Modal Ontology and Generalized Quantifiers

Journal of Philosophical Logic 42 (4):643-678 (2013)
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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.

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Peter Fritz
Australian Catholic University

Citations of this work

Modal science.Timothy Williamson - 2016 - Canadian Journal of Philosophy 46 (4-5):453-492.
Counting Incompossibles.Peter Fritz & Jeremy Goodman - 2017 - Mind 126 (504):1063–1108.
Higher-Order Contingentism, Part 3: Expressive Limitations.Peter Fritz - 2018 - Journal of Philosophical Logic 47 (4):649-671.
Possible Patterns.Jeffrey Sanford Russell & John Hawthorne - 2018 - Oxford Studies in Metaphysics 11.

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Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Past, present and future.Arthur N. Prior - 1967 - Oxford,: Clarendon P..
Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
Generalized quantifiers and natural language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.

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