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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


Mathematics and Its Applications

Mark Colyvan

in The Indispensability of Mathematics

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195137545
eISBN:
9780199833139
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019513754X.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Indispensability arguments are introduced and their connection to scientific realism is discussed. The Quine–Putnam indispensability argument for mathematical realism is then outlined. In particular, ... More


The Argument from the Deliberative Indispensability of Irreducibly Normative Truths

David Enoch

in Taking Morality Seriously: A Defense of Robust Realism

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199579969
eISBN:
9780191729010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199579969.003.0003
Subject:
Philosophy, Moral Philosophy

This chapter develops a positive argument for Robust Metanormative Realism that is modeled after indispensability arguments in the philosophy of mathematics or inferences to the best explanation more ... More


Indispensability

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/9780199757107.003.0009
Subject:
Philosophy, Philosophy of Science

An indispensability argument uses the central role of mathematics in science to argue for a particular interpretation of pure mathematics. This chapter considers three different indispensability ... More


Maddy's Objections

Mark Colyvan

in The Indispensability of Mathematics

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195137545
eISBN:
9780199833139
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019513754X.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

Penelope Maddy's objections to the indispensability argument are considered. In two of her objections – the objection from scientific fictions and the objection from the role of mathematics in ... 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


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


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


Field's Fictionalism

Mark Colyvan

in The Indispensability of Mathematics

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195137545
eISBN:
9780199833139
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019513754X.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

Hartry Field has attacked the indispensability argument by arguing that mathematics is in fact dispensable to science. He does this by showing a way to dispense with quantification over mathematical ... 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


Mathematical Explanation: Why it Matters

Paolo Mancosu

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter offers a broad survey of the literature on mathematical explanation, and shows the importance of this area of work for a philosophical understanding of mathematical practice and for ... 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


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


The Quinean Backdrop

Mark Colyvan

in The Indispensability of Mathematics

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195137545
eISBN:
9780199833139
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019513754X.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

The thesis that philosophy is continuous with science is defended and distinguished from another influential version of naturalism. Holism is then discussed with particular emphasis on the kind of ... 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


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


Explaining with Mathematics? From Cicadas to Symmetry

Otávio Bueno and Steven French

in Applying Mathematics: Immersion, Inference, Interpretation

Published in print:
2018
Published Online:
June 2018
ISBN:
9780198815044
eISBN:
9780191852862
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198815044.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

The putative explanatory role of mathematics is further pursued in this chapter in the context of the so-called indispensability argument. Our conclusion here is that the possibility of mathematical ... More


General Conclusion

Jody Azzouni

in Ontology Without Borders

Published in print:
2017
Published Online:
August 2017
ISBN:
9780190622558
eISBN:
9780190622589
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190622558.003.0012
Subject:
Philosophy, Philosophy of Language, Metaphysics/Epistemology

Some general remarks are given about methods of argument in metaphysics. The importance of indispensability arguments, and the importance of the fact that such arguments don’t succeed, is reiterated. ... More


The Challenge of Platonism

William Lane Craig

in God Over All: Divine Aseity and the Challenge of Platonism

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198786887
eISBN:
9780191829024
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198786887.003.0003
Subject:
Religion, Philosophy of Religion

The Indispensability Argument, the most important contemporary argument in support of Platonism, is summarized and explained. At the heart of that argument lies (i) a criterion of ontological ... More


God Over All: Divine Aseity and the Challenge of Platonism

William Lane Craig

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198786887
eISBN:
9780191829024
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198786887.001.0001
Subject:
Religion, Philosophy of Religion

God Over All is a defence of God’s aseity and unique status as the Creator of all things apart from Himself in the face of the challenge posed by mathematical Platonism, which holds that there are ... More


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