Ulrich Meyer

With the rigorous development of modal logic in the first half of the twentieth century, it became custom amongst philosophers to characterize different views about necessity and possibility in terms of rival axiomatic systems for the modal operators ‘ ’ (‘possibly’) and ‘ ’ (‘necessarily’). From the late 1950s onwards, Arthur Prior began to argue that temporal distinctions ought to be given a similar treatment, in terms of axiomatic systems for sentential tense operators, such as ‘P’ (‘it was the case that’) and ‘F’ (‘it will be the case that’).1 My aim here is to give a brief survey of the extent to which time can be treated on the model of modality. I shall not try to address the further question of whether such ‘modal’ accounts of time are to be preferred over ‘spatial’ accounts that treat times more like places.

This paper explains how to obtain quantification over times in a tense logic in which all temporal distinctions are ultimately spelled out in terms of the two simple tense operators “it was the case that” and “it will be the case that.” The account of times defended here is similar to what is known as “linguistic ersatzism” about possible worlds, but there are noteworthy differences between these two cases. For example, while linguistic ersatzism would support actualism, the view of times defended here does not support presentism.