Online research in philosophy

In this paper I will discuss a rather recondite phenomenon in the area of sequence of tense (SOT), exhibited by sentences like (1): (1) John said that Mary is pregnant. According to traditional grammar, this is a sentence where sequence of tense has failed to apply (i.e., concord has been broken): standard sequence of tense rules would dictate use of a past tense when embedding an event contemporaneous to the embedding verb under a past tense verb, giving the sentence John said that Mary was pregnant. For some verbs breaking concord is impossible (*Mary said that John builds a house) or can only have a present-as-future interpretation (John said that the last spaceship to Mars leaves tomorrow), but with stative verbs, as En¸c (1987) and others have observed, this failure of sequence of tense to apply is associated with a rather special meaning, which we will try to elucidate below. For the moment, let us merely observe that the use of present tense seems to cause such sentences to end up saying something about a larger interval including both the time of utterance and the time of the event described in the main clause. For this reason En¸c calls them “double access sentences”, but that seems a rather dubious name as the interpretation seems to rely on evaluation at a large interval, not just at two points.

There are many parallels between the role of possible worlds in modal logic and that of times in tense logic. But the similarities only go so far, and it is important to note where the two come apart. This paper argues that even though worlds and times play similar roles in the model theories of modal and tense logic, there is no tense analogue of the possible-worlds analysis of modal operators. An important corollary of this result is that presentism cannot be the tense analogue of actualism.

In this paper we show the adequacy of tense logic with unary operators for dealing with finite trees. We prove that models on finite trees can be characterized by tense formulas, and describe an effective method to find an axiomatization of the theory of a given finite tree in tense logic. The strength of the characterization is shown by proving that adding the binary operators "Until" and "Since" to the language does not result in a better description than that given by unary tense logic; although the greater expressive power of "Until" and "Since" can be exploited by using the semantics of e-frames instead of traditional Kripke semantics.

Objections to the traditional view that God knows all of time eternally stand or fall on what one means by “eternally.” The widely held supposition, shared by both eternalists and those who oppose them, such as Open Theists, is that to say God knows all of time eternally entails that he cannot know all of time from atemporal perspective. In this paper I show that Boethius’s characterization of God’s eternal knowledge employs a different meaning of “eternal,” which is incompatible with this supposition. I argue that Boethius’s claim that “the most excellent knowledge is that which by its own nature knows not only its own proper object but also the objects of all lower kinds of knowledge” entails that God is not limited by perspective and so eternally and simultaneously knows every temporal event from a temporal as well as a timeless perspective.

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction.

Boethius' treatise De Hypotheticis Syllogismis provided twelfth-century philosophers with an introduction to the logic of conditional and disjunctive sentences but this work is the only part of the logica vetus which is no longer studied in the twelfth century. In this paper I investigate why interest in Boethius acount of hypothetical syllogisms fell off so quickly. I argue that Boethius' account of compound sentences is not an account of propositions and once a proper notion of propositionality is available the argument forms accepted by Boethius are seen to be incoherent. It was Peter Abaelard who first understood the nature of propositionality and propositional connectives and used this to criticise Boethius' claims in De Hypothetics Syllogismis. In place Boethius' confusion Abaelard offered a simple and correct account of the hypothetical syllogism.

The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.

According to Hans Kamp and Frank Vlach, the two-dimensional tense operators "now" and "then" are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that "now" and "then" are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic.

The syntactic domain of tense is the clause: tense appears in some form in every clause of a tensed language. Semantic interpretation of tense requires information from context, however. This has been clear at least since Partee's 1984 demonstration of the anaphoric properties of tense. In this talk I will show that the facts about context are quite complex, perhaps more so than has been appreciated. There are three patterns of tense interpretation, depending on the type of discourse context in which a clause appears. I will introduce the notion of discourse mode to account for the different types of context.1 I offer an interpretation of tense in Discourse Representation Theory, a framework which is organized to deal with information from the context. I also show that a syntactically based theory can handle contextually-based tense interpretation. In §1 I set out the basic analysis of tense and show how it applies to sentences in isolation. §2 discusses types of discourse context and patterns of tense interpretation; §3 considers the formal analysis of tense; §4 concludes with a summary and a prediction about temporal interpretation in tenseless languages.