David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 32 (2):179-223 (2003)
If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic
|Keywords||modal logic necessity paradox possible worlds|
|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
Alexander Paseau (2009). How to Type: Reply to Halbach. Analysis 69 (2):280-286.
James Kennedy Chase (2012). The Logic of Quinean Revisability. Synthese 184 (3):357-373.
Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (2):114 - 120.
Ming Hsiung (2009). Jump Liars and Jourdain's Card Via the Relativized T-Scheme. Studia Logica 91 (2):239 - 271.
Similar books and articles
William H. Hanson & James Hawthorne (1985). Validity in Intensional Languages: A New Approach. Notre Dame Journal of Formal Logic 26 (1):9-35.
Edward N. Zalta (1997). A Classically-Based Theory of Impossible Worlds. Notre Dame Journal of Formal Logic 38 (4):640-660.
Charles G. Morgan (1975). Weak Liberated Versions of T and S. Journal of Symbolic Logic 40 (1):25-30.
Michael J. Shaffer & Jeremy Morris (2006). A Paradox for Possible World Semantics. Logique Et Analyse 49 (195):307-317.
Holger Sturm & Frank Wolter (2001). First-Order Expressivity for S5-Models: Modal Vs. Two-Sorted Languages. Journal of Philosophical Logic 30 (6):571-591.
Johan Benthem (1984). Possible Worlds Semantics: A Research Program That Cannot Fail? Studia Logica 43 (4):379 - 393.
Theodore Sider (2002). The Ersatz Pluriverse. Journal of Philosophy 99 (6):279-315.
John Divers (2006). Possible-Worlds Semantics Without Possible Worlds: The Agnostic Approach. Mind 115 (458):187-226.
V. Halbach & P. Welch (2009). Necessities and Necessary Truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions. Mind 118 (469):71-100.
Charles G. Morgan (1973). Systems of Modal Logic for Impossible Worlds. Inquiry 16 (1-4):280 – 289.
Added to index2009-01-28
Total downloads60 ( #36,873 of 1,696,507 )
Recent downloads (6 months)8 ( #69,748 of 1,696,507 )
How can I increase my downloads?