We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state formulae in the full `strategically flat' fragment of ATL* is PSPACE-complete, whereas the satisfiability problems in the flat fragments of ATL and (...) ATL$^{+}$ are $\Sigma^P_3$-complete. We note that the nesting hierarchies for fragments of ATL* collapse in terms of expressiveness above nesting depth 1, hence our results cover all such fragments with lower complexities. (shrink)

Logic has sometimes been seen as an alternative to metaphysics and to speculation. In this paper it is argued that a different story should be told when it comes to temporal logic and tense-logic in particular. A. N. Prior’s first formulation of tense logic was mainly established in order to qualify the discussion of certain metaphysical and conceptual problems. Although temporal logic has now been developed in various abstract and rather technical ways, it (...) may still serve as a great help for anyone who wants to clarify the discussion of important existential questions like the nature of time, determinism, future contingency or freedom of choice. (shrink)

In this paper we analyze how the semantics of the Alternating-time Temporal Logic ATL$^*$ deals with agents' commitments to strategies in the process of formula evaluation. In (\acro{atl}$^*$), one can express statements about the strategic ability of an agent (or a coalition of agents) to achieve a goal $\phi$ such as: ``agent $i$ can choose a strategy such that, if $i$ follows this strategy then, no matter what other agents do, $\phi$ will always be true''. However, (...) strategies in \acro{atl} are \emph{revocable} in the sense that in the evaluation of the goal $\phi$ the agent $i$ is no longer restricted by the strategy she has chosen in order to reach the state where the goal is evaluated. -/- Here we discuss some alternatives leading to amendments of that semantics. In particular, we consider variants of \acro{atl}$^*$ where strategies, on the contrary, are \emph{irrevocable}. Unlike in the standard semantics of \acro{atl}, memory plays an essential role in the semantics based on irrevocable strategies. -/- Further, we propose and discuss various syntactic and semantics mechanisms for handling commitments to strategies and release from such commitments in the semantics of ATL$^*$, leading to more expressive and semantically refined versions of that logic. (shrink)

This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible (...) paths. We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees. (shrink)

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted (...) on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

The topic is time travel of the sort depicted in H. G. Wells’ classic novel, The Time Machine—Wellsian time travel. The range of proper applicability of the concept of Wellsian time travel is investigated. The results of this investigation are applied to provide a new argument against the metaphysical possibility of time travel in absolute time. Alternatively, the argument is against the possibility of Wellsian time travel relative to a single temporal frame (...) of reference. The argument leaves open the prospect that an object nontrivially moves relative to one temporal reference frame from one time to another relative to another temporal reference frame. The argument does not turn on closed timelike curves or “causal loops” of any kind. It does however invoke the prospect of backward causation—a consequence of backward time travel in conjunction with common sense—but it invokes this possibility only in the weak sense of mere logical consistency. (shrink)

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 about branching time. (shrink)

ABSTRACT A complete axiomatic system CTLrp is introduced for a temporal logic for finitely branching ω+ -trees in a language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTLrp. 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 about branching time. (shrink)

We develop an approach to temporal logic that replaces the traditional objective, agent- and event-independent notion of time with a constructive, event-dependent notion of time. We show how to make this event-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render event-dependent time functorial and to construct memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We then develop (...) a condensed formalism that represents memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular constructive functor. (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part (...) of a larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

An examination of McTaggart’s [1908] argument for the unreality of time.

In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (...) (\nsbcdt\ for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. (shrink)

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) (...) and of the authors' temporal logic of linear discrete time with gaps follows. (shrink)

I present a new problem for the tense realist concerning the evaluation of cross-temporal claims, such as ‘John is now taller than Michael was in 1984’. Time can play two different roles in the evaluation of an utterance of a sentence: either as an element that completes the content expressed by the utterance (the completion role), or as part of the circumstances against which the content is evaluated (the evaluation role). It is this latter role that time (...) plays in the realist view of tenses. I argue that if the content of a cross-temporal sentence is taken at face value (as an ascription of a crosstemporally instantiated relation), time does not play the evaluation role. Therefore, the world of the tense realist seems to leave no room for cross-temporality. (shrink)

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg (...) Henrik von Wright are developed, and mapped to the ontology of time. (shrink)

In his 1925/26 lecture Logic: The Question of Truth Heidegger turns to an interpretation of the Critique of Pure Reason in order to elucidate his own understanding of time. The largely overlooked lecture series, I argue, is at the root of Heidegger’s exposition of the concept of time and its relationship with human existence (Dasein). Although Heidegger claims that Kant’s concept of time is confined to that of ‘world-time,’ Heidegger develops the first exposition of his (...) understanding of time as ur-temporality via critical analysis of the Critique of Pure Reason. The investigation reveals the conceptual context behind the relationship between time and Dasein, which develops out of Heidegger’s first in-depth interpretation of the Critique of Pure Reason. (shrink)

Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions (...) between time and knowledge. We discuss some complications that occur, even in the single-agent case, when interactions between time and knowledge are assumed and show how the method of incremental tableaux can be adapted to work in EXPSPACE, respectively 2EXPTIME, for these logics, thereby also matching the upper bounds obtained for them by Halpern and Vardi. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory (...) of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time could be replaced with an appropriate (...) justification logic. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed (...) into utilitarian temporal frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

The main question of metasemantics, or foundational semantics, is why an expression token has the meaning (semantic value) that it in fact has. In his reading of Ludwig Wittgenstein’s later work, Saul Kripke presented a skeptical challenge that threatened to make the foundational question unanswerable. My first contention in this paper is that the skeptical challenge indeed poses an insoluble paradox, but only for a certain kind of metasemantic theory, against which the challenge effectively works as a reductio ad absurdum (...) argument. My second contention is that as a result of rejecting the theory which entails a paradoxical outcome, we will see that the foundational question essentially involves a temporal dimension. After arguing that the skeptical challenge gives us a strong reason to adopt a historical view of meaning, I shall further argue against certain authors who claim that meanings not only have histories but futures as well, or that the meaning of a word may change retroactively in time as a consequence of counterfactual change in its future use. The major aim of the paper is thus to bring together the arguably interrelated debates about the skeptical challenge and temporal externalism in philosophy of language. (shrink)

This book reconstructs Heidegger’s philosophy of time by reading his work with and against a series of key interlocutors that he nominates as being central to his own critical history of time. In doing so, it explains what makes time of such significance for Heidegger and argues that Heidegger can contribute to contemporary debates in the philosophy of time. Time is a central concern for Heidegger, yet his thinking on the subject is fragmented, making it (...) difficult to grasp its depth, complexity, and promise. Heidegger traces out a history that focuses on the conceptualisations of time put forward by Aristotle, Plotinus, Augustine, Kant, Hegel, Bergson, and Husserl—an “alternative history of time” that challenges how time has been defined and studied within both philosophy and the sciences. This book explores what happens when we take seriously Heidegger’s claim that these seven figures are essential to any understanding of time, setting out what this can tell us about existence, possibility, and philosophy as a historical discipline. Heidegger’s Alternative History of Time will appeal to scholars and advanced students working on Heidegger, phenomenology, the philosophy of time, and the history of philosophy. (shrink)

Aristotle argues that time depends on soul to count it, but adds that motion, which makes time what it is, may be independent of soul. The claim that time depends on soul or mind implies that there is at least one measurable property of natural beings that exists because of the mind’s activity. This paper argues that for Aristotle time depends partly on soul, but more importantly on motion, which defines a continuum. This argument offers a (...) robust metaphysics of time. In contrast to modern philosophy of physics, for Aristotle the continuum of motion is prior in being to time, while time is a hybrid of the real continuum of motion and the activity of mind. (shrink)

In temporal binding, the temporal interval between one event and another, occurring some time later, is subjectively compressed. We discuss two ways in which temporal binding has been conceptualized. In studies showing temporal binding between a voluntary action and its causal consequences, such binding is typically interpreted as providing a measure of an implicit or pre-reflective “sense of agency”. However, temporal binding has also been observed in contexts not involving voluntary action, but only the (...) passive observation of a cause-effect sequence. In those contexts, it has been interpreted as a top-down effect on perception reflecting a belief in causality. These two views need not be in conflict with one another, if one thinks of them as concerning two separate mechanisms through which temporal binding can occur. In this paper, we explore an alternative possibility: that there is a unitary way of explaining temporal binding both within and outside the context of voluntary action as a top-down effect on perception reflecting a belief in causality. Any such explanation needs to account for ways in which agency, and factors connected with agency, have been shown to affect the strength of temporal binding. We show that principles of causal inference and causal selection already familiar from the literature on causal learning have the potential to explain why the strength of people’s causal beliefs can be affected by the extent to which they are themselves actively involved in bringing about events, thus in turn affecting binding. (shrink)

In this article, I seek to explore Hip Hop as an expression of marronage. I identify marronage as an existential mode of being which restitutes human temporality. Slavery and flight from slavery constituted two inextricable historical processes, therefore logics of marronage must also constitute contemporary human experience. I argue that Hip Hop offers a distinct way of affirming and expressing one’s existence through what has been called a “maroon consciousness.” In the same way that maroons created new worlds free from (...) the tyranny of slavery, Hip Hop offers the Hip Hoppa a space free from colonial logics. (shrink)

The master argument posits a metaphysical thesis: Diodorus does away with Aristotle’s dunamis understood as a power simultaneously oriented toward being and non-being and proclaims that possibilities that fail to actualize are simply nothing. My contention is that this claim is not a mere application of Diodorus’ contribution to modal logic. Rather, Diodorus creates an ontologico-temporal concept of possibility and impossibility. Diodorus envisions the future as the past that the future will become. Since what will have been can (...) never be the accomplishment of a possibility that did not obtain, and since the future is destined to become past, any futural possibility that doesn’t actualize is neither futural nor even possible. (shrink)

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 a merely formal parallel: thus it is held 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. (shrink)

The book deals with conceptualization of time in different languages and in different kinds of discourse (folklore, poetry, fiction). Special attention is paid to some culture-specific models of time as well as to linguistic means related to temporal semantics: nouns, adjectives, adverbs, prepositions, prefixes, particles, and other temporal modifiers. The concept of time is also considered in its logical, axiological and historical aspects.

Empirical work has lately confirmed what many philosophers have taken to be true: people are ‘biased toward the future’. All else being equal, we usually prefer to have positive experiences in the future, and negative experiences in the past. According to one hypothesis, the temporal metaphysics hypothesis, future-bias is explained either by our beliefs about temporal metaphysics—the temporal belief hypothesis—or alternatively by our temporal phenomenology—the temporal phenomenology hypothesis. We empirically investigate a particular version of the (...) temporal belief hypothesis according to which future-bias is explained by the belief that time robustly passes. Our results do not match the apparent predictions of this hypothesis, and so provide evidence against it. But we also find that people give more future-biased responses when asked to simulate a belief in robust passage. We take this to suggest that the phenomenology that attends simulation of that belief may be partially responsible for future-bias, and we examine the implications of these results for debates about the rationality of future-bias. (shrink)

The article reviews some analyses of temporal language in logical approaches to natural language semantics. It considers some asymmetries between past and future, manifested in language, which motivate the “standard view” of the non-reversibility of time and the persistence of the past. It concludes with a puzzle about the changing past which challenges the standard view.

It is surprisingly hard to define presentism. Traditional definitions of the view, in terms of tensed existence statements, have turned out not to to be capable of convincingly distinguishing presentism from eternalism. Picking up on a recent proposal by Tallant, I suggest that we need to locate the break between eternalism and presentism on a much more fundamental level. The problem is that presentists have tried to express their view within a framework that is inherently eternalist. I call that framework (...) the Fregean nexus, as it is defined by Frege’s atemporal understanding of predication. In particular, I show that the tense-logical understanding of tense which is treated as common ground in the debate rests on this very same Fregean nexus, and is thus inadequate for a proper definition of presentism. I contrast the Fregean nexus with what I call the original temporal nexus, which is based on an alternative, inherently temporal form of predication. Finally, I propose to define presentism in terms of the original temporal nexus, yielding original presentism. According to original presentism, temporal propositions are distinguished from atemporal ones not by aspects of their content, as they are on views based on the Fregean nexus, but by their form—in particular, by their form of predication. (shrink)

The basic principles of Cipra's metaphysics (according to his book "Metamorphoses of Metaphysics") are analyzed with respect to Cipra's request for the revision of classical logical principles (of identity, excluded middle and contradiction). In Cipra's metaphysics, the principle of identity holds for being, necessity and past only, the principle of excluded middle does not hold for coming-to-be, possibility and present, and the principle of contradiction does not hold for the actuality, reality (freedom) and future. A propositional and first-order temporal (...) model and semantics are defined for such a concept of metaphysical time. The propositional ockhamistic branching time model is extended, in a first-order model, with a non-empty set of object shapes and an equivalence relation between object shapes in time, so that, for example, different, previously equivalent object shapes can in future contradict one another. (shrink)

John Perry has argued that language, thought and experience often contain unarticulated constituents. I argue that this idea holds the key to explaining away the intuitive appeal of the A-theory of time and the endurance theory of persistence. The A-theory has seemed intuitively appealing because the nature of temporal experience makes it natural for us to use one-place predicates like past to deal with what are really two-place relations, one of whose constituents is unarticulated. The endurance view can (...) be treated in a similar way; the temporal boundaries of temporal parts of objects are unarticulated in experience and this makes it seem that the very same entity exists at different times. (shrink)

The nature of temporal experience is typically explained in one of a small number of ways, most are versions of either retentionalism or extensionalism. After describing these, I make a distinction between two kinds of temporal character that could structure temporal experience: A-ish contents are those that present events as structured in past/present/future terms, and B-ish contents are those that present events as structured in earlier-than/later-than/simultaneous-with relations. There are a few exceptions, but most of the literature ignores (...) this distinction, and silently assumes temporal experience is A-ish. I then argue that temporal character is not scale invariant, but rather that temporal experience is A-ish at larger scales, and B-ish at smaller scales. I then point out that this scale non-invariance opens the possibility of hybrid views. I clarify my own view as a hybrid view, according to which temporal experience is B-ish at small scales – and at this scale my trajectory estimation model applies – but A-ish at larger scales, and at the larger scale my TEM does not apply. I then motivate this hybrid position by first defending it against arguments that have tried to show that the TEM is untenable. Since the hybrid view has TEM as its small-scale component, it must address this objection. I then put pressure on the main alternative account, extentionalism, by showing that its proponents have not adequately dealt with the problem of temporal illusions. The result is a new theory motivated by i) explaining its virtues, ii) showing that objections to it can be met, and iii) showing that objections to its main competitors have not been met. (shrink)

This book surveys the ways in which languages of different types refer to past, present, and future events and how these referents are related to the knowledge and attitudes of discourse participants. The book is the culmination of fifteen years of research by the author. Four major language types are examined in-depth: tense-based English, tense-aspect-based Polish, aspect-based Chinese, and mood-based Kalaallisut. Each contributes to a series of logical representation languages, which together define a common logical language that is argued to (...) underlie all language types. The four types differ in whether they choose to grammaticalize discourse reference to times (tense), events (aspect), and/or attitudes (mood), and how non-grammaticalized elements are inferred. The common logical language is a dynamic update logic, building on DRT and Centering Theory, but with a novel architecture—e.g. the distinction between focal vs. peripheral attention plays a key role, parallel to focal vs. peripheral vision. (shrink)

Open theists argue that God's relationship to time, as conceived in classical theism, is erroneous. They explain that it is contradictory for an atemporal being to act in a temporal universe, including experiencing its temporal successions. Contrary to the atemporalists, redemptive history has shown that God interacts with humans in time. This relational nature of God nullifies the classical notion of God as timelessly eternal. Therefore, it lacks a philosophical and theological basis. Because God is in (...) time, He does not know all future contingencies and, therefore, changes. This study examines open theism's appropriation of the A and B theories of time to the divine-human relationship. The study argues that divine temporality does not solve the tension of divine-human relationships, especially in relation to the future. Further, historical divine temporality does not negate the fact of divine atemporality. It mainly stems from God's choice to create temporal creatures and His relationship with them. Furthermore, if it is not logically and metaphysically contradictory for an omnipresent being to act in space, then it follows that an atemporal being can act in time. Whether time is understood from the metric or psychological point of view, it does not transcend God, and therefore, the limitation it places on human creatures with respect to the future does not apply to God. Lastly, although a few philosophers reject the notion of eternity as timelessly eternal, the doctrine has a philosophical and theological basis in the Scripture. (shrink)

According to the No Alternate Possibilities argument, if time passes then the rate at which it passes could be different. Thus, time cannot pass, since if time passes, then necessarily it passes at a rate of 1 second per second. One response to this argument is to posit hypertime, and to argue that at different worlds, time passes at different rates when measured against hypertime. Since many A-theorists think we can make sense of temporal passage (...) without positing hypertime, we pursue a different response. We describe several worlds that do not contain hypertime, but do contain differential passage: worlds where time passes at different rates in different subregions within the same world. Hence we argue that even if we focus just on the set of worlds that do not contain hypertime (whether this is all, or only some of the worlds) we find that not all these worlds are such that time passes at a rate of 1 second per second. Thus the No Alternate Possibilities argument fails even when restricted to just this set of worlds. (shrink)

The Schwarzschild solution (Schwarzschild, 1915/16) to Einstein’s General Theory of Relativity (GTR) is accepted in theoretical physics as the unique solution to GTR for a central-mass system. In this paper I propose an alternative solution to GTR, and argue it is both logically consistent and empirically realistic as a theory of gravity. This solution is here called K-gravity. The introduction explains the basic concept. The central sections go through the technical detail, defining the basic solution for the geometric tensor, the (...) Christoffel symbols, Ricci tensor, Ricci scalar, Einstein tensor, stress-energy tensor and density-pressure for the system. The density is integrated, and some consistency properties are demonstrated. A notable feature is the disappearance of the event horizon singularity, i.e. there are no black holes. So far this is for a single central mass. A generalization of the solution for multiple masses is then proposed. This is required to support K-gravity as a viable general interpretation of gravity. Then the question of empirical tests is discussed. It is argued that current observational data is almost but not quite sufficient to verify or falsify K-gravity. The Pioneer spacecraft trajectory data is of particular interest, as this is capable of providing a test; but the data (which originally showed anomalies that match K-gravity) is now uncertain. A new and very practical experiment is proposed to settle the matter. This would provide a novel test of GTR, and a novel test of the cause of the Pioneer anomalies. In conclusion, K-gravity has extensive ramifications for gravitational physics and for the philosophy of GTR and space-time. (shrink)

In light of the recent emergence of predictive techniques in law enforcement to forecast crimes before they occur, this paper examines the temporal operation of power exercised by predictive policing algorithms. I argue that predictive policing exercises power through a paranoid style that constitutes a form of temporal governmentality. Temporality is especially pertinent to understanding what is ethically at stake in predictive policing as it is continuous with a historical racialized practice of organizing, managing, controlling, and stealing (...) class='Hi'>time. After first clarifying the concept of temporal governmentality, I apply this lens to Chicago Police Department’s Strategic Subject List. This predictive algorithm operates, I argue, through a paranoid logic that aims to preempt future possibilities of crime on the basis of a criminal past codified in historical crime data. (shrink)

I advocate Time-Slice Rationality, the thesis that the relationship between two time-slices of the same person is not importantly different, for purposes of rational evaluation, from the relationship between time-slices of distinct persons. The locus of rationality, so to speak, is the time-slice rather than the temporally extended agent. This claim is motivated by consideration of puzzle cases for personal identity over time and by a very moderate form of internalism about rationality. Time-Slice Rationality (...) conflicts with two proposed principles of rationality, Conditionalization and Reflection. Conditionalization is a diachronic norm saying how your current degrees of belief should fit with your old ones, while Reflection is a norm enjoining you to defer to the degrees of belief that you expect to have in the future. But they are independently problematic and should be replaced by improved, time-slice-centric principles. Conditionalization should be replaced by a synchronic norm saying what degrees of belief you ought to have given your current evidence and Reflection should be replaced by a norm which instructs you to defer to the degrees of belief of agents you take to be experts. These replacement principles do all the work that the old principles were supposed to do while avoiding their problems. In this way, Time-Slice Rationality puts the theory of rationality on firmer foundations and yields better norms than alternative, non-time-slice-centric approaches. (shrink)

In discussion on consciousness and the hard problem, there is an unquestioned background assumption, namely, our experience is stored in the brain. Yet Bergson argued that this very question, “Is experience stored in the brain?” is the critical issue in the problem of consciousness. His examination of then-current memory research led him, save for motor or procedural memory, to a “no” answer. Others, for example Sheldrake, have continued this negative assessment of the research findings. So, has this assumption actually been (...) proven since Bergson? Do we know how experience is stored? Or that it is stored? Here, a recent review and model of memory is examined to see where this assumption actually stands. Again, the assessment will be that nothing has changed. The core of the problem, it will be argued, lies in two things: Firstly, the search for how/where experience is stored is motivated—rephrasing Bergson—in the classic metaphysic, a framework on space and time whose logic cannot be coherently, logically adhered to in attempting to explain how experience is stored. Secondly, the search generally assumes an inadequate theory of perception that is implicitly based in this classic metaphysic. If framed within Bergson’s model of perception and his temporal metaphysic, conjoined with J. J. Gibson’s model, the storage-search appears misguided from the start. (shrink)

The project format has become a standard and self-evident way to organize research work in today's accelerated university context, leading to the projectification of science. This paper argues that the project format is not a mere technical organizational tool, but that it challenges and reshapes research practices and ideals. The project format is embedded in a specific temporality which is called project time. The key characteristics of project time are scrutinized by distinguishing it from process time, which (...) refers to the internal organizational logic of research. In addition, project time is examined through Barbara Adam's theorizing on the commodification, control, compression and colonization of clock time. In the last part of the paper, temporal conflicts in project-based research are examined empirically by drawing upon interview material with Finnish academics working in the social sciences. (shrink)

As the title suggests, this paper is something of a leftover – or perhaps a new branch – to my "Meaning in Time: on temporal externalism and Kripkenstein’s skeptical challenge". In that work I essayed to portray my understanding of the sceptical challenge uncovered by Saul Kripke’s reading of Wittgenstein’s later works in a nutshell as to its nature and resolution. Here, my task is to dig a little deeper into the key phrase of the earlier paper, namely (...) the claim that meanings, facts grounding meaning facts, and ascriptions of meaning have an important historical dimension to them. In particular, I explore the ideas that (i) the problem of finitude is fundamentally a logical and not a metaphysical problem and (ii) Devitt's development of Kripke's causal-historical theory of reference implies a natural explanation for how at least the meanings of some terms can have a historical dimension. (shrink)

A “conceptual spaces” approach is used to formalize Aristotle’s main intuitions about time and change, and other ideas about temporal points of view. That approach has been used in earlier studies about points of view. Properties of entities are represented by locations in multidimensional conceptual spaces; and concepts of entities are identified with subsets or regions of conceptual spaces. The dimensions of the spaces, called “determinables”, are qualities in a very general sense. A temporal element is introduced (...) by adding a time variable to state functions that map entities into conceptual spaces. That way, states may have some permanency or stability around time instances. Following Aristotle’s intuitions, changes and events will not be necessarily instant phenomena, instead they could be processual and interval dependent. Change is defined relatively to the interval during which the change is taking place. Time intervals themselves are taken to represent points of view. To have a point of view is to look at the world as it is in the selected interval. Many important concepts are relativized to intervals, for instance change, events, identity, ontology, potentiality, etc. The definition of points of view as intervals allows to compare points of view in relation to all these concepts. The conceptual space approach has an immediate semantic and structural character, but it is tempting to develop also logics to describe them. A formal language is introduced to show how this could be done. (shrink)

This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an (...) ultratask (a sequence which includes one task done for each ordinal number—thus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible. (shrink)

According to the No Alternate Possibilities argument, if time passes then the rate at which it passes could be different. Thus, time cannot pass, since if time passes, then necessarily it passes at a rate of 1 second per second. One response to this argument is to posit hypertime, and to argue that at different worlds, time passes at different rates when measured against hypertime. Since many A-theorists think we can make sense of temporal passage (...) without positing hypertime, we pursue a different response. We describe several worlds that do not contain hypertime, but do contain differential passage: worlds where time passes at different rates in different subregions within the same world. Hence we argue that even if we focus just on the set of worlds that do not contain hypertime (whether this is all, or only some of the worlds) we find that not all these worlds are such that time passes at a rate of 1 second per second. Thus the No Alternate Possibilities argument fails even when restricted to just this set of worlds. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

According to the No Alternate Possibilities argument, if time passes then the rate at which it passes could be different but time cannot pass at different rates, and hence time cannot pass. Typically, defenders of the NAP argument have focussed on defending premise, and have taken the truth of for granted: they accept the orthodox view of rate necessitarianism. In this paper we argue that the defender of the NAP argument needs to turn her attention to. We (...) describe a series of worlds that appear to contain differential passage: worlds where time passes at different rates in different subregions. If the NAP argument is to succeed, rate necessitarians must show that each of these worlds is either metaphysically impossible, or does not contain differential passage. (shrink)

I attend to the temporal schema of open/closed by examining its elaboration in Bergson's philosophy and critically parsing the possibilities for its destabilization. Though Bergson wrote in a colonial context, this context barely receives acknowledgement in his work. This obscures the uncomfortable resonances between Bergson's late work, The Two Sources of Morality and Religion, and the temporal narratives that justify French colonialism. Given Bergson's uptake by philosophers, such as Gilles Deleuze, and by contemporary feminist and political theorists (especially (...) “new materialists”), a critical re-examination is called for. The Two Sources not only introduces a new dichotomy into Bergsonian philosophy—that of open/closed—it puts an end to the movement of duration by defining its possibilities as goals already given in advance. By turning the tools of Bergsonian critique onto The Two Sources, I propose an alternative to the open/closed—that of the “half-open”—creating in this way the conditions for decolonizing duration. (shrink)