LP+, K3(+), FDE+, and their 'classical collapse'

J. C. Beall

doi:10.1017/S1755020313000142

LP+, K3(+), FDE+, and their 'classical collapse'

J. C. Beall^*

^*Corresponding author for this work

Philosophy

University of Connecticut

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

Abstract

This paper is a sequel to Beall (2011), in which I both give and discuss the philosophical import of a 'classical collapse' result for the propositional (multiple-conclusion) logic LP+. Feedback on such ideas prompted a spelling out of the first-order case. My aim in this paper is to do just that: namely, explicitly record the first-order result(s), including the collapse results for K3(+) and FDE+.

Original language	English
Pages (from-to)	742-754
Number of pages	13
Journal	Review of Symbolic Logic
Volume	6
Issue number	4
Early online date	1 Jul 2013
DOIs	https://doi.org/10.1017/S1755020313000142
Publication status	Published - Dec 2013

Funding

In addition to very useful comments from anonymous referees, I am very grateful to a number of people whose feedback on the ideas in Beall 2011) directly motivated this note: Michael Glanzberg, Volker Halbach, Ole Hjortland, Leon Horsten, Hannes Leitgeb, Toby Meadows, Julien Murzi, Stephen Read, and Stewart Shapiro. Additionally, I'm grateful for support from the MCMP in Munich, and for a very productive MCMP conference on truth theories that greatly benefited my work. I'm also grateful for ongoing discussion with other travelers in the ideas of this project: Aaron Cotnoir, Hartry Field, Michael Hughes, Graham Priest, Greg Restall, Lionel Shapiro, and Ross Vandegrift - and, out of alphabetical order but perhaps above all, very much David Ripley. Additionally, I want to express special thanks to Henry Towsner, who quickly confirmed the proof idea in an e-mail by in fact formulating his own version, and also to Joshua Schechter who, as noted in a footnote, spotted an error in an earlier formulation of Lemma 3.9 (and, hence, in corresponding proofs of theorems) - and also offered very useful feedback. Finally, I'm grateful to participants in a NELLC meeting at Yale University in April 2012 during which some of these ideas were discussed, including Susanne Bobzien, Phil Bricker, Agustin Rayo, Marcus Rossberg, Zoltan Szabo, Bruno Whittle, and especially Vann McGee, whose subsequent correspondence on the topic(s) continues to be valuable.

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LP+, K3(+), FDE+, and their 'classical collapse'

Abstract

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