Speaker: Thomas Randriamahazaka (University of St Andrews)
Date and Time: Thursday, September 29th 2022, 16:30-18:00
Venue: F1.15 and online.
Title: Aboutness and partiality: a duality-theoretic perspective.
Abstract. A familiar story identifies propositions with sets of possible worlds. This can be understood as the semantic upshot of Stone duality, once it is accepted that propositions form a Boolean algebra. However, possible world semantics is often said to be too coarse-grained to account for some semantic phenomena. To solve this problem, it is possible to distinguish between two popular hyperintensional strategies. The first one is to supplement the space of possible worlds by a mereology of topics and to individuate propositions as pairs consisting of a set of possible worlds and a topic. The second one is to replace possible worlds by partial states. The goal of this talk is to identify a bridge between these two strategies using the tools of duality theory. From an algebraic point of view, the first strategy can be seen as the application of the construction known as Plonka sum. More precisely, the algebra of propositions can be described as the Plonka sum of Boolean algebras over the semilattice of topics. The main result of this talk is the description of the topological dual of the Plonka sum construction, dubbed co-Plonka sum. To do so, a new, weaker notion of topological space will be needed. This dual construction will allow us to lift Stone duality through the Plonka sum and have a description of the dual space of the algebra of propositions. Just like the points of the dual Stone space of a Boolean algebra can be understood as possible worlds, the points of the dual space of the algebra of propositions are best described as partial states, linking the first and the second strategies.