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)

Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of (...) the intermediate truth-value so as to reconstruct Łukasiewicz’s three-valued logic as a kind of extensional modal logic based on partial logic. (shrink)

The problem of future contingents is regarded as an important philosophical problem in connection with determinism and it should be treated by tense logic. Prior’s early work focused on the problem, and later Prior studied branching-time tense logic which was invented by Kripke. However, Prior’s idea to use three-valued logic for the problem seems to be still alive. In this paper, we consider partial and paraconsistent approaches to the problem of future contingents. These (...) approaches theoretically meet Aristotle’s interpretation of future contingents. (shrink)

In Walter Chatton on Future Contingents, Jon Bornholdt presents the first full-length translation, commentary, and analysis of the various attempts by Chatton (14th century C.E.) to solve the ancient problem of the status and significance of statements about the future. At issue is the danger of so-called logical determinism: if it is true now that a human will perform a given action tomorrow, is that human truly free to perform or refrain from performing that action? Bornholdt shows (...) that Chatton constructed an original (though problematic) formal analysis that enabled him to canvass various approaches to the problem at different stages of his career, at all times showing an unusual sensitivity to the tension between formalist and metaphysical types of solution. (shrink)

Avicenna’s discussion of future contingent propositions is sometimes considered to entail metaphysical indeterminism. In this paper, I argue that his logical analysis of future contingent statements is best understood in terms of the epistemic modality of those statements, which has no consequences for modal metaphysics. This interpretation is corroborated by hitherto neglected material concerning the question of God’s knowledge of particulars. In the Taʿlīqāt, Avicenna argues that God knows particulars by knowing their complete causes, and when contrasted with (...) the human knowledge of particulars, this epistemically superior access shows that the contingency of statements about future particulars is not due to the modal properties of real particulars but to the nature of human access to them. (shrink)

This paper deals with the problem of future contingents, and focuses on two classical logical principles, excluded middle and bivalence. One may think that different attitudes are to be adopted towards these two principles in order to solve the problem. According to what seems to be a widely held hypothesis, excluded middle must be accepted while bivalence must be rejected. The paper goes against that line of thought. In the first place, it shows how the rejection of bivalence (...) leads to implausible consequences if excluded middle is accepted. In the second place, it addresses the question of why one should reject bivalence, and finds no satisfactory answer. /// Este artículo trata el problema de los futuros contingentes, y se enfoca en dos principios lógicos clásicos: el tercero excluido y la bivalencia. Se podría pensar que una solución del problema requiere actitudes diferentes hacia estos dos principios. Según una hipótesis que parece ampliamente compartida, el tercero excluido debe ser aceptado, mientras que la bivalencia debe ser rechazada. Este artículo argumenta en contra de esta línea de pensamiento. En primer lugar, se aborda cómo el rechazo de la bivalencia lleva a consecuencias poco plausibles si el tercero excluido es aceptado. En segundo lugar, se enfrenta la cuestión de por qué se debería rechazar la bivalencia, sin encontrar una respuesta satisfactoria. (shrink)

Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of (...) class='Hi'>future contingents. (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)

It is shown how the temporal-modal system of events TM (axiomatized in Appendix) allows for the avoidance of the logical determinism without the rejection of the principle of bivalence. The point is that the temporal and the modal parts of TM are so inter-related that modalities are in-the-real-world-inherent modalities independently of whether they concern actual or only possible events. Though formulated in a tenseless language, whose interpretation does not require the assumption of tense facts at the basic level of reality, (...) TM implies an objective, observer-independent difference between tenses based only on the way in which modalities are distributed along the time continuum. The conclusion is that the arrow of time is an intra-model characteristic of any model of TM that describes the non-deterministic real world up to a certain point of its history, while the flow of time is an inter-model characteristic of the continuous transition between these models. (shrink)

In this paper, we have analyzed a number of solutions to the antinomy between divine foreknowledge and human freedom. If we assume that God is temporal, then a sort of backwards causation of past divine beliefs by future human acts must be acknowledged. Since this solution runs into difficulties, we consider the prospects of the view according to which God is outside time. A timeless and omniscient God seems to imply a B-theory of time and, at least at first (...) glance, seems to jeopardize human freedom. Therefore, we have examined what happens when a non-standard A-theory of time like Fragmentalism is assumed. We demonstrate that in this case the prospects of a timeless view of God are much better: both human freedom and divine knowledge of the results of human choices are preserved if this metaphysics of time is adopted. The costs of this solution are, however, very high. From the logical point of view, it rejects bivalence; from the metaphysical point of view, the world is regarded as fragmentary and incoherent. However, if one is ready to accept these costs, this solution is one of the most successful in the search for a solution to the centuries-old problem of the conciliation between divine foreknowledge and human freedom. (shrink)

This work presents an overview of four different approaches to the problem of future contingency and determinism in temporal logics. All of them are bivalent, viz. they share the assumption that propositions concerning future contingent facts have a determinate truth-value. We introduce Ockhamism, Peirceanism, Actualism and T x W semantics, the four most relevant bivalent alternatives in this area, and compare them from the point of view of their expressiveness and their underlying metaphysics of time.

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 (...) concerning future contingency. But I maintain that, ironically enough, the strategy is less happily applied in this case, where a version of the Field–Williamson argument succeeds. (shrink)

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 (...) concerning future contingency. But I maintain that, ironically enough, the strategy is less happily applied in this case, where a version of the Field–Williamson argument succeeds. (shrink)

In his philosophy, William of Ockham (1285-1347) offered an important and detailed response to the classical argument from the truth of a statement regarding the future to the necessity (unpreventability) of the statement. In this paper, Ockham’s solution and the possible formalisation of it are discussed in terms of modern tense and modal logic. In particular, the famous branching time formalisation suggested by A.N. Prior (1914-19) is discussed. Weaknesses and problems with this suggestion are pointed out, and an (...) alternative formalisation of Ockham’s solution without the use of branching time is presented. (shrink)

ARISTOTLE’S chapter-long digression in the Peri Hermenias to remark a restriction of the law of the excluded middle has touched off reams of commentary, logical, metaphysical and theological. For the theologian, God’s omniscience and human freedom were each at stake; for the metaphysician, the status of time; and logicians professed to find here an application for their remote exercises in trivalent logics. But whatever be the concern of the commentator, a glance at any one of them is likely to discourage (...) a student from pursuing a question which seems destined only to further entangle itself. (shrink)

In The Consolation of Philosophy Boethius addresses two main problems posed by the problem of future contingents that shed important light on his conception of necessity and possibility: (1) a logical problem that alleges that if propositions about the future are true now then they are necessarily true, and (2) a theological problem that centers on a supposed incompatibility between divine foreknowledge and a contingent future. In contrast to established readings of the Consolation, I argue that (...) a proper understanding of Book V requires understanding the modal concepts employed there in atemporal terms. This interpretation requires revising our traditional understanding of the two problems present in the Consolation text, particularly in seeing how timeless knowledge or truth could be conceived as a threat to human freedom. It also stresses the importance of a strategy used by Boethius to disambiguate the scope of modal operators used in his opponent’s arguments and how that strategy unifies his discussion in Book V. (shrink)

This work presents an overview of four different approaches to the problem of future contingency and determinism in temporal logics. All of them are bivalent, viz. they share the assumption that propositions concerning future contingent facts have a determinate truth-value. We introduce Ockhamism, Peirceanism, Actualism and T × W semantics, the four most relevant bivalent alternatives in this area, and compare them from the point of view of their expressiveness and their underlying metaphysics of time.

In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian (...) diagrams can play in organizing and clarifying the debate. After providing a brief survey of the specific ways in which Boyd and Hess make use of Aristotelian relations and diagrams in the debate on the nature of the future, I argue that the position of open theism is best represented by means of a hexagon of opposition. Next, I show that on the classical theist account, this hexagon of opposition ‘collapses’ into a single pair of contradictory statements. This collapse from a hexagon into a pair has several aspects, which can all be seen as different manifestations of a single underlying change. (shrink)

INTRODUCTION OCKHAM'S LIFE AND THE DATE OF THE TREATISE William Ockham, a highly influential philosopher of the fourteenth century and one of the most ...

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this “abundance of the future” is a (...) non-adjunctive paraconsistent formalism based on subvaluations, which has the virtue that all classical laws are valid in it, while no formula like φ ∧ ¬φ is satisfiable (though both φ and ¬φ may be true in a model); (2) The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; (3) abundance preserves some important features of classical logic (not preserved in supervaluationism) when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum. (shrink)

Richard Kilvington (ca. 1302-1361) was one of the most original and influential thinkers among the Oxford Calculators. His impact on late medieval philosophy and theology remains unquestionable. His physical, logical, and ethical solutions were extensively debated and referred to, paving the way for new approaches in philosophy and theology. This volume presents a critical edition of question 4 from Kilvington's Quaestiones super libros Sententiarum, complete with an introduction to the edition and a guide to Kilvington's theological concepts.

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)

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that the logic resulting from this “abundance of the future” is a non-adjunctive (...) paraconsistent formalism based on subvaluations, which has the virtue that all classical laws are valid in it, while no formula like φ ∧ ¬φ is satisfiable ; The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; abundance preserves some important features of classical logic when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum. (shrink)

This paper presents two systems of temporal logic, \Lambda_{CPT} and \Lambda_{CPT@}, with ceteris paribus modalities. The principal aim is to show how this approach can be useful to give an ockhamist solution to the future contingents problem along the same lines of A. Prior. The interest of this work lies also in the fact that \Lambda_{CPT@} represents an alternative modal account of supervaluationist and post-semantics approaches to temporal reasoning.

One concern bothering ancient and medieval philosophers is the logical worry discussed in Aristotle's De Interpretatione 9, that if future contingent propositions are true, then they are settled in a way that is incompatible with freedom. Another is if we grant God foreknowledge of future contingent events then God's foreknowledge will determine those events in a way precluding freedom. ;I begin by discussing the standard compatibilist solution to these problems as represented in Boethius's Consolation of Philosophy and then (...) examine theories that allegedly deviate from the Boethian solution. Boethius's solution to these separate problems involves showing that both problems operate on an ambiguity in the scope of the modal operator 'necessarily' present in the articulation of the problem. Once the ambiguity is removed we see that both disambiguations fail to offer a sound argument against the compatibility of free action with either God's omniscience or future contingent proposition's being true. The only difference between the solutions is that before executing the scope distinction strategy in the theological problem, Boethius reminds us that God knows future contingents rather than foreknowing them, since God is timeless. ;The rest of my discussion examines positions that allegedly deviate from the Boethian solution: positions held by Peter de Rivo, William Ockham and Plotinus. I argue that Ockham doesn't in fact deviate from the Boethian solution to the theological problem as is commonly held. Instead of offering a compatibilist position where God's omniscience includes foreknowledge, Ockham denies that God foreknows the future advocating instead a more sophisticated Boethian position. The other two philosophers, Rivo and Plotinus, deviate from Boethius, but unfortunately neither position appears philosophically plausible. Rivo's incompatibilist solution to the logical problem is inconsistent with his retention of the Boethian solution to the theological problem and is probably implausible on its own. Plotinus's compatibilist account fails not because it claims that necessity and freedom are compatible, but because the account of moral responsibility Plotinus offers to justify the compatibility fails. (shrink)

The doctrine of inerrant divine “middle knowledge” of future contingent events, first developed by the sixteenth century Jesuit theologian Luis de Molina, has resurfaced as a prominent position within contemporary debates over divine foreknowledge, creaturely freedom, and the ontological status of possibilities. As yet, the only substantive response to the new Molinism from a process perspective has come in a brief section on “Hartshorne and the Challenge of Molinism,” in an essay on Hartshorne’s view of “The Logic of (...) Future Contingents” by George W. Shields and Donald W. Viney, in Shields’ edited anthology Process and Analysis.Shields and Viney offer an insightful critique of Molinism. However, their use of Hartshorne’s understanding of possibility presents problems for those, like me, who prefer Whitehead’s more robustly realist notion of eternal objects. Here, I defend Whitehead’s Platonism from the main lines of criticism leveled against itby Hartshorne, while demonstrating that a “thick” conception of the objective content of the possible within the context of the divine understanding need not crossover into a deterministic conception of God’s foreknowledge, à la Molina. (shrink)

For reasons that have more to do with the historiographical traditions of modern Jewish history and the history of critical thought than history itself, Georg Simmel – of Jewish descent – is rarely discussed within the frame of modern Jewish history. Bringing the two together as a theoretical contribution to Simmel studies and modern Jewish history alike, this article explores Simmel’s logic of contingency in the context of modern Jewish history. Which forms and types could Jews realistically seek to (...) fulfill from the perspective of Simmel’s thought? Which could they hope to escape and what could they expect from the future? The author suggests that in answering these questions we disclose a peculiar notion of ‘bounded contingency’ embedded in Simmel’s positing of a non-binary, ‘gray area’ between the necessary and the impossible. This hypothesis is tested in several distinct contexts: a letter on Zionism from around 1900; an odd passage on love in the excursus on ‘The Stranger’ ; and a letter on individuals of Jewish background in German academia. Simmel’s coherency lies in the ‘realist’ approach he adopts to reality as the domain of the contingently possible. When applied to Jewish history in general and Zionism in particular, this notion not only explains why Zionism is unfeasible but also demystifies its emergence as an attempt to escape the status of stranger in Europe. It also evinces why this Jewish national enterprise inevitably carried within it the seeds of the problem it sought to solve. (shrink)

We propose a logic of temporal contingency, which has operators of past and future contingency as primitive modalities. This logic is less expressive than standard temporal logic over the class of bidirectional frames, and cannot define some basic frame properties such as bidirectionality and transitivity. We present a minimal system based on two key ‘bridge axioms’ and a bimodal version of a so-called ‘almost definability’ schema in the literature. The completeness proof is highly nontrivial due to (...) the requirement that the canonical model be bidirectional. We then extend the results to the simplest dynamic case: public announcements. (shrink)

This work concerns the use of operators for past and future contingency in Priorean temporal logic. We will develop a system named C_t, whose language includes a propositional constant and prove that (I) C_t is complete with respect to a certain class of general frames and (II) the usual operators for past and future necessity are definable in such system. Furthermore, we will introduce the extension C_t(lin) that can be interpreted on linear and transitive general frames. The (...) theoretical result of the current work is that contingency can be treated as a primitive notion in reasoning about temporal modalities. (shrink)

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 (...) incitam, com e contra Aristóteles, ao desenvolvimento de uma lógica temporal e plurivalente, ao modo de J. Łukasiewicz ou A. Prior. Esta lógica garante a abertura do futuro sem o oneroso custo metafísico da adesão a uma teo-lógica omni-determinante. A crítica do determinismo lógico, daí resultante, afigura-se mais coadunável com as condições pós-metafísicas ine­rentes à episteme agnóstica contemporânea, mas, nesse caso, a abertura do futuro impli­caria uma profunda redefinição das próprias ideias e funções de “Deus”, “matéria”, “história” e “verdade”. (shrink)

In De interpretatione 9, Aristotle argues against the fatalist view that if statements about future contingent singular events (e.g. ‘There will be a sea battle tomorrow,’ ‘There will not be a sea battle tomorrow’) are already true or false, then the events to which those statements refer will necessarily occur or necessarily not occur. Scholars have generally held that, to refute this argument, Aristotle allows that future contingent statements are exempt from either the principle of bivalence, or the (...) law of excluded middle. This paper offers a new interpretation of Aristotle’s refutation of fatalism. According to this interpretation, each member of a pair of contradictory future contingent statements, in virtue of expressing modal necessity, is simply false. (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)