Modal ontology and generalized quantifiers
type: Item
instance of: scholarly article
title: Modal ontology and generalized quantifiers
zbMATH Open document ID: 1320.03014
author: Peter Fritz
published in: Journal of Philosophical Logic
publication date: 2013-10-21T00:00:00Z
full work available at URL: FRIMOA
review text: The paper focuses on the distinction between two modal metaphysical views, which \textit{T. Williamson} [``Necessitism, contingentism, and plural quantification'', Mind, New Ser. 119, No. 475, 657--748 (2010; \url{doi:10.1093/mind/fzq042})] has called ``necessitism'' and ``contingentism'' and that he has proposed as substitutes for the notions of possibilism and actualism, respectively. Necessitists will subscribe to the thesis that necessarily everything is necessarily something. Contingentists will deny this thesis. Williamson has shown that necessitists can draw distinctions that the contingentists cannot draw on the basis of certain first-order modal theory. The author wants to test Williamson's result in a logical context wider than that of Williamson's. In particular, the author considers the logical context resulting from the addition of generalized quantifiers to the logical syntax of Williamson's first-order modal theory. Reference of those quantifiers is to infinite classes of objects. The formal semantics proposed in the paper for the extended formal language is a possible world semantics with an outer domain and inner domains (i.e., domains associated to each possible world of the semantic models). Each inner domain is a subset of the outer domain. The outer domain is the union of the inner domains. The semantics will also satisfy the so called property actualism condition, i.e., the condition that, at any possible world \(w\), \(n\)-relational symbols are assigned sets of \(n\)-tuples of the domain associated to \(w\). Quantifiers whose range of quantification is based on the outer domain is referred by the author as outer quantifiers; those whose range of quantification is based on inner domains are called inner quantifiers. When the semantics interprets quantifiers on the basis of the outer domain, the author speaks of a logic of outer quantifiers; when it interprets them on the basis of inner domains, he speaks of a logic of inner quantifiers. The au…
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03C80
zbMATH DE Number: 6217459
zbMATH Keywords: possibilism
zbMATH Keywords: actualism
zbMATH Keywords: necessitism
zbMATH Keywords: contingentism
zbMATH Keywords: first-order modal logic
zbMATH Keywords: generalized quantifiers
MaRDI profile type: Publication
OpenAlex ID: W2029002993
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DOI: 10.1007/S10992-012-9243-5
description: scientific article; zbMATH DE number 6217459