Nominal tense logic and other sorted intensional frameworks

This thesis introduces of a system of tense logic called nominal tense logic (NTL), and several extensions. Its primary aim is to establish that these systems are logically interesting, and can provide useful models of natural language tense, temporal reference, and their interaction. Languages of nominal tense logic are a simple augmentation of Priorean tense logic. They add to the familiar Priorean languages a new sort of atomic symbol, nominals. Like propositional variables, nominals are atomic sentences and may be freely combined with other wffs using the usual connectives. When interpreting these languages we handle the Priorean components standardly, but insist that nominals must be true at one and only one time. We can think of nominals as naming this time. Logically, the change increases the expressive power of tensed languages. There are certain intuitions about the flow of time, such as irreflexivity, that cannot be expressed in Priorean languages; with nominals they can. The effects of this increase in expressive power on the usual model theoretic results for tensed languages discussed, and completeness and decidability results for several temporally interesting classes of frames are given. Various extensions of the basic system are also investigated and similar results are proved. In the final chapter a brief treatment of similarly referential interval based logics is presented. As far as natural language semantics is concerned, the change is an important one. A familiar criticism of Priorean tense logic is that as it lacks any mechanism for temporal reference, it cannot provide realistic models of natural language temporal usage. Natural language tense is at least partly about referring to times, and nowadays the deictic and anaphoric properties of tense are a focus of research. The thesis presents a uniform treatment of certain temporally referring expressions such as indexicals, and simple discourse phenomena

Future Contingents, Freedom, And Foreknowledge

This essay is a contribution to the new trend and old tradition of analyzing theological fatalism in light of its relationship to logical fatalism. All results pertain to branching temporal systems that use the A-theory and assume presentism. The project focuses on two kinds of views about branching time. One position is true futurism, which designates what will occur regardless of contingency. The opposing view is open futurism, by which no possible course of events is privileged over others; that is, there are no soft facts. A contextualist theory of temporal standpoints, standpoint inheritance, is designed to enhance Priorian temporal logics. The proposal helps all branching time systems, not only those with an open future. Even though an account of temporal standpoints goes a long way towards aiding various analyses from a linguistic standpoint, theories that designate a true future ultimately succumb to philosophical difficulties. Under open futurism, standpoint inheritance commandeers the best semantic evidence for true futurism. Standpoint inheritance accounts for the evidence, but the evidence does not support true futurism\u27s stronger claims. Furthermore, attempts to explain why one timeline is privileged as the actual future lead to fatalism. Open futurism and a related kind of open theism are the only viable alternatives under dynamic, branching time. If true futurism is feasible at all, it is so only with a static or eternalist basis. Standpoint inheritance is very general. It is applied to every system discussed in this analysis to handle damning linguistic shortcomings of traditional logics. Standpoint inheritance yields several other fruitful results, too. The theory helps clarify what it is for characterizations of God\u27s beliefs to be soft and how his beliefs must differ from normal beliefs to retain softness. For open futurism, all strings of consecutive will\u27s and was\u27s can be reduced to at most two such operators under standpoint inheritance, but not under traditional theories. The open futurist distinction between will and will-inevitably is clarified, too. Standpoint inheritance allows for a supervaluationist semantics using open futurism as its basis instead of the usual true futurism. The theory of standpoint inheritance enhances dynamic, branching accounts of time to better compete with their static correlates

Temporal Operators and (Metaphysical) Presentism

In a paper titled “Tense, Modality, and Semantic Values,” (Philosophical Perspectives, 2003) Jeffrey King argues (in part) that tenses in English do not function as sentential operators but that they are more akin to object-language quantifiers over times. Although not an explicit concern of King’s in the paper under consideration here, his analysis poses several prima facie difficulties for the metaphysical position known as “presentism” (that is, roughly, the view that only what exists at the present is real). Specifically, the commonsense motivation for presentism is threatened because of the discrepancy King proposes between how tense actually functions in the language and how presentism typically insists that tense functions. Additionally, if King is right, the typical presentist paraphrasing project is seemingly jeopardized. Herein we will try to raise some worries about King’s proposal (e.g., without limitation, that he has failed to consider relevant potential sorts of operators) and about the cited linguistic evidence (e.g., that it is too parochial, turns on hard cases, etc.). Finally, we will suggest defenses (e.g., a Matti Eklund-inspired sort of indifferentism ) of both the motivation for presentism and the paraphrasing methods usually employed (which defenses arguably hold up even if King is correct)