In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 249-270 (2019)

Authors
Thomas Ferguson
City University of New York
Abstract
Graham Priest has frequently employed a construction in which a classical first-order model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {A}$$\end{document} may be collapsed into a three-valued model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {A}^{\sim }$$\end{document} suitable for interpretations in Priest’s logic of paradox. The source of this construction’s utility is Priest’s Collapsing Lemma, which guarantees that a formula true in the model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {A}$$\end{document} will continue to be true in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {A}^{\sim }$$\end{document}. In light of the utility and elegance of the Collapsing Lemma, extending variations of the lemma to other deductive calculi becomes very attractive. The aim of this paper is to map out some of the frontiers of the Collapsing Lemma by describing the types of expansions or revisions to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {LP}$$\end{document} for which the Collapsing Lemma continues to hold and a number of cases in which the lemma cannot be salvaged. Among what is shown is that the lemma holds for a strictly more expressive form of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {LP}$$\end{document} including nullary truth and falsity constants, that any conditional connective that can be added to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {LP}$$\end{document} without inhibiting the lemma must be theoremhood-preserving, and that the Collapsing Lemma extends to the paraconsistent weak Kleene logic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {PWK}$$\end{document} as well.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
Buy the book Find it on Amazon.com
DOI 10.1007/978-3-030-25365-3_13
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: 60,795
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

Cofinality of the Laver Ideal.Miroslav Repický - 2016 - Archive for Mathematical Logic 55 (7-8):1025-1036.
Models of Weak Theories of Truth.Mateusz Łełyk & Bartosz Wcisło - 2017 - Archive for Mathematical Logic 56 (5-6):453-474.
A Remark on Hereditarily Nonparadoxical Sets.Péter Komjáth - 2016 - Archive for Mathematical Logic 55 (1-2):165-175.
Minimal Elementary End Extensions.James H. Schmerl - 2017 - Archive for Mathematical Logic 56 (5-6):541-553.
A Covering Lemma for $${K}$$.Daniel W. Cunningham - 2007 - Archive for Mathematical Logic 46 (3):197-221.
$$I_0$$ I 0 and Combinatorics at $$\Lambda ^+$$ Λ +.Nam Trang & Xianghui Shi - 2017 - Archive for Mathematical Logic 56 (1-2):131-154.
Isomorphic and Strongly Connected Components.Miloš S. Kurilić - 2015 - Archive for Mathematical Logic 54 (1-2):35-48.
Σ1-Wellorders Without Collapsing.Peter Holy - 2015 - Archive for Mathematical Logic 54 (3-4):453-462.
Square Principles with Tail-End Agreement.William Chen & Itay Neeman - 2015 - Archive for Mathematical Logic 54 (3-4):439-452.
Set Theory Without Choice: Not Everything on Cofinality is Possible.Saharon Shelah - 1997 - Archive for Mathematical Logic 36 (2):81-125.

Analytics

Added to PP index
2020-06-17

Total views
2 ( #1,390,719 of 2,438,783 )

Recent downloads (6 months)
1 ( #436,491 of 2,438,783 )

How can I increase my downloads?

Downloads

My notes