David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 26 (1):9-35 (1985)
Although the use of possible worlds in semantics has been very fruitful and is now widely accepted, there is a puzzle about the standard definition of validity in possible-worlds semantics that has received little notice and virtually no comment. A sentence of an intensional language is typically said to be valid just in case it is true at every world under every model on every model structure of the language. Each model structure contains a set of possible worlds, and models are defined relative to model structures, assigning truth-values to sentences at each world countenanced by the model structure. The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and just one model structure defined on this class that does correctly the things that model structures are supposed to do. (These include, but need not be limited to, specifying the set of individuals in each world as well as various accessibility relations between worlds.) Why not define validity simply as truth at every world under every model on this one model structure? What is the point of bringing in more model structures than just this one?
We investigate these questions in some detail and conclude that for many intensional languages the puzzle points to a genuine difficulty: the standard definition of validity is insufficiently motivated. We begin (Section 1) by showing that a plausible and natural account of validity for intensional languages can be based on a single model structure, and that validity so defined is analogous in important respects to the standard account of validity for extensional languages. We call this notion of validity "validity!", and in Section 2 we contrast it with the standard notion, which we call "validity2". Several attempts are made to discover a rationale for the almost universal acceptance of validity2, but in most of these attempts we come up empty-handed. So in Section 3 we investigate validity! for some intensional languages. Our investigation includes providing axiomatizations for several propositional and predicate logics, most of which are provably complete. The completeness proofs are given in the Appendix, which also contains a sketch of a compactness proof for one of the predicate logics.
|Keywords||No keywords specified (fix it)|
|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
No citations found.
Similar books and articles
William H. Hanson (2006). Actuality, Necessity, and Logical Truth. Philosophical Studies 130 (3):437 - 459.
Andrea Iacona (2010). Validity and Interpretation. Australasian Journal of Philosophy 88 (2):247-264.
Edwin D. Mares & Robert Goldblatt (2006). An Alternative Semantics for Quantified Relevant Logic. Journal of Symbolic Logic 71 (1):163-187.
Peter Schroeder-Heister (2006). Validity Concepts in Proof-Theoretic Semantics. Synthese 148 (3):525 - 571.
Christopher Gauker (1990). Semantics Without Reference. Notre Dame Journal of Formal Logic 31 (3):437-461.
Roberta Ballarin (2005). Validity and Necessity. Journal of Philosophical Logic 34 (3):275 - 303.
Greg Ray (1996). Ontology-Free Modal Semantics. Journal of Philosophical Logic 25 (4):333 - 361.
Dominic Gregory (2005). Keeping Semantics Pure. Noûs 39 (3):505–528.
Xavier Caicedo & Ricardo O. Rodriguez (2010). Standard Gödel Modal Logics. Studia Logica 94 (2):189 - 214.
Yannis Stephanou (2000). Model Theory and Validity. Synthese 123 (2):165-193.
Added to index2010-03-30
Total downloads18 ( #89,615 of 1,096,840 )
Recent downloads (6 months)2 ( #164,128 of 1,096,840 )
How can I increase my downloads?