Worlds Enough, and Time: Musings on Foundations

Abstract

Belnap’s work on stit theory employs an Ockhamist theory of branching time, in which the fundamental possibilia within models are commonly taken to be moments of time, connected into a tree-like branching structure. In the semantics for alethic modal logic, necessity is characterized by quantification over relevant possible worlds within a model, yet Belnap refers to an entire model of branching time as our world, seemingly leaving no room for non-trivial quantification over worlds within a single model. This chapter explores the question how the notion of possible worlds should be understood in relation to an Ockhamist framework, in order to be able to combine an account of alethic modalities with an account of branching time and stit theory. The advantages and drawbacks of several alternative approaches are examined.