Heinrich Wansing
Ruhr-Universität Bochum
In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox.
Keywords Hyper-contradiction  multilattice  Belnap-trilattice  first-degree entailment
Categories (categorize this paper)
DOI 10.1007/s10849-006-9015-0
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: 64,046
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

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Introduction to Non-Classical Logic.Graham Priest - 2001 - Cambridge and New York: Cambridge University Press.

View all 20 references / Add more references

Citations of this work BETA

Valuations: Bi, Tri, and Tetra.Rohan French & David Ripley - 2019 - Studia Logica 107 (6):1313-1346.
Valuations: Bi, Tri, and Tetra.Rohan French & David Ripley - 2019 - Studia Logica 107 (6):1313-1346.
On Axiomatizing Shramko-Wansing’s Logic.Sergei P. Odintsov - 2009 - Studia Logica 91 (3):407 - 428.

View all 24 citations / Add more citations

Similar books and articles

Many-Valued Logics.Nicholas J. J. Smith - 2012 - In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language. Routledge. pp. 636--51.
Circularity or Lacunae in Tarski’s Truth-Schemata.Dale Jacquette - 2010 - Journal of Logic, Language and Information 19 (3):315-326.
Partiality and its Dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
Entailment and Bivalence.Fred Seymour Michael - 2002 - Journal of Philosophical Logic 31 (4):289-300.
Doubt Truth to Be a Liar.Graham Priest - 2005 - Oxford, England: Oxford University Press.


Added to PP index

Total views
76 ( #142,690 of 2,454,452 )

Recent downloads (6 months)
1 ( #449,269 of 2,454,452 )

How can I increase my downloads?


My notes