Bivalence and Future Contingency

2017

A.N. Prior’s Past, Present and Future [18] was published 50 years ago in 1967 and was clearly a milestone in the development of tense-logic. It is a mature and comprehensive presentation of the basic concepts, systems and issues in tense-logic. In addition it also contains a number of interesting ideas that later led to important further developments of the field. Past, Present and Future represents a culmination of Prior’s struggle with the problem of determinism (including his study of the tension between the doctrines of divine foreknowledge and human freedom). Prior’s study of the problem of determinism led him to a reconstruction of the famous DiodoreanMaster Argument which had for centuries been regarded as a strong argument in favour of determinism. In his further analysis of the problem, hemade extensive use of tense-logic and the idea of branching time. However, in Past, Present and Future Prior also stresses that time as such should not simply be understood in terms of bra...

These criterias (time conception, semantic model structure, truth-value function and truth in the future contingents) will be developed in §3, §4, §5 and §6, respectively. In §3.1, §4.1 and §5.1 I will consider these criterias from a branching-time point of view; while in §3.2, §4.2 and §5.2 I will do the same from a linear-time conception. §6 Includes the fourth criteria and Belnap's branching-time approach to it. Then in §7 I will consider Beall's proposal as the linear 'correlate' of §6. And finally in §8 I will relate the different proposals and argue in favor of the branching-time conception.

Journal of Logic, Language and Information, 2010

Time is the grand stage where human activities take place (rational or otherwise). And the view of a branching temporal universe, or tree of possible events, with our actual history linearly advancing through it, is a widely shared cultural idea, not confined to Academia (cf. Borges brilliant 1941 essay El Jardín de senderos que se bifurcan). Even though logic is often considered a study of timeless propositions, temporal languages and logics over tree structures have a long tradition. Philosophers have studied temporal structure and temporal reasoning since the 1950s, from the 'tense logic' of Prior (1967) to the 'STIT' system of Belnap et al. (2001). Moreover, starting from 1970s, computer scientists have joined in, and developed many further flavours of temporal logic, with major strands such as Pnueli on program correctness (Manna and Pnueli 1991), Emerson and Clarke on process specification and verification (Emerson and Clarke 1980, 1982), Reiter on the situation calculus in AI (Reiter 2001), and Thomas on the automata-theoretic foundations of computing (Thomas 1990). In addition, the pure first-and second-order logic of tree-like structures, starting from Rabin's classic decidability result (Rabin 1969), provides deeper background (cf. Grädel et al. (2002)). The chapter by Hodkinson and Reynolds on 'Temporal Logic' in the Handbook of Modal Logic (Hodkinson and Reynolds 2006) brings together many of these trends in one mathematical narrative. But the field of reasoning in, and about, time can be mapped out in many further ways: Van Benthems chapter 'Temporal Logic' in the

Journal of Logic and Computation, 1996

In formalising temporal reasoning, should a proposition be allowed to change its truth value in nitely often over a nite period of time? It has been widely felt that for many types of proposition this phenomenon, which following Hamblin we call \intermingling", should be outlawed. In this paper we systematically examine the varieties of intermingling, distinguishing intermingling over an interval from intermingling at an instant. We survey the axioms that have been proposed in the literature to rule out intermingling, and determine precisely which varieties of intermingling are ruled out by which axioms. We distinguish \weak" non-intermingling principles, which only rule out one or two forms of intermingling, from \strong" non-intermingling principles which rule out all or most forms of intermingling. We show that none of the rst-order solutions in the literature su ces to rule out all forms of intermingling, though a second-order solution can do so.

2019

This paper argues that A.N. Prior’s invention of tense-logic constitutes a return of medieval logic in the philosophy of time. The argument proceeds from an analysis of W.V. Quine and P.W. Strawson’s 1953 discussion about the inability of formal logic to analyse the tenses of ordinary language. Recent discoveries in the A.N. Prior archive at the Bodleian Library in Oxford reveal that J.J.C. Smart, in a letter to Prior, brought up their discussion in his rejection of Prior’s invention of tense-logic. The correspondence will be discussed in terms of the importance of Prior’s discovery of tense-logic and the presentation of this as a solution to the problem discussed by Strawson and Quine in The Syntax of Time Distinctions (1958, [9]). Recent discoveries reveal a close connection between this discussion and Prior’s discussion of future contingency in Diodoran Modality (1955, [7]). These discoveries support the conclusion of this paper, which argues that Quine’s insistence that modern l...

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this "abundance of the future" is a non-adjunctive paraconsistent formalism based on subvaluations, which has the virtue that all classical laws are valid in it, while no formula like φ ∧ ¬φ is satisfiable (though both φ and ¬φ may be true in a model); (2) The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; (3) abundance preserves some important features of classical logic (not preserved in supervaluationism) when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum.

Applied Logic Series, 2000

Idea. Studia nad strukturą i rozwojem pojęć filozoficznych, 2014

The central point of Brogaard's interesting essay is that temporalism, roughly, the thesis that there are propositions whose evaluation is sensitive to time , is a better alternative to standard semantic eternalism, roughly, the thesis that no proposition is sensitive to temporal variation. Five theoretical roles individuate propositions: (i) semantic values of sentences, (ii) objects of attitudes, (iii) objects of agreement and disagreement, (iv) what is transferred in successful communication, and (v) what intensional operators operate on (5-6, 30). For each of those roles Brogaard aims at showing that temporal propositions fare better than eternal ones, in that the problems that have been traditionally raised against them can be overcome, while more serious problems can be raised against eternal propositions. Although most of the book touches upon issues of philosophy of language and philosophy of mind, as it should be, there are several considerations that Brogaard makes about the relation between the semantic tenets of temporalism and eternalism, on the one side, and the metaphysics of time, on the other. In this note, I will assume that the semantic arguments in the book for preferring temporalism over eternalism are sound, and confine myself to some criticism concerning their metaphysical import.

Journal of Logic, Language and Information - JOLLI, 1999

For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated “restricted variables” called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.