In an influential paper (Bach 1986), Emmon Bach made a distinction between metaphysics, a subfield of philosophy, and natural language metaphysics, a linguistic activity. While metaphysics tries to answer questions such as “What is there?” and “What kind of things are there and how are they related?”, its linguistic cousin looks at parallel questions like “What do people talk as if there is?” and “What kinds of things and relations among them does one need in order to exhibit the structure of meanings that natural languages seem to have?”. Natural language metaphysics, in other words, is the study of the ontological commitments that come with a certain linguistic framework (in Carnap’s sense), in this case the framework imposed by ordinary languages.
My talk will be on natural language metaphysics and will—in a revered metaphysical tradition—be entirely speculative. Its inspiration and point of departure will be the temporal ontology underlying Henk Verkuyl’s recent book (Verkuyl 2021). Readers of this work will know that a central ingredient of the semantic theory proposed in it are certain intervals called indices. Tenseless forms are predicates of indices and consequently have type (i,t), while the operators IMP, PERF, SYN, and POST are functions from predicates of indices to predicates of indices and therefore have type ((i,t)(i,t)), as do temporal adverbials. When tense comes in—but not earlier—a form expressing a truth value is returned.
Indices have attributes. For example, each index i has a leftmost point l(i) and a rightmost point r(i). While these points are not thought of as being temporal (time is kept by a separate linear ordering), they are in fact ordered in the way branching time logic orders temporal instants—by a precedence relation that is irreflexive, transitive, and backwards linear. Each index i also has a world attribute w(i). Worlds can be thought of as (but need not be formally identified with) entire paths in the branching ordering.
What is the ontological status of the points in the branching order? A natural answer seems to be that they are snapshots of worlds at some stage of their development. Let us call them world-stages. If this answer is accepted, a next question forces itself upon us: If end points are world-stages, is it still necessary to additionally provide indices with a full world attribute? The answer here, I will argue, depends on the expressivity that is needed to model operators such as POST. If the semantics of natural language POST is Ockhamist, making reference to some given world, the answer is probably “yes”. But if it is tenable to assume that the linguistic system provides POST with a Peircean semantics that involves only quantification over future world-stages, it seems possible to make do without explicit reference to worlds in the atemporal domain. But then a third question arises. Is this possibility restricted to the untensed domain? Does language quantify over full worlds at all, comprising entire histories, or just over stages that stand in certain accessibility relations? I will argue that assuming the latter is compatible with a model of natural language semantics in which indices rule supreme. In the verbal domain they can function as eventualities, taking additional attributes that encode thematic roles. They can be the carrier of a Davidsonian verb semantics there. But their modal character as connectors of world-stages also makes them a suitable key ingredient of the semantics of modalities and propositional attitudes.