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Caveats

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/9780199273669.003.0022
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter summarizes the many empirical theories and methods involved in this second-philosophical account of logical truth: the KF-structuring of (much of) the world, the experimental paradigms ... More


Vagueness, Metaphysics, and Objectivity

Stewart Shapiro

in Cuts and Clouds: Vagueness, its Nature, & its Logic

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199570386
eISBN:
9780191722134
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570386.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

One much discussed issue concerns the metaphysical nature, or the source or cause, of vagueness. Is vagueness a purely linguistic matter, concerned (merely) with how the world gets represented via ... More


Ontological Reductionism

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/9780199541492.003.0003
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

The concepts of the previous chapter are applied to projectivism. The metaphysical content of projective sentences is given by the presence of internal attitudes but this content is no part of the ... More


Illustrations and Comparisons

Paul Weirich

in Collective Rationality: Equilibrium in Cooperative Games

Published in print:
2010
Published Online:
September 2009
ISBN:
9780195388381
eISBN:
9780199866700
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195388381.003.0010
Subject:
Philosophy, Logic/Philosophy of Mathematics

A concrete game's strategic equilibria depend on the players' pursuit of incentives in the game. This chapter presents illustrations of strategic equilibria. It also compares strategic equilibria to ... More


Compositionality

Paul Weirich

in Collective Rationality: Equilibrium in Cooperative Games

Published in print:
2010
Published Online:
September 2009
ISBN:
9780195388381
eISBN:
9780199866700
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195388381.003.0011
Subject:
Philosophy, Logic/Philosophy of Mathematics

If the members of a group act rationally, so does the group. Moreover, the rationality of the members' acts explains the rationality of the group's act. The general principle of compositionality ... More


Games of Strategy

Paul Weirich

in Collective Rationality: Equilibrium in Cooperative Games

Published in print:
2010
Published Online:
September 2009
ISBN:
9780195388381
eISBN:
9780199866700
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195388381.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

A solution to a game of strategy assigns a strategy to each player so that the players' combination of strategies is a jointly rational act of the players. Principles governing solutions to games ... More


The Realism Debate

Neil Tennant

in The Taming of the True

Published in print:
2002
Published Online:
October 2011
ISBN:
9780199251605
eISBN:
9780191698057
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199251605.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, Philosophy of Language

This chapter provides a comprehensive survey of concepts and issues concerning the realism debate. It explains that realism comes in two basic varieties: realism about things and realism about truth. ... More


Logic, Graded Belief, and Preferences

David Christensen

in Putting Logic in its Place: Formal Constraints on Rational Belief

Published in print:
2004
Published Online:
July 2005
ISBN:
9780199263257
eISBN:
9780191602603
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199263256.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

Defends probabilistic coherence as a logical constraint on graded belief. Standard Dutch Book and Representation Theorem arguments seek to defend coherence by positing very tight—even ... More


Science without Numbers

Hartry Field

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198777915
eISBN:
9780191823381
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198777915.001.0001
Subject:
Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

The book argues that there is no reason to believe in the existence of mathematical entities, or the literal truth of mathematics, and in particular that physical theory does not require this. The ... More


Second Illustration of Why Mathematical Entities are Useful: Geometry and Distance

Hartry Field

in Science without Numbers

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198777915
eISBN:
9780191823381
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198777915.003.0003
Subject:
Philosophy, Philosophy of Science, Logic/Philosophy of Mathematics

Shows that the use of real numbers in geometry can be accounted for by the conservativeness of mathematics, without assuming the truth of the theory of real numbers. Focuses on Hilbert’s ... More


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