The Arithmetization of Syntax and the New Paradoxes of Self-Reference

Authors
T. Parent
Virginia Tech
Abstract
In this paper, I recreate a paradox from my earlier work (“Paradox with just self-reference”) albeit entirely within the language of arithmetic. (In lieu of self-referential expressions, Gödel numbering is used to generate the paradox.) This can suggest that Robinson arithmetic and its extensions are unsound; however, I claim instead that the metalanguage may be to blame, owing to arithmetization of syntax. If so, then the moral would be to restrict arithmetization in the metalanguage somehow, rather than distrust the arithmetical theory in the object language.
Keywords Gödel, Kurt  Paradox  Gödel numbering  Axiomatic arithmetic
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 37,146
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

The Liar Syndrome.Albert A. Johnstone - 2002 - SATS: Northern European Journal of Philosophy 3 (1):37-55.
Gödel's and Other Paradoxes.Hartley Slater - 2016 - Philosophical Investigations 39 (4):353-361.
Kurt Gödel, Paper on the Incompleteness Theorems (1931).Richard Zach - 2004 - In Ivor Grattan-Guinness (ed.), Landmark Writings in Mathematics. Amsterdam: North-Holland. pp. 917-925.
Is Mathematics Syntax of Language?Kurt Gödel - 1953 - In K. Gödel Collected Works. Oxford University Press: Oxford. pp. 334--355.
Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.
Uniform Self-Reference.Raymond M. Smullyan - 1985 - Studia Logica 44 (4):439 - 445.

Analytics

Added to PP index
2018-02-22

Total downloads
54 ( #123,672 of 2,308,512 )

Recent downloads (6 months)
13 ( #41,970 of 2,308,512 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature