Four modal modelings
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.
monadic part of S. Kripke's simple modal predicate calculus S5 *
scientific article; zbMATH DE number 4039854