'Wolterstorff (2009) provides an important explanation to the question: What caused the surprising resurgence in philosophical theology that has occurred over the last 50 years—a resurgence that rivals its zenith in the Middle Ages? This article supplements that with a more fine-grained answer to the question. Recent discoveries in Arthur Norman Prior’s correspondence with J.J.C Smart and Mary Prior, between November 1953 and August 1954 on the possibility of necessary existence, demonstrates the importance of Prior’s discussion of (...) the Barcan formulae in Time and Modality (1957) for the resurgence of analytic theology. The correspondence establishes that Prior’s discovery of tense-logic, and his discussion of quantified tense-logic constituted the perfect opportunity for him to challenge key anti-metaphysical assumptions in analytic philosophy, from which four important consequences can be drawn for the resurgence of philosophical theology. First, Prior’s discussion of time and existence challenged the idea of Russell (1945) and Findlay (1948) on the logical status of a necessary existing being. Second, the discussion challenged the Analytic school’s view of analysis and gave Prior the opportunity to introduce a different perspective on the relationship between logic and metaphysics. Third, it gave Prior a good opportunity to demonstrate that the then-prevailing attitude towards medieval logic was wrong. Fourth, it made it possible for Prior to demonstrate that the highly surprising metaphysical conclusions of quantified tense-logic brings modern logicians into a discussion with the theologically minded medieval logicians. (shrink)

The article discusses Nicholas Wolterstorff’s explanations for the flourishing of philosophical theology in analytic philosophy by taking Arthur Norman Prior’s (1914–1969) development of tense-logic into account. Prior’s work challenged the prevailing anti-metaphysical norms in analytic philosophy and introduced an alternative understanding of the relationship between logic and metaphysics. Prior’s application of tense-logic to an analysis of the concept of existence in quantified tense-logic and his exploration of future contingency in branching time (...) semantics provide a strong reason for why analytic philosophy naturally incorporates philosophical theology. These considerations lead us to modify Wolterstorff’s emphasis on the importance of meta-epistemology for the resurgence of philosophical theology. A development in logic was necessary. Furthermore, Prior’s importance questions the assumption that philosophical theology was a consequence of theistic philosophers seeking ways to defend theistic beliefs in analytic philosophy. This is not true for Prior. His invention of tense-logic and discussion of omniscience was driven by an existential interest in finding answers to philosophical problems concerning divine foreknowledge and human freedom which ultimately led him to reject his Christian beliefs. (shrink)

This is a revised and expanded edition of a seminal work in the logic and philosophy of time, originally published in 1968. Arthur N. Prior was the founding father of temporal logic, and his book offers an excellent introduction to the fundamental questions in the field. Several important papers have been added to the original selection, as well as a comprehensive bibliography of Prior's work and an illuminating interview with his widow, Mary Prior. In addition, the Polish logic which (...) made Prior's writings difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book. (shrink)

Arthur Norman Prior's early theological writings have been relatively neglected for many years. Moreover, to the extent that they have been discussed at all they have been treated mainly as youthful work quite separate from Prior's later work as a philosopher and logician. However, as interest in Prior's achievements has been growing significantly in recent years it has become more important to investigate the development with his overall work. In fact, Prior's putatively "youthful" theological work overlapped his work (...) as a philosopher and logician for many years, as is richly documented by examples discussed in this paper. A particularly important theme is the problem of predestination. This paper presents comprehensive evidence that this theme, which was Prior's most important single preoccupation as a theological writer, was a most important source of inspiration for his development of tense logic. Via questions regarding divine foreknowledge and human free will, predestination was to motivate Prior as a logician to focus on time and tense. Whilst investigating this development, the paper also traces Prior's parallel development from Calvinist Christian believer to a more agnostic position. (shrink)

Arthur Norman Prior (1914-69) was a logician and philosopher from New Zealand who contributed crucially to the development of ‘non-standard’ logics, especially of the modal variety. His greatest achievement was the invention of modern temporal logic, worked out in close connection with modal logic. However, his work in logic had a much broader scope. He was also the founder of hybrid logic, and he made important contributions to deontic logic, modal logic, the theory of quantification, the nature of (...) propositions and the history of logic. In addition, he discussed questions of ethics, free will, and general theology. Prior’s philosophical works comprise about 200 titles. His earliest articles center on philosophical theology and historical studies of Scottish Reformed Theology. This led on to the publication of his first influential work on ethics: Logic and The Basis of Ethics (1949). With the invention of tense-logic in the early 1950s, his focus shifted to investigations into the syntax of tempo-modal logic leading to his seminal Time and Modality (1957), a volume derived from his John Locke Lectures in Oxford in 1956. Furthermore Prior, together with the Irish mathematician and logician C.A. Meredith (1904-76), made important early contributions to the semantics of possible worlds. Prior’s tense-logic provided a strong conceptual framework for problems pertaining to the philosophy of time. In Time and Modality, Prior discussed the philosophical implications of Ruth Barcan’s famous formulae for tense-logic, and in the 1960s he worked on the notion of the present. The most persistent problem running through Prior’s work is his study of the questions surrounding human freedom and divine foreknowledge, and more general philosophical problems emerging from this classical theological question. His thorough analysis of this problem, with the conceptual tools of tense-logic, received a crucial impetus from his correspondence with the young Saul Kripke, when the latter suggested the semantic tool of branching time to Prior. Prior’s development of two solutions based on branching time for the problem of future contingency, the Peircean and the Ockham solution, was most thoroughly developed in Past, Present and Future (1967), the most important work published by Prior. Characteristically for Prior’s methodological approach, the development of these two solutions were at the same time a development of two new systems of tense logic, and vice versa. One of Prior’s significant contributions to logic was his work on world propositions and instant propositions. In the course of developing these notions he also made one of the earliest formulations of hybrid logic. In Papers on Time and Tense (1968), he presented this idea in a more detailed manner in the context of his four grades of tense-logical involvement. (shrink)

Divided into two parts, the first concentrates on the logical properties of propositions, their relation to facts and sentences, and the parallel objects of commands and questions. The second part examines theories of intentionality and discusses the relationship between different theories of naming and different accounts of belief.

This book was designed primarily as a textbook; though the author hopes that it will prove to be of interests to others beside logic students. Part I of this book covers the fundamentals of the subject the propositional calculus and the theory of quantification. Part II deals with the traditional formal logic and with the developments which have taken that as their starting-point. Part III deals with modal, three-valued, and extensional systems.

This book discusses and aims to clarify the issue of describing conduct and character as ‘good’ or ‘bad’, or as ‘right’ or ‘wrong’. The book states that one of the main factors that have made this issue obscure is the illusion of some anti-naturalists that purely logical considerations can settle it. It clearly defines the limitations of the discussions: it is not concerned with the ‘other things’ people use to define conduct and character. The book attempts to consider the issue (...) from the purely logician point of view and suggests to the naturalists and anti-naturalists how their positions may be freed from logical faults. The book also introduces the ‘logic of ethics’, which is not a special kind or branch of logic, but rather an application of it. (shrink)

“Arthur Prior’s Formal logic has been familiar to students for twenty years, but the historical section that was originally meant to accompany it was never published. In this book P. T. Geach and A. J. P. Kenny have selected from those parts of the material that were not superseded by Prior’s later publications a self-contained study of the philosophical prehistory of contemporary logic. Like Prior’s early work Logic and the Basis of Ethics the material here presented is both historical (...) and critical: Prior was not concerned to decide for us the controverted questions of logical doctrine which he discusses. He may be compared to an experienced judge summing up in a complicated civil action: the case for each side is clearly and fairly presented, and although on some issues the summing-up amounts to a pretty clear direction of the jury, the jurymen themselves are left to decide the issues. The value of such an historical survey is to be measured by the ill effects of ignoring our predecessors’ labours. The course of the philosophy of logic in the decades since Prior wrote these pages has continued to illustrate the saying that those who will not learn the history of philosophy are compelled to relive it.” - Publisher. (shrink)

It is commonly presumed that the earliest recoverable writing of the New Zealand born Philosopher Arthur N. Prior is that published in the Australasian Journal of Philosophy and Psychology in 1937. Yet Prior was an extremely active writer as both an undergraduate and as a recent graduate, in a variety of publications. This paper recovers the unknown early Prior and discusses the importance of neo–orthodox Christian theology upon the life and thought of the early Arthur Prior. During (...) the 1930s Prior was primarily a theologian–philosopher and in these early writings there can be discerned important influences upon his thinking. This paper traces Prior’s writings from an early unpublished manuscript through his theological writings and the development of his neo–orthodox thinking to a point where preparatory work for his influential 1942 article ‘Can Religion be Discussed?’ occurs. It ends where Prior bibliographies begin, with a theologian–philosopher remaking himself as a philosopher theologian. Yet to understand the later Prior we need to understand his early life, thought and writing. This paper is an attempt to recover Prior’s early life and note his influences and talent in areas apart from tense logic. (shrink)

In this work Ockham proposes a theory of simple predication, which he uses in explicating the truth conditions of progressively more complicated kinds of propositions. His discussion includes what he takes to be the correct semantic treatment of quantified propositions, past tense and future tense propositions, and modal propositions, all of which are receiving much attention from contemporary philosophers. He also illustrates the use of exponential analysis to deal with propositions that prove troublesome in both semantic theory (...) and other disciplines, such as metaphysics, physics, and theology. This type of analysis plays an essential role in his substantive philosophical and theological works, and in many cases then can hardly be understood without a prior acquaintance with this section of the Summa. An introduction by Alfred J. Freddoso clarifies and summarizes Ockham's theory, discusses certain philosophical problems which it engenders, and proposes new interpretations for parts of it. The essay will be helpful both to those interested in Ockham as a historical figure and to those interested in his substantive systematic contributions to logical theory. (shrink)

One of Arthur Prior’s constructions of the relational calculus for times within tense logic plus propositional quantifiers is considered using Malcolm Rennie’s multimodal semantics and found wantin...

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death. The focus of this paper is a little different. It looks at what Prior himself thought he was accomplishing. In particular it considers Prior’s attitude to the semantic metatheory of the logics that he was interested in. The paper sets out some characteristics of the metalogical study of intensional languages in terms (...) of an indexical theory of truth conditions stated in the language of set theory. In examining Prior’s work using these characteristics, it emerges that Prior had serious reservations about this way of studying modal and tense logics. (shrink)

This is a new edition, revised and expanded, of a seminal work in the logic and philosophy of time, originally published in 1968. Arthur N. Prior was the founding father of temporal logic. His work has attracted increased attention in the decades since his death: its influence stretches beyond philosophy and logic to computer science and formal linguistics. Prior's fundamental ideas about the logic of time are presented here along with his investigations into the formal properties of time and (...) tense. Already in 1969 Prior had been planning a new edition of Papers on Time and Tense, to incorporate his more recent work. Because of his untimely death this plan was never followed through--till now. Seven important papers have been added to the original selection, as well as a comprehensive bibliography of his work and an illuminating interview with his widow, Mary Prior, about his life and work. In addition, the Polish logic which made the original book difficult for many readers has been replaced by standard logical notation. This new edition will secure the classic status of the book. (shrink)

In this paper we argue that Prior and Reichenbach are best viewed as allies, not antagonists. We do so by combining the central insights of Prior and Reichenbach in the framework of hybrid tense logic. This overcomes a well-known defect of Reichenbach’s tense schema, namely that it gives multiple representations to sentences in the future perfect and the future-in-the-past. It also makes it easy to define an iterative schema for tense that allows for multiple points of reference, (...) a possibility noted by Prior and demanded by Comrie, and we sketch how this schema can be generalized to a shift-and-restrict pattern in which special propositional symbols act as restrictors on the range of tense operators. (shrink)

The John Locke Lectures for 1955-6 delivered at the University of Oxford.

1. Lemmon’s stratification. By a “tense logic” I mean a system with the following features: it contains sentential variables which stand for sentences which in some cases are true at some times and false at others; it contains the usual truth-functions, whose truth-conditions are given the obvious modifications, e.g. Np is true when and only when p is false, Kpq is true when and only when both its conjuncts are; and it contains two additional functions which may be interpreted (...) as ‘It will be the case that p’ and ‘It has been the case that p’, the former being true when and only when the plain p will be true later on and the latter when and only when the plain p has been true at some earlier time. (shrink)

Most accounts, including leading textbooks, credit Arthur Norman Prior with the invention of temporal (tense logic). However, (i) Jerzy Łoś delivered his version of temporal logic in 1947, several years before Prior; (ii) Henrk Hiż’s review of Łoś’s system in Journal of Symbolic Logic was published as early as 1951; (iii) there is evidence to the effect that, when constructing his tense calculi, Prior was aware of Łoś’s system. Therefore, although Prior is certainly a key figure (...) in the history tense logic, as well as modal logic in general, it should be accepted both in the literature that temporal logic was invented by Jerzy Łoś. (shrink)

At the beginning of modern logic, propositions were defined as unchangeable entities placed in a certain idealistic realm. These unchangeable propositions contain in themselves so-called indexical, i.e. the place, time and other circumstances of the utterance. This concept of the proposition, which is entitled eternalism, was and is still prevalent among analytic philosophers. Often even the term ‘proposition’ is identified with an idealistic entity located outside the real world. In my paper, I would like to focus on the concept (...) of propositions of two logicians who deviated from the standard understanding of propositions, Arthur N. Prior and Pavel Tichý. They were both proponents of temporalism, i.e. the view that propositions could change their truth-value over time. The paper will discuss the reasons why they were proponents of temporalism and compare their views. It claims that in Prior’s case, his metaphysical views were the main reasons he was a proponent of temporalism. In contrast, when Tichý presented his arguments for temporalism, he focused primarily on natural language. (shrink)

“The Craft of Formal Logic” is Arthur Prior’s unpublished textbook, written in 1950–51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of ‘entities’ with modal character. Although he talks about these ‘entities’ only informally, and hesitates how to name them, using alternately the (...) phrases ‘possible states of affairs’, ‘chances’, ‘cases’ or ‘peculiar objects’, he is nevertheless very clear that they should be the fundamental concept of any theory of modality as a form of quantity. Without the assumption that modal operators quantify over such modal objects, the modal system will be incapable of distinguishing an actually true proposition from a necessarily true one. Due to the fact that Prior never made any direct reference to this theory in his subsequently published papers, it remained largely unknown. The comparison of “The Craft” with some of his papers on tense logic suggests that this early theory of modality underlies his later work on temporality. (shrink)

Tense logic is a branch of contemporary logic which includes formal devices that allow us to deal with the temporal relations between propositions. The aim of our paper is threefold: 1) to reveal how Aristotelian philosophical ideas about time, truth, possibility and necessity were reinterpreted by the founder of contemporay tense logic Arthur Prior; 2) to discuss what novel solutions to the classical problem of future contingents are available using Priorean invention; 3) to describe how the tools (...) of tense logic have transcended their original theoretical purposes. (shrink)

This monograph is designed to provide an introduction to the principal areas of tense logic. Many of the developments in this ever-growing field have been intentionally excluded to fulfill this aim. Length also dictated a choice between the alternative notations of A. N. Prior and Nicholas Rescher - two pioneers of the subject. I choose Prior's because of the syntactical parallels with the language it symbolizes and its close ties with other branches of logi cal theory, especially modal logic. (...) The first chapter presents a wider view of the material than later chapters. Several lines of development are consequently not followed through the remainder of the book, most notably metric systems. Although it is import ant to recognize that the unadorned Prior-symbolism can be enriched in vari ous ways it is an advanced subject as to how to actually carry off these enrichments. Readers desiring more information are referred to the appropri ate literature. Specialists will notice that only the first of several quantifi cational versions of tense logic is proven complete in the final chapter. Again constraints of space are partly to blame. The proof for the 'star' systems is wildly complex and at the time of this writing is not yet ready for publi cation. (shrink)

The author's motivation for constructing the calculi of this paper\nis so that time and tense can be "discussed together in the same\nlanguage" (p. 282). Two types of enriched propositional caluli for\ntense logic are considered, both containing ordinary propositional\nvariables for which any proposition may be substituted. One type\nalso contains "clock-propositional" variables, a,b,c, etc., for\nwhich only clock-propositional variables may be substituted and that\ncorrespond to instants or moments in the semantics. The other type\nalso contains "history-propositional" variables, u,v,w, etc., for\nwhich only history-propositional variables (...) may be substituted and\nthat correspond to maximally linearly ordered subsets of instants.\nThis second type is for tense logics in which time is not linear\nand where at any moment there may exist alternative future courses\nof events. Quantifiers are included in both types but only for clock-\nand history-propositional variables. However, these quantifiers are\ngiven an essentially substitutional interpretation. In addition,\nbesides each clock-propositional variable being true at exactly one\ninstant, the semantics requires that for each instant there be at\nleast one clock-propositional variable true at that instant, which\nin effect amounts to having each instant of the model "denoted" in\nthe formalism by some clock-propositional variable. Thus it is not\nsurprising that quantification over clock-propositional variables\nturns out to have a "well behaved first-order semantics" (p. 284).\n{One axiom relating history- with clock-propositions seems to need\nrevision: CKTauTbuAUabUba. Since the clock-propositional variables\nmight be true at the same instant the consequent should include an\nalternative, namely, LCab.} Besides the standard truth-functional\nand tense operators G,H,F,P, the author includes L for "it is\nalways the case that". The model-theoretic earlier-than relation\nordering instants and the semantic truth-at (an instant) relation\nare formalized by Uab and Taα (for a wff α) which\nare defined respectively as LCbPa (whenever the clock-proposition\nb is the case the clock-proposition a was the case) and LCaα\n(α is the case whenever the clock-proposition a is the case).\nBecause the future tense operators are definable in terms of U\nand T and the latter are definable in terms of L and P, the\ndual of H, the author notes that his completeness proofs can be\nrestricted to L and H as primitive and with the future tense\noperators used for other interpretations, especially Prior, A.'s\nindeterminist "it will be the case that", where time is not linear.\nThe author concludes with some rather technical observations showing\nthat "in ordinary tense logics the instants are nonstandard elements\nof the models. This provides", according to the author, "a semantic\npressure to build the instants into tense logic, so that they will\nappear as standard elements in the models" (p. 283). (shrink)

Recently scholars have discovered a diary entry of Arthur Norman Prior dated the 25 March 1942, in which Prior is reflecting on his own views and attitudes towards theology. The purpose of the present article is to consider what the diary entry can teach us about this period of transition in Prior’s life, and its effects upon his philosophical interests. This article will argue that the diary entry provides an explanation for why theology continued to be (...) significant in Prior’s work. (shrink)

ABSTRACT Analytic philosophy in the mid-twentieth century underwent a major change of direction when a prior consensus in favour of extensionalism and descriptivism made way for approaches using direct reference, the necessity of identity, and modal logic. All three were first defended, in the analytic tradition, by one woman, Ruth Barcan Marcus. But analytic philosophers now tend to credit them to Kripke, or Kripke and Carnap. I argue that seeing Barcan Marcus in her historical context – one (...) dominated by extensionalism and descriptivism – allows us to see how revolutionary she was, in her work and influence on others. I focus on her debate with Quine, who found himself retreating to softened, and more viable, versions of his anti-modal arguments as a result. I make the case that Barcan's formal logic was philosophically well-motivated, connected to her views on reference, and well-matched to her overall views on ontology. Her nominalism led her to reject posits which could not be directly observed and named, such as possibilia. She conceived of modal calculi as facilitating counterfactual discourse about actual existents. I conclude that her contributions ought to be recognized as the first of their kind. Barcan Marcus must be awarded a central place in the canon of analytic philosophy. (shrink)

Arthur N. Prior, in the Preface of Past, Present and Future, made clear his indebtedness to “the very lively tense-logicians of California for many discussions”. Strangely,with a notable exception of Copeland, there is no extensive discussion of these scholars in the literature on the history of tense logic. In this paper, I propose to study how Nino B. Cocchiarella, as one of the Californian tense-logicians, interacted with Prior in the late 1960s. By gathering clues from their (...) correspondence available at Virtual Lab for Prior Studies, I will highlight some of the differences between their views on tense-logic, which might still have far-reaching philosophical implications. I will conclude with a sketchof how to study in what ways Prior and Cocchiarella influenced some other Californian tense-logicians. (shrink)

Logical realism, by Arthur Norman Prior understood as the view that logic is not about language but about reality, is a consistent and strong tenet in all of Prior's philosophical work. Recent disc...

Like the author's first work, this text again develops two advanced logical systems: the formalization of intensional constructions initiated by Arthur Prior, and the refinement of predicate logic instituted by David Hilbert. This book is more historical than the first, but the emphasis is still on the application of the two systems to problems in analytical metaphysics. The natures of provability and possibility are studied further, as well as the natures of opacity and intensional objects.

On the 4th of December 1967, Hans Kamp sent his UCLA seminar notes on the logic of ‘now’ to Arthur N. Prior. Kamp’s two-dimensional analysis stimulated Prior to an intense burst of creativity in which he sought to integrate Kamp’s work into tense logic using a one-dimensional approach. Prior’s search led him through the work of Castañeda, and back to his own work on hybrid logic: the first made temporal reference philosophically respectable, the second made it technically feasible (...) in a modal framework. With the aid of hybrid logic, Prior built a bridge from a two-dimensional UT calculus to a one-dimensional tense logic containing the ‘now’ operator J. Drawing on material from the Prior archive, and the paper “‘Now”’ that detailed Prior’s findings, we retell this story. We focus on Prior’s completeness conjecture for the hybrid system and the role played by temporal reference. (shrink)

I will show how a metaphysical problem of Arthur Prior’s can be solved by a logical tool he developed himself, but did not put to any foundational use: metric logic. The broader context is given by the key question about the metaphysics of time: Is time tenseless, i.e., is time just a structure of instants; or is time tensed, because some facts are irreducibly tensed? I take sides with Prior and the tensed theory. Like him, I therefore I have (...) to deal with a more specific metaphysical question: How can the instants of tenseless time be reduced to tensed facts? This is the point where, on the technical level, hybrid logic and metric logic come in. For present purposes, both can be seen as species of tense logic; and both are creations of Prior. In his argument for the tensed theory of time, Prior used hybrid tense logic to reduce instants. But, as he himself pointed out, this reduction runs into deep problems, because it immediately generalizes to other categories, for example and most importantly to persons. My main aim is to show that metric logic does not run into similar difficulties: It will help the tensed theory reduce instants, but it leaves persons untouched. I will also give reasons for preferring a metric to a hybrid logic of time that are independent of the metaphysical issue of reduction, but concern temporal reasoning, natural language semantics, and the epistemic side of time-keeping. (shrink)

This topical collection is dedicated to the formal representation of arguments involving temporal reasoning and tensed truths; in particular, arguments with a clear significance to everyday life. In a broad perspective, temporal reasoning can be rigorously encoded via intensional logic, treating tenses as modalities, or via extensional logic, quantifying over domains of temporal objects (e.g., instants, intervals, etc.). Nowadays there are several formal devices (languages, systems, semantics, etc.) able to deal with time in many regards. Each of these devices is (...) characterized by peculiar features, such as a certain choice of primitive notions and, arguably, a certain kind of ontological commitment (see, e.g., the surveys of approaches offered by Prior 1967, van Benthem 1983, Gabbay, Hodkinson & Reynolds 1994 and Øhrstrøm & Hasle 1995). The truth-conditions of (the propositions expressed by) statements involving tenses can be explained either in terms of the “past-present-future” opposition (McTaggart’s A-theory) or in terms of the “earlier-later” opposition (McTaggart’s B-theory). Moreover, taking into account the difference between chronologically definite propositions and chronologically indefinite propositions (Rescher 1966), it is possible to distinguish between atemporal and temporal (or tensed) notions of truth. This topical collection will primarily focus on the latter. (shrink)

Contemporary hybrid logic is based on the idea of using formulas as terms, an idea invented and explored by Arthur Prior in the mid-1960s. But Prior’s own work on hybrid logic remains largely undiscussed. This is unfortunate, since hybridisation played a role that was both central to and problematic for his philosophical views on tense. In this paper I introduce hybrid logic from a contemporary perspective, and then examine the role it played in Prior’s work.

Arthur Prior was a truly philosophical logician. Though he believed formal logic to be worthy of study in its own right, of course, the source of Prior’s great passion for logic was his faith in its capacity for clarifying philosophical issues, untangling philosophical puzzles, and solving philosophical problems. Despite the fact that he has received far less attention than he deserves, Prior has had a profound influence on the development of philosophical and formal logic over the past forty years, (...) a fact to which the present volume bears eloquent witness. The genesis of the volume was the 1989 Arthur Prior Memorial Conference, held appropriately enough at the University of Canterbury in Christchurch, New Zealand, where Prior had his first appointment in philosophy. However, this is not a volume of proceedings. Only eight of the twenty-two essays were actually presented at the conference. The rest were solicited by the editor specially for the volume. The subtitle—Essays on the Legacy of Arthur Prior—is an appropriate one. Few of the essays devote much space to Prior’s work per se. Rather, most address issues that, if not first raised by Prior, were revisited by him and subjected to his typically keen and distinctively original analysis. The papers themselves divide pretty evenly into the technical and the less technical. In this short review I will focus on the latter. (shrink)

We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” (for$\forall $) and “sometime in the past” (for$\exists $). It is well known that Prior’s intuitionistic modal logic${\sf MIPC}$axiomatizes the monadic fragment of the intuitionistic predicate logic, and that${\sf MIPC}$is translated fully and faithfully into the monadic fragment${\sf MS4}$of the predicate${\sf S4}$via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension${\sf TS4}$of${\sf S4}$and provide a full and faithful (...) translation of${\sf MIPC}$into${\sf TS4}$. We compare this new translation of${\sf MIPC}$with the Gödel translation by showing that both${\sf TS4}$and${\sf MS4}$can be translated fully and faithfully into a tense extension of${\sf MS4}$, which we denote by${\sf MS4.t}$. This is done by utilizing the relational semantics for these logics. As a result, we arrive at the diagram of full and faithful translations shown in Figure 1 which is commutative up to logical equivalence. We prove the finite model property (fmp) for${\sf MS4.t}$using algebraic semantics, and show that the fmp for the other logics involved can be derived as a consequence of the fullness and faithfulness of the translations considered. (shrink)

Arthur Norman Prior (1914 – 1969) and Georg Henrik von Wright (1916 – 2003) both attended a conference in England sometime in the spring of 1956, after which they corresponded on Anselm’s ontological argument. Prior had at the conference presented a formal treatment of the ontological argument. Based upon notes from the Prior archive at the Bodleian Library, and correspondence with von Wright, we here presents Prior’s and von Wrights’ discussion of Anselm’s argument in light of Prior’s published, (...) as well as unpublished writings on the ontological argument. Three versions of the ontological argument from Prior’s unpublished as well as published papers is presented: a non-modal, an argument from possible existence and finally a modal version. While Prior dismissed the first on the basis of a meta-theorem for proof in argumentation, the second on the basis of a fallacious commutation of operators, he argued that a valid version of the ontological argument can be proven from the distinctive S5 thesis of Lewis modal logic. While Prior gave reasons for a rejection of those distinct S5 thesis, in favour of Lewis S4 system, he also provided a novel argument in favour of accepting the S5 thesis for necessity and possibility. Finally we relate Prior’s work to Plantinga (1974) and consider objections raised by Oppy (2012) and Gale (2007) toward the modal versions of the ontological argument. (shrink)

The revolution in semantics in the late 1960s and 1970s overturned an earlier competing paradigm, ‘translational’ semantics. I revive and defend Prior’s translational semantics for modals and tense-modals. I also show how to extend Prior’s propositional modal semantics to quantificational modal logic, and use the resulting semantics to formalize Prior’s own counterexample to the Barcan Formula.

This paper is a critical discussion of A.N. Prior’s contribution to the modern understanding of indeterminism and human freedom of choice. Prior suggested that these ideas should be conceived in terms of his tense logic. It can be demonstrated that his approach provides an attractive formalization that makes it possible to discuss indeterminism and human freedom of choice in a very precise manner and in a broader metaphysical context. It is also argued that Prior’s development of this approach was (...) closely linked to his very personal struggles with fundamental religious and metaphysical questions. In his opinion, holding the doctrine of divine foreknowledge together with the doctrine of human freewill gives rise to difficult logical and philosophical problems. It appears that Prior, rather early on, decided to support what was later known as the Peircean solution, although he also analysed what he considered to be the most important alternative solution—the Ockhamist solution. This paper offers a discussion of some of Prior’s published books and papers as well as some of the papers in his Nachlass. (shrink)

This chapter contains sections titled: Introduction A Methodology for Ontology The Need for a Criterion of Ontological Commitment The Role of a Canonical Notation The Ontology of Mathematics The Notion of Existence The Ontology of Natural Sciences Do Intensions Belong to the Furniture of the World? How to Treat Intensional Contexts without Positing Intensions Fiction, Intentional Objects and Existence Lesniewski's Ontology Acknowledgments.

This paper traces the course of Prior’s struggles with the concepts and phenomena of modality, and the reasoning that led him to his own rather peculiar modal logic Q. I find myself in almost complete agreement with Prior’s intuitions and the arguments that rest upon them. However, I argue that those intuitions do not of themselves lead to Q, but that one must also accept a certain picture of what it is for a proposition to be possible. That picture. though, (...) is not inevitable. Rather, implicit in Prior’s own account is an alternative picture that has already appeared in various guises, most prominently in the work of Adams, Fine, Deutsch, and Almog. I, too, will opt for this alternative, though I will spell it out rather differently than these philosophers. I will then show that, starting with the alternative picture, Prior’s intuitions can lead instead to a much happier and more standard quantified modal logic than Q. The last section of the paper is devoted to the formal development of the logic and its metatheory. (shrink)

Prior's project of tense logic has both a formal-logical and a philosophical side. Both aspects were important for Prior. The paper suggests viewing Prior's philosophical project as a continuation of the tradition of "logic as language", or "universalism", identified by van Heijenoort and Hintikka, respectively. The label "tense-logical universalism" is chosen in order to stress Prior's emphasis on the foundational role of natural language for the three fields of logic, semantics, and philosophy of science. The paper draws on (...) Prior's works in all three mentioned areas. In particular, we comment on Prior's universalist approach to model theory, which has recently given rise to hybrid logic, and on the interesting perspective on relativity theory offered through his writings. (shrink)

According to many actualists, propositions, singular propositions in particular, are structurally complex, that is, roughly, (i) they have, in some sense, an internal structure that corresponds rather directly to the syntactic structure of the sentences that express them, and (ii) the metaphysical components, or constituents, of that structure are the semantic values — the meanings — of the corresponding syntactic components of those sentences. Given that reference is "direct", i.e., that the meaning of a name is its denotation, an apparent (...) consequence of this view is that any proposition expressed by a sentence containing a name that denotes a contingent being S is itself contingent — notably, the proposition [S does not exist]. Assuming that an entity must exist to have a property, necessarily, [S does not exist] must exist in order to be true. It seems to follow that, necessarily, [S does not exist] is not true and, hence, that S is not contingent after all. Past approaches to the problem — notably, those of Prior and Adams — lead to highly undesirable consequences for quantified modal logic. In this paper, several solutions to this puzzle are developed that preserve actualism, the structured view of propositions, the direct theory of reference, and the intuition that [S does not exist] is indeed possible without the adverse consequences for QML of previous solutions. (shrink)

In his paper ‘The logic of temporal discourse’, Pavel Tichý pointed out that contemporary systems of logic were unable to sufficiently formalise tenses. He therefore suggested temporal specification in transparent intensional logic (TIL), a system of logic that he developed. Discussing contemporary systems of logic, Tichý also took into account the system of Arthur N. Prior, who developed the first systems of modern temporal logic, and his criticism was also addressed to Prior. Tichý only focused, however, on Prior’s early (...) systems of temporal logic. Patrick Blackburn recently raised the awareness that Prior also developed systems of hybrid logic in his latest periods. From the point of view of temporal specification, this system is particularly interesting as the system has greater expressive power than Prior’s early systems of temporal logic. It could also consequently deal with the problematic specifications of tenses that Pavel Tichý pointed out. It is not only the formal criterion that make Tichý and Prior’s approach suitable for comparison. Both logicians shared similar views on time and logic. All these convictions also influenced their systems of logic. The aim of this paper is to demonstrate that the temporal propositions that Tichý introduced as problematic could be formalised in Prior’s hybrid temporal logic. I will also compare formalisations in TIL and hybrid logic and Tichý and Prior’s views that influenced their systems of logic. (shrink)

Arthur Prior states that ‘It will be/was/is that p’ is true iff ‘p’ will be/was/is true, and that is all that needs to be said about the matter. This appears to avoid any need to invoke the existence of non-present entities and accounts for tensed truths with very little ontological cost. However, as David Lewis notes, this version of presentism gives the wrong results when applied to numerically quantified tensed propositions. I show how presentism can accommodate numerical quantification (...) by introducing a more appropriate tense operator. Further, I argue that it is implausible to think that we can have a primitive understanding of it; the correct semantics involves quantification over past and future times. I go on to show what kind of ontology can complement this semantic story, whilst remaining presentist in nature. (shrink)

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. (shrink)

In their simplest form, hybrid languages are propositional modal languages which can refer to states. They were introduced by Arthur Prior, the inventor of tense logic, and played an important role in his work: because they make reference to specific times possible, they remove the most serious obstacle to developing modal approaches to temporal representation and reasoning. However very little is known about the computational complexity of hybrid temporal logics.In this paper we analyze the complexity of the satisfiability (...) problem of a number of hybrid temporal logics: the basic hybrid language over transitive trees; nominal Until logic; and referential interval logic. We discuss the effects of including nominals, the @ operator, the somewhere modality E, and the difference operator D. Adding nominals to tense logic leads for several frame-classes to an increase in complexity of the satisfiability problem from PSPACE to EXPTIME. On transitive trees, however, the satisfiability problem for this language can be decided in PSPACE. Along the way we make a detour through hybrid propositional dynamic logic: we establish upper bounds for a number of temporal logics by generalizing results due to Passy and Tinchev [29] and De Giacomo [16]. We conclude with some remarks on the relevance of our results to description logic, and draw attention to the utility of the spypoint technique for proving upper and lower bounds. (shrink)