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The Knowability Paradox

Jonathan L. Kvanvig

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This book examines and proposes a solution to the knowability paradox. The paradox derives from the proof that if all truths are knowable, then all truths are known, which was first published by ... More


Syntactic Restriction Strategies

Jonathan L. Kvanvig

in The Knowability Paradox

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.003.0004
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter examines approaches to the paradox that wish to save anti-realism from the paradox by denying that the knowability assumption is a commitment of anti-realism. Such approaches contend ... More


The Paradox

Jonathan L. Kvanvig

in The Knowability Paradox

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter examines the logical structure of the knowability paradox, presenting the details of the proofs that underlie the paradox, and clarifying which elements of these proofs give rise to ... More


Semantical Moves

Jonathan L. Kvanvig

in The Knowability Paradox

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.003.0007
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter pursues a strategy for solving the knowability paradox in terms of the general category of the fallacies involved in substituting into intensional contexts. It clarifies and defends the ... More


What's Paradoxical?

Jonathan L. Kvanvig

in The Knowability Paradox

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter explores the different grounds for accepting the claim that all truths are knowable, the assumption central to the derivation of Fitch’s result. It argues that although there is no ... More


Conclusion

Jonathan L. Kvanvig

in The Knowability Paradox

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter discusses the process of developing a solution to knowability paradox. It presents a detailed analysis of the paradox. It argues that the neo-Russellian theory of quantification is the ... More


Introduction

Jonathan L. Kvanvig

in The Knowability Paradox

Published in print:
2006
Published Online:
May 2006
ISBN:
9780199282593
eISBN:
9780191603587
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199282595.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This introductory chapter begins with a brief overview of the knowability paradox — a paradox deriving from a proof that if all truths are knowable, then all truths are known — which was first ... More


New Essays on the Knowability Paradox

Joe Salerno (ed.)

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.001.0001
Subject:
Philosophy, General

In 1945, Alonzo Church issued a pair of referee reports in which he anonymously conveyed to Frederic Fitch a surprising proof showing that wherever there is (empirical) ignorance there is also ... More


Restriction Strategies for Knowability: Some Lessons in False Hope

Jonathan L. Kvanvig

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0014
Subject:
Philosophy, General

The knowability paradox derives from a proof by Frederic Fitch in 1963. The proof purportedly shows that if all truths are knowable, it follows that all truths are known. Antirealists, wed as they ... More


Performance and Paradox

Michael Hand

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0018
Subject:
Philosophy, General

The knowability paradox, or Fitch's paradox, is thought to threaten semantical (Dummettian) antirealism. This chapter suggests that the lesson of the paradox concerns the theoretical location at ... More


Fitch's Paradox of Knowability

Michael Dummett

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0005
Subject:
Philosophy, General

This chapter defends p→¬¬Kp as the best expression of semantic antirealism.


Not Every Truth Can Be Known (at least, not all at once)

Greg Restall

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0022
Subject:
Philosophy, General

According to the ‘knowability thesis’, every truth is knowable. Fitch's paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but ... More


Introduction

Joe Salerno

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0001
Subject:
Philosophy, General

This introductory chapter begins with a discussion of the knowability paradox and how the knowability principle has been claimed for a number of historic non-realisms, including Michael Dummett's ... More


Knowability Noir: 1945–1963

Joe Salerno

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0004
Subject:
Philosophy, General

This chapter analyzes Chapters 1 and 2. It argues that Fitch's intent was to pinpoint a disruptive set of logical properties that lend themselves to the trivialization of conditional analyses. Or, at ... More


Revamping the Restriction Strategy

Neil Tennant

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0015
Subject:
Philosophy, General

This chapter continues the anti-realist's quest for a principled way to avoid Fitch's paradox. It proposes that the Cartesian restriction on the anti-realist's knowability principle ‘φ, therefore ... More


Two Deflationary Approaches to Fitch‐Style Reasoning

Christoph Kelp and Duncan Pritchard

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0021
Subject:
Philosophy, General

This chapter looks at one — perhaps the only — theoretical view to which, on the face of it, the knowability principle is of central importance. It then considers two deflationary responses to ... More


Invincible Ignorance

W. D. Hart

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0020
Subject:
Philosophy, General

This chapter takes Fitch's proof to be evidence for realism. It argues that the prospects are not good for a solution coming from the theory of types.


The Paradox of Knowability and the Mapping Objection

Stig Alstrup Rasmussen

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0006
Subject:
Philosophy, General

This chapter further investigates and defends Dummett's newly favoured knowability principle, p→¬¬Kp. It discusses the ‘mapping objection’, which points out that Gödel's 1933 mapping of ... More


Truth, Indefinite Extensibility, and Fitch's Paradox

José Luis Bermúdez

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0007
Subject:
Philosophy, General

This chapter argues that the Dummett (2001) position is well-motivated. The position restricts the knowability principle to atomic statements, and defines intuitionistic truth inductively from there. ... More


On Keeping Blue Swans and Unknowable Facts at Bay: A Case Study on Fitch's Paradox

Berit Brogaard

in New Essays on the Knowability Paradox

Published in print:
2009
Published Online:
September 2010
ISBN:
9780199285495
eISBN:
9780191713972
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285495.003.0016
Subject:
Philosophy, General

This chapter develops a Fitch-like paradox for strong modal fictionalism. It argues that the most promising strategy to avoid paradox is to reject the claim that modal claims are to be analyzed in ... More


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