The Significance of the Contributions of A.N.Prior and Jerzy Łoś in the Early History of Modern Temporal Logic (original) (raw)
Related papers
Logic and Philosophy of Time: Themes from Prior, Volume 1
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...
Logic and Philosophy of Time: Themes from Prior
2017
A.N. Prior (1914-69) in the course of the 1950s and 1960s founded a new and revolutionary paradigm in philosophy and logic. Its most central feature is the preoccupation with time and the development of the logic of time. However, this was inseparably interwoven with fundamental questions about human freedom, ethics, and existence. This remarkable integration of themes also embodies an original and in fact revolutionary conception of logic. The book series, Logic and Philosophy of Time, is dedicated to a deep investigation and also the further development of Prior's paradigm.
Logic and Philosophy of Time: Further Themes from Prior
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...
Prior’s paradigm for the study of time and its methodological motivation
Synthese, 2016
A. N. Prior's writings should obviously be studied already for historical reasons. His inventions of modern temporal logic and hybrid logic are clearly important events in the history of logic. But the enduring importance of studying his works also rests on his methodological approach, which remains highly relevant also for systematical reasons. In this paper we argue that Prior's formulation in the 1950s of a tense-logical paradigm for the study of time should be understood in the light of at least three other principles or perspectives which were manifest already in his studies during the 1940s and further developed in the 1950s: (1) his emphasis on the value of interdisciplinary studies, (2) his reflections on formalisation and (3) his view of the role of symbolic logic in conceptual studies and in the philosophy of science. Our investigation into Prior's basic tenets and principles makes extensive use of Prior's Nachlass. It is thereby also exemplified how his correspondence and unpublished papers contain important information for a deeper understanding of Prior's paradigm for the study of time. Keywords A. N. Prior • Temporal logic • Interdisciplinary studies • Formalisation A. N. Prior's most important works were written in the period from 1953 to his untimely death in 1969. However, recently his earlier works have attracted growing attention (Hasle 2012; Grimshaw 2002, 2013; Jakobsen 2013). It has become clear that his work preceding his first formulation of formal tense-logic in 1953 had a much stronger B Per Hasle
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
Philosophy in Review, 2013
This book advertises itself as an exploration of the world-time parallel, that is, the parallel between the modal dimension, on the one hand, and the temporal dimension, on the other. It is that, and much more. As the authors point out, there is reasonable agreement that we can model times, through temporal logic, in ways that are analogous to those by which we model modality through the logic of possible worlds. But this formal parallel has almost universally been taken to be merely a formal parallel, that is to say, the assumption has been that no metaphysical conclusions ought to be drawn from it. Thus, it is generally thought that one is free to accept an argument for actualism, say, but to reject a parallel argument for presentism. Rini and Cresswell compellingly argue that this is a mistake: the temporal and the modal are more than merely formally analogous. Abstracting from the interesting central question about the status of the world-time parallel, this book is of interest to anyone who desires clarity about propositional content, de se knowledge (and indexicality more generally) and of course tense and modality. In part because the authors do not wish to prejudge any metaphysical disputes-in particular they do not want to take a stand on whether one ought to be a possibilist rather than an actualist, or an eternalist rather than a presentist-they scrupulously offer very careful explications of current actualist and possibilist modal semantics as well as eternalist and presentist tense semantics. The book is rich with careful detail. It is full of places where various confusions are cleared away. Indeed, there is so much packed into the various discussions that it is difficult to know where to start a review. So rather than try and offer a very potted cook's tour of the book, in what follows I offer just a small taste of one of the issues canvassed.
Two Series of Time in Logic, Natural Language, Computer Science and Artificial Intelligence
FILOSOFIE DNES
J. M. E. McTaggart famously divided time into two time series, which he entitled A-series and B-series. Although he was proponent of neither of them, his division initiated a discussion as to which of the series is prior or real. This paper follows Clifford Williams’s claim that these series are not as distant as their proponents argue they are. It demonstrates their translatability in the case of examples from temporal logic and natural language. It argues that, if there are any deep-rooted differences between these two series, they are only metaphysical. These metaphysical differences could be overcome by focusing on logic or natural language. These two series of time are also used in computer science and in the development of Artificial Intelligence. However, no attempt at unifying them has been suggested in these fields of study. J. M. E. McTaggart rozdělil čas na dvě časové série, A-série a B-série. Třebaže nebyl zastáncem žádné z nich, jeho rozdělení podnítilo diskuzi, která...
Łukasiewicz, Bocheński, and Feys: Their Impact on the Early Prior
Logic and Philosophy of Time, 2023
We investigate how Arthur Prior became a tense-modal logician, and which moderns influenced him in his early thinking about modality. His unpublished manuscript The Craft of Formal Logic, written in the period 1949-51, is in effect a record of his rather isolated apprenticeship as he trained himself in formal logic, during the two years before the commencement of his torrent of publications on modality. We analyse sections of this rich record of his logical development, especially those dealing with modal logic, and we extract a detailed account of the pattern of influences exhibited in The Craft. The Craft reveals that Prior's first encounters with modern symbolic modal logic were the pioneering explorations by Bocheński, Feys, and Lewis. Von Wright was also an early influence. It was through Bocheński's writings that Prior learned of Łukasiewicz's approach to modality, and Łukasiewicz's work quickly became a beacon for Prior. The roles of Lewis and von Wright appear to have been smaller than those of Łukasiewicz, Bocheński, and Feys-hence our focus on these three figures. As well as biographical material on these three outstanding logicians, we
Scrinium, 2019
The article analyzes some key moments in the history of temporal logics in late antiquity (conception of integral time, relationship between temporal and eternal, extended and instant in the systems of Iamblichus, Proclus, Damascius and Simplicius), and genesis of Christian forms of temporal logics, which transform the everlasting homogenous time of κόσμος into history of universal salvation, alterate unextended νῦν, moment of psycho-physical time of late Neoplatonists, with καιρός, eschatologically charged instant of decision and act that can interrupt the continuity of time and to achieve instantaneously the end, τέλος of history.
Between the Time of Physics and the Time of Metaphysics, the Time of Tense Logic?
Einstein vs. Bergson
Accordingt oR ussell, Being is divided into atemporal universals and temporal particulars. But,t ot he extent that the Antisthene'sc aballeity pops up in the topos noeton,the ancestors of the horse must precede the horse in the sublunar. Thus, Being must be divided into Sosein, Dasein and Zeitsein. Onlythe Whiteheadian "eternal objects",s uch as geometricalf orms and colours,a re atemporal universals, while caballeity is in the Zeitsein togetherw ith Conquérant (one among Napoleon'sh orses). In this ontology,a ccordingt ot he Lautmanian shift, Spatiotemporality pertains to the Sosein and has at wo-fold structure: logical and mathematical. The tensel ogic of A.N.P rior describes it,while its link with the mathematics of spacetime is fixed by the Boolean kernel in the vonNeumann algebraf or quantum logic. Thiss peculation will be precededb yanarrative exposition of elementaryt ense logic. *Iam grateful to the all staff at the What is time? symposium for theirinvitation and generous hospitality.Great thanks are especiallydue to RoccoRonchi for his marked concerns, to Elie During for the courtesy of his discussion and to AlessandraC ampof or the truth of her philosophical enthusiasm. As pecial thanks is for the anonymous reviewer of this paper. 1T he Tale of TenseL ogic Tense logic is avariety of temporal logic, and temporallogic is abranch of modal logic. Thus, in order to give ashort history of tenselogic, we must start by tracing as hort genealogyo ft he modal logic.¹ The latter has threem ain moments: the Leibnizian foundation,t he Kripkean mathematization and the creation of tense logic by Arthur Prior. See Blackburn,D eR ijkea nd Venema (2001). Arthur Prior and Hybrid Logic is af ascinating paper which focuses on the morep romisingl ines of thoughti nt he area.