously to the arguments of ... More


Mathematics in application

Penelope Maddy

in Second Philosophy: A Naturalistic Method

Published in print:
2007
Published Online:
January 2009
ISBN:
9780199273669
eISBN:
9780191706264
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199273669.003.0024
Subject:
Philosophy, Logic/Philosophy of Mathematics

Turning now to the role of mathematics in natural science, this chapter takes up a number of themes. First, the Quine/Putnam idea that the indispensability of mathematics for much of science confirms ... More


Does Ontology Rest on a Mistake?

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/9780199266487.003.0006
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

A line of research aimed at determining whether Chicago, April, Spanish, etc., really exist can seem naive to the point of comicality. It's as though one were to call for research into whether April ... More


Apriority and Existence

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/9780199266487.003.0007
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

Quineans think that to establish the existence of so and so's, one must take a holistic a posteriori indispensability argument. Rationalists think that the existence of so and so's follows from a ... More


Go Figure: A Path through Fictionalism

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/9780199266487.003.0008
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

This chapter distinguishes several grades of fictionalism about an area of discourse. Instrumentalists think we assert nothing with a sentence S of the relevant type. Meta-fictionalists have us ... 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


Mathematics and Scientific Representation

Christopher Pincock

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199757107
eISBN:
9780199932313
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199757107.001.0001
Subject:
Philosophy, Philosophy of Science

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this ... More


Quine and the Web of Belief

Michael D. Resnik

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:
10.1093/0195148770.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics

The chapter presents a largely sympathetic account of W. V. O. Quine’s account of mathematics and logic. The themes of naturalism, confirmational holism, and ontological relativity are discussed in ... More


Three Forms of Naturalism

Penelope Maddy

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:
10.1093/0195148770.003.0013
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter compares and contrasts Quine’s naturalism with the versions of two post-Quineans (Burgess and Maddy) on the nature of science, logic, and mathematics. The role of indispensability in the ... More


Nominalism

Charles Chihara

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:
10.1093/0195148770.003.0015
Subject:
Philosophy, Logic/Philosophy of Mathematics

Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of ... More


Explanation

Christopher Pincock

in Mathematics and Scientific Representation

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199757107
eISBN:
9780199932313
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199757107.003.0010
Subject:
Philosophy, Philosophy of Science

This chapter explores the more recent attempts to rescue the indispensability argument for platonism by appeal to the explanatory contributions which mathematics makes in science. Pincock argues that ... More


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