Wherein may be discerned the true essence of moral depravity, or that which really does, like a cesspool, corrupt whatever comes under its influence, as containing within itself all evil and ugliness.

Wherein may be discerned the true essence of moral depravity, or that which really does, like a cesspool, corrupt whatever comes under its influence, as containing within itself all evil and ugliness.

Abstractabstract:Diodorus Cronus reportedly denied that there are truths about present kinēsis (change or movement) but affirmed that there are truths about past kinēsis. Although scholars have argued that Diodorus's atomism about bodies, place, and time supports his rejection of present spatial movement of simple bodies, I argue that Diodorus rejected a broader range of present changes, including qualitative and existential change. I also argue that Diodorus rejected these three sorts of change not only for simples (...) but also for complexes. Furthermore, philosophers since antiquity have claimed that denying truths about present change is incompatible with accepting truths about past change, since each past truth about change corresponds to some present truth about change. I argue that this objection can be overcome. I conclude that Diodorus's arguments against present change are both broader and more successful than is usually maintained. (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)

Det sägs att den gamla grekiska tänkaren Diodorus Cronus argumenterade för uppfattningen att någonting är möjligt endast om det är eller kommer att vara sant. Hans argument går under benämningen ”Mästerargumentet”. I den här uppsatsen tittar jag närmare på detta. Jag tar upp två möjliga tolkningar och går igenom några argument för utgångspunkterna. Jag visar hur det är möjligt att acceptera alla premisser i argumentet, givet att de tolkas på ett visst sätt, samtidigt som man förkastar slutsatsen. Det (...) här innebär positiva nyheter för alla som tycker att det ligger någonting i Diodorus Cronus resonemang men samtidigt tror att det finns möjligheter som aldrig realiseras. (shrink)

The article discusses the biographical and doxographical evidence for Diodorus Cronus, a prominent and influential figure at the start of Hellenistic philosophy. Special emphasis is given to Diodorus’ logic, as well to his controversy with Philo the Dialectician over the truth-criteria for the conditional as to his Master argument, concerning modal notions.

The physician Herophilus of Chalcedon, who lived and worked in Alexandria in the early third centuryb.c., is best known and justly celebrated for his numerous and ground-breaking anatomical discoveries and advances in such areas as pulse theory. His systematic investigations into the human body led to some of the highest achievements of Hellenistic science, among which the best known is probably his discovery and detailed description of the nervous system and its functions. Yet certain aspects of his thought have seemed (...) difficult to harmonize with the aims and methods of his medical research. One such is his attitude to causality. According to Galen, Herophilus had accepted the existence of causes merely on a hypothetical basis, and indeed had made the striking claim that ‘by nature it is not discoverable whether causes do or do not exist’. Galen associates these views directly with a number of arguments designed to prove that there are no such things as causes, but we are otherwise left with little in the way of context, and different interpretations have unsurprisingly suggested themselves. (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)

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

Diodorus cronus was a megaric logician who was reputed to have derived from uncontroversial premises the surprising conclusion that the possible is that which either is or will be the case. Versions of his lost argument have been reconstructed recently by prior, Hintikka, And rescher. I analyze and compare these versions and argue that none of them forms a sound argument.

Diodorus' Master Argument was intended to show that whatever is possible either is or will be true. The intended conclusion does not follow from the extant premisses of the Master Argument. The Near Miss argues however, from those premisses alone, that nothing can be more than momentarily an exception to the Master Argument's intended conclusion. Strong arguments support even the most contentious of those premisses . We therefore cannot easily ignore the Near Miss. Moreover, there are various supplementary premisses (...) that would turn the Near Miss into an argument with the full force of the Master Argument itself. Each of Diodorus' ancient rivals, since they accepted such doctrines as eternal recurrence, temporal atomism, and the "extended" present, would grant him at least one of these supplementary premisses. So too would any modern who holds that time is not circular, has no beginning, and does not branch. (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)

ABSTRACT: Summary presentation of the surviving logic theories of Philo the Dialectician (aka Philo of Megara) and Diodorus Cronus, including some general remarks on propositional logical elements in their logic, a presentation of their theories of the conditional and a presentation of their modal theories, including a brief suggestion for a solution of the Master Argument.

This paper discusses the reports in Diogenes Laertius and in Sextus Empiricus concerning the classification of propositions. It is argued that the material in Sextus uses a source going back to the Dialectical school whose most prominent members were Diodorus Cronus and Philo of Megara. The material preserved in Diogenes Laertius, on the other hand, goes back to Chrysippus.

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)

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)

Controversy has surrounded the interpretation of the so-called 'Diodorean' and 'Chrysippean' conditionals of the Stoics. I critically evaluate and reject two interpretations of each of them: as expressing natural laws, and as strict conditionals. In doing so I engage with the work of authors such as Frede, Gould, Hurst, the Kneales, Mates, and Prior. I conclude by offering my own proposal for where these Stoic conditionals should be located on a 'ladder' of logical strength.

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)

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)

This is a translation of Nicolai Hartmann’s article “Der Megarische und der Aristotelische Möglichkeitsbegriff: ein Beitrag zur Geschichte des ontologischen Modalitätsproblems,” first published in 1937. In this article, Hartmann defends an interpretation of the Megarian conception of possibility, which found its clearest form in Diodorus Cronus’ expression of it and according to which “only what is actual is possible” or “something is possible only if it is actual.” Hartmann defends this interpretation against the then dominant Aristotelian conception of (...) possibility, based on the opposition between dynamis and energeia, and according to which there is always an open multiplicity of simultaneous “possibilities,” the outcome of which remains undetermined. Since, according to Hartmann, reality suffers no indetermination, the Megarian conception of possibility is an account of real possibility, whereas the Aristotelian one is merely an account of epistemic possibility. (shrink)

In antiquity, the dialectician Diodorus Cronus gained reknown as the author of the Master Argument. Unfortunately, this celebrated argument is known to us only as a trio of premises reported by Epictetus.

Aristotle produced several arguments to vindicate the futura contingentia and to refute the conception of modalities which do not allow incidental facts. This conception was coined mainly by Diodorus Cronus and implied the view that whatever may happen, is to happen necessarily. Although Aristotle condemned this view and refuted the theology which it implies, Diodorean modalities were employed by the scholastics to support their theology. Abaelard’s Diodorean formula reads: God wishes no more and no less than what He (...) is able to do – i. e. God’s ability to do something implies necessity. In the Summa theologiae, Thomas Aquinas employed Diodorean modalities along with this result of Abaelard’s. Leibniz himself confessed his debt to Diodorean modalities as well as to the work of Abaelard in formulating his own ontological proof. Kurt Gödel was under the influence of Leibniz when he wrote his »Ontological Proof«, which employs Diodorean modalities. — For the Greek-speaking scholars of the Middle Ages, however, Aristotelian influences were stronger than Diodorean as regards theory building on modalities. Philosophers from the East from the 2nd to the 11th century A.D., such as Alexander of Aphrodisias, John Philoponus and Michael Psellos, condemned Diodorean modalities as fallacious. In the same period, Greek Church Fathers such as Cyril of Alexandria, Maximus Confessor and John of Damascus gave an orthodox account of God and the modalities, according to which God is able to do whatever He wishes. The absence of Leibniz-like modal ontological proofs in the Greek tradition seems more plausible under these circumstances. (shrink)

ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...) of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (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)

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)

This monograph discusses the sources for ancient propositional logic, mainly in Sextus Empiricus and Diogenes Laertius bk. VII. It is argued that most of the sources in Sextus which have hitherto been taken to be sources for Stoic logic either do not report Stoic logic at all or report pre-Chrysippean Stoic logic. These texts report (in the first case) a group labelled the Dialecticians whose most prominent members were Diodorus Cronus and Philo or else (in the second case) (...) early Stoic logicians heavily influenced by the Dialecticians. The texts discussed concern the theory of signs, the theory of proof and the classifications of propositions and of arguments. (shrink)

These books are telling examples which demonstrate that at least some contemporary philosophers have again attained the high level of ‘scholastic’ sophistication which was typical of men like Aristotle, Diodorus Cronus, Chrysippus, Aquinas or Ockham. It can even be said that in an important respect this classical level has been surpassed: Prior’s presentation of the different calculi of tense logic in Past, Present and Future documents the recent progress of symbolic formalization in a domain where the classics had (...) to struggle laboriously with Greek or Latin sentences. (shrink)

The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Megara and by their interest in logical paradoxes, propositional logic and dialectical expertise. . Its two best known members, Diodorus Cronus and Philo the Logician, made groundbreaking contributions to the development of theories of conditionals and modal logic. Philo introduced a version of material implication; Diodorus devised a forerunner of strict implication. Each (...) developed a system of modal notions that satisfies the basic logical requirements laid down by modern standard modal theories. In antiquity, Diodorus Cronus was famous for his so called Master Argument, which aims to prove that only the actual is possible. (shrink)

The first monograph on Stoic modal logic. Part 1 discusses the Stoic notion of propositions (assertibles, axiomata): their definition; their truth-criteria; the relation between sentence and proposition; propositions that perish; propositions that change their truth-value; the temporal dependency of propositions; the temporal dependency of the Stoic notion of truth; pseudo-dates in propositions. Part 2 discusses Stoic modal logic: the Stoic definitions of their modal notions (possibility, impossibility, necessity, non-necessity); the logical relations between the modalities; modalities as properties of propositions; contingent (...) propositions; the relation between the Stoic modal notions and those of Diodorus Cronus and Philo of Megara; the role of ‘external hindrances’ for the modalities; the temporal dependency of the modalities; propositions that change their modalities; the principle that something possible can follow from something impossible; the interpretations of the Stoic modal system by B. Mates, M. Kneale, M. Frede, J. Vuillemin and M. Mignucci are evaluated. -/- For a shorter, updated, English version of Part 1 of the book see S. Bobzien, ‘Stoic Logic’, in K. Algra et al. (eds), The Cambridge History of Hellenistic Philosophy, Cambridge 1999, 92-157. For a shorter, updated, English version of Part 2 of the book see S. Bobzien 'Chrysippus' Modal Logic and its Relation to Philo and Diodorus', in K. Doering / Th. Ebert (eds) Dialektiker und Stoiker (Stuttgart 1993) 63-84. (shrink)

We may distinguish between two ways of understanding tense-logical formulae, depending on whether we construe tense operators as operators on sentences or on predicates. Bearing this distinction in mind helps us formalise the premisses of Diodorus Cronus' Master Argument correctly, and give a formal reconstruction of the Argument itself.

Adversus Mathematicos x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section deals with Diodorus Cronus' arguments concerning movement.

Adversus Mathematicos x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section deals with Diodorus Cronus' arguments concerning movement.