Philosophers have long struggled to understand our perceptual experience of temporal properties such as succession, persistence and change. Indeed, strikingly, a number have felt compelled to deny that we enjoy such experience. Philosophical puzzlement arises as a consequence of assuming that, if one experiences succession or temporal structure at all, then one experiences it at a moment. The two leading types of theory of temporal awareness—specious present theories and memory theories—are best understood as attempts to explain (...) how temporal awareness is possible within the constraints of this principle. I argue that the principle is false. Neither theory of temporal awareness can be made workable unless it is rejected. Our experience of temporal phenomena cannot be understood if we attempt to break experience down into instantaneous slices. In order to understand the perception of temporal properties we must look beyond the instant. (shrink)

According to presentism, everything that exists is present. According to the truthmaker principle, for every true proposition there is a truthmaker – an entity that suffices for the truth of that proposition. According to realism about the past, there are true propositions about the past. Together these claims necessitate presently existing truthmakers for truths about the past (presentist truthmakers). Cameron (2010) argues that temporal distributional properties (TDPs) can play the role of presentist truthmakers. Corkum (2014) argues that they (...) cannot. I argue against Corkum’s objections. In §2, I introduce and outline the motivation for TDPs. In §3, I show that unless TDPs are stipulated to be fundamental, as Cameron does, they can be reduced to temporal non–distributional properties, which are unable to play the role of presentist truthmakers. In §4, I argue against Corkum’s two objections to Cameron’s stipulation. Corkum’s first objection is that Cameron has no grounds on which to stipulate that TDPs are fundamental, and that the reducibility of TDPs to temporal non–distributional properties (as discussed in §3) shows that they are not. I argue that the burden of proof is not on Cameron to argue that TDPs are fundamental, but on Corkum to argue that they are not, and that to argue from the reducibility of TDPs to their non–fundamentality is to beg the question against Cameron: the reduction is only possible once their non–fundamentality is assumed. Corkum’s second objection is that if Cameron is allowed to stipulate that TDPs are fundamental in order to escape objections, then Bigelow's (1996) account is allowed to make the same move, rendering Cameron’s account redundant. I argue that the cases are asymmetric: the alternative account faces a legitimate objection whilst Cameron’s account does not. (shrink)

This paper proposes a semantic description of the linear step-like temporal multi-agent logic with the universal modality \(\mathcal{LTK}.sl_U\) based on the idea of non-reflexive non-transitive nature of time. We proved a finite model property and projective unification for this logic.

We present a technique for automatically verifying cryptographic protocols specified in the mainstream specification language CAPSL. We define a translation from CAPSL models into interpreted systems, a popular semantics for temporal-epistemic logic, and rewrite CAPSL goals as temporal-epistemic specifications. We present a compiler that implements this translation. The compiler links to the symbolic model checker MCMAS. We evaluate the technique on protocols in the Clark-Jacobs library and in the SPORE repository against custom secrecy and authentication requirements.

Some properties and relations take time to be instantiated. They are not instantiated at a time, but through a temporal interval. Cognitive properties and relations such as understanding and thinking are like this, but also many biological, chemical, and microphysical properties and relations such as absorbing, freezing, radiating, and decaying. In this paper, I make a case for taking seriously such temporally extended properties (TEPs). I argue that they are ubiquitous and that our current theories (...) of persistence would do well to make room for them in their ontology. The focus here is on fourdimensionalism and different ways it can accommodate TEPs. I explore four different ways of dealing with TEPs within a fourdimensionalist framework. These are: (a) to make the objects that bear apparent TEPs temporally more extended or “chunky”, while giving TEPs a reductive or eliminativist treatment in favor of instantaneous properties (IPs); (b) to make a series of objects the bearer of TEP predicates, while, again, holding only to IPs; (c) to endorse TEPs in their own right and take them to be temporally extended in a literal sense; and (d) to hold on to TEPs as atemporal properties and make the exemplification relation temporally extended. I discuss each of these options and highlight the types of problems that a fourdimensionalist faces in attempting to accommodate TEPs. I conclude that fourdimensionalists do not yet have a satisfactory account of TEPs in their hands. (shrink)

Most philosophers believe that we have experiences as of temporally extended phenomena like change, motion, and succession. Almost all theories of time consciousness explain these temporal experiences by subscribing to the doctrine of the specious present, the idea that the contents of our experiences embrace temporally extended intervals of time and are presented as temporally structured. Against these theories, I argue that the doctrine is false and present a theory that does not require the notion of a specious present. (...) Furthermore, I argue that the different aspects of temporal experiences arise from different mechanisms operating separately. If the theory is true, then temporal experiences do not tell us anything special about the nature of consciousness and its temporal properties per se. (shrink)

Temporal externalism posits that the meanings of words inherently incorporate properties closely tied to future usage and aims to develop models for the evolution of word meanings within normative-like frameworks. However, these models face significant challenges due to an unwavering focus on how specific words change across diverse practices. A more suitable strategy entails examining the relationship between specific practices and different words, allowing us to naturally replace shifts in agent beliefs for changes in word meanings over time, (...) which may lead to certain contradictions if they insist on asserting changes in word meanings from an external perspective. (shrink)

The Temporal Satisfaction with Life Scale measures judgements of life satisfaction using 15 items, according to three temporal dimensions: past, present, and future. However, only seven studies have looked at the psychometric properties of the Temporal Satisfaction with Life Scale, and this has been individually across vastly different countries and cultures, and with different populations, such as undergraduate students, adults, and older adults. In addition, these studies have highlighted issues regarding the replicability of the validity of (...) the scale structure and optimal number of items. In this study we use a large international and multicultural sample from the International Wellbeing Study and investigate the scale structure of the Temporal Satisfaction with Life Scale, resulting in the recommendation that a shortened 12-item version provides a better model fit compared to the original 15-item version. More in-depth correlates with aspects of wellbeing and illbeing, in relation to past, present, and future life satisfaction, are also presented than have been previously, which found positive correlations between the temporal dimensions of the Temporal Satisfaction with Life Scale and wellbeing, as well as negative correlations with illbeing measures. (shrink)

The paper develops an objection to the extensional model of time consciousness—the view that temporally extended events or processes, and their temporal properties, can be directly perceived as such. Importantly, following James, advocates of the extensional model typically insist that whole experiences of temporal relations between non-simultaneous events are distinct from mere successions of their temporal parts. This means, presumably, that there ought to be some feature(s) differentiating the former from the latter. I try to show (...) why the extensional models offers no credible ground for positing such a difference. (shrink)

European Journal of Philosophy, EarlyView.

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

Three experiments examined whether children and adults would use temporal information as a cue to the causal structure of a three-variable system, and also whether their judgements about the effects of interventions on the system would be affected by the temporal properties of the event sequence. Participants were shown a system in which two events B and C occurred either simultaneously (synchronous condition) or in a temporal sequence (sequential condition) following an initial event A. The causal (...) judgements of adults and 6-7-year-olds differed between the conditions, but this was not the case for 4-year-olds' judgements. However, unlike those of adults, 6-7-year-olds' intervention judgements were not affected by condition, and causal and intervention judgements were not reliably consistent in this age group. The findings support the claim that temporal information provides an important cue to causal structure, at least in older children. However, they raise important issues about the relationship between causal and intervention judgements. (shrink)

A lot of people believe that distinct objects can occupy precisely the same place for the entire time during which they exist. Such people have to provide an answer to the 'grounding problem' – they have to explain how such things, alike in so many ways, nonetheless manage to fall under different sortals, or have different modal properties. I argue in detail that they cannot say that there is anything in virtue of which spatio-temporally coincident things have those (...) class='Hi'>properties. However, I also argue that this may not be as bad as it looks, and that there is a way to make sense of the claim that such properties are primitive. (shrink)

The question I want to explore is whether experience supports an antireductionist ontology of time, that is, whether we should take it to support an ontology that includes a primitive, monadic property of nowness responsible for the special feel of events in the present, and a relation of passage that events instantiate in virtue of literally passing from the future, to the present, and then into the past.

Temporal justification logic is a new family of temporal logics of knowledge in which the knowledge of agents is modelled using a justification logic. In this paper, we present various temporal justification logics involving both past and future time modalities. We combine Artemov’s logic of proofs with linear temporal logic with past, and we also investigate several principles describing the interaction of justification and time. We present two kinds of semantics for our temporal justification logics, (...) one based on interpreted systems and Fitting models and the other based on Mkrtychev models, and further, we establish soundness and completeness. We show that the internalization property holds in some of the temporal justification logics. We further investigate the two well-known epistemic-temporal notions of no forgetting and no learning in the framework of justification logics. Finally, we present temporal justification logics that avoid the logical omniscience problem. (shrink)

In this essay I address the question of the reality of temporal passage through a discussion of some of the implications of Kant's reasoning concerning the necessary conditions of objective judgement. Some theorists have claimed that the attribution of non‐relational temporal properties to objects and events represents a conceptual confusion, or ‘category mistake’. By means of an examination of Kant's Second Analogy, and a comparison between that argument and Cassam's recent exploration of an argument regarding the necessity (...) of the conceptualisation of ourselves as spatially located, I draw out a consequence of Kant's argument: namely, that the representation of temporal becoming is a necessary condition of objective judgement and an a priori element in the representation of objects of experience. I finish by explaining why this would show that the attribution of temporal becoming to objects and events cannot be described as a category mistake. (shrink)

Ross Cameron proposes to reconcile presentism and truth-maker theory by invoking temporal distributional properties, instantiated by present entities, as the truth-makers for truths about the past. This chapter argues that Cameron's proposal fails because objects can change which temporal distributional properties they instantiate and this entails that the truth-values of truths about the past can change in an objectionable way.

In this essay I address the question of the reality of temporal passage through a discussion of some of the implications of Kant's reasoning concerning the necessary conditions of objective judgement. Some theorists have claimed that the attribution of non‐relational temporal properties to objects and events represents a conceptual confusion, or ‘category mistake’. By means of an examination of Kant's Second Analogy, and a comparison between that argument and Cassam's recent exploration of an argument regarding the necessity (...) of the conceptualisation of ourselves as spatially located, I draw out a consequence of Kant's argument: namely, that the representation of temporal becoming is a necessary condition of objective judgement and an a priori element in the representation of objects of experience. I finish by explaining why this would show that the attribution of temporal becoming to objects and events cannot be described as a category mistake. (shrink)

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about (...) the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in DEL. (shrink)

We seem to experience a world abounding with events that exhibit dynamic temporal structure; birds flying, children laughing, rain dripping from an eave, melodies unfolding, etc. Seeing objects in motion, hearing and communicating with sound, and feeling oneself move are such common everyday experiences that one is unlikely to question whether humans are capable of perceiving temporal properties and relations. Despite appearing pre-theoretically uncontroversial, there are longstanding and contentious debates concerning the structure of such experience, how (...) class='Hi'>temporal perception works, and even whether the perception of change, motion, and succession is possible. The overarching goal of my project is to develop a comprehensive model of temporal perception that does justice to the apparent phenomenology, explains how perception functions to represent temporally structured targets, and generates empirically-informed hypotheses for how such perception is neuro-cognitively realized. I also defend my model against the challenges of anti-realist competitors whom deny the possibility of perceiving temporal relations between non-simultaneous events. (shrink)

Summary Verbs of creation (create, make, paint) are not transparent. The object created does not exist during the event time but only thereafter. We may call this type of opacity temporal opacity. I is to be distinguished from modal opacity, which is found in verbs like owe or seek. (Dowty, 1979) offers two analyses of creation verbs. One analysis predicts that no object of the sort created exists before the time of the creation. The other analysis says that the (...) object exists throughout the act of creation. I investigate three theories: Theory I says that no object of the sort created and which is caused by the very act of creation exists before the creation. In this theory, verbs of creation must embed a property. Theory II can regard the indefinite object of a creation verb as a quantifier and gives it wide scope with respect to the verb. The theory has to make sure that the objects quantified over exist only after the event. While Theory I and II start from the assumption that the extension of all nouns depend on time, Theory III says that Individual Level predicates do not depend on time. This ontology will enable us to treat verbs of creation as first order relations. The theory will entail that a picture does not mean the same as there is a picture. The paper discusses various approaches to the problem: Krifka, Parsons, Landman, Kratzer and Zucchi. (shrink)

The expressions “now,” “today,” “tomorrow,” “yesterday,” “last month,” “a year ago,” “past,” “future,” “present,” and others like them are temporal indexicals. Temporal indexicals and dates are both quite different from names. Temporal indexicals often play an important part in philosophical arguments about time. An example is this claim of McTaggart's in his famous essay about the unreality of time. Role‐linking is the key to understanding why temporal indexicals are useful. The system of temporal indexicals and (...) system of dates correspond to two different but interconnecting ways people think about things – role‐based and descriptive. Both contrast with a third way, via detached notions. McTaggart's argument for the unreality of time has two sides. According to McTaggart, these two essential properties of time cannot be combined; people's concept of time is incoherent; there is not and could not be anything that fits the conception; time is unreal. (shrink)

This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional (...) class='Hi'>temporal languages with varying expressivity and varying degrees of transfer of logical properties. The temporalization method and the independent combination method are shown to transfer all three basic logical properties. The method of full join of logic systems generates a considerably more expressive language but fails to transfer completeness and decidability in several cases. So a weaker method of restricted join is proposed and shown to transfer all three basic logical properties. (shrink)

This article reviews some recent research on the development of temporal cognition, with reference to Weist's (1989) account of the development of temporal understanding. Weist's distinction between two levels of temporal decentering is discussed, and empirical studies that may be interpreted as measuring temporal decentering are described. We argue that if temporal decentering is defined simply in terms of the coordination of the temporal locations of three events, it may fail to fully capture the (...) properties of mature temporal understanding. Characterizing the development of mature temporal cognition may require, in addition, distinguishing between event-dependent and event-independent thought about time. Experimental evidence relevant to such a distinction is described; these findings suggest that there may be important changes between 3 and 5 years in children's ability to think about points in time independently of the events that occur at those times. (shrink)

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

In the study of nonmonotonic reasoning the main emphasis has been on static (declarative) aspects. Only recently has there been interest in the dynamic aspects of reasoning processes, particularly in artificial intelligence. We study the dynamics of reasoning processes by using a temporal logic to specify them and to reason about their properties, just as is common in theoretical computer science. This logic is composed of a base temporal epistemic logic with a preference relation on models, and (...) an associated nonmonotonic inference relation, in the style of Shoham, to account for the nonmonotonicity. We present an axiomatic proof system for the base logic and study decidability and complexity for both the base logic and the nonmonotonic inference relation based on it. Then we look at an interesting class of formulas, prove a representation result for it, and provide a link with the rule of monotonicity. (shrink)

The well-known phenomenological argument draws metaphysical conclusions about time, specifically about change through time and the resulting passage or flow of time, from our temporal experience. The argument begins with the phenomenological premise that there is a class of properties which underlies our experience of time and change through time, and its conclusion is that these properties are not merely experienced but exemplified. I argue that the phenomenological argument is best served by the adoption of a representational (...) theory of perception. I then present a representational theory of temporal experience. (shrink)

In conclusion, then, the notion of temporal necessity is certainly queer and perhaps a misnomer. It really has little to do with temporality per se and everything to do with counterfactual openness or closedness. We have seen that the future is as unalterable as the past, but that this purely logical truth is not antithetical to freedom or contingency. Moreover, we have found certain past facts are counterfactually open in that were future events or actualities to be other than (...) they will be, these past facts would have been different as a consequence. God's beliefs about the future are such past facts. Moreover, the effects of actions which God would have taken had He believed differently are also such past facts. Oddly enough, then, virtually any past fact is potentially counterfactually open, and the only necessity that remains is purely de facto. We, of course, do not in general know which events of the past depend counterfactually on present actions, and those cases we do know about seem rather trivial. Our intuitions of the necessity, unalterability, and unpreventability of the past as opposed to the future stem from the impossibility of backward causation, which is precluded by the dynamic nature of time and becoming. But the counterfactual dependence of God's beliefs on future events or actualities is not a case of backward causation: rather future-tense propositions are true in virtue of what will happen, given a view of truth as correspondence, and God simply has the essential property of knowing all and only true propositions. With regard to the future, virtually all facts are counterfactually open, and therefore future-tense propositions are not temporally necessary. Propositions thus move from being temporally contingent to being temporally necessary when all the opportunities to affect things counterfactually have slipped by. Hence, the mere fact that an event is past is no indication that it is counterfactually closed. This is especially evident in the case of God's foreknowledge. If we say that God foreknows that I shall do x and therefore I cannot refrain from doing x, lest I change God's past foreknowledge, we are being deceived by a modality which has nothing to do with my power or freedom. All that is impossible is the conjunction of God's foreknowledge that p and of ~ p; but this modality in sensu composito has no bearing on my ability to act such that ~ p would be true and God would have foreknown differently. Temporal necessity, then, turns out to be only obliquely temporal and modally weak, certainly no threat to freedom or divine foreknowledge. (shrink)

The heart of my dissertation project is the proposal of a new updating rule for responding to learning experiences consisting of continuous streams of evidence. I suggest characterizing this kind of learning experience as a continuous stream of stipulated credal derivatives, and show that Continuous Probability Kinematics is the uniquely coherent response to such a stream which satisfies a continuous analogue of Rigidity – the core property of both Bayesian and Jeffrey conditionalization. In the first chapter, I define neighborhood norms (...) of rationality with reference to Kenny Easwaran’s definition of neighborhood properties. I summarize and comment on some of the key arguments in the dispute between time-slice epistemologists, who argue that there are no fundamentally diachronic norms of rationality, and the proponents of diachronic norms. I am sympathetic to two of the key motivations often given in support of the synchronist position: mentalist internalism and the idea that metaphysical disputes about the identity of persons in bizarre puzzle cases should not play a central role in epistemologists’ assessments of the rationality of agents. However, I argue that time-slice epistemology cannot adequately address the rationality of temporally-extended processes like reasoning and learning. Neighborhood norms present a viable third way between these two positions, capturing much of the spirit of the previously-discussed synchronist motivations while still providing just enough temporal structure to meaningfully guide and evaluate temporally-extended rational processes. Continuous Probability Kinematics is an example of one such neighborhood norm. In the second chapter, I develop my updating rule CPK and establish many of its core properties. Of special note here are the deep connections to Jeffrey’s Probability Kinematics, as well as some key differences. The net result of any CPK updating process will always be representable as a Jeffrey shift on the refined partition generated by the propositions that the agent is receiving direct evidence concerning. However, one crucial difference is that CPK provides an intuitive account of how to combine the effects of learning experiences that are each about fundamentally different underlying partitions. In CPK’s formalism, an agent can receive simultaneous evidence streams about an arbitrary (finite) number of propositions, which can themselves be evidentially related in any way. At any given instant, the result of the combination is a simple sum of the effects that learning about the individual propositions would have separately. CPK is concerned with a novel kind of learning experience and involves a novel characterization of evidence. The third and final chapter of this dissertation is concerned with explaining what this characterization of evidence means and with arguing that it can be the basis for genuine learning. I begin by characterizing learning experiences in terms of the Value of Information, and prove a Value of Information theorem for CPK learning experiences under the assumption of a Martingale constraint on the agent’s prior distribution over the signals that they might receive. I examine Timothy Williamson’s arguments that evidence must be propositional and express my skepticism. I then explore two different routes to model agents who update by CPK as if they are learning some propositional content and updating the rest of their credences by Bayesian conditionalization on this content. The second of these two routes provides a very interesting lens to reexamine the evidential commitments that underwrite updating by CPK, which I analyze. (shrink)

This paper contributes to the debate about ‘tenseless languages’ by defending a tensed analysis of a superficially tenseless language. The language investigated is St’át’imcets (Lillooet Salish). I argue that although St’át’imcets lacks overt tense morphology, every finite clause in the language possesses a phonologically covert tense morpheme; this tense morpheme restricts the reference time to being non-future. Future interpretations, as well as ‘past future’ would-readings, are obtained by the combination of covert tense with an operator analogous to Abusch’s (1985) WOLL. (...) I offer St’át’imcets-internal evidence (of a kind not previously adduced) that the WOLL-like operator is modal in nature. It follows from the analysis presented here that there are only two (probably related) differences between St’át’imcets and English in the area of tense. The first is that St’át’imcets lacks tense morphemes which are pronounced. The second is that the St’át’imcets tense morpheme is semantically underspecified compared to English ones. In each of these respects, the St’át’imcets tense morpheme displays similar properties to pronouns, which may be covert and which may fail to distinguish person, number or gender. Along the way, I point out several striking and subtle similarities in the interpretive possibilities of St’át’imcets and English. I suggest that these similarities may reveal non-accidental properties of tense systems in natural language. I conclude with discussion of the implications of the analysis for cross-linguistic variation, learnability and the possible existence of tenseless languages. (shrink)

The paper argues that four-dimensionalism is incompatible with the existence of additively cumulative properties, including mass, volume, and electrical charge. These properties add up over disjoint objects: for example, the mass of a whole composed of two disjoint objects is a sum of the individual masses of the objects. The difficulty with such properties for four-dimensionalism stems from the way this theory makes persistence depend on the existence of disjoint objects at disjoint times. I consider various possible (...) responses to this difficulty and conclude that they all fail. (shrink)

Even the most Parmenidean-minded of people recognize that quotidian objects somehow undergo change. This claim, nonetheless, is as clearly intuitive as it is apparently incompatible with one of our most widely believed logical principles, namely, Leibniz's Law. This paper focuses briefly on the metaphysical issue underlying this alleged incompatibility in order to provide elements for exploring its semantical counterpart: the analysis of the logical form of sentences attributing complementary temporal properties to current objects. Four analyses are presented, and (...) the ability of each to account for the linguistic data is explained. The semantical issue is preceded by some introductory remarks on the role of temporal references in the evaluation of declarative sentences. (shrink)

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties (...) of the original temporal logic like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time. (shrink)

It is easy to have about the temporal present, the time that is now, thoughts that seem both true and impossible. E.g., ‘Now is the time that matters'. We may reflect that this is not just true but that ‘it is always like that', that is: now is always the time that matters. Yet here we seem to be generalizing the ascription to the temporal present of a property that claims uniqueness, viz., being the time that matters. The (...) present paper explores, in the case of the temporal present, the meaning and implications of this kind of impossible generalisation. (shrink)

It is easy to have about the temporal present, the time that is now, thoughts that seem both true and impossible. E.g., ‘Now is the time that matters'. We may reflect that this is not just true but that ‘it is always like that', that is: now is always the time that matters. Yet here we seem to be generalizing the ascription to the temporal present of a property that claims uniqueness, viz., being the time that matters. The (...) present paper explores, in the case of the temporal present, the meaning and implications of this kind of impossible generalisation. (shrink)

Among philosophers working on modality, there is a common assumption that there is a strong connection between temporal possibility and counterfactual possibility. For example, Sydney Shoemaker 1998, 69 70) writes: It seems to me a general feature of our thought about possibility that how we think that something could have differed from how it in fact is [is] closely related to how we think that the way something is at one time could differ from the way that same thing (...) is at a different time. In possible worlds jargon, the ways one and the same thing of a given sort can differ across worlds correspond to the ways one and the same thing of that sort can differ at different times in the same world. Could I have been a plumber or an accountant instead of a philosopher? The answer seems to be yes -- and this goes with the fact that we acknowledge the possibility of a scenario in which someone who was exactly as I was at some point in my life undergoes a series of changes resulting in his eventually being a plumber or an accountant. In a footnote, he acknowledges that this connection between counterfactual and temporal possibility needs to be qualified in response to an objection by Randy Clarke: «The property of being the child of someone who has visited Paris is not one that one can have and then lose; but it is one that one can have in the actual world and not have in some other possible world.» (1998, 75n.9) Therefore, he restricts the inference from temporal to counterfactual possibility and vice versa to «non historical properties.». (shrink)

ABSTRACT Most theorem provers for Classical Logic transform the input formula into a particular normal form. This tranformation is done before the execution of the algorithm or it is integrated into the deductive algorithm. This situation is no different for Non-Classical Logics and, particularly, for Temporal Logics. However, unlike classical logic, temporal logic does not provide an extension of the notion of non negative normal form. In this work, we define a temporal negative normal form for the (...) future fragment of the linear time propositional temporal logic, named FNext. The definition saves as much information as possible about implicants and implicates of the input formula and its subformulas. This property is the novelty of this normal form; for example, in [Fis97] the normal form is guided by the separation property and in [Ven86] the normal form provided prepares the input formula to be treated by a resolution method. Moreover, we also introduce an algorithm having linear cost, which transforms the input formula into a temporal negative normal form. Furthermore, in this work we present a new structure and a set of operators over it that allows us to efficiently manage the information about unitary implicants and implicates contained in the subformulae. (shrink)

A nonlinear two-variable reaction-diffusion model of bone mineral metabolism, built from an overall self-oscillatory compartmental model of calcium metabolism in vivo, has been studied for its ability to generate spatial and spatio-temporal self-organizations in a two-dimensional space. Analytical and numerical results confirm the theoretical properties previously described for this kind of model. In particular, it is shown that, for a given set of reactional parameter values and certain values of the ratio of the two diffusion coefficients, there exists (...) a set of unstable wavenumbers leading spontaneously to the development, from the homogeneous steady state, of either different types of stationary spatial patterns (hexagonal, striped and re-entrant hexagonal patterns) or more or less complex spatio-temporal expressions. We discuss the relevance of analogies established between some spatial or spatio-temporal structures predicted by the model and some peculiar features of the primary bone trabecular architecture which appear during embryonic ossification. (shrink)

Adopting temporal parts theory is the most popular way of addressing a host of puzzles about diachronic identity. For example, it is not obvious how I am the same person as the baby who shared my name. With the theory, sameness of person, e.g., consists in being comprised by the same temporally extended, four-dimensional object. However, temporal parts theory has unacceptable consequences for notions of freedom and probability. I show that the only acceptable reading of four-dimensionalism entails that (...) the four dimensional object that is me, say, already exists in its entirety. This entails that all of my future properties are already set. This nearly Spinozistic result robs us of familiar notions of choice and possibility. I argue that these notions are more central to our thinking than temporal parts theory, and that on these grounds we must look elsewhere for solutions to our questions about identity across time. (shrink)

Hugh Mellor has proposed what appears to be a new solution to the problem of intrinsic change (Mellor 1998). Assuming endurantism and a B‐theoretic, nonpresentist view of time, facts are supposed to have only enduring things and atemporal properties (or relations) as constituents, but no times. The having of properties and relations is not relativised to times. Instead, the whole of a fact is conceived of as temporally localised. It will be argued that this interesting and novel proposal (...) does not succeed as an account of change in the intrinsic properties of things. The basic difficulty is that the view still leads into contradiction, since it makes it incomprehensible how one and the same thing can have both a property and some incompatible property. The having of these incompatible properties is treated as two facts. But to add that these facts have certain temporal locations is of no help for avoiding the contradiction. (shrink)