Non-classical Metatheory for Non-classical Logics

Journal of Philosophical Logic 42 (2):335-355 (2013)
A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete
Keywords Non-classical logic  Metalogic  Vagueness  Higher order vagueness  Fuzzy logic
Categories (categorize this paper)
DOI 10.1007/s10992-012-9223-9
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive Andrew Bacon, Non-classical Metatheory for Non-classical Logics
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
Vann McGee (1997). How We Learn Mathematical Language. Philosophical Review 106 (1):35-68.

View all 20 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles
Nicholas J. J. Smith (2004). Vagueness and Blurry Sets. Journal of Philosophical Logic 33 (2):165-235.
Greg Restall (forthcoming). Substructural Logics. Stanford Encyclopedia of Philosophy.
Diana Raffman (2009). Demoting Higher-Order Vagueness. In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press 509--22.
Brian Weatherson (2005). True, Truer, Truest. Philosophical Studies 123 (1-2):47-70.
Elia Zardini (2008). A Model of Tolerance. Studia Logica 90 (3):337-368.

Monthly downloads

Added to index


Total downloads

413 ( #4,576 of 1,941,072 )

Recent downloads (6 months)

77 ( #3,549 of 1,941,072 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.