Four modal modelings
type: Item
instance of: scholarly article
title: Four modal modelings
zbMATH Open document ID: 0638.03016
DOI: 10.1007/BF00247906
author: John Bacon
published in: Journal of Philosophical Logic
publication date: 1988-01-01T00:00:00Z
review text: The monadic part of S. Kripke's simple modal predicate calculus S5 *, with all designators rigid and quantification only over individuals, not individual-concepts, can be modeled in four different ways. In the familiar Kripke models, individuals and possible worlds are assumed as primitive. In bundle models, properties are taken as primitive and bundled into individuals by similarity relations, which take the place of possible worlds. In trope models, tropes (abstract particulars; property instances) are assumed as basic, and individuals, properties, and possible worlds are constructed as classes of tropes with the help of appropriate equivalence relations. In situation models, individuals and properties are assumed and possible worlds constructed. All four modelings are proved equivalent. The tropemodeling is extended to polyadic S5 * and completeness proved. The different modelings are compared from a metaphysical point of view. It is suggested that the trope-modeling is the most satisfactory.
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 4039854
zbMATH Keywords: monadic part of S. Kripke's simple modal predicate calculus S5 *
zbMATH Keywords: Kripke models
zbMATH Keywords: possible worlds
zbMATH Keywords: bundle models
zbMATH Keywords: trope models
zbMATH Keywords: situation models
zbMATH Keywords: polyadic S5 *
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4039854