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At the centre of Arthur Prior’s ‘Thank goodness’ argument for the Atheory of time is a particular form of relief. Time must objectively pass, Prior argues, or else the relief felt when a painful experience has ended is not intelligible. In this paper, I offer a detailed analysis of the type of relief at issue in this argument, which I call temporal relief, and distinguish it from another form of relief, which I refer to as counterfactual relief. I also argue (...) 

Worlds, Lewis says this: Let us say that something persists iff, somehow or other, it exists at various times; this is the neutral word. Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is wholly present at more than one time; whereas it endures iff it persists by being wholly present at more than one time. Perdurance corresponds to the way a road persists through space; part of it (...) 

This paper aims to clarify the connection between the logic of temporal distinctions and the temporal features of propositions. Contra Prior, it argues that the adoption of tense operators does not commit one to the view that propositions can change their truth value over time. 

Todd (2016) proposes an analysis of futuredirected sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further (...) 

The future is different from the past. What is past is fixed and set in stone. The future, on the other hand, is open insofar as it holds numerous possibilities. Branchingtree models of time account for this asymmetry by positing an ontological difference between the past and the future. Given a time t, a unique unified past lies behind t, whereas multiple alternative existing futures lie ahead of t. My goal in this paper is to show that there is an (...) 

Branching spacetime is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to EinsteinPodolskyRosen distant correlations. 

The logic of 'elsewhere,' i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions, as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which (...) 

There is a longstanding disagreement among BranchingTime theorists. Even though they all believe that the branching representation accurately grasps the idea that the future, contrary to the past, is open, they argue whether this representation is compatible with the claim that one among many possible futures is distinguished—the single future that will come to be. This disagreement is paralleled in an argument about the bivalence of future contingents. The single, privileged future is often called the Thin Red Line. I reconstruct (...) 

Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted secondorder quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to wellknown results on the relative expressivity of quantified modal logics with socalled inner and outer (...) 

The Epistemic Objection says that certain theories of time imply that it is impossible to know which time is absolutely present. Standard presentations of the Epistemic Objection are elliptical—and some of the most natural premises one might fill in to complete the argument end up leading to radical skepticism. But there is a way of filling in the details which avoids this problem, using epistemic safety. The new version has two interesting upshots. First, while Ross Cameron alleges that the Epistemic (...) 

Mights plug gaps. If p lacks a truthvalue, then ‘It might be that p’ should also lack truthvalue. Yet epistemic hedges often turn an unassertible statement into an assertible one. The phenomenon is illustrated in detail for two kinds of statements that are frequently alleged to be counterexamples to the principle of bivalence: future contingents and statements that apply predicates to borderline cases. The paper concludes by exploring the prospects for generalizing this gapplugging strategy. 

Situations serving as partial worlds as well as events in natural language semantics are constructed from a typetheoretic interpretation of firstorder formulae and (after a type reduction) temporal formulae. Limitations of the RussellWienerKamp derivation of time from events are discussed and overcome to give a more widely applicable account of temporal granularity. Finite situations are formulated as strings of observations, conceptualized to persist inertially (in the absence of forces). 

In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...) 

This article traces the development of possible worlds semantics through the work of: Wittgenstein, 19131921; Feys, 1924; McKinsey, 1945; Carnap, 19451947; McKinsey, Tarski and Jónsson, 19471952; von Wright, 1951; Becker, 1952; Prior, 19531954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 19551957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 19581959; Drake, 19591961; Kripke, 19581965. 

RESUMO: A presente investigação questiona a essência teológica dos futuros contingentes. Para o efeito, analisase, primeiramente, a argumentação segundo a qual, sob certas condições lógicas, teológicas, ontológicas e cosmológicas antinecessitantes, detetadas por G. W. Leibniz, a abertura contingente do futuro parece ser compatível com o regime das "verdades contingentes prédeterminadas", regime enquadrado teologicamente pelo princípio do "futuro melhor" ou do "único futuro verdadeiro". No entanto, os futuros contingentes incitam, com e contra Aristóteles, ao desenvolvimento de uma lógica temporal e plurivalente, (...) 

In this paper we develop a novel propositional semantics based on the framework of branching time. The basic idea is to replace the momenthistory pairs employed as parameters of truth in the standard Ockhamist semantics by pairs consisting of a moment and a consistent, downward closed set of socalled transitions. Whereas histories represent complete possible courses of events, sets of transitions can represent incomplete parts thereof as well. Each transition captures one of the alternative immediate future possibilities open at a (...) 

This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are threevalued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con sequence in PWK – that is, we individuate necessary and sufficient conditions for a set. 

The struggle to delineate the relationship between theology and logic flourished in the thirteenth century and culminated in two condemnations in early 1277, one in Paris and the other in Oxford. To see how much and what kind of effect ecclesiastical actions such as condemnations and prohibitions to teach had on the development of logic in the Middle Ages, we investigate the events leading up to the 1277 actions, the condemned propositions, and the parts of these condemnations connected to modal (...) 



This paper follows Part I of our essay on caseintensional firstorder logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BHCIFOL adds structure to the cases, which in Part I formed just a set: a case in BHCIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment (...) 

In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language to the strong Priorean language . We show that hybrid logic offers a genuinely firstorder perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the (...) 

Hamblin's ActionState Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic (...) 

Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in MontagueLewisEarman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are not rich enough to study (...) 

Branching theories are popular frameworks for modeling objective indeterminism in the form of a future of open possibilities. In such theories, the notion of a history plays a crucial role: it is both a basic ingredient in the axiomatic definition of the framework, and it is used as a parameter of truth in semantics for languages with a future tense. Furthermore, histories—complete possible courses of events—ground the notion of modal consistency: a set of events is modally consistent iff there is (...) 

In a recent article, ‘Tensed Time and Our Differential Experience of the Past and Future,’ William Lane Craig attempts to resuscitate A. N. Prior's ‘Thank Goodness’ argument against the Btheory by combining it with Plantinga's views about basic beliefs. In essence Craig's view is that since there is a universal experience and belief in the objectivity of tense and the reality of becoming, ‘this belief constitutes an intrinsic defeaterdefeater which overwhelms the objections brought against it.’ An intrinsic defeaterdefeater is a (...) 

Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his groundbreaking innovations in the 1950s and 1960s. Because of the important rôle played by Prior's research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, temporal logic, or hybrid logic should be (...) 





In this paper the class of minimal models C ZI for Kiczuk's system of physical change ZI is provided and soundness and completeness proofs of ZI with respect to these models are given. ZI logic consists of propositional logic von Wright's And Then and six specific axioms characterizing the meaning of unary propositional operator "Zm", read "there is a change in the fact that". ZI is intended to be a logic which provides a formal account for describing two kinds of (...) 

The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only 'real' time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of firstorder predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the (...) 

The current trend in knowledge revision in the Dynamic Epistemic Logic tradition focuses on the addition of new knowledge, rather than the possibility of losing knowledge. Yet there are natural situations, such as an agent who does not want another agent to know that she knows a certain piece of information, where there is a need to be able to model the retraction of a proposition from a knowledge base. One situation where this is systematically required is the variant of (...) 

Open future is incompatible with realism about possible worlds. Since realistically conceived (concrete or abstract) possible worlds are maximal in the sense that they contain/represent the full history of a possible spacetime, past and future included, if such a world is actual now, the future is fully settled now, which rules out openness. The kind of metaphysical indeterminacy required for open future is incompatible with the kind of maximality which is built into the concept of possible worlds. The paper discusses (...) 

I present a variant of with time, called, interpreted in standard Kripke semantics. On the syntactic level, is nothing but the extension of atemporal individual by: the future tense and past tense operators, and the operator of group agency for the grand coalition. A sound and complete axiomatisation for is given. Moreover, it is shown that supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment. 

Two new infinitary modal logics are simply obtained from a Gentzentype sequent calculus for infinitary logic by adding a nexttime operator, and a program operator, respectively. It is shown that an anytime operator and a programiteration operator can respectively be expressed using infinitary conjunction in these logics. The cutelimination and completeness theorems for these logics are proved using some theorems for embedding these logics into (classical) infinitary logic. 

In recent publications, Kit Fine devises a classification of Atheories of time and defends a nonstandard Atheory he calls fragmentalism, according to which reality as a whole is incoherent but fragments into classes of mutually coherent tensed facts. We argue that Fine's classification in not exhaustive, as it ignores another nonstandard Atheory we dub dynamic absolutism, according to which there are tensed facts that stay numerically the same and yet undergo qualitative changes as time goes by. We expound this theory (...) 

A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL$^{*}$ into CTL$_{rp}$. In particular, that yields a complete axiomatization for the translations of all valid CTL$^{*}$formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive medium for reasoning (...) 

The apparent 'flow' of time is one of its most mysterious features, and one which discomforts both scientists and philosophers. One of the most striking assaults upon it is McTaggart's argument that the idea of temporal flow is demonstratively incoherent. In this paper I first urge that the idea of temporal flow is an important part of our intuitive understanding of time, underpinning several of our notions about rationality and time. Second, I try to undercut McTaggart's argument by showing that (...) 

This paper discusses the fallacies of combination and division as they are presented by Aristotle in chapter 4 of his Sophistici Elenchi. Aristotle's examples are concise, their discussion is unclear, and it is difficult to distinguish the cases of combination from those of division. I analyse the Aristotelian examples and the interpretations offered so far. I show that these interpretations suffer from a major defect: they fail to identify a common characteristic whereby the Aristotelian examples can be classified as instances (...) 



A view of individuals as constituted of quantities of matter, both understood as continuants enduring over time, is elaborated in some detail. Constitution is a threeplace relation which can't be collapsed to identity because of the placeholder for a time and because individuals and quantities of matter have such a radically different character. Individuals are transient entities with limited lifetimes, whereas quantities are permanent existents undergoing change in physical and chemical properties from time to time. Coincidence, considered as a matter (...) 

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkinstyle completeness proofs even when the modal logic being hybridized is higherorder. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and firstorder hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of type $a$ that (...) 

A structure is described that can serve as a foundation for a semantics for a modal agentive construction such as sees to it that Q ([ stit: Q]). The primitives are Tree,,Instant, Agent, choice. Eleven simple postulates governing this structure are set forth and motivated. Tree and encode a picture of branching time consisting of moments gathered into maximal chains called histories. Instant imposes a timelike ordering. Agent consists of agents, and choice assigns to each agent and each moment in (...) 

A conjecture of Gabbay (1981) states that any class of flows of time having the property known as finite Hdimension admits a finite set of expressively complete onedimensional temporal connectives. Here we show that the class of 'circular' structures refutes the generalisation of this conjecture to Kripke frames. We then construct from this class, by a general method, a new class of irreflexive transitive flows of time that refutes the original conjecture. Our paper includes full descriptions of a method for (...) 

This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching spacetime’—in terms of their respective A and Btheoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a model with (...) 

We propose a nonstandard interpretation of Alternatingtime Temporal Logic with imperfect information, for which no commonly accepted semantics has been proposed yet. Rather than changing the semantic structures, we generalize the usual interpretation of formulae in single states to sets of states. We also propose a new epistemic operator for ?practical? or ?constructive? knowledge, and we show that the new logic (which we call Constructive Strategic Logic) is strictly more expressive than most existing solutions, while it retains the same model (...) 

The paper puts forward a theory of historical modalities that is framed in terms of possible continuations rather than possible worlds or histories. The proposal is tested as a semantic theory for a language with historical modalities, tenses, and indexicals. 

The situation calculus is one of the most established formalisms for reasoning about action and change. In this paper we will review the basics of Reiter’s version of the situation calculus, show how knowledge and time have been addressed in this framework, and point to some of the weaknesses of the situation calculus with respect to time. We then present a modal version of the situation calculus where these problems can be overcome with relative ease and without sacrificing the advantages (...) 

The paper attempts to give a solution to the Fitch's paradox though the strategy of the reformulation of the paradox in temporal logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism. 

The paper defends an Aristotelian notion of indeterminism, as rigorously formulated in the framework of branching spacetimes (BST) of Belnap (1992), against the modeltheoretic characterization of indeterminism that Montague (1962) introduced into the philosophy of science. It delineates BST branching against the background provided by Earman's (2008) distinction between individual vs. ensemble branching. It describes a construction of physicallymotivated BST models, in which histories are isomorphic to Minkowski spacetime. Finally it responds to criticism leveled against BST by addressing some semantical (...) 