Outline for a Truth Conditional Semantics for Tense

Ernest Lepore and Kirk Ludwig

Abstract

The use of verbs inflected or modified for tense, and temporal adverbs, indexicals, and quantifiers, pervades everyday speech. Getting clearer about their semantics promises not only to help us to understand how we understand each other but is also a step toward clarifying the nature of time and temporally located thoughts. Our aim in the present paper is to investigate, from the standpoint of truth-theoretic semantics, English tense, temporal designators and quantifiers, and other expressions we use to relate ourselves and other things to the temporal order. Truth-theoretic semantics provides a particularly illuminating standpoint from which to discuss issues about the semantics of tense, and their relation to thoughts at, and about, times. Tense, and temporal modifiers, contribute systematically to conditions under which sentences we utter are true or false. A Tarski-style truth-theoretic semantics, by requiring explicitly represented truth conditions, helps to sharpen questions about the function of tense, and to deepen our insight into the contribution the tenses and temporal modifiers make to what we say by using them.

We are interested in a semantic, rather than syntactic, phenomenon. Although tense is identified traditionally with verb inflection, our concern is with linguistic devices used for indicating a time interval, relative to, or in, which a state or activity is to be understood to occur or obtain. For ease of exposition, we will press into use ‘tense’ to cover any verb form we use to indicate time intervals in which the event or state expressed by a verb is to occur or obtain. In English, verb inflection, such as adding ‘-ed’ to a truncation of an infinitive, is one such device. But the phenomenon occurs even in languages like Chinese that lack inflection for tense. Though we will be concerned solely with tense in English, we are interested in it as an example of a semantic phenomenon common to natural language. The structure of a semantic phenomenon may be expected to reflect underlying facts about the structure of our thoughts about contingent particulars. We expect that all languages share basic expressive resources, even when they are realized by diverse syntactical devices.

Our basic approach, which goes back to Frege and Russell and, treats tense as an indexical device for referring to times or time intervals at which events take place or states obtain. Where the time interval picked out is not the present, tense involves what we will call indexically restricted quantifiers. The indexical element functions to pick out a time of utterance as a reference point for indicating quantificationally the relative location of temporally bound states and events. While the central idea is intuitively appealing, it has not been systematically explored within a truth-theoretic framework. It turns out to be particularly powerful in its application to systematizing the often puzzling interaction of tense with other temporal devices. Treating tense as quantificational will enable us to give a uniform account of tense and temporal modifiers and quantifiers in English, and it can be shown to complement in a compelling way the standard event/state analyses of adverbial modification. If the basic account is correct, in our most ordinary remarks we reveal a commitment to the existence of time intervals. Hence, time is real, or virtually everything we say is false.

We begin with an overview of how to deploy a truth theory as a compositional meaning theory. We show that the requirement that the theory be interpersonal precludes a semantics for tense which employs tense operators. Next, we present an account of the simple tenses (present, past, future) and of the present progressive, and discuss several methodological points about tense and semantics. One initially surprising result is that a semantic for natural languages like English cannot be given in those languages, because they lack the non-context sensitive relational verbs relating things to times required in the metalanguage. Next, we give an account of deictic and structured temporal referring expressions, representing them as directly referring terms that have a semantic rule with a privileged description that picks out their referent. Next, we consider how our basic account interacts with temporal adverbials, and then how it interacts with >before= and >after=, used as sentential connectives. We then consider how tense interacts with temporal quantifiers. Next we treat so-called habitual sentences and frequency adverbials. Then we show how our account of tense interacts with the event analysis of adverbial modification. Next, we consider the interaction of tense in main and complement clauses of indirect discourse reports and attitude sentences. We show, in particular, that on the quantificational approach, the interaction of the tense of the main verb with that of the complement clause is properly represented as a matter of the quantifier introduced by the main verb binding the argument place for reference time in the complement verb. Thus, very many indirect discourse sentences and attitude reports involve quantification into the complement clause in virtue of tense alone. Next, we apply the account to issues in the philosophy of time, and discuss the limitations of semantics in metaphysics. We conclude our semantics supports the B-series conception of time, that is, the conception of time as not having changing properties of being past, present and future. In the appendix we provide a truth-conditional semantics for the perfect tenses.