Talk: Edward N. Zalta (Stanford)

Authors: Uri Nodelman and Edward N. Zalta

Title:

The Metaphysics of Possibility Semantics

Abstract:

A number of researchers have suggested that there is a mismatch between the use of complete, possible worlds in the semantics of our modal language and the fact that the particular possibility claims such worlds are used to interpret only specify incomplete "ways things might have been". They have attempted to interpret our possibility (and necessity) claims in terms of a background of "less determinate entities than possible worlds" (Humberstone 1981), and have called these entities "possibilities". Edgington (1985) suggested that they are possible situations that "differ from possible worlds in leaving many details unspecified". In technical developments of this notion (Humberstone 1981, 2011; van Benthem 1981, 2016; Holliday 2014, forthcoming; and Ding \&\ Holliday 2020), one finds that: (a) "possibilities" are taken as primitive entities in a semantics, (b) semantic principles governing these entities (Ordering, Persistence, Refinement, Cofinality, Negation, and Conjunction) are then stipulated, and (c) a modal language is then interpreted via this semantic structure.
In this talk, we show that "possibilities" in the technical sense used in these papers can be defined in object theory (OT), and that the semantic principles that have been stipulated to characterize them can be derived from the definition as theorems. The analysis deploys the theory of situations developed within OT in Zalta 1993 ("Twenty-Five Basic Theorems in Situation and World Theory") and 1997 ("A Classically-Based Theory of Impossible Worlds"). I'll briefly review OT and the results in these two papers and then show how to formally define a "possibility" as a situation that is consistent and modally closed. I then sketch the basic theorems that follow from this definition and sketch how the main semantic axioms governing possibilities become derivable as theorems in OT. The analysis shows that a primitive modal operator is needed to fully capture the notion of a "possibility", but that such a modal operator hasn't been used by those who offer semantic characterizations.