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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


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.


Logical Types in Some Arguments about Knowability and Belief

Bernard Linsky

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/9780199285495.003.0012
Subject:
Philosophy, General

Over the years a number of arguments have been formulated in elementary modal logic purporting to show that there are limits to what can be known or believed. These include the ‘Fitch’ style ... 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


Fitch's Paradox and the Philosophy of Mathematics

Otávio Bueno

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/9780199285495.003.0017
Subject:
Philosophy, General

This chapter considers the impact of the Fitch paradox on particular epistemological views about mathematics. It assumes therefore, for the sake of argument, that the reasoning leading to Fitch's ... 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


The Mystery of the Disappearing Diamond

C. S. Jenkins

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/9780199285495.003.0019
Subject:
Philosophy, General

This chapter agrees that the knowability principle fails as an expression of anti-realism. It takes issue with Kvanvig (2006), in which it is argued that the real paradoxicality of Fitch's proof is ... 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.


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


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


Referee Reports on Fitch's “A Definition of Value”

Alonzo Church

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/9780199285495.003.0002
Subject:
Philosophy, General

This chapter presents the earliest version of the knowability proof by Alonzo Church which appears in a 1945 referee report for the Journal of Symbolic Logic. Church anonymously conveyed the proof to ... 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


Tennant's Troubles

Timothy Williamson

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/9780199285495.003.0013
Subject:
Philosophy, General

In The Taming of the True (1997), Neil Tennant objects to the specific intuitionistic anti-realist response to Fitch envisaged by the author, and proposes his own alternative responses, still of a ... More


Knowability and Possible Epistemic Oddities

Jc Beall

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/9780199285495.003.0009
Subject:
Philosophy, General

This chapter explores alternatives, some of which avoid the epistemic oddities of the framework presented in Chapter 7. It presents a semantic framework that is paracomplete, but not paraconsistent, ... More


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


Beyond the Limits of Knowledge

Graham Priest

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/9780199285495.003.0008
Subject:
Philosophy, General

This chapter develops the Routley/Beall proposal by countenancing the mere possibility of truth-value gluts and appealing to a paraconsistent logic with excluded middle.


Actions That Make Us Know

Johan van Benthem

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/9780199285495.003.0010
Subject:
Philosophy, General

This chapter looks at the Paradox of the Knower in a dynamic-epistemic perspective where learning means changing the current epistemic model. The problematic Moore sentence driving the paradox turns ... 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


Can Truth Out?

John Burgess

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/9780199285495.003.0011
Subject:
Philosophy, General

It is rather discouraging that forty years have passed since Frederic Fitch first propounded his paradox of knowability without philosophers having achieved agreement on a solution. As a general ... More


A Logical * Analysis of Some Value Concepts 1

Frederic B. Fitch

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/9780199285495.003.0003
Subject:
Philosophy, General

This chapter presents Fitch's seminal 1963 paper, which has been the logical fuel or foil for the literature on the knowability paradox. The paper provides a partial logical analysis of a few ... More


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