A Formal Framework for Future Contingents

In this article, I present a formal semantic framework that renders explicit how to reconcile the condition that a proposition about a contingent future event is true at a moment t0 with the idea that at t0, this proposition is ‘truth-maker indeterminate’: a state of affairs making it true will obtain later on, though no such state of affairs obtains at t0. The semantics I formulate employs ‘open temporal models’. They represent the passage of time by a specific component termed time-resource, which acts on durations construed as model-external inputs. A model does not by itself specify which course of events gets actualized in a given duration depending on the latest moment that has already got actualized. A time-resource merely represents schematically the dependence between a moment t and a course of events that gets actualized in a time-span of a given length counted from t; until that much time has indeed passed, it is not fixed which course of events actually extends t. Further, I introduce evaluations as a fine-grained tool for studying truth-conditions of tensed formulas, and I use this tool to define the notion of truth-maker. I define what it means that a truth-maker will obtain but does not, and what it means for a truth-maker to be determinate. It is proven that my semantic analysis retains the desirable link between determinacy and historical necessity—namely, a truth-maker of a proposition being determinate entails that the proposition is historically necessary.