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Gödel’s incompleteness theorems, free will and mathematical thought

SOLOMON FEFERMAN

in Free Will and Modern Science

Published in print:
2011
Published Online:
January 2013
ISBN:
9780197264898
eISBN:
9780191754074
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197264898.003.0007
Subject:
Philosophy, Philosophy of Mind

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical ... More


Gödel's Theorem

Graham Priest

in In Contradiction

Published in print:
2006
Published Online:
May 2007
ISBN:
9780199263301
eISBN:
9780191718823
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199263301.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter presents an argument for dialetheism which draws on Gödel's first incompleteness theorem. This is a non-constructive argument, which does not produce dialetheias explicitly, but shows ... More


The Transaction-Cost Approach

Pol Antràs

in Global Production: Firms, Contracts, and Trade Structure

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691168272
eISBN:
9781400873746
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691168272.003.0006
Subject:
Economics and Finance, Macro- and Monetary Economics

This chapter develops a transaction-cost model of the internalization decision of multinational firms. A key organizational decision of firms is the extent of control that firms choose to exert over ... More


The Property-Rights Approach

Pol Antràs

in Global Production: Firms, Contracts, and Trade Structure

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691168272
eISBN:
9781400873746
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691168272.003.0007
Subject:
Economics and Finance, Macro- and Monetary Economics

This chapter turns to the property-rights theory of the firm, which arguably constitutes the most compelling and influential theory of the firm explaining in a unified framework both the benefits as ... More


Saving Truth From Paradox

Hartry Field

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

The book is an opinionated survey of philosophical work on paradoxes of truth and of related notions, such as property-instantiation, with occasional forays into related topics such as vagueness, the ... More


Are Supervaluational and Revision Theories Self‐Undermining?

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0013
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter is concerned with the extent to which supervaluation and revision theories can declare that their rules all preserve truth. The extent varies from one such theory to another, but none ... More


Validity, Truth‐Preservation, and the Second Incompleteness Theorem

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0020
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter begins with a survey of possible responses to the Curry paradox, and argues that the one offered by the theory of Chapters 15 through 18 is least disruptive of ordinary reasoning. Based ... More


Paraconsistent Dialetheism and Soundness

Hartry Field

in Saving Truth From Paradox

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199230747
eISBN:
9780191710933
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230747.003.0027
Subject:
Philosophy, Logic/Philosophy of Mathematics

Priest has argued that his dialetheic theories declare themselves sound and in this regard are better than non-dialetheic theories. This chapter shows this to be unfounded. Indeed, dialetheic ... More


The past is another country: is evidence for prehistoric, historical, and present-day extinction really comparable?

Samuel T. Turvey and Joanne H. Cooper

in Holocene Extinctions

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199535095
eISBN:
9780191715754
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535095.003.0010
Subject:
Biology, Evolutionary Biology / Genetics

Our understanding of Late Quaternary ecosystems and the timing and causation of prehistoric extinctions is based almost entirely on studies of the recent fossil record. However, palaeontological and ... More


Singularities

Yvonne Choquet-Bruhat

in General Relativity and the Einstein Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780199230723
eISBN:
9780191710872
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199230723.003.0013
Subject:
Mathematics, Applied Mathematics

This chapter presents a computable sufficient condition for the future causal completeness of a spacetime, and then a sufficient condition for its future or null incompleteness. It gives the ... More


Propositionalism and Some Problem Cases

Emma Borg

in Pursuing Meaning

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199588374
eISBN:
9780191741487
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199588374.003.0003
Subject:
Philosophy, Philosophy of Language, Philosophy of Mind

This chapter looks at the examples commonly appealed to in recent literature which appear to show that at least some well-formed declarative sentences fail to express propositions on the basis of ... More


Moderate Relativism

François Recanati

in Relative Truth

Published in print:
2008
Published Online:
May 2010
ISBN:
9780199234950
eISBN:
9780191715846
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199234950.003.0002
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Language

This chapter discusses two classical objections to the view that the content of a tensed utterance is a ‘temporal proposition’, true relative to certain times and false relative to others. The first ... More


Objections and Comparisons

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/9780199541492.003.0005
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

Relativism is distinguished from pluralism; mathematical theses which are true in some systems but not others are held to express different propositions which different truth values in each. ... More


Range, Information, and Process

Sabina Alkire

in Valuing Freedoms: Sen's Capability Approach and Poverty Reduction

Published in print:
2002
Published Online:
April 2004
ISBN:
9780199245796
eISBN:
9780191600838
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199245797.003.0003
Subject:
Economics and Finance, Development, Growth, and Environmental

Each of the four chapters of Part I of the book synthesizes one aspect that must be specified in the operationalization of the capability approach, then proposes a framework for doing so. This third ... More


Consciousness of Abstract Objects *

Richard Tieszen

in Phenomenology and Philosophy of Mind

Published in print:
2005
Published Online:
May 2010
ISBN:
9780199272457
eISBN:
9780191709951
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199272457.003.0009
Subject:
Philosophy, Philosophy of Mind

Edmund Husserl is one of only a few major philosophers in the last one hundred years or so who holds that it is possible to develop a philosophy of mind in which one can account for the consciousness ... More


Toils of Patriarchy

Derek Hirst and Steven N. Zwicker

in Andrew Marvell, Orphan of the Hurricane

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199655373
eISBN:
9780191742118
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199655373.003.0003
Subject:
Literature, 17th-century and Restoration Literature, Poetry

This chapter uses the early modern construct of patriarchy as a way to understand Marvell's idealizing but often troubled address to the dominant male figures of his life: Thomas Lord Fairfax, Oliver ... More


The Limits of Human Mathematics (2001)

Nathan Salmon

in Metaphysics, Mathematics, and Meaning: Philosophical Papers, Volume I

Published in print:
2005
Published Online:
February 2006
ISBN:
9780199284719
eISBN:
9780191603235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199284717.003.0014
Subject:
Philosophy, General

Gödel’s claim is defended that his famous incompleteness theorems yield the result, as a mathematically established fact, that the mathematical problem-solving capacity of the human mind either ... More


Formalism

Michael Detlefsen

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:
10.1093/0195148770.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter traces the philosophical and mathematical origins of formalist ideas. On the philosophical side, the key element is a certain freedom the mathematician is taken to have—namely, the ... More


Structuralism Reconsidered

Fraser MacBride

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:
10.1093/0195148770.003.0018
Subject:
Philosophy, Logic/Philosophy of Mathematics

The basic relations and functions that mathematicians use to identify mathematical objects fail to settle whether mathematical objects of one kind are identical to or distinct from objects of ... More


The Not-Two: Logic and God in Lacan

Lorenzo Chiesa

Published in print:
2016
Published Online:
January 2017
ISBN:
9780262529037
eISBN:
9780262335034
Item type:
book
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262529037.001.0001
Subject:
Philosophy, General

The Not-Two examines the treatment of logic and God in Lacan’s later work. The book draws from Lacan’s axiom “There is no sexual relationship.” It provides both a close reading of Lacan’s strive to ... More


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