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The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Megara and by their interest in logical paradoxes, propositional logic and dialectical expertise. . Its two best known members, Diodorus Cronus and Philo the Logician, made groundbreaking contributions to the development of theories of conditionals and modal logic. Philo introduced a version of material implication; Diodorus devised a forerunner of strict implication. Each developed a system (...) |
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Most of us would want to say that it is true that Socrates taught Plato. According to realists about past facts,1 this is made true by the fact that there is, located in the past, i.e., earlier than now, at least one real event that is the teaching of Plato by Socrates. Presentists, however, in denying that past events and facts exist2 cannot appeal to such facts to make their past-tensed statements true. So what is a presentist to do? |
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Investigation into the reality of time can be pursued within the ontological domain or it can also span human thought and natural language. I propose to approach time by correlating three domains of inquiry: metaphysical time, the human concept of time, and temporal reference in natural language, entertaining the possibility of what I call a ‘horizontal reduction’ and ‘vertical reduction’. I present a view of temporalityL/E as epistemic modality, drawing on evidence from the L domain and its correlates in the (...) |
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Many languages have past-and-counterfactuality markers such as English simple past. There have been various attempts to find a common definition for both uses, but I will argue in this paper that they all have problems with ruling out unacceptable interpretations, or accounting for the contrary-to-fact implicature of counterfactual conditionals, or predicting the observed cross-linguistic variation, or a combination thereof. By combining insights from two basic lines of reasoning, I will propose a simple and transparent approach that solves all the observed (...) |
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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 (...) |
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The concept of event is one of the key notions of many theories dealing with causality or agency. In this paper we study different approaches to events that share the basic assumption that events can be analyzed fruitfully in branching-time structures. The terminological framework developed thereby may be helpful for further analyses in the fields of causality and agency and also in those fields of computational semantics, where similar concepts are considered. |
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Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) |
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On the historic Cross, it is God Himself Who has actually met the last dark limits of our life, and has brought Himself face to face with that inescapable something (or Someone) which seems to keep us forever strangers (physically, morally, logically and in every other way) to the Absolute and Eternal. And because it is God Himself Who has thus in life and in death personally encountered sin, death, time and corruption, He has overthrown them and raised and transformed (...) |
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We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. (...) |
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In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...) |
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We spend much of our adult lives thinking and reminiscing about particular events of the past, which, by their very nature, can never be repeated. What is involved in a capacity to think thoughts of this kind? In this paper, I propose that such thoughts are essentially connected with a capacity to communicate about past events, and specifically in the special way in which events of the past are valued and shared in our relationships with one another. I motivate this (...) |
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This paper starts the systematic study of inconsistency measures for propositional logics enriched with operators involving time. We use Prior’s operators for tense logic: H, G, P, and F; however, we apply different semantics to them. We define two logics. The first one, ATPL, allows formulas with the application of any of the four operators any number of times to propositional logic formulas. The semantics is given in terms of TPL structures. We then show how to measure the inconsistency of (...) |
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Over the past several decades, in the field of temporal logic there have been created a great number of semantical theories that provide different truth conditions for tensed propositions. In this article we deal with five non-bivalent semantical interpretations of the temporal logic systems CL and Kb : 1) Ł3 by J. Łukasiewicz; 2) K3 by S. C. Kleene; 3) Ockhamism by A. Prior; 4) supervaluationism by R. Thomason; 5) relativism by J. MacFarlane. The aim of this article is to (...) |
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In ‘Many-valued Logics’, a lecture broadcast over New Zealand's public radio in 1957, Arthur N. Prior (1914–1969) complained that conjunctions are put ‘to something like forced labour’ in Łukasiewicz's three-valued semantics, Ł3. In this paper, we discuss what Prior might have meant by this. |
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Presentism states that everything is present. Crucial to our understanding of this thesis is how we interpret the ‘is’. Recently, several philosophers have claimed that on any interpretation presentism comes out as either trivially true or manifestly false. Yet, presentism is meant to be a substantive and interesting thesis. I outline in detail the nature of the problem and the standard interpretative options. After unfavourably assessing several popular responses in the literature, I offer an alternative interpretation that provides the desired (...) |
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A presente investigação questiona a essência teo-lógica dos futuros contingentes. Para o efeito, analisa-se, primeiramente, a argumentação segundo a qual, sob certas condições lógicas, teológicas, ontológicas e cosmológicas anti-necessitantes, detetadas por G. W. Leibniz (conciliando a posição de St. Agostinho com a de L. Molina e W. Ockham), a abertura contingente do futuro parece ser compatível com o regime das “verdades contingentes pré-determinadas”, regime enquadrado teologicamente pelo princípio do “futuro melhor” ou do “único futuro verdadeiro”. No entanto, os futuros contingentes (...) |
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Typical presentism asserts that whatever exists is present. Moderate presentism more modestly claims that all events are present and thus acknowledges past and future times understood in a substantivalist sense, and past objects understood, following Williamson, as “ex-concrete.” It is argued that moderate presentism retains the most valuable features of typical presentism, while having considerable advantages in dealing with its most prominent difficulties. |
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This paper presents two general results of decidability concerning logics based on an indeterministic metric tense logic, which can be applied to, among others, logics combining knowledge, time and agency. We provide a general Kripke semantics based on a variation of the notion of synchronized Ockhamist frames. Our proof of the decidability is by way of the finite frame property, applying subframe transformations and a variant of the filtration technique. |
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Like modal logic, temporal logic, and description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoare-style proof systems with the goal to perform automatic program analysis. In a broad sense, separation logic is often understood as a programming language, an assertion language and a family of rules involving Hoare triples. In this survey, we present similarities between separation logic as an assertion language and modal and temporal logics. Moreover, we (...) |
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Presentism is held by most to be the intuitive theory of time, due in large part to the view's supposed preservation of time's passage. In this paper, I strike a blow against presentism's intuitive pull by showing how the presentist, contrary to overwhelming popular belief, is unable to establish temporal change upon which the passage of time is based. I begin by arguing that the presentist's two central ontological commitments, the Present Thesis and the Change Thesis, are incompatible. The main (...) |
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The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we (...) |
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I present a variant of with time, called, interpreted in standard Kripke semantics. On the syntactic level, is nothing but the extension of atemporal individual by: the future tense and past tense operators, and the operator of group agency for the grand coalition. A sound and complete axiomatisation for is given. Moreover, it is shown that supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment. |
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The man who is isolated over against God is as such rejected by God. But to be this man can only be the choice of the Godless man himself. The witness of the Community of God to every individual man points in this direction: that this choice of the Godless is null and void, that he belongs to Jesus Christ from eternity and thus is not rejected, but rather chosen by God in Jesus Christ, that the reprobation which he deserves (...) |
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For twenty years, D. H. Mellor has promoted an influential defence of a view of time he first called the ‘tenseless’ view, but now associates with what he calls the ‘B-theory.’ It is his defence of this view, not the view itself, which is generally taken to be novel. It is organized around a forcefully presented attack on rival views which he claims to be a development of McTaggart's celebrated argument that the ‘A-series’ is contradictory. I will call this attack (...) |
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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 (...) |
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Multiple-conclusion Hilbert-style systems allow us to finitely axiomatize every logic defined by a finite matrix. Having obtained such axiomatizations for Paraconsistent Weak Kleene and Bochvar–Kleene logics, we modify them by replacing the multiple-conclusion rules with carefully selected single-conclusion ones. In this way we manage to introduce the first finite Hilbert-style single-conclusion axiomatizations for these logics. |
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Indicative conditionals with present tense antecedents can have ‘shifted’ readings that are unexpected given the semantic behavior of the tenses outside of conditionals. In this paper, we compare two accounts of this phenomenon due to Kaufmann (J Semant 22(3):231–280, 2005) and Schulz (SALT XVIII, pp. 694–710, 2008), by reconstructing them in the framework of branching time. We then propose a novel account of indicative conditionals based on the branching time semantics suggested in Rumberg (J Logic Lang Inf 25(1):77–108, 2016), viz. (...) |
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Propositional modal logic over relational frames is naturally extended with propositional quantifiers by letting them range over arbitrary sets of worlds of the relevant frame. This is also known as second-order propositional modal logic. The propositionally quantified modal logic of a class of relational frames is often not axiomatizable, although there are known exceptions, most notably the case of frames validating the strong modal logic $\mathrm {S5}$. Here, we develop new general methods with which many of the open questions in (...) |
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This paper presents the link between Arthur N. Prior and logicians that belonged to the Lvov-Warsaw School. Although certain members of the Lvov-Warsaw School influenced Prior’s views, the amount and the form of the impact are still under discussion. Prior also cooperated with some of them in the development of his systems of logic. This paper focuses on four main areas in which Prior admitted adopting ideas from the Lvov-Warsaw School: systems of propositional logic, the history of logic, modal and (...) |
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Two new infinitary modal logics are simply obtained from a Gentzen-type sequent calculus for infinitary logic by adding a next-time operator, and a program operator, respectively. It is shown that an any-time operator and a program-iteration operator can respectively be expressed using infinitary conjunction in these logics. The cut-elimination and completeness theorems for these logics are proved using some theorems for embedding these logics into (classical) infinitary logic. |
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Le concept du possible a pris récemment dans les sciences de la vie une place plus importante, en raison de réflexions nouvelles sur l’évolution biologique ainsi que du développement très important des biotechnologies. On souhaite ici explorer l’idée que les choses contingentes, celles qui pourraient être un peu différentes, sont modifiables. La contingence de l’évolution biologique a souvent été notée, et définie en des sens notoirement différents. Certains biologistes ont fait usage du conditionnel contrefactuel, en définissant la contingence par l’idée (...) |
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It has been argued that the primary acquisition of genericity in early child speech poses a problem for standard quantificational approaches to generics and instead motivates the claim that generics give voice to an innate, default mode of generalising. This article argues that analogous puzzles involving the acquisition of A‐quantifiers undermine the empirical support for a purely cognition‐based approach to generics. Instead, these acquisition puzzles should be solved by generalising the core insight of the cognitive defaults theory to these expressions, (...) |
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Although it receives less attention, (Lewis in Noûs 13:455–476, 1979. https://doi.org/10.2307/2215339) admitted that the branching-time(-like) model fits a wide range of counterfactuals, including (Nix) ‘If Nixon had pressed the button, there would have been a nuclear war’, which was raised by (Fine in Mind 84:451–458, 1975). However, Lewis then claimed that similarity analysis is more general than temporality analysis. In this paper, we do not scrutinise his claim. Instead, we re-analyse (Nix) not only model-theoretically but also proof-theoretically from the ‘meaning-as-use’ (...) |
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I examine Quine’s and Davidson’s arguments to the effect that classical logic is the one and only correct logic. This conclusion is drawn from their views on radical translation and interpretation, respectively. I focus on the latter, but I first address, independently, Quine’s argument to the effect that the ‘deviant’ logician, who departs from classical logic, is merely changing the subject. Regarding logical pluralism, the question is whether there is more than one correct logic. I argue that bivalence may be (...) |
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A position that has been called ‘classical indeterminism’ has recently been developed in order to model vagueness: this approach appeals to an object-language ‘determinately’ operator, the semantics of which are defined in such a way as to preserve the principle of bivalence. I suggest that a prominent argument against this strategy, which I call the Field–Williamson argument, fails. The classical indeterminist position in its general form was anticipated by the Aristotelian commentators in their discussions of Aristotle’s famous ‘sea battle’ passage (...) |
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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. |
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