The issues I explore in this paper are best introduced by the table with which it begins. The left-hand entry in each row gives expression to a kind objectivity; the right-hand entry affirms the existence of a special kind of object. When philosophers believe in any of the entities on the right, it is typically because they think them necessary to ground the facts on the left. By the same token, when philosophers deny any of the facts on the left, (...) it is often because they cannot bring themselves to believe in the associated kind of object on the right. My project is to explore the extent to which it is possible to have the objectivity without the objects—for example, absolute motion without substantival space, objective predication without universals, objective synonymy without propositions, and objective modality without possible worlds. Each of these combinations would have been congenial to A.N. Prior. (shrink)

David Lewis’s analysis of “can” in “The Paradoxes of Time Travel” has been widely accepted both as a definitive analysis of “can” and as a successful resolution of the Grandfather Paradox for time travel. I argue that the central feature of his analysis puts it on all fours with a fallacy frequently imputed to fatalists such as Richard Taylor. I go on to consider two moves that might be made to avoid the fallacy, arguing that one of them leads to (...) the unavailability of an all-things-considered “can” and the other to a new primitive modality, not analyzable in Lewis’s way. (shrink)

This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary for assigning (...) them a probability distribution. The “historical” state of a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed. An age operator computes the informational depth of historical states and its standard deviation can be used to provide a universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence of the subject’s activity of measuring, which defines the flow of time-information. (shrink)

I illustrate with three classical examples the mistakes arising from using a modal operator admitting multiple interpretations in the same argument; the flaws arise especially easily if no attention is paid to the range of propositional variables. Premisses taken separately might seem convincing and a substitution for a propositional variable in a modal context might seem legitimate. But there is no single interpretation of the modal operators involved under which all the premisses are plausible and the substitution successful.

Though Arthur Prior is now best known for his founding of modern temporal logic and hybrid logic, much of his early philosophical career was devoted to history of logic and historical logic. This interest laid the foundations for both of his ground-breaking innovations in the 1950s and 1960s. Because of the important rôle played by Prior's research in ancient and medieval logic in his development of temporal and hybrid logic, any student of Prior, temporal logic, or hybrid logic should be (...) familiar with the medieval logicians and their work. In this article we give an overview of Prior's work in ancient and medieval logic. (shrink)

The current trend in knowledge revision in the Dynamic Epistemic Logic tradition focuses on the addition of new knowledge, rather than the possibility of losing knowledge. Yet there are natural situations, such as an agent who does not want another agent to know that she knows a certain piece of information, where there is a need to be able to model the retraction of a proposition from a knowledge base. One situation where this is systematically required is the variant of (...) the medieval theory of obligationes known as dubitatio, where one of the agents in the dialogue is obliged to hold the initial proposition, the dubitatum, as doubtful, regardless of what other propositions she may concede or deny during the disputation. In this paper, we use dubitatio as a motivation for studying deceitful agents, and we discuss various ways that an agent can move from a model where f is known to one where f is not known. (shrink)

In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching space-time models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract space-time structures based on the real numbers and the integers, considering three different accessibility relations between spatio-temporal (...) points. (shrink)

In Prior’s tense-logical analysis, we can avoid mentioning instants in our language by construing them as propositions of a special kind. Instead of qualifying instants by predicates, we may qualify propositions by modalities. Prior shows that by changing the informal interpretation of our modal-like language, we can similarly attempt to avoid ontological commitments to worlds and even to selves and other bona fide individuals. As he notes, the paraphrasing strategy works too generally to be of direct metaphysical use. I wish (...) to speak of several types of entities within one and the same language. This leads to the issue of cross-context identity: how to make sense of speaking of the same entity of one type relative to distinct entities of another type. My analysis employs the notion of world line. I discern a structure of mutually interrelated categories with three informal interpretations: tense, modal and egocentric. They correspond to different metaphysical views on the interrelations of time, logical alternatives and individuals. Prior’s dilemma regarding the possibility of modalizing, not only our talk concerning times and worlds, but even our discourse pertaining to the ‘real world of individuals’ does not vanish but reappears also in my setting. (shrink)

In this paper the class of minimal models C ZI for Kiczuk's system of physical change ZI is provided and soundness and completeness proofs of ZI with respect to these models are given. ZI logic consists of propositional logic von Wright's And Then and six specific axioms characterizing the meaning of unary propositional operator "Zm", read "there is a change in the fact that". ZI is intended to be a logic which provides a formal account for describing two kinds of (...) process change: the change from one state of the process to its other state (e.g., transmitting or absorbing energy with greater or less than the usual intensity) and the perishing of the process (e.g., cessation of the energetic activity of the sun). (shrink)

Will it rain tomorrow? Will there be a sea battle tomorrow? Will my death be painful? Wondering about the future plays a central role in our cognitive lives. It is integral to our inquiries, our planning, our hopes, and our fears. The aim of this paper is to consider various accounts of future contingents and the implications that they have for wondering about the future. I argue that reflecting on the nature of wondering about the future supports an Ockhamist account (...) of future contingents according to which many of them are true. Alternative accounts which maintain that no future contingents are true, either by claiming that they are all false or by claiming that they are neither true nor false, face difficulties concerning why it is appropriate to wonder about them. Reflecting on wondering in general, and wondering about the future in particular, suggests that in wondering how the future will go, we implicitly assume that there is a determinate fact of the matter. After presenting an attractive account of interrogative attitudes that has been recently proposed by Jane Friedman and outlining some norms governing wondering, I argue that all accounts of future contingents except Ockhamism face difficulties concerning why it is appropriate to wonder about them. (shrink)

Various philosophers have long since been attracted to the doctrine that future contingent propositions systematically fail to be true—what is sometimes called the doctrine of the open future. However, open futurists have always struggled to articulate how their view interacts with standard principles of classical logic—most notably, with the Law of Excluded Middle. For consider the following two claims: Trump will be impeached tomorrow; Trump will not be impeached tomorrow. According to the kind of open futurist at issue, both of (...) these claims may well fail to be true. According to many, however, the disjunction of these claims can be represented as p ∨ ~p—that is, as an instance of LEM. In this essay, however, I wish to defend the view that the disjunction these claims cannot be represented as an instance of p ∨ ~p. And this is for the following reason: the latter claim is not, in fact, the strict negation of the former. More particularly, there is an important semantic distinction between the strict negation of the first claim [~] and the latter claim. However, the viability of this approach has been denied by Thomason, and more recently by MacFarlane and Cariani and Santorio, the latter of whom call the denial of the given semantic distinction “scopelessness”. According to these authors, that is, will is “scopeless” with respect to negation; whereas there is perhaps a syntactic distinction between ‘~Will p’ and ‘Will ~p’, there is no corresponding semantic distinction. And if this is so, the approach in question fails. In this paper, then, I criticize the claim that will is “scopeless” with respect to negation. I argue that will is a so-called “neg-raising” predicate—and that, in this light, we can see that the requisite scope distinctions aren’t missing, but are simply being masked. The result: a under-appreciated solution to the problem of future contingents that sees and as contraries, not contradictories. (shrink)

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 (...) that, looking backwards, it was the case that there would be a sea battle? This tension forms, in large part, what might be called the problem of future contingents. A dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition--including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et. al (2001) and MacFarlane (2003, 2014)--have argued that the apparent tension between the intuitions is in fact merely apparent. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions. (shrink)

A‐theorists of time postulate a deep distinction between the present, past and future. Settling on an appropriate logic for such a view is no easy matter. This Philosophy Compass article describes one of the most vexing formal problems facing A‐theorists. It is commonly thought that A‐theories can only be formally expressed in a tense logic: a logic with operators like P and F . And it seems natural to think that we live in a world where objects come to exist (...) and cease to exist as time passes. Indeed, this is typically a key component of the most prominent kind of A‐theory, presentism. But the temporary existence assumption cannot be upheld in any tense logic with a standard quantification theory. I will explain the problem and outline the philosophical and logical considerations that generate it. I will then consider two possible solutions to the problem – one that targets our logic of quantification and one that targets our assumptions about change. I survey the costs of each solution. (shrink)

A-theorists think there is a fundamental difference between the present and other times. This concern shows up in what kinds of properties they take to be instantiated, what objects they think exist and how they formalize their views. Nearly every contemporary A-theorist assumes that her metaphysics requires a tense logic – a logic with operators like and. In this paper, I show that there is at least one viable A-theory that does not require a logic with tense operators. And I (...) will argue that three common indispensability arguments for tense operators are unsound. (shrink)

Open futurism is the indeterministic position according to which the future is ‘open’, i.e., there is now no fact of the matter as to what future contingent events will actually obtain. Many open futurists hold a branching conception of time, in which a variety of possible futures exist. This paper introduces two challenges to branching-time open futurism, which are similar in spirit to a challenge posed by Fine to tense realism. The paper argues that, to address the new challenges, open (...) futurists must adopt an objective, non-perspectival notion of actuality and subscribe to an A-theoretic, dynamic conception of reality. Moreover, given a natural understanding of “actual future”, it is perfectly sensible for open futurists to hold that a unique, objectively actual future exists, contrary to a common assumption in the current debate. The paper also contends that recognising the existence of a unique actual future helps open futurists to avoid potential misconceptions. (shrink)

Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon (...) a specific formal treatment of time and agency, that of so-called stit logics. Moreover, a complete axiomatic theory of fiction-making TFM is defined, where fiction-making is understood as the exercise of agency and choice in time over what is fictionally true. The language \ of TFM is an extension of the language of propositional logic, with the addition of temporal and modal operators. A distinctive feature of \ with respect to other modal languages is a variety of operators having to do with fictional truth, including a ‘fictionality’ operator \ . Some applications of TFM are outlined, and some interesting linguistic and inferential phenomena, which are not so easily dealt with in other frameworks, are accounted for. (shrink)

Mights plug gaps. If p lacks a truth-value, then ‘It might be that p’ should also lack truth-value. Yet epistemic hedges often turn an unassertible statement into an assertible one. The phenomenon is illustrated in detail for two kinds of statements that are frequently alleged to be counterexamples to the principle of bivalence: future contingents and statements that apply predicates to borderline cases. The paper concludes by exploring the prospects for generalizing this gap-plugging strategy.

Why is it that philosophers find it so hard to come to agreement? Many disputes that have gone on for centuries or even millennia are still unresolved, even though there has been increased conceptual sophistication on the part of the contending parties. Consider, for example, the question of free will, where libertarians still contest the field with determinists and compatibilists.

Why can I not appropriately utter ‘It must be raining’ while standing outside in the rain, even though every world consistent with my knowledge is one in which it is raining? The common response to this problem is to hold that epistemic must, in addition to quantifying over epistemic possibilities, carries some additional evidential information concerning the source of one'S evidence. I argue that this is a mistake: epistemic modals are mere quantifiers over epistemic possibilities. My central claim is that (...) the seeming anomaly of the data above arises from a mistaken conception of what a possibility is. Instead of conceiving of possibilities as possible worlds, I argue that we should conceive of possibilities as answers to open questions. (shrink)

The goal of this paper is to re-examine some aspects of the nature of specificational copular constructions by looking at the ways in which the semantics of tense interacts with the semantics of the copula in English. I propose that Tense Harmony (restrictions on the tense of a relative clause in the subject position of specificational copular constructions) is imposed by the interaction between the matrix and embedded tenses.

The apparent 'flow' of time is one of its most mysterious features, and one which discomforts both scientists and philosophers. One of the most striking assaults upon it is McTaggart's argument that the idea of temporal flow is demonstratively incoherent. In this paper I first urge that the idea of temporal flow is an important part of our intuitive understanding of time, underpinning several of our notions about rationality and time. Second, I try to undercut McTaggart's argument by showing that (...) it is not temporal flow which is illusory but rather the vicious regress McTaggart saw in that idea. A steadfast clinging to the notion of now, along with an analysis of McTaggart's argument reveals that the regress halts after but two steps. (shrink)

In the fourteenth century, Duns Scotus suggested that the proper analysis of modality required not just moments of time but also “moments of nature”. In making this suggestion, he broke with an influential view first presented by Diodorus in the early Hellenistic period, and might even be said to have been the inventor of “possible worlds”. In this essay we take Scotus’ suggestion seriously devising first a double-index logic and then introducing the temporal order. Finally, using the temporal order, we (...) define a modal order. This allows us to present modal logic without the usual interpretive questions arising concerning the relation called variously ‘accessibility’, ‘alternativeness’, and, ‘relative possibility.’ The system in which this analysis is done is one of those which have come to be called a hybrid logic. (shrink)

We report two experiments on temporal reasoning with problems, such as: John has cleaned the house. John is taking a shower. John is going to read the paper. Mary always does the dishes when John cleans the house. Mary always drinks her coffee when John reads the paper. What for Mary is the relation between doing the dishes and drinking coffee? The experiments showed that problems such as this one, which require one mental model, elicited correct answers more often than (...) did those requiring multiple models (e.g. with the second premise modified to "John has taken a shower", so that the order between the events in the first two premises is not fixed). These multiple-model problems, in turn, elicited more correct answers than did multiple-model problems with no valid answers (e.g. with the second premise modified to "John has taken a shower", and the fifth premise modified to "Mary always drinks her coffee when John takes a shower"). One-model problems were also solved more quickly than multiple-model problems, which were solved more quickly than problems with no valid answers. These results corroborated the predictions of the mental model theory of reasoning. (shrink)

This paper reports three studies of temporal reasoning. A problem of the following sort, where the letters denote common everyday events: A happens before B. C happens before B. D happens while B. E happens while C. What is the relation between D and EEfficacylls for at least two alternative models to be constructed in order to give the right answer for the right reason. However, the first premise is irrelevant to this answer, and so if reasoners were to ignore (...) it, then they would need to construct only one model. Experiment 1 showed that one-model problems were answered faster and more accurately than multiple-model problems. When the question preceded the premises in the statement of the multiple-model problems there was a slight tendency for the latencies of response to speed up in the predicted way. Experiment 2 modified the procedure, in part by using practice problems with many irrelevant premises, so that reasoners might grasp the advantage of ignoring them. Its results showed that when the premises preceded the question, the multiple-model problems were significantly harder than one-model problems. But when the question was presented first, the difference was significantly reduced in line with the theory's prediction. Experiment 3 used only problems with valid conclusions, and so the construction of multiple models was never necessary. However, there was still a significant difference between one-model problems and multiple-model problems. (shrink)

When an agent undergoes fission, how should the beliefs of the fission results relate to the pre-fission beliefs? This question is important for the Everett interpretation of quantum mechanics, but it is of independent philosophical interest. Among other things, fission scenarios demonstrate that ‘self-locating’ information can affect the probability of uncentred propositions even if an agent has no essentially self-locating uncertainty. I present a general update rule for centred beliefs that gives sensible verdicts in cases of fission, without relying on (...) controversial metaphysical or linguistic assumptions. The rule is supported by the same considerations that support standard conditioning in the traditional framework of uncentred propositions. (shrink)

Todd (2016) proposes an analysis of future-directed sentences, in particular sentences of the form 'will(φ)', that is based on the classic Russellian analysis of definite descriptions. Todd's analysis is supposed to vindicate the claim that the future is metaphysically open while retaining a simple Ockhamist semantics of future contingents and the principles of classical logic, i.e. bivalence and the law of excluded middle. Consequently, an open futurist can straightforwardly retain classical logic without appeal to supervaluations, determinacy operators, or any further (...) controversial semantical or metaphysical complication. In this paper, we will show that this quasi-Russellian analysis of 'will' both lacks linguistic motivation and faces a variety of significant problems. In particular, we show that the standard arguments for Russell's treatment of definite descriptions fail to apply to statements of the form 'will(φ)'. (shrink)

According to an influential line of thought, from the assumption that indeterminism makes future contingents neither true nor false, one can conclude that assertions of future contingents are never permissible. This conclusion, however, fails to recognize that we ordinarily assert future contingents even when we take the future to be unsettled. Several attempts have been made to solve this puzzle, either by arguing that, albeit truth-valueless, future contingents can be correctly assertable, or by rejecting the claim that future contingents are (...) truth-valueless. The paper examines three of most representative accounts in line with the first attempt, and concludes that none of them succeed in providing a persuasive answer as to why we felicitously assert future contingents. (shrink)

According to an influential line of thought, from the assumption that indeterminism makes future contingents neither true nor false, one can conclude that assertions of future contingents are never permissible. This conclusion, however, fails to recognize that we ordinarily assert future contingents even when we take the future to be unsettled. Several attempts have been made to solve this puzzle, either by arguing that, albeit truth-valueless, future contingents can be correctly assertable, or by rejecting the claim that future contingents are (...) truth-valueless. The paper examines three of most representative accounts in line with the first attempt, and concludes that none of them succeed in providing a persuasive answer as to why we felicitously assert future contingents. (shrink)

The aim of this paper is to present a new perspective under which branching-time semantics can be viewed. The set of histories (maximal linearly ordered sets) in a tree structure can be endowed in a natural way with a topological structure. Properties of trees and of bundled trees can be expressed in topological terms. In particular, we can consider the new notion of topological validity for Ockhamist temporal formulae. It will be proved that this notion of validity is equivalent to (...) validity with respect to bundled trees. (shrink)

Arthur Prior was one of the logicians who participated in the invention of the possible worlds’ semantics. The ontology, which is connected with his systems of modal logic, is unique. Prior tried to reduce the number of abstract entities as much as possible. Hence he did not elect to introduce possible worlds and possibilia into his ontology. In addition, he held a reductionist view, which is called modal actualism by Fine or modalism by Melia. Prior was inspired by various authors (...) but this paper mainly discusses the influence of two prominent sources, Wittgenstein and logicians from Warsaw School. Prior acknowledged Wittgenstein’s influence, when he discuss the view that possible worlds consist of propositions. The second important feature of Prior’s concept is the denial of the real existence of possible worlds and the denial of the existence of entities which are in them. It was probably enabled by Prior’s adoption of some systems of logic invented by logicians from the Warsaw school, especially Lesniewski’s and Łukasiewicz’s systems. (shrink)

The Epistemic Objection says that certain theories of time imply that it is impossible to know which time is absolutely present. Standard presentations of the Epistemic Objection are elliptical—and some of the most natural premises one might fill in to complete the argument end up leading to radical skepticism. But there is a way of filling in the details which avoids this problem, using epistemic safety. The new version has two interesting upshots. First, while Ross Cameron alleges that the Epistemic (...) Objection applies to presentism as much as to theories like the growing block, the safety version does not overgeneralize this way. Second, the Epistemic Objection does generalize in a different, overlooked way. The safety objection is a serious problem for a widely held combination of views: “propositional temporalism” together with “metaphysical eternalism”. (shrink)

This paper proves a precisification of Hume’s Law—the thesis that one cannot get an ought from an is—as an instance of a more general theorem which establishes several other philosophically interesting, though less controversial, barriers to logical consequence.

In this paper we develop a novel propositional semantics based on the framework of branching time. The basic idea is to replace the moment-history pairs employed as parameters of truth in the standard Ockhamist semantics by pairs consisting of a moment and a consistent, downward closed set of so-called transitions. Whereas histories represent complete possible courses of events, sets of transitions can represent incomplete parts thereof as well. Each transition captures one of the alternative immediate future possibilities open at a (...) branching point. The transition semantics exploits the structural resources a branching time structure has to offer and provides a fine-grained picture of the interrelation of modality and time. In addition to temporal and modal operators, a so-called stability operator becomes interpretable as a universal quantifier over the possible future extensions of a given transition set. The stability operator allows us to specify how and how far time has to unfold for the truth value of a sentence at a moment to become settled and enables a perspicuous treatment of future contingents. We show that the semantics developed along those lines generalizes and extends extant approaches: both Peirceanism and Ockhamism can be viewed as limiting cases of the transition approach that build on restricted resources only, and on both accounts, stability collapses into truth. (shrink)

The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...) w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language L_t by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

The transition semantics presented in Rumberg :77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language \ are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves \-validity w.r.t. transition structures. As a consequence, for a certain fragment of \, validity w.r.t. transition structures turns (...) out to be axiomatizable. The result is then extended to the entire language \ by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

Ockhamism implies that future contingents may be true, their historical contingency notwithstanding. It is thus opposed to both the Peircean view according to which all future contingents are false, and Supervaluationist Indeterminism according to which all future contingents are neither true nor false. The paper seeks to defend Ockhamism against two charges: the charge that it cannot meet the requirement that truths be grounded in reality, and the charge that it proves incompatible with objective indeterminism about the future. In each (...) case, the defence draws on the idea that certain truths are truths only courtesy of others and of what makes the latter true. After introduction of the Ockhamist view, its competitors and implications, a suitable definition of grounded truth is being devised that both is faithful to the spirit of the grounding-requirement and allows the Ockhamist to heed that requirement quite comfortably. Then two senses in which the future might be open are being introduced, indeterminacy as failure of predetermination by past and present facts, and indeterminacy as failure of entailment by past and present truths. It is argued that while openness in the former sense, but not in the latter sense, coheres with the Ockhamist view, it is only openness in the former sense that matters for objective indeterminism. (shrink)

Besides their ordinary cardinal and proportional meanings, many and few have been argued to allow for a ‘reverse proportional’ reading. This reading has later been characterised in two opposite directions: Cohen’s reading where the proportion \ matters and Herburger’s where it does not. We develop a compositional analysis that derives the correct truth conditions for both characterisations of Westerståhl-style sentences while maintaining conservativity, assuming a standard syntax/semantics mapping and reducing their context-dependence to mechanisms independently needed for degree constructions in general. (...) In a nutshell, mirroring the decomposition of other degree expressions like tall, many is decomposed into the parametrized determiner many and the operator POS, where POS combines with a contextually salient comparison class C matching the alternatives triggered by some element X\ in the sentence. Non-reverse readings obtain when X\ is external to the original host NP and reverse readings when X\ is internal to the host NP. Cohen’s truth conditions for Westerståhl-style sentences are derived as a reverse proportional reading and Herburger’s interpretation as a sub-case of the non-reverse cardinal reading. (shrink)

The Moral Law is fulfilled iff everything that ought to be the case is the case, and The Good is realised in a possible world w at a time t iff w is deontically accessible from w at t. In this paper, I will introduce a set of temporal modal deontic systems with propositional quantifiers that can be used to prove some interesting theorems about The Moral Law and The Good. First, I will describe a set of systems without any (...) propositional quantifiers. Then, I will show how these systems can be extended by a couple of propositional quantifiers. I will use a kind of TxW semantics to describe the systems semantically and semantic tableaux to describe them syntactically. Every system will include a constant · that stands for The Good. ‘·’ is read as ‘The Good is realised’. All systems that contain the propositional quantifiers will also include a constant '*' that stands for The Moral Law. '*' is read as ‘The Moral Law is fulfilled’. I will prove that all systems (without the propositional quantifiers) are sound and complete with respect to their semantics and that all systems (including the extended systems) are sound with respect to their semantics. It is left as an open question whether or not the extended systems are complete. (shrink)

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of$$T \times W$$T×Wmodels, and the (...) proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper. (shrink)

Hamblin's Action-State Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic (...) tense logic captures intuitions of the Hamblinian model of imperatives. The logic implements a direct mapping of each of Hamblin's key concepts: strategies, partial strategies and wholehearted satisfaction. (shrink)