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)

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)

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

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)

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)

My dissertation deals with the Master Argument of Diodorus Cronus, a contemporary of Aristotle's. The argument was one of the most famous pieces of temporal and modal reasoning in ancient philosophy. It purports to prove that a proposition is possible if and only if it is true or will be true. The argument runs as follows: Everything that is past and true is necessary; The impossible does not follow the possible; Therefore, nothing is possible which (...) neither is nor will be true. Unfortunately, all accounts of the Master that have survived are so sketchy that we cannot determine whether the argument is valid or not. ;Several reconstructions of Diodorus' argument have been proposed. The purpose of the reconstructions is to show, using the resources of modal and tense logics, that the argument is valid. I analyze and critique most of these proposals, arguing in the final chapter for a new reconstruction which I believe to be more defensible than existing ones. ;The Master Argument is important for several reasons. It elicited much discussion among ancient philosophers and logicians both because of its reduction of modal logic to tense logic and its bearing on the free will/determinism debate. But, its influence also extends to contemporary philosophy and logic. In the 1950s and 60s, the Master inspired formal work on Diodorean systems. Much of the work on the calculus of tenses, e.g., by Prior, was undertaken in view of investigating Diodorus' argument. Finally, the literature that the argument has spawned has enriched and deepened our understanding of the connections between matters modal and temporal. (shrink)

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)

This book is an English version of a book published in 1984 in French, the aim of which was to give a reconstruction of Diodorus Cronus's Master Argument, together with a historical analysis of some of the central modal notions on which it draws. In preparing the English text, Vuillemin has made some changes to the logic of his reconstruction of Diodorus's Argument and added an epilogue. The Master Argument consisted of three premises: Every (...) past truth is necessary, The impossible does not follow from the possible, and Something is possible which neither is nor will be true. Diodorus claimed that these premises are inconsistent, and purported to derive the negation of the third premise, which is plausibly to be identified with the principle of plenitude, from the first two premises. (shrink)

Almost all the chapters of this book have appeared earlier as separate articles in American and Finnish journals between 1957 and 1971, but are now reprinted together as dealing with Aristotle’s theory of modal notions and its underlying doctrines and assumptions. Recital of the chapter headings illustrates the scope of the book: "Aristotle and the Ambiguity of Ambiguity" ; "Aristotle’s Different Possibilities" ; "On the Interpretation of De Interpretatione 12-13" ; "Time, Truth and Knowledge in Aristotle and Other Greek Philosophers" (...) ; "Aristotle on the Realization of Possibilities in Time" ; "Aristotelian Infinity" ; "On Aristotle’s Modal Syllogistic" ; "The Once and Future Sea Fight: Aristotle’s Discussion of Future Contingents in De Interpretatione 9" ; and "Aristotle and the ‘Master Argument’ of Diodorus". The volume ends with "Index of Texts" cited from Aristotle and other Greek authors and "General Index". (shrink)

The master argument posits a metaphysical thesis: Diodorus does away with Aristotle’s dunamis understood as a power simultaneously oriented toward being and non-being and proclaims that possibilities that fail to actualize are simply nothing. My contention is that this claim is not a mere application of Diodorus’ contribution to modal logic. Rather, Diodorus creates an ontologico-temporal concept of possibility and impossibility. Diodorus envisions the future as the past that the future will become. Since what will have been can (...) never be the accomplishment of a possibility that did not obtain, and since the future is destined to become past, any futural possibility that doesn’t actualize is neither futural nor even possible. (shrink)

A revised version of the author’s Göttingen doctoral dissertation, this book is as much an independent essay in modal logic as it is an interpretation of Aristotle’s modal syllogistic. In chapter 1 the author develops what he calls a "rich framework" including speech-act operators as well as epistemic and alethic modal operators, all expressed in a notation of his own devising; for example, "Pc if ENj Pc RNc S, Rc ENj Pa Rp S" translates as "The speaker claims that if (...) he is not justified in claiming that it is not certain that S, it is certain that he is not justified in allowing that it is possible that S." A dual system of quantification is then introduced, with and without existential import for both universal and particular propositions. In chapters 2 and 3 the author uses his framework as a model for discussing various difficulties in Aristotle’s assertoric and modal logic, insisting that his results are relevant to Aristotle’s even when they do not "correspond" to them. An appendix takes up the famous sea-battle of De interpretatione 9. The author is at his best when examining particular problems in Aristotle’s logic; in this regard his criticism of the operation of conversion stands out as especially effective. He is at his worst when pursuing the "intrinsic interest" of his model above and beyond its usefulness in studying Aristotle and when making unwarranted claims of originality for his objectives. One such objective is to stress what he calls the "teleological" character of Aristotle’s logic, a character which he says "is lost sight of in modern accounts" of Aristotle’s work. He appears to be unaware of Ernst Kapp’s classic Greek Foundations of Traditional Logic, which repeatedly calls attention to just this character. The author acknowledges the existence of twentieth century modal logic only once, in a one page criticism of Prior’s defense of the distinction between de dicto and de re modalities. This occurs within a curious argument, based on a premise taken from Ammonius and Abelard, that the concept of logical necessity is "bogus."—J.D. (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)

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)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Aristotle’s “De Interpretatione”: Contradiction and Dialectic by C. W. A. WhitakerEugene GarverC. W. A. Whitaker, Aristotle’s “De Interpretatione”: Contradiction and Dialectic. Oxford: Clarendon Press, 1996. Pp. x + 235. Cloth, $60.00.Traditionally, the De Interpretatione is placed in the Organon between the Categories and the Prior Analytics. Where the Categories is about single terms and the Analytics about inferences, the De Interpretatione is about propositions. That traditional view is (...) presupposed by most contemporary studies of the work, which “concentrate on a small number of passages, which have been treated as isolated oases of philosophical interest in an otherwise barren work,” highlights which include “Aristotle’s semantic theory of philosophy of language” in the first chapter, the first four “linguistic chapters,” and chapter 9 on the Sea Battle (1). I suppose that the square of opposition could be added to Whitaker’s list.Whitaker, in this republication of a doctoral dissertation, wants to challenge both the traditional view and the contemporary concentration by instead studying the work as a coherent whole, whose subject, it turns out, is not propositions after all but “contradictory pairs, which are central to the working of dialectic” (2). The book then proceeds through the De Interpretatione, chapter by chapter. If he succeeds, the De Interpretatione will henceforth be read as preparation for the Topics, rather than for the Analytics. There are also three appendices examining the use of such contradictory pairs in Metaphysics IV, the Topics, and the Posterior Analytics.Thus, the first five chapters of the De Interpretatione explain the nature of assertions, name and verb, and “before that, how language is related to thought and to the real world, and how it is that utterances can make claims about things which are true or false” (8). Where names, verbs, and propositions are part of our ordinary understanding of language, contradictory pairs are not, but are a philosophical understanding of a linguistic structure that has a specifically philosophical, dialectical, purpose. The rest of the De Interpretatione, from chapter 6 on, is the examination of contradiction. Chapters 7–9 classify contradictory pairs by different criteria. Each of these chapters isolates an exception to “the rule that, in every contradictory pair, one member is true and the other false” (79). Chapter 7 looks at the first exception to the rule, “non-universal statements about universals” (91). Whitaker’s project looks good here, since he then shows the dialectical uses of such propositions, and denies their value for the deductive logic of the Analytics. Similarly, in Chapter 8 Aristotle looks at “apparently simple assertions... which are not single” (105), which also have important uses in dialectic. Finally, chapter 9 looks at the third exception to the rule, future singular assertions. One payoff of this book is to place the sea battle discussion in its Aristotelian context. [End Page 459] Whitaker says that most discussions of the sea battle assume that what is at stake is what he calls the “Principle of Bivalence” in which every assertion is either true or false. He instead insists that it is contradictory pairs, not single assertions, that are being tested by future contingents. He thus concludes: “Dialectic is a universal discipline, and its questioning can cover any subject where a question can be posed which has a right and a wrong answer. Chapters 7 to 9... demonstrate that there are limits to the universality of dialectic” (128).Whitaker follows the De Interpretatione chapter by chapter in the remainder of the book. He shows how the later chapters assist the dialectician in “sorting assertions into contradictory pairs” (181). And just as De Interpretatione begins with a consideration of the relation of language, thought, and the world, so it ends by showing the connection between contradictory propositions and opposed beliefs.Whitaker rarely strays from the De Interpretatione to show how our understanding of dialectic is improved by attention to this prerequisite. When he does, for example in a very short discussion of the relation of problems and propositions in the Topics, the results are illuminating. I would have liked more. This book should be useful to the growing numbers of scholars interested in Aristotle’s art of dialectic... (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 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)

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)

ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to make (...) clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy. (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)

Chrysippus claims that some propositions perish. including some true conditionals whose consequent is impossible and antecedent is possible, to which he appeals against Diodorus?s Master Argument. On the standard interpretation. perished propositions lack truth values. and these conditionals are true at the same time as their antecedents arc possible and consequents impossible. But perished propositions are false, and Chrysippus?s conditionals are true when their antecedent and consequent arc possible, and false when their antecedent is possible and consequent impossible. (...) The claim of the Master Argument that Chrysippus rejects, then, is stronger ihan usually supposed. (shrink)

The Master Argument, recorded by Epictetus, indicates that Diodorus had deduced a contradiction from the conjoint assertion of three propositions. The Argument, which has to do with necessity and contingency and therefore with freedom, has attracted the attention of logicians above all. There have been many attempts at reconstructing it in logical terms, without excessive worry about historical plausibility and with the foregone conclusion that it was sophistic since it directly imperilled our common sense notion of (...) freedom. This text takes exception to recent tradition, translating the propositions into logical terms. The propositions figuring in The Master Argument are interpreted in terms of temporal modal logic where both the modalities and the statements they govern have chronological indices. This means that the force of the argument comes not from purely logical or modal considerations, but from our experience of time. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:FATALISM AND TRUTH ABOUT THE FUTURE }AMES w. FELT, S.J. Santa Clara University Santa Clara, California WHEN WE SPEAK of future events, does today's ruth mean tomorrow's necessity? The question is as old as Aristotle's sea battle tomorrow. The last ships should have been sunk long ago, but after two thousand years the textual analysis of this passage is still controverted. Yet I think something new can be (...) said about it if we consider afresh the philosophic issues themselves. What philosophic consequences must we accept if we suppose that predictions, that is, propositions referring to future events, are either true or false antecedently to the events themselves? In particular, if a prediction be true now, does its present truth imply a fixity inherent in the future such that fatalism is unavoidable? 1 It has been argued that it does. Aristotle sketched such an argument in the sea battle passage already alluded to:... [If anything] is white now it was true to say earlier that it would be white; so that it was always true to say of anything that has happened that it would be so. But if it was always true to say that it was so, or would be so, it could not not be so, or not be going to be so. But if something cannot not happen it is impossible for it not to happen; and if it is impossible for something not to happen it is necessary for it to happen. Everything that will be, therefore, happens necessarily. So nothing will come about as chance has it or by chance; for if by chance, not of necessity.2 1 Whether it makes any sense to speak of a proposition as true " now " or at any other time will be considered below. 2 De Interpretatione (trans. J. L. Ackrill; Oxford University Press: 1963), ch. 9, 18b9 ff. 209 210 JAMES W. FELT, S.J. If, then, a prediction is true in the present or false in the present, its very truth value today seems to create an ineluctable fixity upon tomorrow's event such that fatalism would be unavoidable. And as is implied in Aristotle's example, it seems natural to suppose that a prediction must, after all, be either true or, if not true, then false. Does not the law of excluded middle demand this? Thus the logic of truth relations seems to impose a fatalistic view of events. Indeed, fatalism is sometimes defined precisely in terms of logic, so that a contemporary author writes : " Fatalism is the thesis that the laws of logic alone suffice to prove that no man has free will, suffice to prove that the only actions which a man can perform are the actions which he does, in fact, perform, and suffice to prove that a man can bring about only those events which do, in fact, occur and can prevent only those events which do not, in fact, occur." 3 I shall, however, argue that ( 1) neither the law of excluded middle nor any other logical consideration requires that predictions be true or else false when they are asserted; (2) the antecedent truth (or falsity) of predictions would not necessitate fatalism by reason of any logical considerations, (3) though it could necessitate fatalism for causal reasons; and (4) predictions are never, absolutely speaking, true or false before the occurrence of the events to which they refer, though they may be true or false in an attenuated, relative sense. Thesis 1: Neither the law of excluded middle nor any other logical consideration requires that a prediction be, prior to the event, true or, if not true, then false. I understand the law of excluded middle (LEM) to mean that, for any meaningful proposition p, it is (logically) necessary that p be true or, if not true, then false. By ordinary usage a proposition referring to a state of affairs in the world, as distinguished from one referring to logical re3 Steven M. Cahn. Fate, Logic, and Time (New Haven: Yale University Press, 1967), p. 8. FATALISM AND TRUTH ABOUT THE FUTURE 211 lationships, is called ' true' if and only if that state of affairs obtains. The... (shrink)

A Master-like argument, in the usage of the present paper, is an argument that employs a reductio ad impossibile principle to transmit the necessity of what are or become past truths to the remainder of time by means of necessary conditionals of some sort. The conclusion of such an argument is some no-unactualized-possibilities principle. This paper argues that the formulation of a Master-like argument by A. N. Prior in a mixed modal temporal propositional logic (...) introduces certain artifacts into the logical analysis of the argument. One of these, a principle of temporal discreteness, is not essential to a Master-like argument. Another, a principle of forwards temporal linearity, is technically essential; but it is usually tacitly presupposed by the necessary temporal conditionals employed to 'tie together' past and future time in less formal accounts of Master-like arguments. (shrink)

My aim is to figure out whether Aristotle’s response to the argument for fatalism in De Interpretatione 9 is successful. By “response” here I mean not simply the reasons he offers to highlight why fatalism does not accord with how we conduct our lives, but also the solution he devises to block the argument he provides for it. Achieving my aim hence demands that I figure out what exactly is the argument for fatalism he voices, what exactly (...) is his solution, whether his solution is coherent, and whether it does indeed succeed. I find that the argument is essentially bivalence plus that the truth of a proposition stating that an event will happen in the future entails that this event will necessarily happen, that Aristotle’s solution is to restrict bivalence when it comes to propositions about contingent future events, that this solution is coherent, and that while it does not rule out the possibility of fatalism, it does succeed in blocking the argument for fatalism offered within chapter 9. (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)

This chapter contains sections titled: The Origins: Parmenides and Zeno Dialectic and the Beginnings of Logical Theory Aristotle and the Theory of Demonstration The Regress Argument of Posterior Analytics I.3 Time and Modality: The Sea‐Battle and the Master Argument Sentential Logic in Aristotle and Afterwards.

Everyman’s Library commemorates its fiftieth anniversary very aptly with this issue as its thousandth volume of a classic text of some 2,300 years of age, which through varying fortunes has been a major influence in European culture. As a transcendental science Metaphysics makes no concession to the semi-curious; Aristotle’s inaugurating textbook is understandably concentrated and obscure. A literal version of this formidable text would have no appeal to the general reader, innocent largely of the Greek idiom and of philosophical jargon, (...) while a personal paraphrase could not carry the authentic voice of a past master. Mr. Warrington simply takes the existing Oxford version, retranslating it into easier, more fluent English and rearranging its fourteen books into a free, logical order. In this he is guided by their matter and by the critico-historical views of Jaeger and Ross, outlined in a short Introduction by Sir David himself. He has added chapter titles, numbered sections, prefixing their main groups with a short summary of contents and has courageously kept clear the main line of Aristotle’s argument by relegating all parentheses to footnotes, to which he adds his own identification of historical references. Radical re-arrangement justifies itself by success—here a forbidding classic is presented with the immediate, systematic clarity of a modern text. (shrink)

In the field of philosophy, Plato's view of rhetoric as a potentially treacherous craft has long overshadowed Aristotle's view, which focuses on rhetoric as an independent discipline that relates in complex ways to dialectic and logic and to ethics and moral psychology. This volume, composed of essays by internationally renowned philosophers and classicists, provides the first extensive examination of Aristotle's Rhetoric and its subject matter in many years. One aim is to locate both Aristotle's treatise and its (...) subject within the more general context of his philosophical treatment of other disciplines, including moral and political theory as well as poetics. The contributors also seek to illuminate the structure of Aristotle's own conception of rhetoric as presented in his treatise. The first section of the book, which deals with the arguments of rhetoric, contains essays by M. F. Burnyeat and Jacques Brunschwig. A section treating the status of the art of rhetoric features pieces by Eckart Schütrumpf, Jürgen Sprute, M. M. McCabe, and Glenn W. Most. Essays by John M. Cooper, Stephen Halliwell, and Jean-Louis Labarrière address topics related to rhetoric, ethics, and politics. The final section, on rhetoric and literary art, comprises essays by Alexander Nehamas and André Laks. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

This light revision of Bornholdt's doctoral thesis (Würzburg, 2015) is effectively a medievally-oriented follow-up to Richard Gaskin’s 'The Sea Battle and the Master Argument' (1995). The book is stimulating from a philosophical point of view, but the exegesis is disappointingly unreliable.

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 dissertation is a study of John Buridan's (c.1300-c.1361) conception of modalities. Modal concepts - concepts of necessity, possibility, impossibility, and contingency - describe the ways in which things could and could not be otherwise. These concepts became notoriously central for philosophical discourse in the late Middle Ages. In recent years, Buridan's philosophy and modal theory have received sophisticated scholarly attention. The main contribution of the dissertation is to show new ways in which Buridan's modal theory is embedded in its (...) contextual practical aims, as providing methods for argumentation schemes and analysis used in his natural philosophy and metaphysics. The dissertation is divided into two parts. In Part I, I conduct a detailed analysis of Buridan's account of varieties of modality in logical contexts. In Chapter 2, I show that Buridan distinguishes between broad and restricted forms of necessity in his treatment of logical consequence. Moreover, I show how the distinction between these forms of necessity underpins his modal syllogistics. I argue in Chapter 3 that Buridan acknowledged a variety of modal concepts that are distinguished as a matter of degree. I identify the main modal concepts Buridan's theory reckons with, show how he motivates the distinctions among them, and clarify how they are logically related. Part II turns to applications of Buridan's modal analyses to natural philosophy. In Chapter 4, I address the relationship between necessity with sempiternal truth in Buridan's commentary on Aristotle's De Caelo and compare Buridan's treatment of a key passage in that commentary with the treatment by John of Jandun (c. 1285-1328), a near-contemporary master of arts at Paris. Chapter 5 focuses on Buridan's account of the relationship between power-based concepts of modality and his modal semantics. Chapter 6 describes Buridan's account of contingency in the Physics, and sets Buridan's account of the relationship between forms of contingency and chance against the background of a received debate between Avicenna's and Averroes' views on the subject. Finally, in Chapter 7, I analyse some important applications of Buridan's distinction between logical and metaphysical possibility in physical contexts. I conclude this section by showing how Buridan considered merely conceivable possibilities useful in natural philosophy, and draw further conclusions for investigating the connections between logic and natural philosophy in the later Middle Ages. (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 well known Master Argument of ancient Stoic logician Diodorus Cronus is an argument in favour of the philosophical doctrine of fatalism. Perhaps in antiquity this argument was a subject of the most celebrated controversy about temporal truth and modality. This argument is a subject of logical analysis, especially in connection with temporal logic, also today. 1 The most elegant tense-logical formulation of the Master Argument has been given by A. N. (...) Prior. Discreteness and irreflexivity of time are semantical assumptions of Prior’s formulation of the argument. The assumption of discreness is troublesome. 2 The problem of this assumption is a subject of M. J. White’s paper “The Necessity of the Past and ModalTense Logic Incompleteness”. 3. (shrink)

The main idea animating the present paper is that the general aim of debates, such as the one involving the notorious case of the Master Argument, is the ponderation of logical principles by confronting them with some set of assertions and other endorsed principles on the meaning explanation of connectives, quantifiers and modality. As suggested by Seel (2017), the point of the specific case of the MA is about examining Aristotle’s notion of possibility – as implemented by (...) the Possibility Principle (i.e., If it is necessary that if A then B, then B is possible if A is) and the Possibility Rule (i.e., If A is possible, and if B follows from the assumption of A, then B is is possible) in the context of a dialectical debate where it has been asserted that a given proposition is possible, even it is neither true now nor it will ever be, and where at the same time the irrevocability of the past has been endorsed. This suggests to study the MA debate in a setting based on Marion’s (2020) reconstruction of Aristotle’s Dialectical Bouts, adapted to propositions affected by modalities. The setting of Dialectical Bouts for the MA proposed includes•Propositions affected by Reichenbach’s (1948, § 5) three-folded temporal reference, namely: the point of speech S, the point of reference R and the point of the event E. This constitutes our take on Vuillemin’s (1977, 1979, 1984, 1996) suggestion of a “double indexation”.•The dialogical meaning explanation for modalities understood as involving hypotheticals. •The dialogical rules that settle the commitments undertaken when endorsing Aristotle’s Possibility Principle. In fact, in relation to the notion of possibility at work in Vuillemin’s (1996) reconstruction we explored different formulations of the Possibility Rule. Still, there remains a dearth of researches confronting the different formulations of the Possibility Rule with the texts studied by Crubellier (2010) and Rosen and Malink (2012). More generally and coming back to my remarks above, one of the most fruitful insights that can be gained from Vuillemin’s writings on the MA, is that such kind of debates provide an instance of a general pattern for reasoning that I shall call Dialectical Bouts of Material Admissibility (BMA). The rationale behind such kind of argumentation-pattern is to examine the incorporation of new (epistemological, ontological or logical) principles against the background of the commitments undertaken by endorsing a specific set of assertions and meaning explanations. They display the kind of abductive procedure stressed by Crubellier’s (2014) study of syllogism. Under this perspective Ebbinghaus’s (1964) casting of the inferential moves that reduce imperfect syllogisms to perfect ones as implementing an admissibility procedure, represents a logical generalization of the material procedures at stake in the Dialectical Bouts of Material Admissibility. Furthermore if, as stressed by Duthil-Novaes (2005) Medieval Obligations represent a development of Aristotelian Bouts aimed at the ludic exercise of consistency maintenance, DMA should be rather linked to the Islamic tradition of dialectical theory [jadal, munāẓara, ādāb al-baḥth], aimed at the epistemological task of what Young (2017) calls the forging of principles, including legal and deontic ones. In a more contemporary setting, DMA can be related to Brandom’s (2000, pp. 66-77) considerations on Non-Conservative Extensions, where the point of dialectical procedures is put under public Socratic scrutiny the discovery and elucidation of concepts. This general point on Dialectical Bouts of Material Admissibility can be seen as underlying Vuillemin’s project of linking the study of the MA with the classification of philosophical systems.The present paper does not contain a fully developed study on such Dialectical Bouts, but it is rather is an invitation to pick up the gauntlet that Jules Vuillemin threw into the ring. (shrink)

Comment: This translation contains a correction of an argument in the original English edition, a correction that was subsequently made in the 1999 English Paperback edition, The correction is described below in the final paragraph. Differences in language can seriously restrict one's access to, and knowledge of, the philosophical work that's being done in other countries, and before the publication in 1997 of my book Time, Tense, and Causation, I was not aware of the depth of interest, in Italy, (...) in analytical philosophy in general, and metaphysics in particular. Since that time, however, I've had the opportunity of talking to, and corresponding with, Italian philosophers who are currently working very intensely on problems in the philosophy of time. I very much enjoyed those discussions, and so I'm very pleased indeed that my book has now been translated into Italian. -/- The introduction to the book will provide readers with quite a detailed overview of my approach to the philosophy of time, and of the main theses that I am defending. But perhaps it will be helpful here if I try to sketch, very briefly, the big picture. -/- The central issue in the philosophy of time concerns the choice between tensed and tenseless accounts of the nature of time – or, as I prefer to express it, between dynamic and static conceptions of reality. According to tensed (or dynamic) accounts, there are significant ontological differences between the past, the present, and the future – either because the world contains intrinsic tensed properties of passiveness, presentness, and futurity, or else because the past, the present, and the future are not all equally real. In contrast, according to tenseless (or static) views of the nature of time, there are no intrinsic tensed properties, and the past, the present, and the future are all equally real. In this book, I defend a dynamic view of time dash specifically, one according to which, while the past and the present are now real, the future is not. This view has, of course, a very long history, with a version of it having been defended by Aristotle in his famous discussion of the sea battle tomorrow, in which he argued that, although it is now true – indeed necessarily so – that either there will be a sea battle tomorrow or there will not be one, it is not now true that there will be a sea battle tomorrow, and not now true that there will not be one. Only when tomorrow comes will the world contain states of affairs that make one of these propositions true, and the other false. -/- But while this general view of the nature of time has a very long and distinguished history – and also seems, intuitively, quite appealing – it has become clear, especially in this century, that it is exposed to very strong objections – objections moreover, that come not merely from philosophy, but also from contemporary physics, and especially from Einstein's special theory of relativity. One of the main challenges accordingly, for any defense of a tensed or dynamic view of time, is to show that those objections can be answered. -/- In grappling with those objections, however, one thing that emerged very clearly was that some theses that defenders of tensed approaches to time have traditionally viewed as absolutely essential must be abandoned as unsound. The result is that. I was led to a view of the nature of time that is, in many respects, intermediate between tenseless views of time and traditional tensed approaches. In particular, advocates of traditional tensed views almost always maintain that the simplest temporal facts are themselves inherently tensed: they consist of facts such as, for example, that is certain apple is now red. But I maintain that, on the contrary, the simplest temporal facts, rather than being intrinsically tensed, are facts to the effect, for example, that a certain apple is now red at time t. On this fundamental issue, then, I agree with those who accept a tenseless or static view of time, since they too hold that the simplest tensed facts ¬– and indeed all tensed facts – are not tensed facts. How, then, does my approach to the nature time differ from a tenseless or static approach? The answer is that I also maintain that, although basic tensed facts are not inherently tensed, the world is nevertheless a dynamic one, since every present moment is a point at which things come into existence. Events, therefore, are not merely actual or nonactual – as is maintained by advocates of tenseless approaches to time. Rather an event is actual as of some time, and not actual as of other times. One needs, therefore, a temporally indexed notion of actuality, according to which an event is not actual until the time at which it occurs, and given that notion, one can explain, in a straightforward fashion, what it is for events to lie in the past, the present, and the future, and in the way that entails that the past and the present are real, but the future is not. -/- One task, as I have said, is to show that the many objections that have been advanced against dynamic conceptions of the world dash by philosophers – such as McTaggart, Quine, Smart, Putnam, and Mellor – can be answered. But even if, as I claim, this can be done, one is still left, of course, with the question of what positive reason there is, if any, for accepting a tensed or dynamic view of the world. -/- The argument that I develop in response to this question centers upon the concept of causation, and here I argue, first, that there are decisive objections to reductionist approaches to causation; secondly, that it is possible to set out a very plausible realistic account of the nature of causation; and, thirdly, that the crucial postulates that are involved in that account can only be satisfied in a dynamic world – indeed only in a dynamic world in which the past and the present are real, but the future is not. -/- This way of defending the view that our world is a dynamic one also has implications for some other issues – in particular, issues connected with the subtle and very difficult metaphysical question of the relation between time and causation. Thus, after setting out the above argument, I attempt to show that if causation can exist only in a dynamic world, then one can both demonstrate that backward causation is logically impossible and defend the view that the direction of time is to be defined in terms of the direction of causation, rather than vice versa. -/- Finally, a comment on the text. It involves one major change from the original English edition – namely in sections 4. 6.2 and 4.7. The change in those sections involves the crucial part in my argument both for the claim that our world is one where the past and present are real, but the future is not, and for the claim that backward causation is logically impossible. It was pointed out to me by Kenji Murota, a graduate student of philosophy at Keio University, that there was a problem in my original formulation of that argument. I'm grateful to him for his incisive criticism, and I'm pleased that I've had the opportunity of correcting that argument in the present edition. (shrink)

In 1951 Lukasiewicz [[sic]] linked Aristotle's Prior Analytics with modern formal logic. This book attempts to analyze Aristotle's syllogistic theory in the light of Lukasiewcz's work and the whole tradition of classic interpretations of Aristotle's logic. The first of the book's five chapters shows that for Aristotle the syllogism is basically a relationship of terms couched in conditional form; a relationship of variables rather than concrete terms; and a relationship that sees S linked with P not by (...) the copula but by less metaphysical expressions. The classical S is P form is not Aristotelian at all but a much later renovation. The second chapter maintains that Aristotle distinguishes "relative necessity" from "absolute necessity." Aristotle himself ignores his own distinction at times and thus creates logical difficulties for himself. The oft-fought sea battle is fought again in this chapter. Chapter three deals with the controversial notions of "perfect" and "imperfect" syllogisms. The author asserts that by "perfect syllogism" Aristotle means self-evident syllogisms that serve as axioms for deducing other proofs. Chapters four and five deal with the figures of the syllogism and the syllogism as a deductive system respectively. Patzig concludes that Aristotle's syllogistic theory is purely formal in its structure and can only be properly understood if it is not tied to a metaphysics and converted into a philosophical logic. He denies that it is a universal logic, but rather sees it as a specialized theory of relations.--J. J. R. (shrink)

The article focuses on the New Rhetoric’s concept of quasi-logical arguments imitating logical or mathematical demonstrations, and examines it from point of view of pragma-dialectics as a device contributing towards resolving the difference of opinion. It is shown that the category of quasi-logical arguments cannot be considered as an argument scheme or a united type of strategic maneuvering. It is suggested to consider the category of quasi-logical arguments as a cluster of specific strategic maneuvers increasing (...) the efficiency of arguments under certain circumstances. This approach is demonstrated in a case study of pragma-dialectical analysis of the quasi-logical scheme of probability. (shrink)

The debate over the value of pleasure among Eudoxus, Speusippus, and Aristotle is dramatically documented by the Nicomachean Ethics, particularly in the dialectical pros-and-cons concerning the so-called argument from contraries. Two similar versions of this argument are preserved at EN VII. 13, 1153b1–4, and X. 2, 1172b18–20. Many scholars believe that the argument at EN VII is either a report or an appropriation of the Eudoxean argument in EN X. This essay aims to revise this received (...) view. It will explain why these two arguments differ in premises, contents and purposes, and why these distinctions matter for a proper assessment of Aristotle’s understanding of pleasure and pain in general and his dialectical art in particular. (shrink)

Is it a mistake to use "true" or "false" in certain contexts? White sets the stage for dealing with this issue by laying out a field of usages. He develops his position by characterizing and criticizing contemporary treatments of these data, moving rapidly from case to case. His numerous summaries and conclusions, obviously based on a wider view of the material than is presented in the text, may leave the uninitiated alternately puzzled, bristling, or suspicious. While White's data are expressed (...) clearly, the goal of his arguments and his organizational principles are frequently less apparent. White's discussions of fiction and modality are of particular historic interest. Here we find Frege and Russell arguing about whether they can argue about the King of France. We meet with Aristotle's ancient problem of the future naval battle, witness latter-day skirmishes over the nature of moral language, and find Leibniz, Hume, and Kant debating the logic of necessity and contingency. Are there really different types of truth which correspond with different modalities and existence presuppositions, as White seems to assume? This question, harking back to books 5 and 6 of Plato's Republic, is passed over by White in his usage-oriented quest for the sense of "truth." Truth will suit both student and researcher alike and is to be recommended for its breadth of concern and for its 18 pages of bibliography.--M. D. P. [[sic]]. (shrink)

This article investigates Abelard’s defence of the compatibility between universal bivalence and the existence of future contingent events. It first considers the standard strategy put forward by twelfth-century commentators to solve Aristotle’s dilemma in De Interpretatione 9, which fundamentally relies on Boethius’ distinction between definite and indefinite truth values. Abelard’s own position on the dilemma is then introduced, focusing on a specific deterministic argument considered in his logical works that aims to demonstrate that, given the determinacy of present-tense (...) propositions such as ‘“that Socrates will eat tomorrow” is true’, future contingent events such as that Socrates will eat tomorrow are determinate in advance. In addition to presenting Abelard’s reply to the argument, the article offers an analysis of his notions of contingency, determinacy, and future events, and a comparison between Abelard’s position and other twelfth-century discussions on future contingents. (shrink)