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)

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)

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)

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)

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)

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)

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)

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)

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.

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)

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)

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)

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)

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)

Dâwûd al-Qarisî (Dâvûd al-Karsî) was a versatile and prolific 18th century Ottoman scholar who studied in İstanbul and Egypt and then taught for long years in various centers of learning like Egypt, Cyprus, Karaman, and İstanbul. He held high esteem for Mehmed Efendi of Birgi (Imâm Birgivî/Birgili, d.1573), out of respect for whom, towards the end of his life, Karsî, like Birgivî, occupied himself with teaching in the town of Birgi, where he died in 1756 and was buried next to (...) Birgivî. Better known for his following works on Arabic language and rhetoric and on the prophetic traditions (hadith): Sharḥu uṣûli’l-ḥadîth li’l-Birgivî; Sharḥu’l-Ḳaṣîdati’n-nûniyya (two commentaries, in Arabic and Turkish); Şarḥu’l-Emsileti’l-mukhtalifa fi’ṣ-ṣarf (two commentaries, in Arabic and Turkish); Sharḥu’l-Binâʾ; Sharḥu’l-ʿAvâmil; and Sharḥu İzhâri’l-asrâr, Karsî has actually composed textbooks in quite different fields. Hence the hundreds of manuscript copies of his works in world libraries. Many of his works were also recurrently printed in the Ottoman period. One of the neglected aspects of Karsî is his identity as a logician. Although he authored ambitious and potent works in the field of logic, this aspect of him has not been subject to modern studies. Even his bibliography has not been established so far (with scattered manuscript copies of his works and incomplete catalogue entries). This article primarily and in a long research based on manuscript copies and bibliographic sources, identifies twelve works on logic that Karsî has authored. We have clarified the works that are frequently mistaken for each other, and, especially, have definitively established his authorship of a voluminous commentary on al-Kâtibî’s al-Shamsiyya, of which commentary a second manuscript copy has been identified and described together with the other copy. Next is handled his most famous work of logic, the Sharhu Îsâghûcî, which constitutes an important and assertive ring in the tradition of commentaries on Îsâghûcî. We describe in detail the nine manuscript copies of this work that have been identified in various libraries. The critical text of Karsî’s Sharhu Îsâghûcî, whose composition was finished on 5 March 1745, has been prepared based on the following four manuscripts: (1) MS Kayseri Raşid Efendi Kütüphanesi, No. 857, ff.1v-3v, dated 1746, that is, only one year after the composition of the work; (2) MS Bursa İnebey Yazma Eser Kütüphanesi, Genel, No.794B, ff.96v-114v, dated 1755; (3) MS Millet Kütüphanesi, Ali Emiri Efendi Arapça, No. 1752, ff.48v-58r, dated 1760; (4) MS Beyazıt Yazma Eser Kütüphanesi, Beyazıt, No. 3129, ff.41v-55v, dated 8 March 1772. While preparing the critical text, we have applied the Center for Islamic Studies (İslam Araştırmaları Merkezi, İSAM)’s method of optional text choice. The critical text is preceded by a content analysis. Karsî is well aware of the preceding tradition of commentary on Îsâghûcî, and has composed his own commentary as a ‘simile’ or alternative to the commentary by Mollâ Fanârî which was famous and current in his own day. Karsî’s statement “the commentary in one day and one night” is a reference to Mollâ Fanârî who had stated that he started writing his commentary in the morning and finished it by the evening. Karsî, who spent long years in the Egyptian scholarly and cultural basin, adopted the religious-sciences-centered ‘instrumentalist’ understanding of logic that was dominant in the Egypt-Maghrib region. Therefore, no matter how famous they were, he criticized those theoretical, long, and detailed works of logic which mingled with philosophy; and defended and favored authoring functional and cogent logic texts that were beneficial, in terms of religious sciences, to the seekers of knowledge and the scholars. Therefore, in a manner not frequently encountered in other texts of its kind, he refers to the writings and views of Muhammad b. Yûsuf al-Sanûsî (d.1490), the great representative of this logical school in the Egyptian-Maghrib region. Where there is divergence between the views of the ‘earlier scholars’ (mutaqaddimûn) like Ibn Sînâ and his followers and the ‘later scholars’ (muta’akhkhirûn), i.e., post-Fakhr al-dîn al-Râzî logicians, Karsî is careful to distance himself from partisanship, preferring sometimes the views of the earliers, other times those of the laters. For instance, on the eight conditions proposed for the realization of contradiction, he finds truth to be with al-Fârâbî, who proposed “unity in the predicative attribution” as the single condition for the realization of contradiction. Similarly, on the subject matter of Logic, he tried to reconcile the mutaqaddimûn’s notion of ‘second intelligibles’ with the muta’akhkhirûn’s notion of ‘apprehensional and declarational knowledge,’ suggesting that not much difference exists between the two, on the grounds that both notions are limited to the aspect of ‘known things that lead to the knowledge of unknown things.’ Karsî asserts that established and commonly used metaphors have, according to the verifying scholars, signification by correspondence (dalâlat al-mutâbaqah), adding also that it should not be ignored that such metaphors may change from society to society and from time to time. Karsî also endorses the earlier scholars’ position concerning the impossibility of quiddity (mâhiyya) being composed of two co-extensive parts, and emphasizes that credit should not be given to later scholars’ position who see it possible. According to the verifying scholars (muhaqqîqûn), it is possible to make definition (hadd) by mentioning only difference (fasl), in which case it becomes an imperfect definition (hadd nâqis). He is of the opinion that the definition of the proposition (qadiyya) in al-Taftâzânî’s Tahdhîb is clearer and more complete: “a proposition is an expression that bears the possibility of being true or false”. He states that in the division of proposition according to quantity what is taken into consideration is the subject (mawdû‘) in categorical propositions, and the temporal aspect of the antecedent (muqaddam) in hypothetical propositions. As for the unquantified, indefinite proposition (qadiyya muhmalah), Karsî assumes that if it is not about the problems of the sciences, then it is virtually/potentially a particular proposition (qadiyya juz’iyyah); but if it is about the problems of the sciences, then it is virtually/potentially a universal proposition (qadiyya kulliyyah). This being the general rule about the ambiguous (muhmal) propositions, he nevertheless contends that, because its subject (mawdû‘) is negated, it is preferable to consider a negative ambiguous (sâliba muhmalah) proposition like “human (insân) is not standing” to be a virtually/potentially universal negative (sâliba kulliyyâh) proposition. He states that a disjunctive hypothetical proposition (shartiyya al-munfasila) that is composed of more than two parts/units is only seemingly so, and that in reality it cannot be composed of more than two units. Syllogism (qiyâs), according to Karsî, is the ultimate purpose (al-maqsad al-aqsâ) and the most valuable subject-matter of the science of Logic. For him, the entire range of topics that are handled before this one are only prolegomena to it. This approach of Karsî clearly reveals how much the ‘demonstration (burhân)-centered’ approach of the founding figures of the Muslim tradition of logic like al-Fârâbî and Ibn Sînâ has changed. al-Abharî, in his Îsâghûjî makes no mention of ‘conversion by contradiction’ (‘aks al-naqîd). Therefore, Karsî, too, in his commentary, does not touch upon the issue. However, in his Îsâghûjî al-jadîd Karsî does handle the conversion by contradiction and its rules. Following the method of Îsâghûjî, in his commentary Karsî shortly touches on the four figures (shakl) of conjuctive syllogism (qiyâs iqtirânî) and their conditions, after which he passes to the first figure (shakl), which is considered ‘the balance of the sciences’ (mi‘yâr al-‘ulûm), explaining the four moods (darb) of it. In his Îsâghûjî al-jadîd, however, Karsî handles all the four figures (shakl) with all their related moods (darb), where he speaks of fife moods (darb) of the fourth figure (shakl). The topic of ‘modal propositions’ (al-muwajjahât) and of ‘modal syllogism’ (al-mukhtalitât), both of which do not take place in the Îsâghûjî, are not mentioned by Karsî as well, either in his commentary on Îsâghûjî or in his Îsâghûjî al-jadîd. Karsî proposes that the certainties (yaqîniyyât), of which demonstration (burhân) is made, have seven, not six, divisions. After mentioning (1) axioms/first principles (awwaliyyât), (2) observata/sensuals (mushâhadât), (3) experta/empiricals (mujarrabât), (4) acumenalia (hadthiyyât), (5) testata (mutawâtirât), and (6) instictives (fitriyyât), that is, all the ‘propositions accompanied by their demonstrations,’ Karsî states that these six divisions, which do not need research and reflection (nazar), are called badîhiyyât (self-evidents), and constitute the foundations (usûl) of certainties (yaqîniyyât). As the seventh division he mentions (7) the nazariyyât (theoreticals), which are known via the badîhiyyât, end up in them, and therefore convey certainty (yaqîn). For Karsî, the nazariyyât/theoreticals, which constitute the seventh division of yaqîniyyât/certainties, are too numerous, and constitute the branches (far‘) of yaqîniyyât. Every time the concept of ‘Mughâlata’ (sophistry) comes forth in the traditional sections on the five arts usually appended to logic works, Karsî often gives examples from what he sees as extreme sûfî sayings, lamenting that these expressions are so widespread and held in esteem. He sometimes criticizes these expressions. However, it is observed that he does not reject tasawwuf in toto, but excludes from his criticism the mystical views and approaches of the truth-abiding (ahl al-haqq), shârî‘â-observant (mutasharri‘) leading sufis who have reached to the highest level of karâmah. (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)

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)

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)

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)

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)

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)

Much of the work in moral philosophy and the political debate on abortion has focused on when in human development personhood begins. In this article, using a variant of Derek Parfit’s view on personal identity, I instead frame the question as one of victimhood. I argue for what I call the Victim Requirement for the wrongness of killing–killing is wrong only if there is an identifiable victim. An identifiable victim is, temporally speaking, in the midst of a chain of psychological (...) connections in the sense of “Relation R.” I go on to argue for a version of psychological identity which makes consciousness a necessary condition of rational self-interest and numerical identity across time. The implications for the abortion debate, based upon the best neurological evidence, are that abortion cannot be wrong before at least 22 weeks of pregnancy and perhaps significantly later. I then respond to alternatives to my Victim Requirement and argue that they either fail on their own merits or are deeply problematic. Finally, I discuss the role of autonomy and consent in a world where fetal consciousness develops much earlier. (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.

The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or (...) “complimentary” to its model. The historical reality by itself can be seen as mathematical if one considers it in Hegel’s manner as a specific interpretation of the totality being in a permanent self-movement due to being just the totality, i.e. by means of the “speculative dialectics” of history, however realized as a theory both mathematical and empirical and thus falsifiable as by logical contradictions within itself as emprical discrepancies to facts. Not less, a Husserlian kind of “historical phenomenology” is possible along with Hegel’s historical dialectics sharing the postulate of the totality (and thus, that of transcendentalism). One would be to suggest the transcendental counterpart: an “eternal”, i.e. atemporal and aspatial history to the usual, descriptive temporal history, and equating the real course of history as with its alternative, actually happened branches of the regions of the world as with only imaginable, counterfactual histories. That universal and transcendental history is properly mathematical by itself, even in a neo-Pythagorean model. It is only represented on the temporal screen of the standard historiography as a discrete series of unique events. An analogy to the readings of the apparatus in quantum mechanics can be useful. Even more, that analogy is considered rigorously and logically as implied by the mathematical transcendental history and sharing with it the same quantity of information as an invariant to all possible alternative or counterfactual histories. One can involve the hypothetical external viewpoint to history (as if outside of history or from “God’s viewpoint to it), to which all alternative or counterfactual histories can be granted as a class of equivalence sharing the same information (i.e. the number choices, but realized in different sequence or adding redundant ones in each branch) being similar and even mathematically isomorphic to Feynman trajectories in quantum mechanics. Particularly, a fundamental law of mathematical history, the law of least choice of the real historical pathway is deducible from the same approach. Its counterpart in physics is the well-known and confirmed law of least action as far as the quantity of action corresponds equivocally to the quantity of information or that of number elementary historical choices. (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)

In discussion on consciousness and the hard problem, there is an unquestioned background assumption, namely, our experience is stored in the brain. Yet Bergson (1896) 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 (2012), 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)

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 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)

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 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.

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)

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)

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)

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)

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)

Time and space are conflated in time-warps when asleep we dream. Our wakeful cognitive ability to keep them separate indicates different ways of envisaging self-hood. Awareness that dream-time and life-time are separate is itself a propensity of human minds that has evolved by natural selection with adaptive developments in cerebral neuronal circuitry that underpin human behavioural complexity. The contrast is highlighted between how memory of our spatio-temporal experiences appears to be treated by our brain one (...) way when we are wide-awake and thus well aware of our unfolding personal life-history, and in a different way when, fast asleep, our dreaming dissolves any such awareness and our oneiric self-hood seems different from our real-life self-hood. The difference is considered from two angles. Regarding simultaneous memory-storage for an experience recalled from alternative perspectives, a theoretical possibility is proposed of a pro-system comparable to Cantor Ternary Set topology. Regarding the brain, the difference is considered in relation to the temporo-spatial theory of consciousness and the compatible concept of active inference forestalling surprisal by minimising variational free energy according to the free energy principle. (shrink)

What is the temporal structure of conscious experience? While it is popular to think that our most basic conscious experiences are temporally extended, we will be arguing against this view, on the grounds that it makes our conscious experiences depend on the future in an implausible way. We then defend an alternative view of the temporal structure of experience from a variety of different objections. Along the way, we hope to illustrate the wider philosophical ramifications of the relationship (...) between experience and time. What one thinks about the temporal structure of experience is, we believe, deeply interconnected with issues concerning whether consciousness is vague or precise, whether conscious states can be reduced to physical states, whether phenomenal properties are intrinsic properties, and whether phenomenal consciousness can “overflow” access consciousness. As we will see, even seemingly unrelated metaphysical questions, such as the debate between Humean and Non-Humean accounts of natural necessity, bear on questions about the relationship between experience and time. (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)

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)

In the philosophy of time, the neo-positivist is focussed above all else on sustaining the view called the static theory of time, as the very foundation of their scientific metaphysics. This is the deeply held metaphysical conviction of almost all ‘modern philosophical-scientific’ writers on time. In fact it is hardly too much to say that the entire official modern 20th Century philosophy of physics rests on the assumption that the static theory of space-time is the only (...) concept of time we can use in physics. The static theory of time prescribes the representational space for physics as being logically based on space-time – to the point physicists are incapable of conceiving a theory without space-time any longer, and mutter superstitiously among themselves if someone suggests such a thing. By extension, this space-time provides the representation of all reality for the modern scientific materialists, since they believe that everything ultimately reduces to physics. This agenda simultaneously requires discrediting the alternative concept of time flow and the associated traditional metaphysical concepts that it supports. This Chapter explains the concept of time flow and contrasts it with the static or block universe theory as a genuine and natural alternative for a physical ontology. (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)

The topic of exemplarity has attracted considerable interest in philosophy, legal theory, literary studies and art recently. There is broad consensus that exemplary cases mediate between singular instances and general concepts or norms. The aim of this article is to provide an additional perspective on the logic of exemplarity. First, inspired by Jacques Derrida’s discussion of exemplarity, I shall argue that there is a kind of différance between (singular) examples and (general) exemplars. What an example exemplifies, the exemplarity of (...) the example, eludes any fixed identity and follows a logic of supplement. Second, I shall present the so-called logic of exemplarity. The received paraconsistent view has it that the exemplar of X is an X and, at the same time, is not an X. Inspired by Ludwig Wittgenstein’s discussion of the standard metre, I would like to present an alternative paracomplete view whereby we can say of an exemplar of X neither that it is an X nor that it is not an X. (shrink)

This paper presents an attempt to define temporal coincidence starting from the first principles. The temporal coincidence defined here differs from Einstein’s simultaneity for it is invariant across inertial frames - not relative. The meaning and significance of temporal coincidence is derived from axioms of existence and it somehow relates to Kant’s notion of simultaneity. Consistentl y applied to the Special Theory of Relativity framework, temporal coincidence does not in any way create mathematical contradictions; however it (...) allows looking at some common relativity claims with a dose of scepticism. Time, as derived from Lorentz transformations, appears to be conventional in order to match the postulate of constancy of the speed of light. The relative simultaneity is only apparent due to that convention. There are insufficient grounds to claim that inertial systems moving relatively to each other have their own different temporal realities. Overall, the innate temporal logic we have is not erroneous and does not need to be replaced contrary to the claims of some relativity educators. (shrink)