Diodorus Cronus Research Articles

La figure du labyrinthe entre philosophie, art et littérature

The Figure of the Labyrinth between Philosophy, Art and Literature The aim of this article is to draw analogies between the Prisons by Piranesi and The Castle by Franz Kafka in the light of the figure of the labyrinth. In these specific cases, the architectonics (as a pseudo- arrangement of perspective planes) and the plot (as a factitious connection between action sequences) enclose the illusion of depth and the impression of duration in the vicious circles of the lines of rupture and of the missed events, respectively. The Piranesian atopic topic (from atopos, « out of place ») and the Kafkaesque apraxic practice (from apraktos, « inconclusive ») are both based on unsurpassable antinomies and, in this particular respect, seem to revive Zeno of Elea’s paradoxes of motion and Diodorus Cronus’ aporia of becoming, which Gottfried W. Leibniz considers to be two labyrinths.

Diodorus Cronus on Present and Past Change

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.

Chrysippus’ counterargument against the Master Argument: a reappraisal

Abstract It is widely held that as a nego suppositum, Chrysippus’ response to Diodorus Cronus’ Master Argument is that the impossible “this man has died” follows from the possible “Dio has died”. A principal claim of this article is that Chrysippus was not actually committed, against Diodorus, to the tenet that there are deductions and conditionals whereby from the possible the impossible follows. I argue that this is most likely part of a Chrysippean exemplum fictum of a real dialectical discussion and it merely reflects a Chrysippean dialectical strategy, a merely instrumental agreement (συγχώρησις) with Diodorus on the admissibility of some single-premised arguments. As historical evidence for my conjecture I highlight two key passages by Sextus Empiricus which help to understand that Chrysippus’ real tenet was an ancient implicational counterpart of a deictic version of the Identity-Elimination Rule, whereas most likely, according to Diodorus the identitarian major premiss of this rule is redundant, so that it must be eliminated.

The Megarian and the Aristotelian Concept of Possibility: A Contribution to the History of the Ontological Problem of Modality

This is a translation of Nicolai Hartmann’s article “Der Megarische und der Aristotelische Moglichkeitsbegriff: ein Beitrag zur Geschichte des ontologischen Modalitatsproblems,” 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 (Frederic Tremblay).

DISPUTAS DE EPICURO Y CRISIPO EN TORNO A LA NECESIDAD LÓGICA

Este artículo se centrará en las propuestas de Epicuro y Crisipo frente a la tesis de la necesidad lógica de todos los eventos del mundo defendida por Diodoro Crono. Se argumentará que Epicuro rechazaba este tipo de necesidad sosteniendo que el principio de bivalencia no es aplicable a las proposiciones sobre eventos futuros e indicando que no existen causas eternas que garanticen la verdad de dichas proposiciones dado que la causa de dichos eventos puede ser una desviación repentina de los átomos. Se mostrará que Crisipo, en contraste, se sirvió de la validez irrestricta del principio de bivalencia para demostrar que existen causas eternas de todas las cosas y, no obstante, defendía que esto no implica la necesidad lógica de los eventos específicos del mundo.

‘God kan net doen wat God wel doen’: Petrus Abelardus se Megariaanse argument in Theologia ‘Scholarium’, Opera Theologica III

‘God can only do what God does do’: Peter Abelard’s Megarian argument in Theologia ‘Scholarium’, Opera Theologica III Peter Abelard’s contribution to a constellation of central themes in post-Carolingian medieval philosophy, namely on causation, necessity and contingency, with its discursive undertone of the relation between potentiality and actuality, is worked out in a rather informal way in one of his later works, Theologia ‘Scholarium’. Typical of the fusion of philosophical questions and theological premises in medieval philosophy, Abelard addresses the issue by asking whether God can only do what God does. Abelard argues that God can do or not do or omit doing only those things which God does do or does not do or omits doing and that God can do or can not do or omit doing those things only in the way or at the time at which God does and not at any other. Given Abelard’s fragmented and restricted access to the Aristotelian corpus regarding causality, how did he come to this Aristotelian-orientated conclusion? This article stresses the ancient quality of Abelard’s argument from another angle, reminiscent of the so-called Master Argument of the Megarians, with specific reference to the dialectical legacy of Diodorus Cronus, according to whom what can be is what is: what is, in turn, is what must be. Actuality, for the Megarians, exhausts potentiality. The path of actuality cannot be undermined or compromised by issues of potentiality. God’s actions are thus for both the Megarians and Abelard strictly determined and determining. God, in the end, can only do what God does. This article contributes to scholarship in medieval philosophy or theology by making this connection explicit and by thoroughly exploring the link between Abelard and his ancient predecessors.

Aristotle and Diodorus Cronus: Principle of bivalence and principle of plenitude

Aristotle in De Interpretatione 9 considers the use of predicates in combination with subjects which are forming propositions, each of which is necessarily either true or false. This necessity was later named as Principle of bivalence (of truth values). Although he grants the truth or falsity of propositions about past and present events, propositions about the future seem problematic. If a proposition about tomorrow is true (or false) today, then the future event it describes will happen (or not happen) necessary. It leads to (logical) determinism. Aristotle attempts to avoid it. His solution was to maintain that the disjunction is necessarily true today even though neither of its disjuncts is. Thus, it is necessary that either tomorrow's event will occur or it will not, but it is neither necessary that it will occur nor necessary that it will not occur. Because of fact that according to Aristotle Principle of bivalence is not valid for a propositions about future, for him is not valid Principle of plenitude also. On the other side, according to his Master argument and his definitions of modalities for Diodorus Cronus possible is something what is or will be. In opposition to Aristotle, for him does not exists any non-actualized possibility. In some sense Diodorus implicit respects Principle of bivalence. It is compatible with the Principle of plenitude which is also respected from Diodorus Cronus. Aristotle attempts to save difference between modal categories (necessity and possibility), and trys to reject logical determinism. According to his definition of possibility in Diodorus Cronus conception this difference collapses in to determinism.

Wenn die Möglichkeit in Notwendigkeit umschlägt

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 (at least since Abaelard, as Leibniz pointed out) to support their theology. Abaelard’s Diodorean formula reads: God wishes (and ultimately cannot but do) 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 (contrary to what Abaelard says) 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.

Neglected Evidence for Diodorus Cronus

Neglected Evidence for Diodorus Cronus

Necessity or Contingency: The Master Argument.

Introduction Part I. The Master Argument: 1. The Master Argument: on the shortcomings of some past interpretations: Conditions to be fulfilled by any acceptable interpretation 2. Reconstruction of the master argument Part II. Systems of Necessity: The Megarians and the Stoics: 3. The system of logical fatalism: Diodorus Cronus 4. Eternal return and cyclical time: Cleanth's solution 5. Freedom as an element of fate: Chrysippus Part III. System of Contigency: The Lyceum, the garden, the academy: 6. Aristotle 7. Epicurus and intuitionism 8. Carneades and the skeptical nominalism of the modalities 9. Platonism and conditional necessity Epilogue.

The Stoic Analysis of Tense and of Plural Propositions in Sextus Empiricus, Adversus Mathematicos x 99

Adversus Mathematicos (M.) x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section (M. x 85–120) deals with Diodorus Cronus' arguments concerning movement.

What Worried the Crows?

A well-known epigram by Callimachus on the philosopher Diodorus Cronus (fr. 393 Pfeiffer) reads as follows:The question of the third line, while perhaps recondite from a contemporary perspective, was clear in antiquity. The crows are asking ‘What follows (from what)?’, in allusion to the Hellenistic disputes concerning the truth conditions of conditional propositions (συνημμ⋯να), disputes in which the views of Diodorus figured prominently.I agree with Sedley that the question of the last line is ‘much more problematic’. The common interpretation has been to read the αὖθι as a form of αὖθις and to interpret it temporally. The result, in Pfeiffer's estimation, is ‘quomodo posthac erimus?’.This interpretation derives from Sextus Empiricus' discussion at M. 1.309–12 of the last two lines of the epigram. After crediting the grammarian with the ability to understand the allusion in the crows' first question (M. 1.310: κα⋯ μ⋯χρι τούτου συνήσει τ⋯ κα⋯ παιδίοις γνώριμον), he proceeds to argue that the philosopher has a better chance than the grammarian of understanding the second question. But, to quote Sedley, Sextus ‘makes a ghastly mess of it’ when he attempts his own elucidation. According to an argument of Diodorus, a living thing does not die in the time in which it lives nor in a time in which it does not live. Hence, Sextus concludes, it must be the case that it never dies and, ‘if this is the case, we are always living and, according to him, we shall come to be hereafter (αὖθις γενησόμεθα)’ (M. 1.312).

Time and modality in Diodorus Cronus

TheoriaVolume 47, Issue 1 p. 31-53 Time and modality in Diodorus Cronus Nicholas Denyer, Nicholas Denyer University of CambridgeSearch for more papers by this author Nicholas Denyer, Nicholas Denyer University of CambridgeSearch for more papers by this author First published: April 1981 https://doi.org/10.1111/j.1755-2567.1981.tb01236.xCitations: 7AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume47, Issue1April 1981Pages 31-53 RelatedInformation

Facets of Megarian Fatalism: Aristotelian Criticisms and the Stoic Doctrine of Eternal Recurrence

The Megarians, as well as their Stoic heirs, are known to have been fatalists or logical determinists in the following, very broad sense of these terms: with respect to at least certain classes or kinds of nontautologous propositions, they held that the mere truth of a proposition entails its necessity. This paper explores, in a very tentative fashion, the relation between several versions of logical determinism and two passages in the Aristotelian corpus, one of which is specifically directed against Megarian doctrine and the other of which is an argument purporting to establish a thesis concerning the necessity of future events which Aristotle wished to reject but which the Megarian logician Diodorus Cronus apparently accepted.

The Fatalism of 'Diodorus Cronus'

The fatalism of ‘Diodorus Cronus’ Get access Rod Bertolet, Rod Bertolet Purdue University Search for other works by this author on: Oxford Academic Google Scholar William L. Rowe William L. Rowe Purdue University Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 39, Issue 3, June 1979, Pages 137–138, https://doi.org/10.1093/analys/39.3.137 Published: 01 June 1979

The fatalism of 'Diodorus Cronus'

The fatalism of 'Diodorus Cronus'

Diodorus Cronus and Hellenistic Philosophy

During the last four decades historians of ancient logic have become increasingly aware of the importance of Diodorus Cronus and his pupil Philo as pioneers of the propositional logic which came to flourish in the Stoa. Their direct influence has so far been recognised in two main areas of Hellenistic controversy – the validity-criteria for conditional propositions, and the definition of the modal terms ‘possible’ and ‘necessary’. But some broader questions have not been satisfactorily answered. What were Diodorus' own philosophical allegiances and antecedents? What is his place in the history of Greek philosophy? How far-reaching was his influence on the post-Aristotelian philosophers?There was little chance of tackling these questions confidently until 1972, when Klaus Döring published for the first time the collected fragments of Diodorus, in his important volume Die Megariker. Meagre though they are, these fragments confirm my suspicion that Diodorus' philosophical background has not been fully explored, and also that his influence on the three emerging Hellenistic schools – the Stoics, Epicureans, and Sceptics – was far wider than has hitherto been recognised. There has been much discussion as to which earlier philosophers played the most decisive part in shaping Hellenistic philosophy, and the respective claims of the Platonists and of Aristotle have never lacked expert advocacy. In all this, the claims of so obscure a figure as Diodorus have been underrated.

Die Megariker: Kommentierte Sammlung der Testimonien (review)

Book Reviews Die Megariker: Kommentierte Sammlung der Testimonien. By Klaus D~ring. (Amsterdam : Verlag B. R. Griiner N.V., 1972. Pp. xii q- 185) D~Sring has assembled the first complete collection of textual fragments concerning the Megarian philosophers of the fourth and third centuries B.c., together with a commentary. The fragments are divided by the author into four groups, each centered around one of the better-known figures of the school: Euclid, Eubulides, Diodorus Cronus, Stilpo. Evidences concerning lesser-known personalities are included under the figure to whose "circle" they belonged. A fifth group of texts appears in an Anhang devoted to the sophist Bryson (often mistakenly associated with the Megarians) and his student Polyxenus. Divisions in the commentary parallel those in the text. The author also adds a stemma summarizing his conclusions about teacher-pupil relationships within the school, and there is a selective bibliography and a SteUenregister. An index, which in view of the work's organization would be helpful, is not included. Simply as a collection of texts, this is a major addition to the scholarship in its field; with the author's commentary, it is the most important work on the Megarians since Kurt von Fritz's Real-Encyclopiidie article.1 D~Sringpresents convincing evidence that some widely disseminated opinions about the school have little or no foundation. Some of his alternative views have important consequences, and not only for the history of the Megarians. DSring rejects the dates customarily assigned to the school's founder Euclid (ca. 450ca . 380), pointing out that there is actually no good evidence for them (pp. 73-74). His own figures (ca. 435-ca. 365) rely on the evidence of Plato's Theaetetus to give the year 369 as a terminus post quem for Euclid's death. The first consequence of this chronology is that the story of Euclid stealing into Athens disguised as a woman in order to avoid the anti-Megarian decree of 432 must be rejected; Dfiring feels that it is probably one of a family of tales elaborated by later writers "urn die Macht der Philosophie zu demonstrieren " (p. 74). A more important consequence is in store when this chronology is combined with a reassessment of the evidence relating to Euclid's philosophical position. D6ring rejects the traditional description of Euclid as a "neo-Eleatic" who attempted to combine a strict Parmenidean monism with Socrates' ethical views by identifying the "One" with the "Good." Following yon Fritz, he sees this as "eine ziemlich gewaltsame antike Doxographenkonstruktion" (p. 83). His own view reverses the importance of Socratic and Eleatic elements in Euclid's thought, making him "[ein] Sokratiker, der die dem Sokratischen Denken inh~ente eleatische Komponente weiterentwickelt hat" (p. 87). Together with the revision of Euclid's dates, this would appear to eliminate decisively Kr~imer's thesis that Euclid originated the "Gleichsetzung ontologischer und axiologischer Momente''e fundamental to Platonic metaphysics. First, Euclid was only a few years older than Plato (not "at least two decades," as KrOner requires); second, there is no evidence whatever that he had studied the Eleatic doctrines before meeting Socrates; and finally, the purported "Gleichsetzung" appears to be rather the work of doxographers (pp. 87-89). When we add DSring's skeptical assessment of the story of Plato's Megarian period (p. 76), there remains little evidence to support the theory that Euclid was the ultimate source of Plato'S metaphysics. The most famous achievements of the M~garians were in the sphere of logic. Here, x Suppl. V (1931), s. v. "Megariker." H. J. Kr~mer, Arete bei Platon und Aristoteles (Heidelberg, 1959), p. 506. [52H 522 HISTORY OF PHILOSOPHY Dtring's work should provide the impetus for further research; his collection of texts is much more comprehensive than anything previously available, and his commentary, although deliberately limited to an overview, at least provides a good account of the status quaestionis. The material on the paradoxes attributed to the Megarians (pp. 106-114) is particularly valuable; he gives a good conspectus of the extensive literature on the "Liar" and "sorites," and his remarks on the lesser-known paradoxes (the "Man Who Escapes Notice," the "Electra," the "Hooded...

Time, truth and ability

Time, truth and ability Get access Diodorus Cronus Diodorus Cronus New York City Search for other works by this author on: Oxford Academic Google Scholar Analysis, Volume 25, Issue 4, March 1965, Pages 137–141, https://doi.org/10.1093/analys/25.4.137 Published: 01 March 1965

Fate and Possibility in Early Stoic Philosophy

THE SToIC CoNCEPTS of and in Physics depended ultimately upon the distinction which the Stoics made between principal and initiating causes. In this paper I hope to prove that possibility is to be found in the principal cause, which was a quality and the cause of a predicate, and that a possible event was one which followed from the principal cause. I wish to show also, that the term fate was applied to both the principal and the initiating cause. When it was used to refer to the principal cause, it denoted only its relationship to its substratum. On the other hand, all initiating causes which included particulars and events external to the object, and the circumstances in which the object was placed, were according to fate.' Since there is a close connection between Stoic Physics and Logic it will be necessary to consider the evidence given for the views of Cleanthes and Chrysippus by their criticisms of the Master Argument of Diodorus Cronus, a Megarian philosopher who was born about 350 B.c. The Master Argument contained three propositions dealing with the necessary and the possible, which were considered to be incompatible. Since Cleanthes and Chrysippus each rejected a different proposition, and since both disagreed with Diodorus Cronus, I shall point out the differences in the treatment of this subject by the two Stoic philosophers, and I shall show how Chrysippus' interpretation of the Master Argument was related to his Physics. Later we shall see that the definitions of the possible, non-necessary, necessary, and impossible in Stoic Logic are in complete accord with their concepts of and in Physics. In fact, definitions in Logic which would be otherwise unintelligible become clear when they are viewed in the light of Physics. The close connection which I shall demonstrate between these two aspects of Stoic philosophy will, I hope, justify my inclusion of the logical propositions in my paper. The Stoics themselves insisted that the three divisions of their philosophy, Physics, Logic, and Ethics were inseparable, and that no part was independent of the other two (D. L. 7.40; cf. Sext. Emp. Math. 7.19).