Prior on the semantics of modal and tense logic

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death, and it is right that this should be so, since a philosopher’s greatness is marked by his legacy. My focus however will be a little different. I want in this talk to look at what Prior himself thought he was accomplishing. In particular I want to investigate Prior’s attitude to the semantic metatheory of the logics that he was interested in, specifically modal and tense logics. Even a brief glance at Prior’s writings shews a lack of interest in metalogic. His earlier writings of course predated the development of the possible worlds model theory for modal logic, and its generalisation to intensional logic, often called ‘modal logic’ in a wider sense of that term. For this reason there is little explicit discussion there of model theory. His later work did span the semantic developments pursued by Kripke and others, and while he has a few comments, it is hard to get a clear statement of his views. What I propose to do therefore is list a number of features possessed by the current possible worlds semantics — where by that I mean a semantics in which the indices are called ‘worlds’ though they could be moments of time, states in the execution of a computer program, or whatever. I shall use these features to compare them with Prior’s views on these particular questions. The features I shall list are related, though many are independent, and it is this which makes it a not insignificant task to get a unified view from Prior’s work. In looking at Prior’s logical writings we have to remember the time frame. Beginning in the early 1950s, at the height of the ordinary language movement, and emerging in the John Locke lectures in 1956, it continued until his death in 1969. It was during this period that the possible worlds semantics was being developed for modal logic. Prior was writing throughout the whole period, and his own work contributed to it, yet, despite this, his attitude was increasingly ambivalent. As early as 1952 we find a ‘possible worlds’ account of modality in In what sense is modal logic many-valued?: