Modal Ontology and Generalized Quantifiers

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

Authors
Peter Fritz
University of Oslo
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
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DOI 10.1007/s10992-012-9243-5
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford University Press.
Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Past, Present and Future.Arthur Prior - 1967 - Clarendon Press.

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Citations of this work BETA

Counting Incompossibles.Peter Fritz & Jeremy Goodman - 2017 - Mind 126 (504):1063–1108.
First-Order Modal Logic in the Necessary Framework of Objects.Peter Fritz - 2016 - Canadian Journal of Philosophy 46 (4-5):584-609.
Logics for Propositional Contingentism.Peter Fritz - 2017 - Review of Symbolic Logic 10 (2):203-236.
Higher-Order Contingentism, Part 3: Expressive Limitations.Peter Fritz - 2018 - Journal of Philosophical Logic 47 (4):649-671.

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