A theory of embedded tense that derives SOT effects from an SOT rule is compared with a theory that derives SOT effects without appealing to an SOT rule, and an argument is provided in favor of the former. The argument relies mostly on examples where a tense is embedded under future-in-the-past. Such an argument was originally presented in and later dismissed in Proceedings of Sinn und Bedeutung 17, ENS-Paris, 45–62, 2013a). An additional argument is provided in favor of (...) supplementing the SOT rule with a ‘de re’ mechanism. (shrink)

Next SectionLanguages that are classified as non-Sequence-of-Tense come in more than one variety (e.g., Arregui & Kusumoto 1998): some of these languages allow a past tense in before-clauses while others do not. We propose that some languages have quantificational (existential) tenses, while others have pronominal (referential/bound) tenses. The past tense in before-clauses is ill-formed in a language that has quantificational tenses, because the semantics of before is incompatible with existential quantification over times. A language with pronominal (...) tenses does not have this problem. The pronominal/quantificational tense distinction interacts with the Sequence-of-Tense parameter, providing a general theory of possible and impossible languages. (shrink)

Languages that are classified as non-Sequence-of-Tense come in more than one variety : some of these languages allow a past tense in before -clauses while others do not. We propose that some languages have quantificational tenses, while others have pronominal tenses. The past tense in before -clauses is ill-formed in a language that has quantificational tenses, because the semantics of before is incompatible with existential quantification over times. A language with pronominal tenses does not have this (...) problem. The pronominal/quantificational tense distinction interacts with the Sequence-of-Tense parameter, providing a general theory of possible and impossible languages. (shrink)

In this article I defend the view that many central aspects of the semantics of tense are determined by independently-motivated principles of syntactic theory. I begin by decomposing tenses syntactically into a temporal ordering predicate (the true tense, on this approach) and two time-denoting arguments corresponding to covert a reference time (RT) argument and an eventuality time (ET) argument containing the verb phrase. Control theory accounts for the denotation of the RT argument, deriving the distinction between main clause (...) and subordinate clause tenses. The theory of covert movement is used to account for the independent/indexical interpretation of relative clause tenses, and for the correlation between independent tense interpretation and a de re construal of the relative clause. A theory of “past polarity”, based on traditional negative polarity theory, accounts both for the simultaneous “sequence of tense” construal of past tenses in subordinate clauses embedded within past tense contexts, and for the obligatory indexical/independent interpretation of present tense in a relative clause embedded within a past tense context. Combined with the copy theory of movement, the polarity theory also provides an account of the semantics of double access sentences, treating them as involving a special kind of reconstruction effect. (shrink)

On the basis of an experimental investigation of the construals of present under past in child French, we argue that French children, just like Japanese adult speakers, but unlike French adult speakers, allow pure simultaneous construals of present under past, where the present denotes an interval that lies completely in the past, be it in relative or complement clauses. We conclude that French children have two presents: an indexical present and a zero present (just like Japanese adults, cf. Ogihara 1999, (...) 2008), suggesting that French children have both the Japanese and the French setting for the Sequence of Tense parameter since they allow simultaneous construals of both present and past under past. This multiple grammar approach to tense interpretation in child French extends to child Japanese in so far as Japanese children have been argued to allow simultaneous readings of past under past, although this reading is unavailable in the target grammar (Matsuo & Hollebrandse 1999). (shrink)

American Academy of Pediatrics (AAP) and American College of Medical Genetics (ACMG) recently provided two recommendations about predictive genetic testing of children. The Clinical Sequencing Exploratory Research Consortium's Pediatrics Working Group compared these recommendations, focusing on operational and ethical issues specific to decision making for children. Content analysis of the statements addresses two issues: (1) how these recommendations characterize and analyze locus of decision making, as well as the risks and benefits of testing, and (2) whether the guidelines conflict or (...) come to different but compatible conclusions because they consider different testing scenarios. These statements differ in ethically significant ways. AAP/ACMG analyzes risks and benefits using best interests of the child and recommends that, absent ameliorative interventions available during childhood, clinicians should generally decline to order testing. Parents authorize focused tests. ACMG analyzes risks and benefits using the interests of the child and other family members and recommends that sequencing results be examined for additional variants that can lead to ameliorative interventions, regardless of age, which laboratories should report to clinicians who should contextualize the results. Parents must accept additional analysis. The ethical arguments in these statements appear to be in tension with each other. (shrink)

Viewing the language of modal logic as a language for describing directed graphs, a natural type of directed graph to study modally is one where the nodes are sets and the edge relation is the subset or superset relation. A well-known example from the literature on intuitionistic logic is the class of Medvedev frames $\langle W,R\rangle$ where $W$ is the set of nonempty subsets of some nonempty finite set $S$, and $xRy$ iff $x\supseteq y$, or more liberally, where $\langle W,R\rangle$ (...) is isomorphic as a directed graph to $\langle \wp(S)\setminus\{\emptyset\},\supseteq\rangle$. Prucnal [32] proved that the modal logic of Medvedev frames is not finitely axiomatizable. Here we continue the study of Medvedev frames with extended modal languages. Our results concern definability. We show that the class of Medvedev frames is definable by a formula in the language of tense logic, i.e., with a converse modality for quantifying over supersets in Medvedev frames, extended with any one of the following standard devices: nominals (for naming nodes), a difference modality (for quantifying over those $y$ such that $x\not= y$), or a complement modality (for quantifying over those $y$ such that $x\not\supseteq y$). It follows that either the logic of Medvedev frames in one of these tense languages is finitely axiomatizable---which would answer the open question of whether Medvedev's [31] "logic of finite problems'' is decidable---or else the minimal logics in these languages extended with our defining formulas are the beginnings of infinite sequences of frame-incomplete logics. (shrink)

The apparent very close similarity between the learning of the past tense by Adam and the Plunkett and Marchman model is exaggerated by several misleading comparisons--including arbitrary, unexplained changes in how graphs were plotted. The model's development differs from Adam's in three important ways: Children show a U-shaped sequence of development which does not depend on abrupt changes in input; U-shaped development in the simulation occurs only after an abrupt change in training regimen. Children overregularize vowel-change verbs more (...) than no-change verbs; the simulation overregularizes vowel-change verbs less often than no-change verbs. Children, including Adam, overregularize more than they irregularize; the simulation overregularized less than it irregularized. Interestingly, the RM model--widely criticized as being inadequate--does somewhat better, correctly overregularizing vowel-change verbs more often than no-change verbs, and overregularizing more often than it irregularizes. Although Plunkett and Marchman's (1993) state of the art model incorporated hidden layers and back-propagation, used a more realistic phonological coding scheme, and explored a broader range of parameters than Rumelhart and McClelland's model, their results are farther from psychological reality. It is unknown whether any connectionist model can mimic a child's performance without resorting to unrealistic exogenous changes in the training or input, but it is clear that adding a hidden-layer and back-propagation does not ensure a solution. (shrink)

: Consider mental states of the type that relate a subject to a content expressed by a sentence. I propose that some of these states necessarily include as constituents of their contents the states themselves. These reflexive states arise when one locates a content as belonging, for example, to one's own present or past. That content is then a tense% thought, ordering one's present state with respect to the content. Anaphoric cross‐reference between an event or state and a constituent (...) of its own content is responsible, I argue, for the phenomenon of sequence of tense in English. Conversely, the fact that some states are necessarily reflexive supports the view that the elaborations of logical form that account for sequence of tense are no mere artefact of semantics, but even intrinsic to some of our utterances and thoughts. (shrink)

In Section 1, we questioned the evidence for iteration of tenses, even with abstraction. To permit abstraction would in any case risk neutralizing our distinction between tensed and untensed sentences. Sequence of tense phenomena, far from supporting iteration, were incompatible with it. Instead, we argued, tense always retains its full deictic character; tenses never have scope over each other. The future modal WILL is exceptional (Section 2), but abstraction is not required to deal with this.An important suggestion, (...) first made in Section 1 and developed further in Section 3, would restrict quantification induced by the interpretation of Past to a domain determined by pragmatic factors. When Past serves as a reference time, e.g. when it forms part of would, as inSam believed that he would be in BostonJames bought a stamp that would be priceless then a previous occurrence of Past serves to define the domain relevant to the quantificational element of Past. Without semantic binding or reference, the two cases of Past in such sentences will thus be satisfied by the same interval in the past.The extension of this idea in Section 3, permits an account of the supposed incompleteness of the past tense without invoking a hidden THEN in e.g. I turned the lights off. In this case, restriction of the relevant domain does not proceed via an earlier occurrence of Past but depends solely on discourse factors.In Section 4, the analysis of have given in Part I is modified to introduce an element of ‘pastness’. The relevant sub-interval must be non-final-and perhaps need not even be a sub-interval of the evaluation interval itself. Empirically necessary, this change makes the incompatibility of Pres,have and a definite adverb like at 6 o'clock in a single sentence even harder to explain semantically. However, the vague restrictions on domain imposed by the present tense and relevant to the sub-interval required by an embedded have below it seem clearly pragmatically incompatible with the explicit restriction of that same interval to a very specific interval in the past — a restriction which, we argue, is imposed by a definite time adverb.Thus, Part II represents a consistent, though entirely informal plea for the embedding of the semantics of Part I in a framework in which pragmatic considerations can interact freely with the semantics, to restrict the domains within which quantification is permitted. It is in effect a plea for the introduction of partial models along the lines suggested by Barwise and Perry (1981). The advantages of the basic distinctions between tense, aspect and adverbs introduced in Part I would, we have suggested in the second part, be yet more obvious in such a framework. Formalization in a system of partial models must await further work. (shrink)

By force of _causes precede effects_, causality contributes to the temporal meaning of discourse. In case of semantic causal relations, this contribution is straightforward, but in case of epistemic causal relations, it is not. In order to gain insight into the semantics of epistemic causal relations, paradoxical cases are analyzed of text fragments in which temporal and causal meaning seem to be irreconcilable. A solution is proposed consisting of several parts: First, an analysis of epistemic causal coherence relations, in which (...) the effect sentence is argued to be a _belief_ sentence. Secondly, a method for deriving causal coherence relations. And thirdly, a format for representing temporal meaning in which contributions of tense and causality can be reconciled. Finally, it is argued that _understanding_ epistemically causally connected sequences is not equal to being persuaded to _believing_ them. The difference is shown to be expressible in the representation format proposed. (shrink)

This monograph investigates the temporal interpretation of narrative discourse in two parts. The theme of the first part is narrative progression. It begins with a case study of the adverb ‘now’ and its interaction with the meaning of tense. The case study motivates an ontological distinction between events, states and times and proposes that ‘now’ seeks a prominent state that holds throughout the time described by the tense. Building on prior research, prominence is shown to be influenced by (...) principles of discourse coherence and two coherence principles, NARRATION and RESULT, are given a formally explicit characterization. The key innovation is a new method for testing the definitional adequacy of NARRATION and RESULT, namely by an abductive argument. This contribution opens a new way of thinking about how eventive and stative descriptions contribute to the perceived narrative progression in a discourse. -/- The theme of the second part of the monograph is the semantics and pragmatics of tense. A key innovation is that the present and past tenses are treated as scalar alternatives, a view that is motivated by adopting a particular hypothesis concerning stative predication. The proposed analysis accounts for tense in both matrix clauses and in complements of propositional attitudes, where the notorious double access reading arises. This reading is explored as part of a corpus study that provides a glimpse of how tense semantics interacts with Gricean principles and at-issueness. Several cross-linguistic predictions of the analysis are considered, including their consequences for the Sequence of Tense phenomenon and the Upper Limit Constraint. Finally, a hypothesis is provided about how tense meanings compose with temporal adverbs and verb phrases. Two influential analysis of viewpoint aspect are then compared in light of the hypothesis. (shrink)

In this work Ockham proposes a theory of simple predication, which he uses in explicating the truth conditions of progressively more complicated kinds of propositions. His discussion includes what he takes to be the correct semantic treatment of quantified propositions, past tense and future tense propositions, and modal propositions, all of which are receiving much attention from contemporary philosophers. He also illustrates the use of exponential analysis to deal with propositions that prove troublesome in both semantic theory and (...) other disciplines, such as metaphysics, physics, and theology. This type of analysis plays an essential role in his substantive philosophical and theological works, and in many cases then can hardly be understood without a prior acquaintance with this section of the Summa. An introduction by Alfred J. Freddoso clarifies and summarizes Ockham's theory, discusses certain philosophical problems which it engenders, and proposes new interpretations for parts of it. The essay will be helpful both to those interested in Ockham as a historical figure and to those interested in his substantive systematic contributions to logical theory. (shrink)

The article deals with two problems that arise within moorean style act-utilitarianism (a.u.): (i) how is the notion of 'the alternatives to' a particular action to be explicated? (ii) how should a.u. be formulated in order for it to validate the laws of standard deontic logic? it is argued that these intertwined problems can be solved only if the traditional formulations a a.u. are rejected in favor of some new and more viable ones. in the literature the two problems seem (...) to have been seriously considered only by bergstrom and castaneda. in a final section the author extends his new versions of a.u. to 'sequences' of "single" particular actions and argues for the necessity of working with 'tensed' deontic notions as well as for a combination of deontic logic with tense-logic. (shrink)

In recent years combinations of tense and modality have moved intothe focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of (...) predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T x W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T x Wsemantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed. (shrink)

Children with specific language impairment (SLI) show a protracted period of inconsistent use of tense/agreement morphemes. The purpose of this investigation was to determine whether this inconsistent use could be attributed to the children's misinterpretations of particular syntactic structures in the input. In Study 1, preschool-aged children with SLI and typically developing peers heard sentences containing novel verbs preceded by auxiliarywasor sentences in which the novel verb formed part of a nonfinite subject-verb sequence within a larger syntactic structure (...) (e.g.We saw the dog relling). The children were then tested on their use of the novel verbs in contexts that obligated use of auxiliaryis. The children with SLI were less accurate than their peers and more likely to produce the novel verb withoutisif the verb had been heard in a nonfinite subject-verb sequence. In Study 2, children with SLI and typically developing peers were tested on their comprehension of sentences such asThe cow sees the horse eating. The children with SLI were less accurate than their peers and were disproportionately influenced by the nonfinite subject-verb clause at the end of the sentence. We interpret these findings within the framework of construction learning. (shrink)

In his Quadratura, Paul of Venice considers a sophism involving time and tense which appears to show that there is a valid inference which is also invalid. Consider this inference concerning some proposition A : A will signify only that everything true will be false, so A will be false. Call this inference B. A and B are the basis of an insoluble-that is, a Liar-like paradox. Like the sequence of statements in Yablo's paradox, B looks ahead to (...) a moment when A will be false, yet that moment may never come. In the Quadratura, Paul follows the solution to insolubles found in the collection of elementary treatises known as the Logica Oxoniensis, which posits an implicit assertion of its own truth in insolubles like B. However, in the treatise on insolubles in his Logica Magna, Paul develops and endorses a different solution that takes insolubles at face value. We consider how both types of solution apply to A and B : on both, B is valid. But on one, B has true premises and false conclusion, and contradictories can be false together; on the other (following the Logica Oxoniensis), the counterexample is rejected. (shrink)

The paper has two parts preceded by quite comprehensive preliminaries.In the first part it is shown that a subvariety of the variety ${\cal T}$ of all tense algebras is discriminator if and only if it is semisimple. The variety ${\cal T}$ turns out to be the join of an increasing chain of varieties ${\cal D}_n$, which are discriminator varieties. The argument carries over to all finite type varieties of boolean algebras with operators satisfying some term conditions. In the case (...) of tense algebras, the varieties ${\cal D}_n$ can be further characterised by certain natural conditions on Kripke frames.In the second part it is shown that the lattice of subvarieties of ${\cal D}_0$ has two atoms, the lattice of subvarieties of ${\cal D}_1$ has countably many atoms, and for $n>1$, the lattice of subvarieties of ${\cal D}_n$ has continuum atoms. The proof of the second of the above statements involves a rather detailed description of zero-generated simple algebras in ${\cal D}_1$.Almost all the arguments are cast in algebraic form, but both parts begin with an outline describing their contents from the dual point of view of tense logics. (shrink)

For given Boolean algebras$\mathbb {A}$and$\mathbb {B}$we endow the space$\mathcal {H}(\mathbb {A},\mathbb {B})$of all Boolean homomorphisms from$\mathbb {A}$to$\mathbb {B}$with various topologies and study convergence properties of sequences in$\mathcal {H}(\mathbb {A},\mathbb {B})$. We are in particular interested in the situation when$\mathbb {B}$is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on$\mathbb {A}$in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result stating (...) that there are Efimov spaces in the random model. We also investigate relations between topologies on$\mathcal {H}(\mathbb {A},\mathbb {B})$for a Boolean algebra$\mathbb {B}$carrying a strictly positive measure and convergence properties of sequences of measures on$\mathbb {A}$. (shrink)

Abstract This paper compares Heidegger's conception of time with more prevalent physical and broadly psychological analyses of time. The ?vulgar? notion of time, as Heidegger understands it, is based on the assumption that time, regardless of whether it is identified with tense or not, is something that is essentially measurable by clocks. Heidegger maintains that the vulgar notion of time is a distortion of his own preferred conception of temporality. I show how temporality may be understood as the non?sequential (...) tensed structure underlying tensed discourse. I argue against any straightforward reduction of this tensed structure and the direction of time to physical occurrences. Nevertheless I argue that temporality can be distinguished from purely psychological analyses of temporal experience and from traditional conceptions of time as tensed experience. The selectiveness of demonstrative discourse provides the basis for Heidegger's critique and reconstruction of time understood as tensed discourse about things. Heidegger's scepticism about the interpretation of time as a sequence of nows that underlies the dominant interpretation of tense is due to his appropriation of the relativity of simultaneity from special relativity. But his interpretation of physical theory leads him to the thesis that time is pre?supposed but not completely analysed in physical theory. The meta?language of physical theory makes covert use of temporal notions, for entities can themselves only be understood in covertly temporal ways. I show how this claim may be understood and defended in the light of current physical theory. Heidegger's analysis gives us some basis for thinking that his own notion of temporality is built into an understanding of temporal experience. But I argue that Heidegger fails to make the case that physical time is ontologically dependent on human existence. (shrink)

Shows that both anaphoricity and egocentric de se binding play a crucial role in the interpretation of tense in discourse. Uses the English backwards shifted reading of the past tense in a mistaken time scenario to bring out the tension between these two features. Provides a suitable representational framework for the observed clash in the form of an extension of DRT in which updates of the common ground are accompanied by updates of each relevant agent's complex attitudinal state.

Based on the results of [11] this paper delivers uniform algorithms for deciding whether a finitely axiomatizable tense logic has the finite model property, is complete with respect to Kripke semantics, is strongly complete with respect to Kripke semantics, is d-persistent, is r-persistent.It is also proved that a tense logic is strongly complete iff the corresponding variety of bimodal algebras is complex, and that a tense logic is d-persistent iff it is complete and its Kripke frames form (...) a first order definable class. From this we obtain many natural non-d-persistent tense logics whose corresponding varieties of bimodal algebras are complex. (shrink)

We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles.

McTaggart has an insight that changes of property rely on changes of tense (McTaggart 1908). As I show in this paper, he fails to define A-series as a series for changes of tense, and therefore his proof for the unreality of time is unsuccessful. A-series found in the proof is reduced to a number of mere indexicals of time, and this reduction is pushed forward in Dummett's defense. My aim in this paper is not only to check the (...) validity of their arguments but to investigate invincible difficulties faced in defining changes of tense. The latter is my main aim, and the former is a preliminary argument for it. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Christopher Gill PLATO'S ATLANTIS STORY AND THE BIRTH OF FICTION There is a sense in which Plato's Atlantis story is the earliest example of narrative fiction in Greek literature; which is also to say it is the earliest example in Western literature. This may seem a surprising claim. Plato's story is introduced in the Timaeus as the record of a factual event and as one which is "absolutely true." (...) If the story is conceded, nonetheless, to be an invention, one might suppose that earlier works of literature, such as Homer's epics, have an equal claim to be considered fictional. On the other hand, it might be objected that the genre of narrative fiction (what we call the romance or novel) did not emerge in Greece until considerably later, in or around the first century B.C. A better understanding both of fiction and of the Atlantis story will, however, show my claim to be justified. If we describe a narrative as a fiction, we usually mean that it is an account of events which did not actually take place as they are described but which have been invented by the author. This, however, does not distinguish between falsehood and fiction. And, indeed, fiction is distinguishable from falsehood only by the presumptions of author and audience: the author of fiction does not intend to deceive (nor is the audience generally deceived) about the status of the narrative. It is also true (though in a different sense) that it is the presumptions of author and audience that distinguish fictional from factual accounts. For a fictional narrative in the past tense is not formally distinguishable from a narrative of past factual events; and it is only certain conventional and extrinsic signals (like the title of a book) which denote the class of the narrative. Moreover, an audience follows a fictional narrative with much the same kind of mental attention and emotional involvement as it does a factual narrative: fictional events may seem, in a sense, as real as, or more real than, factual events. Yet, at some level, the audience is aware that the fictional events are not real in the ordinary sense of the word but invented by the author; this awareness underlies 64 Christopher Gill65 and characterizes the kind of attention, and involvement, elicited by fictional narrative. Fiction, one may say, is a kind of game, in which both participants share in a willed pretense, treating what is unreal as real, and what is invented as actual. The rules of the game of fiction are not intuitively obvious, but presuppose a degree of cultural sophistication in a society or individual: in particular, the capacity to draw a clear distinction between fact and fiction. This capacity cannot be reasonably attributed to the composers of Homeric epic, nor can the poems (which are a chemical fusion of legends about the past and creative invention) accurately be classified by either term. The genre of deliberately fictional narrative (that is, the romance) did not emerge until historiography, factual recording of the past, was an established technique. Indeed, the romance seems to have grown up as an imitation of history, in which the author played the game of recounting a sequence of past events. Xenophon's Education of Cyrus (c. 360 b.c.), the first self-consciously semi-fictional history, served as a suggestive prototype for later, more completely fictional narratives. It is perhaps not accidental that Thucydides' attempt in the fifth century to lay down criteria for wholly factual historiography (with none of the romantic elaborations of the Homeric epics, 1.3, 1.10, 1.22) was succeeded in the fourth century by the first philosophical accounts ofthe truth-status of literature; Aristotle, in fact, defines literary truth through a contrast with historical truth (Poetics, 9). The clearer delineation of fact promoted the desire to define fiction (or, at least, literary invention), as well as creating the preconditions for the self-conscious production of fiction. Plato may seem to be an enemy rather than an analyst of literature; and his discussions undeniably have a polemical tone. But, closely examined, his treatment of literature in the Republic, and of the kinds of... (shrink)

I argue for a version of tense-logical realism that privileges tensed facts without privileging any particular temporal standpoint from which they obtain.

The paper argues that metaphysics depends upon science when it comes to claims about the constitution of the real world. That thesis is illustrated by considering the examples of global supervenience, the tenseless vs. the tensed theory of time and existence, events vs. substances, and relations vs. intrinsic properties. An argument is sketched out for a metaphysics of a four-dimensional block universe whose content are events and their sequences, events consisting in physical properties instantiated at space-time points, these properties being (...) relations rather than intrinsic properties. (shrink)

This paper is mainly concerned with tense in embedded constructions. I believe that recent research – notably the work by Ogihara (1989) and Abusch (1993) – has contributed much to our better understanding of its semantics. The proposals made by the two authors are, however, still too simplistic in some regards. Among other things, they neglect the interplay of tense with temporal adverbs of quantification and with frame-setters. To get this composition right is a touchstone for every theory (...) of tense and tense semanticists have been concerned with this problem from the beginning on, as witnessed by the analyses in Kratzer (1978), Bäuerle (1979), Dowty (1979/1982), to mention a few. (shrink)

The aim of this essay is to characterize the issue whether tense is real. Roughly, this is the issue whether, given any tensed representation, its tense corresponds in some suitably direct way to some feature of reality. The task is to make this less rough. Eight characterizations of the issue are considered and rejected, before one is endorsed. On this characterization, the unreality of tense is equivalent to the unity of temporal reality. The issue whether tense (...) is real, so characterized, is then related to Kant’s deduction of the categories in his Critique of Pure Reason. It is argued that Kant’s deduction does not provide the argument for the unreality of tense that it may appear to. The conclusion drawn at the end of the essay is that the unreality of tense cannot be argued for—not because tense is real, but because, even if it is unreal, its unreality is basic. (shrink)

The tense tree method extends Jeffrey’s well-known formulation of classical propositional logic to tense logic (Jeffrey 1991).1 Tense trees combine pure tense logic with features of Prior’s U-calculi (where ‘U’ is the earlier-than relation; see Prior 1967 and the Introduction to this volume). The tree method has a number of virtues: trees are well suited to computational applications; semantically, the tree systems presented here are no less illuminating than model theory; the metatheory associated with tree formulations (...) is often more tractable than that required in a model-theoretic setting; and last but not least the tree method is ideal for pedagogical purposes. (shrink)

Although we believe the results reported below to have direct philosophical import, we shall for the most part confine our remarks to the realm of mathematics. The reader is referred to [4] for a philosophically oriented discussion, comprehensible to mathematicians, of tense logic.The “minimal” tense logicT0is the system having connectives ∼, →,F(“at some future time”), andP(“at some past time”); the following axioms:(whereGandHabbreviate ∼F∼ and ∼P∼ respectively); and the following rules:(8) fromαandα → β, inferβ,(9) fromα, infer any substitution instance (...) ofα,(10) fromα, inferGα,(11) fromα, inferHα.A tense logic is a systemTwhose language is that ofT0and whose axioms and rules include (1)–(11). The axioms and rules ofTother than (1)–(11) are calledproperaxioms and rules.We shall investigate three systems of semantics for tense logics, i.e. three notions ofstructureand three relations ⊧ which stand between structures and formulas. One reads⊧αas “αis valid in.” A structureis amodelof a tense logicTif every formula provable inTis valid in. A semantics isadequateforTif the set of models ofTin the semantics is characteristic forT, i.e. if wheneverT ∀ αthen there is a modelofTin the semantics such that∀ α. Two structuresand, possibly from different semantics, are calledequivalent(∼) if exactly the same formulas are valid inas in. (shrink)