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Realism in Mathematics

Penelope Maddy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort ... More


Causality, Reliabilism, and Mathematical Knowledge

Albert Casullo

in Essays on a Priori Knowledge and Justification: Essays

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199777860
eISBN:
9780199933525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199777860.003.0004
Subject:
Philosophy, Metaphysics/Epistemology, General

Benacerraf maintains that causal constraints on knowledge, such as those imposed by the causal theory of knowledge, are incompatible with knowledge of statements, such as mathematical statements, ... More


Second philosophy of mathematics

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/9780199273669.003.0026
Subject:
Philosophy, Logic/Philosophy of Mathematics

Though extra-mathematical philosophy is irrelevant to the methodological decisions of mathematics, a second-philosophical understanding of the human practice of mathematics requires answers to ... 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


Doubts About Realism

Michael D. Resnik

in Mathematics as a Science of Patterns

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250142
eISBN:
9780191598296
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250142.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

One of the strongest motivations for being an anti‐realist with regard to mathematics is the difficulty in formulating a plausible realist epistemology, given that there seems to be a lack of ties ... More


Conclusion

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.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

The varieties of mathematical realism that are consistent with the indispensability argument are outlined. It is shown that the argument is silent on many issues such as whether numbers are sets, and ... More


Epistemology and Reference

Stewart Shapiro

in Philosophy of Mathematics: Structure and Ontology

Published in print:
2000
Published Online:
November 2003
ISBN:
9780195139303
eISBN:
9780199833658
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195139305.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter deals with matters of epistemology and reference, resolving the well‐known problems with realism or platonism due to Paul Benacerraf. A series of speculative epistemic strategies is ... More


Perception and Intuition

Penelope Maddy

in Realism in Mathematics

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

Begins with a presentation and elaboration of Benacerraf's epistemic challenge to realism: how can we gain knowledge of an acausal world of non‐spatio‐temporal abstracts? I then outline a theory of ... More


Numbers

Penelope Maddy

in Realism in Mathematics

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

Begins with a review of Benacerraf's metaphysical challenge to mathematical realism based on sets: how, for example, can number theory be the study of particular sets when other sets with the same ... More


Mathematical Objectivity and Mathematical Objects

Hartry Field

in Truth and the Absence of Fact

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199242894
eISBN:
9780191597381
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199242895.003.0011
Subject:
Philosophy, General

Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the ... More


On what Possible Worlds could not be (1996)

Robert C. Stalnaker

in Ways a World Might Be: Metaphysical and Anti-Metaphysical Essays

Published in print:
2003
Published Online:
April 2005
ISBN:
9780199251483
eISBN:
9780191602320
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199251487.003.0003
Subject:
Philosophy, Metaphysics/Epistemology

This paper explores the analogy between mathematical Platonism and modal realism, and between Benacerraf’s dilemma and the epistemological objection. It is argued that the parallels and contrasts may ... More


Morality and Mathematics

Justin Clarke-Doane

Published in print:
2020
Published Online:
July 2020
ISBN:
9780198823667
eISBN:
9780191862274
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198823667.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics, Moral Philosophy

This book explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. It argues that ... 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


Could Evolution Explain Our Reliability about Logic?

Joshua Schechter

in Oxford Studies in Epistemology Volume 4

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199672707
eISBN:
9780191751905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199672707.003.0008
Subject:
Philosophy, Metaphysics/Epistemology

We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a ... More


Cognitive Accomplishment in Logic and Mathematics

Agustín Rayo

in The Construction of Logical Space

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199662623
eISBN:
9780191755392
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199662623.003.0004
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

This chapter develops a model of cognitive accomplishment in logic and mathematics. The model is based on the idea that mathematical achievement is not just a matter of acquiring information but also ... More


Intuition as a Source of Evidence?

Jonathan Jenkins Ichikawa and Benjamin W. Jarvis

in The Rules of Thought

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199661800
eISBN:
9780191748325
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199661800.003.0014
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Mind

This chapter generalizes the principal argument from the previous chapter in order to refute weak experientialist rationalism, the view that intuitions are a source of original, a priori ... More


Explaining our Reliability

Justin Clarke-Doane

in Morality and Mathematics

Published in print:
2020
Published Online:
July 2020
ISBN:
9780198823667
eISBN:
9780191862274
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198823667.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics, Moral Philosophy

This chapter discusses the Benacerraf–Field Challenge – i.e., the reliability challenge. It argues that neither Benacerraf’s formulation of the challenge, nor any simple variations on it, satisfies ... More


The Reliability Challenge in Moral Epistemology

Matt Lutz

in Oxford Studies in Metaethics Volume 15

Published in print:
2020
Published Online:
August 2020
ISBN:
9780198859512
eISBN:
9780191891861
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198859512.003.0013
Subject:
Philosophy, Metaphysics/Epistemology, Moral Philosophy

The Reliability Challenge to moral non-naturalism has received substantial attention recently in the literature on moral epistemology. While the popularity of this particular challenge is a recent ... More


Should the Mathematical Fictionalist Be a Moral Fictionalist, Too?

Mary Leng

in Fictionalism in Philosophy

Published in print:
2020
Published Online:
January 2020
ISBN:
9780190689605
eISBN:
9780190689636
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190689605.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

On the face of it, the same motivations that lead some philosophers to adopt mathematical fictionalism seem also to push in the direction of moral fictionalism. In particular, to the extent that ... More


An Unmysterious Color Primitivism

Joshua Gert

in Primitive Colors: A Case Study in Neo-pragmatist Metaphysics and Philosophy of Perception

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198785910
eISBN:
9780191840579
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198785910.003.0002
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Mind

This chapter argues for a primitivist view of color: a view according to which colors are primitive properties—not reducible to such things as sets of spectral reflectances, disjunctions of ... More


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