Quantification over Sets of Possible Worlds in Branching-Time Semantics

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quanti\uafcation over histories, which is a second-order quanti\uafcation over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as \uafrst-order counterparts of the original semantics

Future Contingents. Indeterminism, Temporal Logic and Semantics

This essay is about the problem of future contingents, that is, statements predicting future events that are neither historically impossible, nor inevitable. The analysis intersects metaphysics, logic, philosophy of language and philosophy of science. In particular, the essay explores why indeterminism – viz., the doctrine that the present, the past, and the laws of nature do not necessitate the future – may be taken as a sensible thesis. Furthermore, several semantics for indeterministic, modal temporal languages will be considered. It is argued that the modal, temporal logic that best fits indeterminism is a version that mirrors the so-called TRL metaphysics. The advocates of the TRL metaphysics, indeed, can evoke a substantive notion of actuality to tell themselves apart from determinist, many worlds theorists. And the notion of substantive actuality assumed by TRL theorists may be easily reflected at the (post)semantic level, yield- ing a temporal logic which meets several desiderata