Journal of Philosophical Logic (forthcoming)
|Abstract||Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer quantifiers. The present paper deals with these issues in the context of quantified modal logics with generalized quantifiers. Its main aim is to establish two results for such a logic: Firstly, contingentists can draw the distinctions necessitists can draw if and only if the logic with inner quantifiers is at least as expressive as the logic with outer quantifiers, and necessitists can draw the distinctions contingentists can draw if and only if the logic with outer quantifiers is at least as expressive as the logic with inner quantifiers. Secondly, the former two items are the case if and only if all of the generalized quantifiers are first-order definable, and the latter two items are the case if and only if first-order logic with these generalized quantifiers relativizes.|
|Keywords||Modality Ontology Generalized quantifiers Contingentism Necessitism Actualism Possibilism|
|Through your library||Configure|
Similar books and articles
Wiebe Van Der Hoek & Maarten De Rijke (1993). Generalized Quantifiers and Modal Logic. Journal of Logic, Language and Information 2 (1).
Johan van Benthem & Dag Westerståhl (1995). Directions in Generalized Quantifier Theory. Studia Logica 55 (3):389-419.
Juha Kontinen & Jakub Szymanik (2011). Characterizing Definability of Second-Order Generalized Quantifiers. In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
Juha Kontinen (2006). The Hierarchy Theorem for Second Order Generalized Quantifiers. Journal of Symbolic Logic 71 (1):188 - 202.
Fredrik Engström (2012). Generalized Quantifiers in Dependence Logic. Journal of Logic, Language and Information 21 (3):299-324.
Dorit Ben Shalom (2003). One Connection Between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers. Journal of Logic, Language and Information 12 (1).
Dorit Ben Shalom (2003). One Connection Between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers. Journal of Logic, Language and Information 12 (1):47-52.
Martin van den Berg (1996). Dynamic Generalized Quantifiers. In J. van der Does & Van J. Eijck (eds.), Quantifiers, Logic, and Language. Stanford University.
Georg Gottlob (1997). Relativized Logspace and Generalized Quantifiers Over Finite Ordered Structures. Journal of Symbolic Logic 62 (2):545-574.
Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. Journal of Logic, Language and Information 6 (3):305-335.
Lauri Hella, Kerkko Luosto & Jouko Väänänen (1996). The Hierarchy Theorem for Generalized Quantifiers. Journal of Symbolic Logic 61 (3):802-817.
M. Mostowski (1995). Quantifiers Definable by Second Order Means. In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers.
Dag Westerståhl (1989). Aristotelian Syllogisms and Generalized Quantifiers. Studia Logica 48 (4):577-585.
Per Lindström (1966). First Order Predicate Logic with Generalized Quantifiers. Theoria 32:186--195.
Jouko Väänänen & Dag Westerståhl (2002). On the Expressive Power of Monotone Natural Language Quantifiers Over Finite Models. Journal of Philosophical Logic 31 (4):327-358.
Added to index2012-02-10
Total downloads77 ( #10,364 of 549,069 )
Recent downloads (6 months)21 ( #2,591 of 549,069 )
How can I increase my downloads?