Hyper-contradictions, generalized truth values and logics of truth and falsehood
Journal of Logic, Language and Information 15 (4):403-424 (2006)
Abstract
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.Author's Profile
DOI
10.1007/s10849-006-9015-0
My notes
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.
A few more useful 8-valued logics for reasoning with tetralattice eight.Dmitry Zaitsev - 2009 - Studia Logica 92 (2):265 - 280.
Circularity or Lacunae in Tarski’s Truth-Schemata.Dale Jacquette - 2010 - Journal of Logic, Language and Information 19 (3):315-326.
Entailment and bivalence.Fred Seymour Michael - 2002 - Journal of Philosophical Logic 31 (4):289-300.
Analytics
Added to PP
2009-01-28
Downloads
78 (#157,240)
6 months
2 (#297,737)
2009-01-28
Downloads
78 (#157,240)
6 months
2 (#297,737)
Historical graph of downloads
Author's Profile
Citations of this work
Truth and Falsehood: An Inquiry Into Generalized Logical Values.Yaroslav Shramko & Heinrich Wansing - 2011 - Dordrecht, Netherland: Springer.
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.
Shifting Priorities: Simple Representations for Twenty-seven Iterated Theory Change Operators.Hans Rott - 2006 - In David Makinson, Jacek Malinowski & Heinrich Wansing (eds.), Towards Mathematical Philosophy. Dordrecht: Springer. pp. 269–296.
Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System.Heinrich Wansing & Yaroslav Shramko - 2008 - Studia Logica 88 (3):405-429.
References found in this work
Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan Ross Anderson & Nuel D. Belnap - 1975 - Princeton University Press.
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.
Intuitive semantics for first-degree entailments and 'coupled trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.