Difference between revisions of "Read2019"

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(Created page with "{{BibEntry |BibType=ARTICLE |Author(s)=Rupert Read; Christian Greiffenhagen; |Title=Can sentences self-refer? Gödel and the liar |Tag(s)=EMCA; Reference |Key=Read2019 |Year=2...")
 
 
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|Journal=Ethnographic Studies
 
|Journal=Ethnographic Studies
 
|Volume=16
 
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|Pages=181-201
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|Pages=181–201
|URL=https://zenodo.org/record/3459372#.XZmWz0YzaUk
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|URL=https://zenodo.org/record/3459372
 
|DOI=10.5281/zenodo.3459372
 
|DOI=10.5281/zenodo.3459372
 
|Abstract=In this article we discuss the issue of ‘self-reference’, i.e., the question whether (or in which sense) sentences may be said to refer to themselves. Following Wittgenstein, we suggest that the clearest thing to say is that sentences cannot of themselves ‘do’ or ‘say’ anything, but that it is human beings that ‘do’ and ‘say’. Consequently, instances of self-reference have to be considered as part of specific human practices. We illustrate these general remarks through the examination of the Liar Paradox and Gödel’s Incompleteness Theorem (which uses a formally undecidable sentence, which is sometimes taken to ‘say’ ‘I am not provable.’). We emphasise that in the context of the ‘foundations of mathematics’ it is important to separate technical/mathematical from philosophical questions, and argue (again following Wittgenstein) that Gödel’s Incompleteness Theorem was more a contribution to the former than the latter. In other words, Gödel’s result runs the risk of being over-interpreted, and of falling foul of Wittgensteinian philosophy, if it is interpreted philosophically to include focally a sentence that literally self-refers.
 
|Abstract=In this article we discuss the issue of ‘self-reference’, i.e., the question whether (or in which sense) sentences may be said to refer to themselves. Following Wittgenstein, we suggest that the clearest thing to say is that sentences cannot of themselves ‘do’ or ‘say’ anything, but that it is human beings that ‘do’ and ‘say’. Consequently, instances of self-reference have to be considered as part of specific human practices. We illustrate these general remarks through the examination of the Liar Paradox and Gödel’s Incompleteness Theorem (which uses a formally undecidable sentence, which is sometimes taken to ‘say’ ‘I am not provable.’). We emphasise that in the context of the ‘foundations of mathematics’ it is important to separate technical/mathematical from philosophical questions, and argue (again following Wittgenstein) that Gödel’s Incompleteness Theorem was more a contribution to the former than the latter. In other words, Gödel’s result runs the risk of being over-interpreted, and of falling foul of Wittgensteinian philosophy, if it is interpreted philosophically to include focally a sentence that literally self-refers.
 
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}}

Latest revision as of 09:39, 16 January 2020

Read2019
BibType ARTICLE
Key Read2019
Author(s) Rupert Read, Christian Greiffenhagen
Title Can sentences self-refer? Gödel and the liar
Editor(s)
Tag(s) EMCA, Reference
Publisher
Year 2019
Language English
City
Month
Journal Ethnographic Studies
Volume 16
Number
Pages 181–201
URL Link
DOI 10.5281/zenodo.3459372
ISBN
Organization
Institution
School
Type
Edition
Series
Howpublished
Book title
Chapter

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Abstract

In this article we discuss the issue of ‘self-reference’, i.e., the question whether (or in which sense) sentences may be said to refer to themselves. Following Wittgenstein, we suggest that the clearest thing to say is that sentences cannot of themselves ‘do’ or ‘say’ anything, but that it is human beings that ‘do’ and ‘say’. Consequently, instances of self-reference have to be considered as part of specific human practices. We illustrate these general remarks through the examination of the Liar Paradox and Gödel’s Incompleteness Theorem (which uses a formally undecidable sentence, which is sometimes taken to ‘say’ ‘I am not provable.’). We emphasise that in the context of the ‘foundations of mathematics’ it is important to separate technical/mathematical from philosophical questions, and argue (again following Wittgenstein) that Gödel’s Incompleteness Theorem was more a contribution to the former than the latter. In other words, Gödel’s result runs the risk of being over-interpreted, and of falling foul of Wittgensteinian philosophy, if it is interpreted philosophically to include focally a sentence that literally self-refers.

Notes