David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 50 (3):275-301 (2009)
We present $\in_I$-Logic (Epsilon-I-Logic), a non-Fregean intuitionistic logic with a truth predicate and a falsity predicate as intuitionistic negation. $\in_I$ is an extension and intuitionistic generalization of the classical logic $\in_T$ (without quantifiers) designed by Sträter as a theory of truth with propositional self-reference. The intensional semantics of $\in_T$ offers a new solution to semantic paradoxes. In the present paper we introduce an intuitionistic semantics and study some semantic notions in this broader context. Also we enrich the quantifier-free language by the new connective < that expresses reference between statements and yields a finer characterization of intensional models. Our results in the intuitionistic setting lead to a clear distinction between the notion of denotation of a sentence and the here-proposed notion of extension of a sentence (both concepts are equivalent in the classical context). We generalize the Fregean Axiom to an intuitionistic version not valid in $\in_I$. A main result of the paper is the development of several model constructions. We construct intensional models and present a method for the construction of standard models which contain specific (self-)referential propositions
|Keywords||truth theory non-Fregean logics self-reference intuitionistic logic semantic paradoxes intensional semantics extension intension denotation|
|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
No references found.
Citations of this work BETA
Steffen Lewitzka (2011). ?K: A Non-Fregean Logic of Explicit Knowledge. Studia Logica 97 (2):233-264.
Similar books and articles
Yaroslav Shramko (2005). Dual Intuitionistic Logic and a Variety of Negations: The Logic of Scientific Research. Studia Logica 80 (2-3):347 - 367.
Torben Braüner (2006). Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic. Journal of Logic, Language and Information 15 (3):179-194.
Kevin Scharp (2010). Falsity. In Cory D. Wright & Nikolaj Jang Lee Linding Pedersen (eds.), New Waves in Truth. Palgrave Macmillan.
A. D. Yashin (1999). Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness. Journal of Philosophical Logic 28 (2):175-197.
Ignacio Jané & Gabriel Uzquiano (2004). Well- and Non-Well-Founded Fregean Extensions. Journal of Philosophical Logic 33 (5):437-465.
Friederike Moltmann (forthcoming). 'Truth Predicates' in Natural Language. In Dora Achourioti, Henri Galinon & José Martinez (eds.), Unifying Theories of Truth. Springer.
Fan Yang (2013). Expressing Second-Order Sentences in Intuitionistic Dependence Logic. Studia Logica 101 (2):323-342.
Gary M. Hardegree (1981). An Axiom System for Orthomodular Quantum Logic. Studia Logica 40 (1):1 - 12.
Giambattista Amati, Luigia Carlucci-Aiello & Fiora Pirri (1997). Intuitionistic Autoepistemic Logic. Studia Logica 59 (1):103-120.
David H. Sanford (1975). Borderline Logic. American Philosophical Quarterly 12 (1):29-39.
Giacomo Bonanno (1999). Varieties of Interpersonal Compatibility of Beliefs. In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema (eds.), Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Amsterdam University Press.
Added to index2010-09-13
Total downloads13 ( #127,289 of 1,101,847 )
Recent downloads (6 months)2 ( #191,964 of 1,101,847 )
How can I increase my downloads?