Classical Logic is not Uniquely Characterizable

Journal of Philosophical Logic:1-21 (forthcoming)
  Copy   BIBTEX

Abstract

I show that it is not possible to uniquely characterize classical logic when working within classical set theory. By building on recent work by Eduardo Barrio, Federico Pailos, and Damian Szmuc, I show that for every inferential level, either classical logic is not unique at that level or there exist intuitively valid inferences of that level that are not definable in modern classical set theory. The classical logician is thereby faced with a three-horned dilemma: Give up uniqueness but preserve characterizability, give up characterizability and preserve uniqueness, or preserve both but give up modern classical set theory. After proving the main result, I briefly explore this third option by developing an account of classical logic within a paraconsistent set theory. This account of classical logic ensures unique characterizability in some sense, but the non-classical set theory also produces highly non-classical meta-results about classical logic.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,649

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Possibilities, Models, and Intuitionistic Logic: Ian Rumfitt’s The Boundary Stones of Thought.Stewart Shapiro - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (7):812-825.
Pluralism in Logic.Hartry Field - 2009 - Review of Symbolic Logic 2 (2):342-359.
Classical Negation Can Be Expressed by One of its Halves.J.-Y. Beziau - 1999 - Logic Journal of the IGPL 7 (2):145-151.
Classical Negation Can Be Expressed by One of its Halves.Jean-Yves Beziau - 1999 - Logic Journal of the IGPL 7 (2):145-151.
On the Non-Confluence of Cut-Elimination.Matthias Baaz & Stefan Hetzl - 2011 - Journal of Symbolic Logic 76 (1):313 - 340.
Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.

Analytics

Added to PP
2022-01-21

Downloads
29 (#399,891)

6 months
7 (#108,849)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

Beyond the Limits of Thought.Graham Priest - 1995 - Cambridge, England: Cambridge University Press.
Classical Logic and the Strict Tolerant Hierarchy.Chris Scambler - 2020 - Journal of Philosophical Logic 49 (2):351-370.
ST, LP and Tolerant Metainferences.Bogdan Dicher & Francesco Paoli - 2019 - In Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency. Springer Verlag. pp. 383-407.

View all 18 references / Add more references