The logic of temporal discourse

Abstract

Despite the extensiveness of the literature on the topic, the logic of tenses is still in a rudimentary stage. Not only have we no satisfactory account of tensed statements' truth-conditions; it is not even clear what the correct logical types of tenses are. It seems well established, for instance, that conjunction is, semantically speaking, a function which takes couples of truth-values to truth-values, and that necessitation is a function which takes propositions to truth-values. There seems, on the other hand, no generally agreed typological classification of the Simple Past or the Present Perfect. If tenses are to be semantically understood, they too must be construed as functions; but functions from what to what? As has been recognized by leading tense logicians', the first step on the way to understanding temporal discourse is to liberate oneself from the received dogma that truth is timeless. If truth were atemporal, tenses would be idle, for to say that something was true in the past would be tantamount to saying that it is true in the present or that it will be true in the future. Tenses can only make a difference if what is true at one time may be false at other times and vice versa. And since it is propositions which may be true or false, what must be recognized is that the truth-value of a proposition depends, in general, on time. The truth-value of a proposition depends, in fact, on exactly two factors: on which of the possible world histories (briefly: possible worlds) is actualized, and on what the time is. A proposition is thus best identified with a function which takes each possible world to the class of moments of time at which the proposition is true in that world; we shall speak of that class as the chronology of the proposition in that world. When a proposition is put into, say, the present perfect, its chronology will normally change. Consider, for instance, the proposition that Tom is drunk; call it A. The actual chronology of A (i.e., the set of times at which Tom was, is, or will be actually drunk) is, we may suppose, scattered irregularly along the time axis. But the chronology of the present perfect of A, i.e., of the proposition that Tom has been drunk, is entirely different: it consists of all times which come after the time of Tom's maiden drunkenness.