David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
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
Alexander Chagrov (1997). Modal Logic. Oxford University Press.
George Bealer (1982). Quality and Concept. Oxford University Press.
Citations of this work BETA
Federico L. G. Faroldi (forthcoming). Ethical Copula, Negation, and Responsibility Judgments. Synthese:1-8.
Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (2):114 - 120.
Johannes Stern & Martin Fischer (2015). Paradoxes of Interaction? Journal of Philosophical Logic 44 (3):287-308.
James Kennedy Chase (2012). The Logic of Quinean Revisability. Synthese 184 (3):357-373.
Alexander Paseau (2009). How to Type: Reply to Halbach. Analysis 69 (2):280-286.
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 downloads71 ( #57,018 of 1,790,397 )
Recent downloads (6 months)9 ( #94,427 of 1,790,397 )
How can I increase my downloads?