David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 15 (4):403-424 (2006)
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)|
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
Alan R. Anderson & Nuel D. Belnap (1975). Entailment: The Logic of Relevance and Neccessity, Vol. I. Princeton University Press.
Graham Priest (2001). Introduction to Non-Classical Logic. Cambridge University Press.
Alan Ross Anderson, Nuel D. Belnap & J. Michael Dunn (1992). Entailment: The Logic of Relevance and Necessity, Vol. II. Princeton University Press.
J. Michael Dunn (2001). Algebraic Methods in Philosophical Logic. Oxford University Press.
N. D. Belnap (1977). A Useful Four-Valued Logic. In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel
Citations of this work BETA
Sergei P. Odintsov (2009). On Axiomatizing Shramko-Wansing's Logic. Studia Logica 91 (3):407 - 428.
Heinrich Wansing & Yaroslav Shramko (2008). Suszko's Thesis, Inferential Many-Valuedness, and the Notion of a Logical System. Studia Logica 88 (3):405 - 429.
Norihiro Kamide & Heinrich Wansing (2009). Sequent Calculi for Some Trilattice Logics. Review of Symbolic Logic 2 (2):374-395.
Graham Priest (2008). Jaina Logic: A Contemporary Perspective. History and Philosophy of Logic 29 (3):263-278.
Sergei P. Odintsov & Heinrich Wansing (2015). The Logic of Generalized Truth Values and the Logic of Bilattices. Studia Logica 103 (1):91-112.
Similar books and articles
Nicholas J. J. Smith (2012). Many-Valued Logics. In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language. Routledge 636--51.
Graham Priest (2006). Doubt Truth to Be a Liar. Oxford University Press.
Josep Maria Font (2009). Taking Degrees of Truth Seriously. Studia Logica 91 (3):383 - 406.
Fred Seymour Michael (2002). Entailment and Bivalence. Journal of Philosophical Logic 31 (4):289-300.
J. Michael Dunn (2000). Partiality and its Dual. Studia Logica 66 (1):5-40.
Roy T. Cook (2009). What is a Truth Value and How Many Are There? Studia Logica 92 (2):183 - 201.
Dale Jacquette (2010). Circularity or Lacunae in Tarski's Truth-Schemata. Journal of Logic, Language and Information 19 (3):315-326.
Dmitry Zaitsev (2009). A Few More Useful 8-Valued Logics for Reasoning with Tetralattice Eight. Studia Logica 92 (2):265 - 280.
Yaroslav Shramko & Heinrich Wansing (2005). Some Useful 16-Valued Logics: How a Computer Network Should Think. [REVIEW] Journal of Philosophical Logic 34 (2):121 - 153.
Added to index2009-01-28
Total downloads49 ( #82,503 of 1,790,308 )
Recent downloads (6 months)8 ( #106,127 of 1,790,308 )
How can I increase my downloads?