Determinism and the Origins of Temporal Logic

Abstract

The founder of symbolic temporal logic, A. N. Prior was to a great extent motivated by philosophical concerns. The philosophical problem with which he was most concerned was determinism versus free will. The aim of this paper is to point out some crucial interrelations between this philosophical problem and temporal logic. First, we sketch how Prior’s personal reasons for studying the problems related to determinism were philosophical — initially, indeed theological. Second, we discuss his reconstruction of the classical Master Argument, which has since Antiquity been considered a strong argument for determinism. Furthermore, the treatment of determinism in two of Prior’s proposed temporal systems, namely the Ockhamistic and the Peircean systems, is investigated. Third, we illustrate the fundamental role of the very same issue in more recent discussions of some tempo-modal systems: The ‚Leibniz-system‘ based on ideas of Nishimura (1979) as well as Belnap and Green’s argument (! 1994), to which we add some necessary revisions.KeywordsModal LogicTemporal LogicTense OperatorTense LogicContingent FutureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.