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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


Truth and the Absence of Fact

Hartry Field

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199242894
eISBN:
9780191597381
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199242895.001.0001
Subject:
Philosophy, General

This is a collection of papers, written over many years, with substantial postscripts tying them together and giving an updated perspective on them. The first five are on the notions of truth and ... 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


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


Science Without Numbers

Charles S. Chihara

in Constructibility and Mathematical Existence

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

Focuses on Hartry Field's Instrumentalism. The ‘Conservation Theorems’, upon which Field bases so much of his form of Instrumentalism, are examined in detail, as is Field's attempt to ‘nominalize’ ... More


Apriority as an Evaluative Notion

Hartry Field

in New Essays on the A Priori

Published in print:
2000
Published Online:
November 2003
ISBN:
9780199241279
eISBN:
9780191597107
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199241279.003.0006
Subject:
Philosophy, Metaphysics/Epistemology

Hartry Field argues that meaning‐based approaches to explaining the apriority of certain propositions fail to succeed in their endeavour. He suggests that adopting what one calls a ‘non‐factualist’ ... More


Is Platonism Epistemologically Bankrupt?

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:
10.1093/0198236395.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper argues that the epistemological challenge against a Platonist conception of mathematics can be met. The challenge is expounded in a general version and does not rely on the specific ... More


Field and Fregean Platonism

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:
10.1093/0198236395.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper starts by offering a brief reconstruction of the Neo‐Fregean approach as suggested in Frege's Conception of Numbers as Objects and distinguishes various challenges against the method of ... More


Implicit Definition and the a Priori

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:
10.1093/0198236395.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

This paper discusses the idea, labelled as “the traditional connection” that implicit definitions aim to found a priori knowledge of logic and mathematics. In the first part, it discusses and rejects ... More


What Is Mathematics About ?

Michael Dummett

in The Seas of Language

Published in print:
1996
Published Online:
November 2003
ISBN:
9780198236214
eISBN:
9780191597350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198236212.003.0018
Subject:
Philosophy, Philosophy of Language

While it is relatively clear what the subject matter of empirical sciences is, puzzles persist about the proper subject matter of mathematics. The logicists took mathematics to be concerned solely ... More


Deflationism and Mathematical Truth

Charles S. Chihara

in Constructibility and Mathematical Existence

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics

Takes up Field's version of Logicism—a position that he calls ‘deflationism’. Unlike traditional Logicists, Field does not analyse mathematical propositions into purely logical ones, but he does ... More


The Impossibility of Perfection

Micheal Slote

in The Impossibility of Perfection: Aristotle, Feminism, and the Complexities of Ethics

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199790821
eISBN:
9780199919185
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199790821.003.0003
Subject:
Philosophy, Moral Philosophy

This chapter homes in on Aristotle and recent Aristotelianism, which have mainly assumed that the virtues are unified, that in order to have one virtue one must have them all. What can be said about ... More


Epistemology

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/9780199579969.003.0007
Subject:
Philosophy, Moral Philosophy

A common objection to realism (robust or otherwise) is that realists owe us — very roughly speaking — an account of how it is that we can have epistemic access to the normative truths about which ... More


Temporal Substantivalism

Ulrich Meyer

in The Nature of Time

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199599332
eISBN:
9780191760648
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199599332.003.0003
Subject:
Philosophy, Philosophy of Science

This chapter argues against the view that the time-series is made up of metaphysically basic time points. It shows that the only plausible version of such a temporal substantivalism is an ... More


Philosophical Challenges for Scientism (and How to Meet Them?)

Alex Rosenberg

in Scientism: Prospects and Problems

Published in print:
2018
Published Online:
August 2018
ISBN:
9780190462758
eISBN:
9780190462772
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190462758.003.0004
Subject:
Philosophy, Philosophy of Science, General

Scientism is expounded. Then its two major challenges are stated and responses to them sketched. The first challenge is to its epistemology of mathematics-how we know the necessary truths of ... More


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