Tense logic is a branch of contemporary logic which includes formal devices that allow us to deal with the temporal relations between propositions. The aim of our paper is threefold: 1) to reveal how Aristotelian philosophical ideas about time, truth, possibility and necessity were reinterpreted by the founder of contemporay tense logic Arthur Prior; 2) to discuss what novel solutions to the classical problem of future contingents are available using Priorean invention; 3) to describe how the tools of tense logic (...) have transcended their original theoretical purposes. (shrink)

While philosophers feel relatively comfortable about talking of the present and the past, some of them feel uncomfortable about talking in just the same way of future events. They feel that, in general, discourse about the future differs significantly from discourse about the past and present, and that these differences reflect a logical asymmetry between the past and future beyond the merely defining fact that the future succeeds, and the past precedes, the present time. The problem is: how can we (...) talk about events which have not yet happened, or at any rate are not yet bound to happen, or whose participants do not yet exist? The effect of these worries has led them to claim to recognise restrictions on our talk about the future which do not govern talk about the past and present. The most famous of these views is Aristotle's. According to one familiar interpretation, he holds that a statement about a future event which is not yet settled, a contingent event in the future, is neither true nor false, even though the statement that the event either will or will not happen is necessarily true. Proponents of this view felt that if a future-tensed statement were already true then the fact that it stated would already be settled. I do not propose to discuss this well-known and muchdiscussed doctrine of Aristotle's, but I do want to consider some allied views which have been aired recently, and to look at their philosophical significance. Before I look at these, however, it will be convenient to recall three of the main reasons why the Aristotelian doctrine is unpopular. In the first place it is paradoxical to accept that a statement of the form p v ∼ p is true while claiming that neither of its disjuncts is true. Then there are misgivings about the notion of truth involved: many feel that truth is essentially an attribute of timeless propositions and that it is nonsense to talk of a statement's becoming true as you would of Aristotle's views if the event described became inevitable. There is also the difficulty of accounting for the meaning of a future-tensed sentence which may express a statement that is neither true nor false simply because what it states is not yet settled. It could not be said of the sentence expressing such a statement that you know what it means if you know what it is for the sentence to express a true statement. I know the meaning of the present-tensed sentence ‘A sea-battle is now being waged’ if I know that it can normally be used to make a true statement precisely in the event of there being a sea-battle being waged at present. But I do not know the meaning of the future-tensed sentence ‘A sea-battle will be waged tomorrow’ simply by knowing that the sentence expresses a true statement if it is already settled that there is going to be a battle: the statement doesn't mean that the battle is already settled, otherwise it would not lack a truth-value when the matter was still open – it would be false. (shrink)

The assumption that the future is open makes well known problems for traditional semantics. According to a commonly held intuition, today's occurrence of the sentence 'There will be a sea battle tomorrow', while truth-valueless today, will have a determinate truth-value by tomorrow night. Yet given traditional semantics, sentences that are truth-valueless now cannot later 'become' true. Relativistic semantics has been claimed to do a better job of accommodating intuitions about future contingents than non-relativistic semantics does. However, intuitions about future (...) contingents cannot by themselves give good reasons for shifting to a new paradigm, for despite the initial appearances, standard non-relativistic semantics (plus an account of truth-value gaps) can accommodate both intuitions about future contingents. (shrink)

Preliminaries: Terminology and Notation We may make a distinction between temporally definite and temporally indefinite sentences. ...

This note provides a review of the book 'On the Sea-Battle Tomorrow That May Not Happen' by Tomasz Jarmużek.

Ancient commentators like Ammonius and Boethius tried to solve Aristotle's “sea battle argument” in On Interpretation 9 by saying that statements about future contingents are “indefinitely” true or false. They were followed by al-Fārābī in his commentary on On Interpretation. The article sets out two possible interpretations of what “indefinitely” means here, and shows that al-Fārābī actually has both conceptions: one applied in his interpretation of Aristotle, and another that he is forced into by the problem of divine foreknowledge. (...) It also explains the relevance of al-Fārābī's remarks as a link between the non-statistical modal theories of Philo and Avicenna. (shrink)

In this paper, I present a formal reconstruction of the classical argument for fatalism set forth by Aristotle in On Interpretation 9. From there, I expose two different formal solutions for avoiding the unwanted conclusion based on the traditional interpretation of Aristotle’s rejection of the Principle of Bivalence: On the one hand, Łukasiewicz's three-valued logic and, on the other hand, supervaluation semantics. I also address some criticisms made against these two proposals. To finish, I remark on some alternative interpretations of (...) Aristotle’s intentions maintaining that the Stagirite philosopher rejected fatalism without abandoning the Principle of Bivalence. (shrink)

I explore the application of the “no-go” theorems of quantum mechanics to the problem of the openness of the future. The notion of fatalism can be made precise if we think of it as a claim that the future has a Boolean property structure. However, if this is correct, then it may be the case that by the “no-go” theorems of quantum mechanics the future must be at least partially open in the precise sense that there cannot be a fact (...) of the matter at a given time about some events at later times. (shrink)

In chapter 9 of De Interpretatione, Aristotle offers a defense of free will against the threat of fatalism. According to the traditional interpretation, Aristotle concedes the validity of the fatalist's arguments and then proceeds to reject the Principle of Bivalence in order to avoid the fatalist's conclusion. Assuming that the traditional interpretation is right on this point, it remains to be seen why Aristotle felt compelled to reject such an intuitive semantic principle rather than challenge the fatalist's inference from truth (...) to necessity. The answer, I contend, lies in Aristotle's theory of truth and truthmakers. (shrink)

This dialogue between Achilles and the Tortoise – in the spirit of those of Carroll and Hofstadter – argues against the idea, identified with the “traditional” interpretation of Aristotle’s “sea battle argument”, that future contingents are an exception to the Principle of Bivalence. It presents examples of correct everyday predictions, without which one would not be able to decide and to act; however, doing this is incompatible with the belief that the content of these predictions lacks a truth-value. The (...) cost of using a non-classical logic to cope with that may be too high for Stagirite’s defenders, and they would still need to explain why our ordinary predictions seem to have a binary truth-value. In the end, the paper suggests that the problem of future contingents – and of free will – is not a logical problem at all, but rather a limit on what an agent can believe before taking a decision. (shrink)

The talk deals with Aristotle’s famous sea-battle problem concerning the truth values of sentences about contingent future events: If an utterance of the sentence “There will be a sea battle tomorrow” is true, then it seems that it is determined that there will be a sea battle tomorrow. For otherwise, how could the utterance be true? If, however, an utterance of the sentence “There will be a sea battle tomorrow” is false, then it seems that it (...) is determined that there will be no sea battle tomorrow. For otherwise, how could the utterance be false? Thus, it seems that it is determined whether there will be a sea battle tomorrow or not – and so for any future event whatsoever. This, however, is in conflict with the assumption that there is such a thing as an open future, i.e., that at least for some future events, it is not determined whether they will take place or not. Some have argued, in light of this problem, that sentences about f uture events are neither true nor false. In this talk, however, it shall be argued that the sea-battle problem can be resolved in an intuitively plausible manner without giving up the principle of bivalence. (shrink)

The hold of the fatalistic reasoning that Aristotle criticizes is dependent, first, on the idea, articulated by Frege, that the real candidates for truth and falsity are something other than particular contingent happenings such as affirmations or thinkings, and, second, on the idea that the demand for speculative reflection overrides any demand for practical deliberation. Standard challenges to the reasoning embody the same presuppositions and so simply perpetuate the core confusions. They do so most fundamentally in the assumption that we (...) need a ‘metaphysical’ grounding for our idea of ourselves as agents who have influence on the course of events. (shrink)

A Schrödinger-like formalism of relativistic quantum theory is presented based on an alternative Lagrangian formalism of relativistic mechanics with the proper time as the evolution parameter. The Schrödinger-like formalism resolves the great difficulties of negative probability density, Klein paradox, and Zitterbewegung. Ehrenfest's theorem is preserved in the Schrödinger-like formalism.

Using Aristotle's well-known sea battle as our example, we offer a precise, intelligible analysis of future contingent assertions in the presence of indeterminism. After explaining our view of the problem, we present a picture of indeterminism in the context of a tree ofbranching histories. There follows a brief description ofthe semantic bases for our double-time-reference theory of future contingents. We then set out our account. Before concluding, we discuss some ramifications of, and alternatives to, a double-time-reference approach to the (...) problem of future contingents. There are some technical ideas at the foundation of our analysis, ideas of which most philosophers are largely ignorant; on our view, in the absence of mastery ofthese ideas it is quite impossible to speak responsibly about either indeterminism or free will. (shrink)

This article investigates a puzzle in the rapidly evolving profession of advertising in post-socialist Hungary: young professionals who came of age during the shift to market-driven practices want to produce advertising that is uncompromised by clients and consumers, and to educate others about western modernity. It is their older colleagues—trained during customer-hostile socialism—who emphasize that good professionals serve their clients’ needs. These unexpected generational positions show that 1) professions are more than groups expanding their jurisdiction. They are fields structured by (...) two conflicting demands: autonomy of expertise and dependence on clients. We can explain the puzzle by noting that actors are positioning themselves on one or the other side based on their trajectory or movement in the field relative to other actors. Old and new groups vie for power in the transforming post-socialist professional field, responding to each other’s claims and vulnerabilities, exploiting the professional field’s contradictory demands on its actors. 2) The struggle is not between those who are oriented to the west and those that are not. Rather, the west is both the means and the stake of the struggle over historical continuity and professional power. Imposing a definition of the west is almost the same as imposing a definition of the profession on the field. In this historical case, “field” appears less as a stable structure based on actors’ equipment with capital, than as dynamic relations moved forward by contestation of the field’s relevant capital. (shrink)

This paper considers traditional debates and position regarding time and the future in relation to Einstein's physics of space-time.

The purpose of the present study is the understanding of Gentili's position on the law of the sea as expressed in his classic De iure belli . The key constitutive elements turn out to be: 1) the idea of the sea as 'res communis' to all mankind, which amounts to the concept of 'freedom of the sea'; 2) 'jurisdiction' of the coastal state on the adjacent sea, even on the high seas, in order to police crime and prevent/punish piracy. As (...) such these two key elements, if taken in isolation, are rooted in the civil law tradition, but their true meaning can only be captured by placing them in the intellectual framework of which they constitute an integral part. Firstly, the epistemic structure of discourse hinges on the new science of natural jurisprudence, as applied to the subject of 'ius gentium bellicum'; secondly, the constituent theoretical languages emanate from a distinctive combination of civil law, scholastic-theological and humanist traditions. This procedure enables us to highlight the strikingly original and distinctly modern traits of Gentili's perspective on the law of the sea, which emerges as a corollary of his project of international/global order. A project that is based on the crucial notion of 'respublica magna' of mankind, a notion encompassing the two notions of 'freedom' and 'jurisdiction' that constitute and define the legal regime of the sea.The Stoic humanist notion of universal human society as 'corpus unum' implies, first of all, 'freedom of intercourse', or 'ius communicationis', to start from 'free passage' and 'freedom of commerce'. It is in the context of his argument about these basic freedoms that Gentili is finally led to discuss the subject of the 'law of the sea'. But, not only the concept of 'res communis', or 'freedom of use', but also the concept of 'jurisdiction', or 'protection', are strictly related to the same foundational concept of 'respublica magna'. This is a crucial characteristic of Gentili's approach to world order that is proved by reference to two cardinal points of his new 'cosmopolitan justice': 1) the 'international right to punish', as exemplified by the legitimacy of the wars of 'humanitarian intervention' and of the wars in support of the 'common law of mankind'; 2) the 'occupation of vacant land', which again underlines the relevance of the principle of 'jurisdiction' by striking a balance between the principle of 'free use' of nature and the 'jurisdiction' of the local ruler.Such a reconstruction definitely rejects the traditional image of Gentili as a supporter of 'maritime protectionism', on the ground of his Advocatio Hispanica published posthumously in 1613 and containing his pleadings as Spanish advocate before the Court of Admiralty. The guiding assumption here is that the book is strictly of a forensic character and as such devoid of any coherent theoretical substance. To the contrary, in his De iure belli, far from anticipating the English position in favour of 'mare clausum', Gentili tends to anticipate the essentials of Grotius' position, especially at the level of the ethic of the 'modern cosmopolis' and the related theme of colonial empire. On this very plane of discourse, Gentili's thinking transcends the so-called battle of the books and emerges as especially significant in illuminating the wider and deeper intellectual currents that contributed to the development of what were to become basic standard positions of modern international theory. (shrink)

Leadership praxis, development and succession can become a bloody battlefield in Africa, mainly because of economic, cultural, theological and political factors. Just like some secular leaders who fail to serve their mandate paradoxically fight for further conquest and retention of power at all costs, certain spiritual leaders miscarry Christian leadership, struggle to deliver their missionary service and tragically battle to stay in power, instead of passing the baton. Church leadership ought to be successional, transformational and intergenerational enough to disciple (...) and develop leaders to sustain and promote other-centred missio Dei and missio Ecclesiae. Yet, the majority of Pentecostal church founders and leaders are neo-patrimonial, authoritarian and serving themselves at the expense of God’s mission. That way, they deface the missionary identity of the Church. Engaging with available literature and observing multifarious leadership trends in Africa, this article unravels problematic Christian leadership development and succession in view of Jesus Christ’s servant leadership model. It disconnects self-centred incumbents and connects the few who are Christ-like with tomorrow’s leaders. Contribution: This article advances Christian leadership development and succession in view of Jesus Christ’s intergenerational servant leadership model. (shrink)

In the course of the military operations at Pylos three major actions were fought. The first was the series of attacks by land and sea launched by the Peloponnesians against the forces under Demosthenes occupying the peninsulaof Pylos ; the second was the naval battle in the harbour ; the third was the Athenian assault on the Spartans cut off on Sphacteria. The second of these actions does not appear to have had less influenceon the development of the situation (...) or to have been militarily less interestingand instructive than the other two. The account of it by Thucydides is, however, less detailed than his accounts of the first and third major actions andmay be thought to be lacking in the clarity which is normally a conspicuousfeature of his battle narratives. (shrink)

The arrival of coronavirus disease 2019 in South Africa was responded to by a lockdown, which barred people from moving out of their homes unless for serious and stipulated reasons by government. Amongst other things, one of the most remarkable repercussions of the lockdown was the closing of the educational system. The call to reopen the public schools by the Minister of Basic Education after almost 2 months brought contestations from different sects of life, for instance, labour unions, parents and (...) School Governing Body representatives. Mistrust and suspicions developed amongst parents, SGB's unions and the Department of Basic Education as a result. This has seen certain political parties and unions lodging court cases against the reopening decision. This was likely to be a protracted battle as the issue is between life and education. The aim of this research is to discover if these contestations are for the good of the school children or if there is another underlying issue.CONTRIBUTION: This article unveils the different contestations which are important for the South Africans regarding the shaping of the future through educational weapon. The contestations help open our eyes and make awareness as to where our democracy has done well and where it is still lacking. (shrink)

“Je doute qu'il y ait un dialogue de la chenille et du papillon”A. MatrauxThe most ordinary events astonish only those who think about them. What can be more natural than two people talking? They are from the same country, they speak the same language, they understand one another. They have things to say to each other and they say them. Anyone who would try to question such evident truisms would be seen as attempting to be a spinner of paradoxes. And (...) yet…First of all is it as natural as it appears that two people should stop and speak? To an impartial observer of the behavior of one's peers this would not seem to be the case. Most of the people we rub elbows with daily—in the street, in the subway, on a beach, in a hotel or even in the apartment building where we have lived for ten years—are people whom we do not accost and to whom we never speak. In order for people to speak to one another, certain circumstances must exist; there must be a ritual of introduction and a mutual consent that often occurs only after a certain resistance has been overcome. There are important differences to be observed in this respect among different peoples and, within the same nation, among people of different classes. But in every case dialogue is preceded by a preparatory phase of prudent observation, reserve and mistrust during which the partners size one another up and seek to situate themselves in relation to each other. (shrink)

This article investigates the figurative role of water in martial similes, metaphors, and personifications in the Iliad. Such imagery, it is argued, is generally informed by a thematic association of Greeks and their camp with the sea, and Trojans and their territory with rivers; as heroes sound and move like waves and streams, bodies of water become sympathetically animated warriors, and gods of sea and river rush into battle. The conclusion is that an ancient antithesis between saltwater and freshwater (...) lends the Iliad a sense of unity in setting and plot and endows heroic action with greater cosmic and theological significance. (shrink)

Verificationism is the doctrine stating that all truths are knowable. Fitch’s knowability paradox, however, demonstrates that the verificationist claim (all truths are knowable) leads to “epistemic collapse”, i.e., everything which is true is (actually) known. The aim of this article is to investigate whether or not verificationism can be saved from the effects of Fitch’s paradox. First, I will examine different strategies used to resolve Fitch’s paradox, such as Edgington’s and Kvanvig’s modal strategy, Dummett’s and Tennant’s restriction (...) strategy, Beall’s paraconsistent strategy, and Williamson’s intuitionistic strategy. After considering these strategies I will propose a solution that remains within the scope of classical logic. This solution is based on the introduction of a truth operator. Though this solution avoids the shortcomings of the non-standard (intuitionistic) solution, it has its own problems. Truth, on this approach, is not closed under the rule of conjunction-introduction. I will conclude that verificationism is defensible, though only at a rather great expense. (shrink)

Memphis Elvis is cool; Vegas Elvis is cheesy. How come? To call something cheesy is, ostensibly, to disparage it, and yet cheesy acts are some of the most popular in popular culture today. How is this possible? The concepts of cheese, cheesy, and cheesiness play an important and increasingly ubiquitous role in popular culture today. I offer an analysis of these concepts, distinguishing them from nearby concepts like kitchy and campy. Along the way I draw attention to the important roles (...) of cultural/historical context, background knowledge, and especially artist’s intentions as they are relevant to aesthetic assessments involving cheese and related concepts. I go on to contend that these concepts, properly understood, serve as helpful test cases concerning some important issues in contemporary aesthetics, such as the paradox of negative art and the contentious debate between intentionalists and anti-intentionalists. (shrink)

Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to (...) the complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

Regarding the famous Sea Battle Argument, which Aristotle presents in De Interpretatione 9, there has never been a general agreement not only about its correctness but also, and mainly, about what the argument really is. According to the most natural reading of the chapter, the argument appeals to a temporal concept of truth and concludes that not every statement is always either true or false. However, many of Aristotle’s followers and commentators have not adopted this reading. I believe that (...) it has faced so much resistance for reasons of hermeneutic charity: denying the law of universal bivalence seems to be overly disruptive to logical orthodoxy – the kind of logical orthodoxy represented by what we now call classical propositional logic, much of which Aristotle clearly supports in many texts. I intend to show that the logical-semantic theses that the traditional reading finds in De Interpretatione 9 are much more conservative than they may seem to be at first glance. First, I will show that they complement, and do not contradict in any way, the orthodox definitions of the concepts of truth and statement that Aristotle advances in other texts. Second, by resorting in an anachronistic vein to concepts and methods peculiar to contemporary logic, I will show that a trivalent modal semantics conforming to those theses can be built for a standard formal language of the classical propositional calculus. It is remarkable that reasonable concepts of logical truth and logical consequence that may be defined on the basis of this trivalent modal semantics are coextensive with their orthodox counterparts, the concepts of tautology and tautological consequence of classical bivalent and extensional semantics. (shrink)

In this paper, I start by describing and examining the main results about the option of formalizing the Yablo Paradox in arithmetic. As it is known, although it is natural to assume that there is a right representation of that paradox in first order arithmetic, there are some technical results that give rise to doubts about this possibility. Then, I present some arguments that have challenged that Yablo’s construction is non-circular. Just like that, Priest (1997) has argued that (...) such formalization shows that Yablo’s Paradox involves implicit circularity. In the same direction, Beall (2001) has introduced epistemic factors in this discussion. Even more, Priest has also argued that the introduction of infinitary reasoning would be of little help. Finally, one could reject definitions of circularity in term of fixed-point adopting non-well-founded set theory. Then, one could hold that the Yablo paradox and the Liar paradox share the same non-well-founded structure. So, if the latter is circular, the first is too. In all such cases, I survey Cook’s approach (2006, forthcoming) on those arguments for the charge of circularity. In the end, I present my position and summarize the discussion involved in this volume. En este artículo, describo y examino los principales resultados vinculados a la formalización de la paradoja de Yablo en la aritmética. Aunque es natural suponer que hay una representación correcta de la paradoja en la aritmética de primer orden, hay algunos resultados técnicos que hacen surgir dudas acerca de esta posibilidad. Más aún, presento algunos argumentos que han cuestionado que la construcción de Yablo no sea circular. Así, Priest (1997) ha argumentado que la formalización de la paradoja de Yablo en la aritmética de primer orden muestra que la misma involucra implícitamente circularidad. En la misma dirección, Beall (2001) ha introducido factores epistémicos en esta discusión. Más aún, Priest ha también argumentado que la introducción de razonamiento infinitario como complemento de la formalización en la aritmética sería de poca ayuda. Finalmente, se podría rechazar todo intento de dar definiciones de circularidad en términos de puntos fijos adoptando teoría de conjuntos infundados. Entonces, se podría sostener que la paradoja de Yablo y la del mentiroso comparten la misma estructura infundada. Por eso, si la última es circular, también lo es la primera. En todos los casos, presento el enfoque de Roy Cook (2006, en prensa) sobre estos argumentos que atribuyen circularidad a la construcción de Yablo. En el final, presento mi posición y un breve resumen de la discusión involucrada en este volumen. (shrink)

Redefining god -- The battle between grace and truth -- Qualifying the unqualified -- Breaking cultural rules -- Rejected to redeemed -- Who wants the oil? -- Sweet vindication -- Falling forward -- Pushing boundaries -- The power of again -- The now and the next -- A clean slate.

This paper examines issues of ontology and methodology in behavioral economics: the attempt to increase the explanatory and predictive power of economic theory by providing it with more psychologically plausible foundations. Of special interest is the epistemological status of neoclassical economic theory within behavioral economics, the runaway success story of contemporary economics. Behavioral economists aspire to replace the fundamental assumptions of orthodox, neoclassical economic theory. Yet, behavioral economists have gone out of their way to praise those very assumptions. Matthew Rabin, (...) for example, writes that behavioral economics “is not only built on the premise that [orthodox] economic methods are great, but also that most mainstream economic assumptions are great.” These apparently contradictory attitudes toward neoclassical theory raises the question of what, exactly, its epistemological status within behavioral economics is. This paper argues that the paradox can be resolved, and the question answered, by thinking of the epistemological status of neoclassical theory within behavioral economics in terms of Max Weber’s ideal types: analytical constructs that are not intended to be descriptively true of anything but which nevertheless can be used for a variety of theoretical purposes. The analysis is consistent with many of the insights from the philosophical literature on models in science and has important implications for the practice of economics—behavioral and neoclassical—as well as for the very nature of rationality. (shrink)