Objects and modalities. A study in the semantics of modal logic
This work characterizes a formal semantic framework based on a distinction between possible worlds, local objects and individuals. A local object is an object that exists in a possible world or another and it is world-bound, that is, it cannot exist in more than one world. For its part, individuals are trans-world, that is, they do not exist in possible worlds. Rather, they are realized at possible worlds as local objects, although they do not have to be realized at every possible world. Individuals connect different local objects across possible worlds and, for this reason, they are also referred as world lines. At some point in the book, the author compares his approach to individuals with other views, in particular, those by S. Kripke, D. Lewis and K. Fine. Predicates are assumed by the author to be true or false of local objects only and never of individuals. That is, at a possible world \(w\), \(n\)-ary predicates are true or false only of the local objects of \(w\). However, complex formulas might be true or false of individuals. The ranges of first-order quantifiers at a possible world are not the set of local objects of that world but rather a (possibly empty) set of individuals. These ranges might vary from one possible world to another. Two sorts of world lines or individuals are distinguished, viz.: those that are physically individuated and those that are intentionally individuated. On the basis of this distinction, a further distinction is introduced between physical and intentional first-order quantifiers. The range of a physical quantifier at a given world consists of world lines that are realized in that world, while that of an intentional quantifier might not include world lines fulfilling such a condition. Behind this difference is the idea that intentional quantifiers might quantify over non-existent intentional individuals, while physical quantifiers cannot. They are the individuals in an agent's thought at the world at which an intentional quantificational reference is made. All of the above philosophical notions are set-theorically represented in two different formal semantics systems. The first system constitutes a possible world relational semantics for a first-order modal language with only one sort of first-order quantifiers. The range of these quantifiers, at a possible world, is a certain set of individuals associated to the world. An individual is set-theoretically represented as a partial function from the set of possible worlds into the set of all local objects such that, at each world \(w\) at which the function is defined, its value is to be a local object of \(w\). For each possible world, there is an associated set of local objects. The second system is a possible world multi-relational semantics for a first-order modal language with individual constants, two sorts of first-order quantifiers and a set of indexed necessity operators. In addition to the set-theoretic representation of individuals of the first semantics and its association of sets of local objects to each possible world, the semantic system also includes a set representing agents and a set of different accessibility relations that formally stand for intentional states of the agents. The different accessibility relations are correlated with the indexed necessity operators in the definition of a satisfaction of formula by a model of the semantics. The semantics also associates to each possible world two different sets of individuals. These correspond to the ranges of the two sorts of quantifiers, which formally represent the author's distinction between physical and intentional quantifiers. Finally, the semantic values of individual constants are local objects In connection with his semantic framework, the author discusses several important topics, such as the distinction between extensional and intentional predicates, modes of predication, the Barcan formulas, intensional verbs, intentional states, and non-existent objects.
scientific article; zbMATH DE number 6755684