Review of Symbolic Logic 10 (1):92–115 (2017)

Authors
Bruno Whittle
University of Wisconsin, Madison
Abstract
This paper addresses the question: given some theory T that we accept, is there some natural, generally applicable way of extending T to a theory S that can prove a range of things about what it itself (i.e. S) can prove, including a range of things about what it cannot prove, such as claims to the effect that it cannot prove certain particular sentences (e.g. 0 = 1), or the claim that it is consistent? Typical characterizations of Gödel’s second incompleteness theorem, and its significance, would lead us to believe that the answer is ‘no’. But the present paper explores a positive answer. The general approach is to follow the lead of recent (and not so recent) approaches to truth and the Liar paradox.
Keywords provability  Gödel’s second incompleteness theorem  truth  the Liar paradox
Categories (categorize this paper)
Reprint years 2017
DOI 10.1017/s1755020316000216
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,291
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

New Work for a Theory of Universals.David Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.

View all 20 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Rosser-Type Undecidable Sentences Based on Yablo’s Paradox.Taishi Kurahashi - 2014 - Journal of Philosophical Logic 43 (5):999-1017.
Query the Triple Loophole of the Proof of Gödel Incompleteness Theorem.Fangwen Yuan - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:77-94.
Herbrand Consistency of Some Arithmetical Theories.Saeed Salehi - 2012 - Journal of Symbolic Logic 77 (3):807-827.
Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
A Note on Boolos' Proof of the Incompleteness Theorem.Makoto Kikuchi - 1994 - Mathematical Logic Quarterly 40 (4):528-532.
Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.
A Simple Exposition Of Gödel's Theorem.John Lucas - 2003 - Etica E Politica 5 (1):1.
Samozwrotność i odrzucanie.Jan Woleński - 1993 - Filozofia Nauki 1.
On the Philosophical Relevance of Gödel's Incompleteness Theorems.Panu Raatikainen - 2005 - Revue Internationale de Philosophie 59 (4):513-534.
Gödel's Incompleteness Theorems.Panu Raatikainen - 2013 - The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), Edward N. Zalta (Ed.).

Analytics

Added to PP index
2016-10-05

Total views
53 ( #203,178 of 2,456,092 )

Recent downloads (6 months)
3 ( #225,826 of 2,456,092 )

How can I increase my downloads?

Downloads

My notes