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  1. A model of the ontology of time.Marian Călborean - manuscript
    I this paper I give minimal axioms for the ontology of time, especially A-theories and B-theories and I derive philosophically interesting lemmas. The exercise is set-theoretical, defining all notions and indicating assumptions and philosophical points of disagreement, while being easy to translate to other formal expressions . The issue of a logic for A-theories of time is treated towards the end, where I sketch ‘copresent’ operators for capturing the idea of temporal passage. The main conclusion will be that, while circularity (...)
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  2. Two-Dimensional Time.Michael Kowalik - manuscript
    Philosophical views about the logical structure of time are typically divided between proponents of A and B theories, based on McTaggart's A and B series. Drawing on Paul Ricoeur's hermeneutic phenomenology, I develop and defend McTaggart's thesis that the C series and the A series working together give a consistent description of temporal experience, provided that the two series are treated as distinct dimensions internal to time. In the proposed two-dimensional model, the C series expresses a nesting order of the (...)
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  3. The Apparent Nature of Relative Simultaneity.Andrew Wutke - manuscript
    This paper presents the proof of the apparent nature of relative simultaneity originally derived from Einstein’s Special Theory of Relativity (STR). The proof does not challenge the validity of the STR but uncovers fundamental and widespread error in understanding of practical implications of Lorentz transformations. It is demonstrated that more than a century long debates generally miss the point. This results in counterintuitive claims of coexisting multiple time realities by mere equivalence of equal clock indications and simultaneity. Such claims have (...)
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  4. L. Farinas and E. ORLOWSKA, Preface 115 P. WOLPER, The tableau method for temporal logic: an over-view 119 M. MICHEL, Computation of temporal operators 137. [REVIEW]L. Farinas del Cerro - forthcoming - Logique Et Analyse.
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  5. Meyer’s Struggle with Presentism or How We Can Understand the Debate between Presentism and Eternalism.Jerzy Gołosz - forthcoming - Logic and Logical Philosophy:1.
    The paper consists of two parts. The first critically analyses Meyer’s [2005] version of the triviality objection to presentism (according to which, presentism is either trivial or untenable), and tries to show that his argument is untenable because – contrary to what he claimed – he did not take into account the entire possible spectrum of interpretations of the presentist’s thesis. In the second, positive part of the paper, it is shown that a leading form of tensed theory of time (...)
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  6. Review of Patrick Todd, The Open Future. Why Future Contingents are All False. [REVIEW]David P. Hunt - forthcoming - Zeitschrift Für Theologie Und Philosophie.
  7. Syntactic Proofs for Yablo’s Paradoxes in Temporal Logic.Ahmad Karimi - forthcoming - Logic and Logical Philosophy:1.
    Temporal logic is of importance in theoretical computer science for its application in formal verification, to state requirements of hardware or software systems. Linear temporal logic is an appropriate logical environment to formalize Yablo’s paradox which is seemingly non-self-referential and basically has a sequential structure. We give a brief review of Yablo’s paradox and its various versions. Formalization of these paradoxes yields some theorems in Linear Temporal Logic (LTL) for which we give syntactic proofs using an appropriate axiomatization of LTL.
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  8. Temporal logic.Temporal Logic - forthcoming - Stanford Encyclopedia of Philosophy.
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  9. About time, concisely. [REVIEW]Matias Slavov - forthcoming - Metascience.
    Adrian Bardon has produced a new version of his historical introduction to the philosophy of time. Originally published in 2013, the second edition of 2024 is partly rewritten and supplemented with a more extensive discussion on our disposition to project the passage of time [...] Although the book’s title emphasizes history, most of the chapters are directed at issues in systematic philosophy of time: the realism/antirealism debate, temporal passage, temporal experience, spacetime, direction, time travel, time and free will, and the (...)
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  10. Jerzy Łoś Positional Calculus and the Origin of Temporal Logic.Marcin Tkaczyk & Tomasz Jarmużek - forthcoming - Logic and Logical Philosophy:1.
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  11. Probabilistic temporal logic with countably additive semantics.Dragan Doder & Zoran Ognjanović - 2024 - Annals of Pure and Applied Logic 175 (9):103389.
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  12. Temporal Interpretation of Monadic Intuitionistic Quantifiers.Guram Bezhanishvili & Luca Carai - 2023 - Review of Symbolic Logic 16 (1):164-187.
    We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” (for$\forall $) and “sometime in the past” (for$\exists $). It is well known that Prior’s intuitionistic modal logic${\sf MIPC}$axiomatizes the monadic fragment of the intuitionistic predicate logic, and that${\sf MIPC}$is translated fully and faithfully into the monadic fragment${\sf MS4}$of the predicate${\sf S4}$via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension${\sf TS4}$of${\sf S4}$and provide a full and faithful translation (...)
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  13. The Modal Future, by Fabrizio Cariani. [REVIEW]David Boylan - 2023 - Philosophical Review 132 (2).
  14. Discrete Duality for Nelson Algebras with Tense Operators.Aldo V. Figallo, Gustavo Pelaitay & Jonathan Sarmiento - 2023 - Studia Logica 111 (1):1-19.
    In this paper, we continue with the study of tense operators on Nelson algebras (Figallo et al. in Studia Logica 109(2):285–312, 2021, Studia Logica 110(1):241–263, 2022). We define the variety of algebras, which we call tense Nelson D-algebras, as a natural extension of tense De Morgan algebras (Figallo and Pelaitay in Logic J IGPL 22(2):255–267, 2014). In particular, we give a discrete duality for these algebras. To do this, we will extend the representation theorems for Nelson algebras given in Sendlewski (...)
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  15. Temporal logic of surjective bounded morphisms between finite linear processes.David Gabelaia, Evgeny Kuznetsov, Radu Casian Mihailescu, Konstantine Razmadze & Levan Uridia - 2023 - Journal of Applied Non-Classical Logics 34 (1):1-30.
    In this paper, we study temporal logic for finite linear structures and surjective bounded morphisms between them. We give a characterisation of such structures by modal formulas and show that every pair of linear structures with a bounded morphism between them can be uniquely characterised by a temporal formula up to an isomorphism. As the main result, we prove Kripke completeness of the logic with respect to the class of finite linear structures with bounded morphisms between them.
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  16. Postsemantic Peirceanism.Andrea Iacona & Samuele Iaquinto - 2023 - American Philosophical Quarterly 60:249-256.
    There are essentially two ways to develop the Peircean idea that future contingents are all false. One is to provide a quantificational semantics for "will," as is usually done. The other is to define a quantificational postsemantics based on a linear semantics for "will." As we will suggest, the second option, although less conventional, is more plausible than the first in some crucial respects. The postsemantic approach overcomes three major troubles that have been raised in connection with Peirceanism: the apparent (...)
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  17. The Logic of Past-Alteration.Alex Kaiserman - 2023 - In Dean W. Zimmerman & Karen Bennett (eds.), Oxford Studies in Metaphysics: Volume 13. Oxford: Oxford University Press. pp. 283-314.
    Is it possible to change the past—to make something that has happened not have happened? Past-alteration is widely believed to be ‘logically impossible’. But despite this, there have been few attempts to actually apply logical resources to the question of whether it is possible to change the past. This chapter articulates a novel tense logic and uses it to argue that past-alteration is possible—with just a single dimension of time—so long as it’s possible for time to have a certain kind (...)
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  18. Refutation-Aware Gentzen-Style Calculi for Propositional Until-Free Linear-Time Temporal Logic.Norihiro Kamide - 2023 - Studia Logica 111 (6):979-1014.
    This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson’s paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven.
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  19. Detecting bots with temporal logic.Mina Young Pedersen, Marija Slavkovik & Sonja Smets - 2023 - Synthese 202 (3):1-39.
    Social bots are computer programs that act like human users on social media platforms. Social bot detection is a rapidly growing field dominated by machine learning approaches. In this paper, we propose a complementary method to machine learning by exploring bot detection as a model checking problem. We introduce Temporal Network Logic (TNL) which we use to specify social networks where agents can post and follow each other. Using this logic, we formalize different types of social bot behavior with formulas (...)
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  20. A problem with the fixed past fixed.Jacek Wawer - 2023 - Synthese 202 (5):1-15.
    A novel fatalistic argument that combines elements of modal, temporal, and epistemic logic to prove that the fixed past is not compatible with the open future has recently been presented by Lampert (Analysis 82(3):426–434, 2022). By the construction of a countermodel, it is shown that his line of reasoning is defective. However, it is also explained how Lampert’s argument could be corrected if it were supported with an extra premise regarding the temporal status of a priori knowledge. This additional assumption—which (...)
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  21. Computational complexity of hybrid interval temporal logics.Przemysław Andrzej Wałęga - 2023 - Annals of Pure and Applied Logic 174 (1):103165.
  22. Knowledge-of-own-factivity, the definition of surprise, and a solution to the Surprise Examination paradox.Alessandro Aldini, Samuel Allen Alexander & Pierluigi Graziani - 2022 - Cifma.
    Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal characterisations of the surprise notion, (...)
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  23. Loop-Check Specification for a Sequent Calculus of Temporal Logic.Romas Alonderis, Regimantas Pliuškevičius, Aida Pliuškevičienė & Haroldas Giedra - 2022 - Studia Logica 110 (6):1507-1536.
    In our previous work we have introduced loop-type sequent calculi for propositional linear discrete tense logic and proved that these calculi are sound and complete. Decision procedures using the calculi have been constructed for the considered logic. In the present paper we restrict ourselves to the logic with the unary temporal operators “next” and “henceforth always”. Proof-theory of the sequent calculus of this logic is considered, focusing on loop specification in backward proof-search. We describe cyclic sequents and prove that any (...)
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  24. Branching time and doomsday.Giacomo Andreoletti - 2022 - Ratio 35 (2):79-90.
    Branching time is a popular theory of time that is intended to account for the openness of the future. Generally, branching-time models the openness of the future by positing a multiplicity of concrete alternative futures mirroring all the possible ways the future could unfold. A distinction is drawn in the literature among branching-time theories: those that make use of moment-based structures and those that employ history-based ones. In this paper, I introduce and discuss a particular kind of openness relative to (...)
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  25. Complete Intuitionistic Temporal Logics for Topological Dynamics.Joseph Boudou, Martín Diéguez & David Fernández-Duque - 2022 - Journal of Symbolic Logic 87 (3):995-1022.
    The language of linear temporal logic can be interpreted on the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${\sf ITL}^{\sf c}_{\Diamond \forall }$, recently shown to be decidable by Fernández-Duque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.
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  26. In Search of Modal Hypodoxes using Paradox Hypodox Duality.Peter Eldridge-Smith - 2022 - Philosophia 50 (5):2457-2476.
    The concept of hypodox is dual to the concept of paradox. Whereas a paradox is incompatibly overdetermined, a hypodox is underdetermined. Indeed, many particular paradoxes have dual hypodoxes. So, naively the dual of Russell’s Paradox is whether the set of all sets that are members of themselves is self-membered. The dual of the Liar Paradox is the Truth-teller, and a hypodoxical dual of the Heterological paradox is whether ‘autological’ is autological. I provide some analysis of the duality and I search (...)
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  27. Lvov-Warsaw School. Past and Present Logic. [REVIEW]K. Gan-Krzywoszyńska & P. Leśniewski - 2022 - History and Philosophy of Logic 44 (3):343-349.
    1. First, a short anecdote. In the mid-1980s, Professor Jerzy Pogonowski gave a series of lectures entitled The Lvov-Warsaw School at the Institute of Philosophy at the Adam Mickiewicz University i...
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  28. Measuring Inconsistency in Some Logics with Tense Operators.John Grant - 2022 - Notre Dame Journal of Formal Logic 63 (3):415-440.
    This paper starts the systematic study of inconsistency measures for propositional logics enriched with operators involving time. We use Prior’s operators for tense logic: H, G, P, and F; however, we apply different semantics to them. We define two logics. The first one, ATPL, allows formulas with the application of any of the four operators any number of times to propositional logic formulas. The semantics is given in terms of TPL structures. We then show how to measure the inconsistency of (...)
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  29. A separation theorem for discrete-time interval temporal logic.Dimitar P. Guelev & Ben Moszkowski - 2022 - Journal of Applied Non-Classical Logics 32 (1):28-54.
    Gabbay's separation theorem about linear temporal logic with past has proved to be one of the most useful theoretical results in temporal logic. In this paper, we establish an analogous statement a...
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  30. Revising System Specifications in Temporal Logic.Paulo T. Guerra & Renata Wassermann - 2022 - Journal of Logic, Language and Information 31 (4):591-618.
    Although formal system verification has been around for many years, little attention was given to the case where the specification of the system has to be changed. This may occur due to a failure in capturing the clients’ requirements or due to some change in the domain (think for example of banking systems that have to adapt to different taxes being imposed). We are interested in having methods not only to verify properties, but also to suggest how the system model (...)
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  31. Is Time a Physical Unit?Yang I. Pachankis - 2022 - Science Set Journal of Physics 1 (1):1-4.
    The article approaches the epistemological question on the concept of time from an anthropological psychology perspective. The differentiation between imminent perceptions and existence beyond imminent perception has been the earliest conceptualization of time found so far in the traces of human civilizations. The research differentiated psychological time from modern physics and astronomy as the basic hypothesis in the inquiries on the concept of time in physics and modern astronomy – is the physical unit of time an ontological existence of things (...)
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  32. Permanence vs. termination: a logical analysis.Matteo Pascucci & Claudio E. A. Pizzi - 2022 - Logique Et Analyse 257:57-78.
    The present article is devoted to a logical inquiry on the notions of permanence and termination, which play a central role in many areas of temporal reasoning. In the first part, we introduce a bimodal framework to represent these notions and provide a syntactic and semantic comparison with a monomodal framework representing the notion of future necessity. In the second part, we focus on the problem of defining synonymous logical systems over the two frameworks; as an example, we provide an (...)
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  33. Ockhamism and Philosophy of Time.Alessio Santelli (ed.) - 2022 - Springer Cham.
    This book discusses fundamental topics on contemporary Ockhamism. The collected essays show how contemporary Ockhamism can impact areas of research such as semantics, metaphysics and also the philosophy of science. In addition, the volume hosts one historian of Medieval philosophy who investigates the way in which William of Ockham “in flesh and bone” construed time and, more generally, future contingency. The essays explore the different meanings of this theory. They cover three main topics, in particular. The first examines the thesis (...)
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  34. Non-classical Comparative Logic I: Standard Categorical Logic–from SLe to IFLe.Amer Amikhteh & Seyed Ahmad Mirsanei - 2021 - Logical Studies 12 (1):1-24.
    n this paper, a non-classical axiomatic system was introduced to classify all moods of Aristotelian syllogisms, in addition to the axiom "Every a is an a" and the bilateral rules of obversion of E and O propositions. This system consists of only 2 definitions, 2 axioms, 1 rule of a premise, and moods of Barbara and Datisi. By adding first-degree propositional negation to this system, we prove that the square of opposition holds without using many of the other rules of (...)
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  35. The future ain’t what it used to be: Strengthening the case for mutable futurism.Giacomo Andreoletti & Giuseppe Spolaore - 2021 - Synthese 199 (3-4):10569-10585.
    This paper explores mutable futurism, the view according to which the future can literally change—that is, it can happen that a future time t changes from containing an event E to lacking it. Mutable futurism has received little attention so far, and the details and implications of the view are underexplored in the literature. For instance, it currently lacks a precise metaphysical model and a formal semantics. Although we do not endorse mutable futurism, our goal here is to strengthen the (...)
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  36. Level theory, part 2: Axiomatizing the bare idea of a potential hierarchy.Tim Button - 2021 - Bulletin of Symbolic Logic 27 (4):461-484.
    Potentialists think that the concept of set is importantly modal. Using tensed language as an heuristic, the following bar-bones story introduces the idea of a potential hierarchy of sets: 'Always: for any sets that existed, there is a set whose members are exactly those sets; there are no other sets.' Surprisingly, this story already guarantees well-foundedness and persistence. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories; specifically, with (...)
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  37. Assertions and future tense semantics.Ciro De Florio & Aldo Frigerio - 2021 - Synthese 199 (1-2):4729-4747.
    Non-bivalent semantics of the future tense assert that propositions regarding future contingents are neither true nor false. One of the most relevant non-bivalent semantics is supervaluationism :264–281, 1970; Thomason, in: Gabbay, Guenthner Handbook of philosophical logic, Springer, Berlin, 1984), which preserves important logical principles. Recently, non-bivalent semantics are under attack from some pragmatics arguments: these semantics would be incompatible with our practices of asserting future contingents and with the probability we ascribe to such assertions :251–271, 2014; Cariani and Santorio in (...)
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  38. Temporal Logic of Minkowski Spacetime.Robin Hirsch & Brett McLean - 2021 - In Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Springer Verlag. pp. 389-409.
    We present the proof that the temporal logic of two-dimensional Minkowski spacetime is decidable, PSPACE-complete. The proof is based on a type of two-dimensional mosaic. Then, we present the modification of the proof so as to work for slower-than-light signals. Finally, a subframe of the slower-than-light Minkowski frame is used to prove the new result that the temporal logic of real intervals with during as the accessibility relation is also PSPACE-complete.
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  39. Possibility Semantics.Wesley H. Holliday - 2021 - In Melvin Fitting (ed.), Selected Topics from Contemporary Logics. London: College Publications. pp. 363-476.
    In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness—a world makes a disjunction true only if it makes one of the disjuncts true—which classically implies totality—for each proposition, a world either (...)
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  40. Credible Futures.Andrea Iacona & Samuele Iaquinto - 2021 - Synthese 199:10953-10968.
    This paper articulates in formal terms a crucial distinction concerning future contingents, the distinction between what is true about the future and what is reasonable to believe about the future. Its key idea is that the branching structures that have been used so far to model truth can be employed to define an epistemic property, credibility, which we take to be closely related to knowledge and assertibility, and which is ultimately reducible to probability. As a result, two kinds of claims (...)
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  41. Discrete Linear Temporal Logic with Knowing-Value Operator.Kaiyang Lin - 2021 - In Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 141-148.
    In epistemic logic we are not only interested in the propositional knowledge expressed by “knowing that” operators, but also care about other types of knowledge used in natural language. In [1], Plaza proposed the “knowing value” operators and gave the complete axiomatization for the logic of knowledge with nonrigid designators. Moreover, in [2] Halpern and colleagues holds that, when analyzing a system in terms of knowledge, not only is the current state of knowledge of the agents in the system relevant, (...)
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  42. Social Bot Detection as a Temporal Logic Model Checking Problem.Mina Young Pedersen, Marija Slavkovik & Sonja Smets - 2021 - In Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 158-173.
    Software-controlled bots, also called social bots, are computer programs that act like human users on social media platforms. Recent work on detection of social bots is dominated by machine learning approaches. In this paper we explore bot detection as a model checking problem. We introduce Temporal Network Logic which we use to specify social networks where agents can post and follow each other. In this logic we formalize different types of social bot behavior. These are formulas that are satisfied in (...)
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  43. Philosophy of Time: A Contemporary Introduction.Sean Enda Power - 2021 - Routledge.
    As a growing area of research, the philosophy of time is increasingly relevant to different areas of philosophy and even other disciplines. This book describes and evaluates the most important debates in philosophy of time, under several subject areas: metaphysics, epistemology, physics, philosophy of language, philosophy of mind, cognitive science, rationality, and art. -/- Questions this book investigates include: Can we know what time really is? Is time possible, especially given modern physics? Must there be time because we cannot think (...)
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  44. Tense Logic and Ontology of Time.Avril Styrman - 2021 - Emilio M. Sanfilippo Et Al, Eds., Proceedings of FOUST 2021: 5th Workshop on Foundational Ontology, Held at JOWO 2021: Episode VII The Bolzano Summer of Knowledge, September 11–18, 2021, Bolzano, Italy, CEURWS, Vol. 2969, 2021.
    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 (...)
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  45. The Open Future: Why Future Contingents Are All False.Patrick Todd - 2021 - Oxford: Oxford University Press.
    This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.
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  46. Future Contingents and the Logic of Temporal Omniscience.Patrick Todd & Brian Rabern - 2021 - Noûs 55 (1):102-127.
    At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) it was the case that it would happen. How can it be that, looking forwards, it isn’t true that there will be a sea battle, while also being true (...)
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  47. Satisfiability, Lattices, Temporal Logic and Constraint Logic Programming on Intervals.André Vellino - 2021 - In Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Springer Verlag. pp. 521-536.
    This essay narrates some of the influences that Alasdair Urquhart has had on computer science at the intersection of automated theorem proving, temporal logic and lattice theory—topics that have no obvious relationship to one another. I illustrate this by showing how Allen’s temporal relations are represented in a system for constraint logic programming over intervals and how the combination of a linear-resolution theorem prover and an interval constraint satisfaction system are connected via a lattice-theoretical semantic model. I also speculate on (...)
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  48. The Formalities of Temporaryism without Presentness.Fabrice Correia & Sven Rosenkranz - 2020 - Notre Dame Journal of Formal Logic 61 (2):181-202.
    Temporaryism—the view that not always everything always exists—comes in two main versions: presentism and expansionism (aka the growing block theory of time). Both versions of the view are commonly formulated using the notion of being present, which we, among others, find problematic. Expansionism is also sometimes accused of requiring extraordinary conceptual tools for its formulation. In this paper, we put forward systematic characterizations of presentism and expansionism which involve neither the notion of being present nor unfamiliar conceptual tools. These characterizations (...)
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  49. On the relation between modality and tense.Fabrice Correia & Sven Rosenkranz - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):586-604.
    ABSTRACT We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical views that (...)
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  50. Temporal location of events in language and (non) persistence of the past.Fabio Del Prete - 2020 - Critical Hermeneutics 4 (II):25-68.
    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.
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