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Selected Bibliography on the Master Argument of Diodorus Cronus

BIBLIOGRAPHY

  1. Akama, Seiki, Murai, Tetsuya, and Miyamoto, Sadaaki. 2011. "A three-valued modal tense logic for the Master Argument." Logique et Analyse no. 213:19-30.

    Abstract: "The Master Argument was shown by Diodorus Cronos to conclude that nothing is possible that neither is true nor will be true and that therefore every (present) possibility must be realized at a present or future time. It leads to logical determinism. Prior tried to reconstruct the argument by means of modal tense logic. As a consequence, Prior proposed several branching time tense logics to resolve the fallacy of the Master Argument. In this paper, we propose a three-valued modal tense logic with a Kripke semantics to defend Prior's original argument."

  2. Akama, Seiki, and Nagata, Yasunori. 2011. A Three-Valued Approach to the Master Argument. Paper read at 41st IEEE International Symposium on Multiple-Valued Logic, Tuusula Finland.

  3. Alessandrelli, Michele. 2019. "Giannantoni, logica di Aristotele e logica megarica." In Méghiston agathón. La storiografia filosofica di Gabriele Giannantoni. Atti della giornata di studio (Roma, 30 novembre 2018), edited by Brancacci, Aldo, 71-92. Bologna: Diogene Multimedia.

    All'articolo di G. Giannantoni sull'argomento dominatore: "Il kyrieuon logos di Diodoro Crono" (1981) sono dedicate le pagine 82-92.

  4. Angstl, Helmut. 1986. "Bemerkungen zu Jules Vuillemin, Die Aporie des Meisterschlusses von Diodoros Kronos und ihre Lösungen." Allgemeine Zeitschrift für Philosophie no. 11:79-82.

  5. Bar-Hillel, Yehoshua. 1965. "Et Tu, Diodorus Cronus?" Analysis no. 26:54-56.

  6. Barreau, Hervé. 1975. "Le Maître Argument de Diodore: son interprétation traditionnelle, sa signification historique, sa reconstitution contemporaine." Cahiers Fundamenta Scientiae no. 46:1-51.

  7. ———. 2006. "Cléanthe et Chrysippe face au maître-argument de Diodore." In Les Stoiciens et leur logique, edited by Brunschwig, Jacques, 283-301. Paris: Vrin.

    Deuxième édition revue, augmentée et mise a jour (Première edition 1978, pp. 21-40).

  8. Barreau, Hervé, and Picolet, Françoise. 1978. "Suite et fin sur le Maître Argument de Diodore." Cahiers Fundamenta Scientiae no. 88:1-53.

    Françoise Picolet: Nouvelles remarques à propos de Diodore, pp. 7-11; Hervé Barreau: Conception diodoréenne et conception stoicienne du Maître Argument, pp. 15-53.

  9. Becker, Oskar. 1956. "Über den Κυριεύων λόγος des Diodoros Kronos." Rheinisches Museum für Philologie no. 99:289-304.

  10. ———. 1961. "Zur Rekonstruktion des ‘kurieuon logos’ des Diodoros Kronos." In Erkenntnis und Verantwortung: Festschrift für Theodor Litt, edited by Derbolav, Josef and Nicolin, Friedhelm, 250-263. Düsseldorf: Schwann.

  11. Bertolet, Rod, and Rowe, William L. 1979. "The Fatalism of 'Diodorus Cronus'." Analysis no. 39:137-138.

  12. Blanché, Robert. 1965. "Sur l'interprétation du κυριεύων λóyоς." Revue Philosophique no. 155:133-149.

  13. Bolduc, Ghyslain. 2011. "L'appropriation critique de la pensée aristotélicienne par Diodore Kronos." Gnosis no. 12:1-14.

  14. Boudot, Maurice. 1983. "L'argument dominateur et le temps cyclique." Les Études Philosophiques:271-298.

  15. Bouveresse, Jacques. 2013. "Le Dominateur, les possibles et le problème de la liberté." In Dans le labyrinthe: nécessité, contingence et liberté chez Leibniz. Cours 2009 et 2010, 1-25. Paris: Collège de France.

  16. Bull, R. A. 1965. "An Algebraic Study of Diodorean Modal Systems." The Journal of Symbolic Logic no. 30:58-64.

    "I shall consider two Diodorean models: what I call the D-model, constructed on the set of non-negative reals, and the D-model - in effect the usual one - on that of positive integers. I show that these characterise S4.3 and D, respectively. All the Diodorean models verify S4.3. It is easy to adapt the completeness proof for S4.3 given here to Diodorean models on the non-negative rationals and various other linearly-ordered sets. (The proof depends, in fact, on the linearly-ordered set having a suitable sub-set of ordinal W2.) There are other Diodorean systems, but they do not seem to be of any interest." (p. 59)

  17. Buzzetti, Dino. 2000. "L'Argomento Dominante e la posizione di Scoto. A proposito di un 'errore' interpretativo di Jules Vuillemin." In Ob rogatum meorum sociorum. Studi in memoria di Lorenzo Pozzi, edited by Caroti, Stefano and Pinzani, Roberto. Milano: Franco Angeli.

  18. Celluprica, Vincenza. 1977. "L'argomento dominatore di Diodoro Crono e il concetto di possibile in Crisippo." In Scuole socratiche minori e filosofia ellenistica, edited by Giannantoni, Gabriele, 55-73. Bologna: Il Mulino.

  19. ———. 1984. "Necessità megarica e fatalità stoica." Elenchos no. 3:361-385.

  20. Christian, Curt. 1964. "Zur Interpretation der Diodoreischen Modalgesetze und der Diodoreischen Implikation." Anzeiger der Philosophisch-Historischen Klasse / Österreichische Akademie der Wissenschaften:235-243.

  21. Ciuni, Roberto. 2009. "The Search for the Diodorean Frame." Humana Mente: Journal of Philosophical Studies no. 8:47-65.

    Abstract: "Diodorean modalities are logical notions that specify, in a precise way, how sentences may be true with respect to time: a sentence is diodoreanly necessary at a given instant iff it is true since that instant on. Arthur Prior has treated them as sentential operators and built up a logic for such modalities (DIOD) conjecturing that the frame for such a logic (the "diodorean frame") was the frame for S4. The Conjecture was soon proved false, through a number of counterexamples that played a role in the research on modal logics between S4 and S5. The present paper aims at showing that (i) the search for the diodorean frame benefited from such a research, and that (ii) there has been a mutual interaction between the search of the diodorean frame and some characterisation results. The paper is divided into five parts. In section 1, I will introduce diodorean modalities, while in Section 2 I will be focusing on Prior's reconstruction of the Master Argument and his characterisation of DIOD. In section 3, I present a conjecture Prior advanced about the characterisation of DIOD and some counterexamples to it. The notions of "frame" and "frame for" will be also introduced. In section 4 I summarise the connections between the search of the diodorean frame and some researches in modal logic. Section 5 presents a short conclusion.

  22. Corpina, Fabio. 2016. " The Ancient Master Argument and Some Examples of Tense Logic." Argumenta no. 1:245-258.

    Abstract: "The Master Argument of Diodorus Cronus has been long debated by logicians and philosophers. During the Hellenistic period it was so famous that doxographers and commentators took for granted its notoriety and none of them gave us a detailed report. The first section presents a philosophical account of the ancient Master Argument, by trying to retrace its meaning, originated from the Megarian context, and so halfway between ancient logic and metaphysics. The second section introduces a logical analysis of the Master Argument against the backdrop of the Jarmużek-Pietruszczak semantics for the tense logic Kt4P; but the main aim of the section is to deal with one of the most fascinating attempts to peruse the Master Argument, i.e. A. Prior’s reconstruction. Prior stays true to the Diodorean philosophical stance even if he uses modern logical tools. The significance of the work by Prior marks the beginning of tense logic. The third section expounds an argument by Øhrstrøm-Hasle. Danish logicians do not consider additional premises for the Master Argument. They give, in primis, a sentential example for the third premise, proving its inconsistency with the first two. The deterministic conclusion is the implicit result of this stratagem. Finally, in the fourth section, we compare the strategies by Prior and Øhrstrøm-Hasle."

    References

    Jarmużek, T. and Pietruszczak A. 2009, “The Tense Logic for Master Argument in Prior’s Reconstruction”, Studia Logica, 92, 85-108

    Øhrstrøm, P. and Hasle, P. 1995, Temporal Logic. From Ancient Ideas to Artificial Intelligence, Dordrecht: Kluwer.

  23. Corpina, Fabio, and Øhrstrøm, Peter. 2017. "The Diodorean approach to time and modality from a historical and a philosophical perspective." In Logic and Philosophy of Time: Themes from Prior, Volume 1, edited by Hasle, Per, Blackburn, Patrick Rowan and Øhrstrøm, Peter, 83-101. Aalborg: Aalborg Universitetsforlag.

    Abstract: "Diodorus Cronus (ca. 340–280 B.C.) was an important philosopher and logician of the Megaric School. His principal contribution consists in a strong, logically oriented, characterisation of metaphysics, focused on the temporal aspects of important logical notions, in particular the understanding of conditionals and modality. Furthermore, he is well known for his so-called Master Argument which was designed to demonstrate that if something is possible then either it is the case already or it will be the case later. In this way Diodorus suggested a close connection between time and modality. According to Diodorus time can be seen as a series of temporal atoms. At any such atomic moment a proposition may be true or false.

    Since we do not have the details of Diodorus’ original argument, several scholars have tried to reconstruct the Master Argument as it might have been. In this paper, we consider two attempted reconstructions of the argument: one based on a certain interpretation of Diodorus’ notion of implication, and one suggested by A.N. Prior and based on a tense-logical approach to time and reasoning. We argue that both reconstructions are possible from a historical point of view, but that the latter is more interesting than the former if the argument should be conceived as an argument in favour of determinism."

  24. de los Ríos Gutiérrez, Iván. 2018. "Kyrieuon Logos. Diodoro Crono y el problema del determinismo a la luz de Metaphysica IX, 9, 3." Trans/Form/Ação no. 41:9-30.

    Resumen: "El presente artículo tiene por objetivo la reconstrucción del argumento dominador (kyrieuon logos) atribuido a Diodoro Crono y su revisión filosófica a la luz de la crítica aristotélica al actualismo extremo de la Escuela de Mégara en Metafísica IX, 3. Desde esta perspectiva, el trabajo aspira a situar el proyecto teórico de Diodoro en el marco de su disputa filosófica con la metafísica aristotélica y su concepto de δύναμις, con el fin de traducir esta querella dialéctica en lo que, a nuestro juicio, constituye una disputa teórica de importantes consecuencias prácticas: la disyunción excluyente entre el azar y el destino como paradigmas de interpretación conceptual y de acción moral."

  25. Denyer, Nicholas. 1981. "Time and Modality in Diodorus Cronus." Theoria no. 47:31-53.

  26. ———. 1996. "Gaskin on the Master Argument." Archiv für Geschichte der Philosophie no. 78:166-180.

    "Richard Gaskin's The Sea Battle and the Master Argument (1995) falls into two roughly equal sections each corresponding to one half of its title. The first explores Aristotle's treatment in De Interpretatione 9 of his puzzle about tomorrow’s sea-battle; the second puts some of these results to work in developing a novel account of the Master Argument of Diodorus Cronus. Moreover, throughout the book, Gaskin pays detailed attention to rival interpretations from the mass of commentary that has accumulated around these topics since ancient times, and that continues to accumulate ever faster in our own. On this aspect of Gaskin’s book, I will have little more to say than that he discusses all the rival interpretations with a general good sense, and with a patience that I for one could not so long sustain. Moreover, I propose merely to summarise the salient points in Gaskin’s own understanding of Aristotle. In the bulk of this critical notice, I will examine at much greater length what I myself take to be Gaskin's most interesting achievement: a reconstruction of the Master Argument that, whatever its faults, is both more plausible historically and more interesting philosophically than all but a handful of the umpteen reconstructions that are now on offer." (p. 166)

  27. ———. 1999. "The Master Argument of Diodorus Cronus. A Near Miss." Logical Analysis and History of Philosophy /Philosophiegeschichte und logische Analyse no. 2:239-252.

    Abstract: "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 ("every past truth is necessary"). 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."

  28. ———. 2009. "Diodorus Cronus: Modality, the Master Argument and Formalisation." Humana Mente: Journal of Philosophical Studies no. 8:33-46.

  29. Diodorus Cronus, [pseudonym]. 1965. "Time, Truth and Ability." Analysis no. 25:137-141.

    Pseudonym of Richard Taylor and Steven M. Cahn.

  30. Fernández-García, Socorro. 2005. "Leibniz y el argumento dominante." Anuario Filosófico no. 38:255-267.

  31. Ferre, Julien. 2015. "Logique modale temporelle: Arthur Prior, Jules Vuillemin et l'aporie de Diodore." Les Études philosophiques no. 154:581-609.

  32. Gaskin, Richard. 1995. The Sea Battle and the Master Argument. Aristotle and Diodorus Cronus on the Metaphysics of the Future. Berlin: Walter de Gruyter.

  33. ———. 1996. "Reconstructing the Master Argument:Response to Denyer." Archiv für Geschichte der Philosophie no. 78:181-191.

  34. ———. 1999. "Tense Logic and the Master Argument." Logical Analysis and History of Philosophy / Philosophiegeschichte und logische Analyse no. 2:203-224.

    Abstract: "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 ("every past truth is necessary"). 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."

  35. Giannantoni, Gabriele. 1981. "Il kyrieuon logos di Diodoro Crono." Elenchos no. 2:239-272.

  36. Gómez Espíndola, Laura Liliana. 2012. "Disputa de Aristoteles y Diodoro Crono en torno a la necesidad logica." Praxis Filosófica no. 35:39-57.

  37. Goodman, Lenn E. 1999. "The Diodorean Modalities and the Master Argument." In From Puzzles to Principles? Essays on Aristotle's Dialectic, edited by Sim, May, 15-37. Lanham: Lexington Books.

    "My purpose in this chapter is to examine the modalities of Diodorus and the logic of his argument in their behalf, the so-called Master4 Argument." (p. 19)

    (...)

    "What Diodorus seems to me to be saying is that if there is a state of affairs that will never occur, then (for example) it was always true that it would never occur (and always true to say so, as in the version of the argument that Aristotle considers). So the event cannot occur without falsifying that truth or claim, thus, without making over the past, which Aristotle concedes is impossible. Diodorus seems to me to generalize this approach, by assuming that there is always some truth about the past that any falsehood about the future will contradict. The inference is that all falsehoods about the future are impossible and all truths about the future necessary.

    We need not speculate that this line of argument was in fact taken by Diodorus, for we have the testimony of Cicero's De Fato to confirm our reconstruction. The core of the argument that Cicero links to the name of Diodorus is this: If p ('Fabius was born at the rising of the Dogstar') entails q ('Fabius will not die at sea'), then the entailment of q by p (a necessary proposition, since it deals with the past) renders q necessary as well, and it becomes impossible for Fabius to die at sea. (27)

    The strength of the Diodorean position lay in its capacity to refute the conception of possibility put forward by Aristotle, and that by arguing from his own premises.(28) If real possibility is indeed an incoherent notion and there are no possibilities that are not at some time to be realized, then all truths become necessary and the time dimension itself is called into question. For necessity is timeless. Even though Diodorean necessity was achieved through quantification over time, it has the effect of bracketing or erasing time." (pp. 21-22)

    (...)

    "With the elimination of real possibility, modality as an independent category is effectively suppressed. A system of modality which does not allow for possibilities that may never be realized cannot distinguish possibility from actuality except in point of temporal placement. Modality as such becomes vacuous; and the distinction of, say, natural from logical necessity, otiose. The Aristotelian, then, and indeed anyone who would retain modal concepts in describing change, causality, or nature has an interest in refuting the Master Argument." (p.22)

    27. See Cicero, De Fato, vi 12, vii 13; cf. Michael J. White's discussion in "Facets of Megarian Fatalism: Aristotelian Criticisms and the Stoic Doctrine of Eternal Recurrence," Canadian Journal of Philosophy 10 (1980): 203-4.

    28. For the reliance of the Master Argument on Aristotelian premises, sec, Peter Øhlstrom, "A New Reconstruction," 61 ; and O. Becker, "Zur Rekonstruktion des 'Kyrieuon Logos' des Diodorus Kronos," in Festschrift für Theodor Litt, J. Derbolav and F. Nicolin, eds. (Düsseldorf, 1960).

  38. Guerry, Herbert. 1967. "Rescher's Master Argument." The Journal of Philosophy no. 64:310-312.

  39. Gundersen, Lars. 1997. "The Master Argument and Branching Time." Logic and Logical Philosophy no. 5:49-60.

    Abstract: "It is argued that reconstructions of the so-called ‘Master Argument’ of Diodorus Cronos to the effect that possibility should be understood as present or future truth, essentially relies on two axioms: i) that every true proposition concerning the past is necessary, and ii) that it follows necessarily from a proposition being true that it always has been the case that it would be true. It is furthermore argued that these two axioms are inconsistent in the sense that any tense/modal semantics which incorporates both collapses either modally (fails to distinguish between truth simpliciter and modalised truth) or temporally (fails to offer a plausible semantical account for propositions about the future). This finding is, furthermore, taken as indicator for the more generel claim that there are principled difficulties involved in construing semantics for combined tense/modal logical systems."

  40. Hafemann, Burkhard. 1999. "Indefinite Aussagen und das kontingent Zukünftige.

    Akzidenzien allgemeiner Gegenstände und graduelle Wahrheit in Aristoteles’

    De Interpretatione 7 und 9." Philosophiegeschichte und logische Analyse / Logical Analysis and History of Philosophy no. 2.

    Abstract: "Die von Aristoteles in De Int. 7 eingeführte „indefinite Aussage“ verweist nach meiner Deutung auf ein Universale, welches anteilig an widersprüchlichen akzidentellen Prädikaten teilhat. Dem korrespondiert auf semantischer Ebene die graduelle Wahrheit beider Widerspruchsglieder. In gleicher Weise ist für Aristoteles auch die Aussage, daß ein Individuum zu einem Zeitpunkt seiner kontingenten

    Zukunft so-und-so bestimmt sein wird, nach De Int. 9 offenbar als graduell-wahr einzustufen. Das Einzelne kann hinsichtlich seiner kontingenten Zukunft nämlich noch nicht betrachtet werden, sofern es faktisch wäre, sondern nur, sofern es zeitübergreifend ein Universale exemplifiziert. In diesem Zusammenhang werden zugleich fundamentale Bezüge zwischen indefiniter Aussage einerseits und Aristotelischer Modallogik, Statistik und Wissenschaftstheorie andererseits deutlich."

  41. Hartmann, Nicolai. 1993. "Le concept mégarique et aristotélicien de possibilité. Contribution à l'histoire du problème ontologique de la modalité." Laval Théologique et Philosophique no. 49:131-146.

    Traduit par Jean-Pierre Narbonne.

  42. ———. 2017. "The Megarian and the Aristotelian Concept of Possibility: A Contribution to the History of the Ontological Problem of Modality." Axiomathes.

    Translated by Frédéric Tremblay and Keith Peterson.

    Abstract: "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 (Frédéric Tremblay)."

  43. Hintikka, Jaakko. 1964. "Aristotle and the 'Master Argument' of Diodorus." American Philosophical Quarterly no. 1:101-114.

    Revised reprint as Chapter IX in: J. Hintikka, Time and Necessity. Studies in Aristotle's Theory of Modality, New York: Oxford University Press, 1973, pp. 179-213.

  44. Hintikka, Jaakko, Knuuttila, Simo, and Remes, Unto. 1977. "Aristotle on Modality and Determinism." Acta Philosophica Fennica no. 29.

    In collaboration with Unto Remes and Simo Knuuttila.

  45. Ide, Harry A. 1992. "Chrysippus’s Response to Diodorus’s Master Argument." History and Philosophy no. 13:133-148.

    Abstract: "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 are possible and consequents impossible. But perished propositions are false. and Chrysippus's conditionals are true when their antecedent and consequent are possible, and false when their antecedent is possible and consequent impossible. The claim of the Master Argument that Chrysippus rejects, then, is stronger that usually supposed."

  46. Jansen, Ludger. 2011. "The Master Argument of Diodorus Cronus." In Just the Arguments: 100 of the Most Important Arguments in Western Philosophy, edited by Bruce, Michael and Barbone, Steven, 73-75. Malden: Blackwell.

  47. Jarmużek, Tomasz. 2009. "Master Argument vs. Sea-Fight Tomorrow." Bulletin of the Section of Logic no. 38:205-214.

    Abstract: "This paper deals with the Aristotelian problem of Sea-fight tomorrow, but it is analyzed from a Diodorean point of view. Precisely, we examine whether the lost argument of Diodor Cronus, called Master Argument, could be conducted within a frame of future open time. Since we do not know the argument itself, we follow the known reconstructions of Master Argument. Each of them requires special logical assumptions, but also semantic constraints concerning a frame of time. The last detail interests us the most. Showing shortly, step by step, all constraints, we come to the conclusion that the strictly treated reconstructions of Master Argument must prefer a linear model of future."

  48. ———. 2018. On the Sea Battle Tomorrow That May Not Happen. Berlin: Peter Lang.

    A Logical and Philosophical Analysis of the Master Argument.

  49. Jarmużek, Tomasz, and Pietruszczak, Andrzej. 2009. "The Tense Logic for Master Argument in Prior's Reconstruction." Studia Logica no. 92:85-108.

  50. Kutschera, Franz von. 1986. "Zwei Modallogische Argumente für den Determinismus: Aristoteles und Diodor." Erkenntnins no. 24:201-217.

  51. Lapied, André. 2006. "Aporie de Diodore et formalisation de l'incertitude." Cahiers d'économie Politique no. 50:155-164.

  52. Mariani, Mauro. 2009. "Commentary: The Sea Battle and the Master Argument. Aristotle and Diodorus Cronus on the Metaphysics of the Future, R. Gaskin, de Gruyter, Berlin-New York, 1995." Humana Mente: Journal of Philosophical Studies no. 8:191-200.

    Ristampato in: M. Mariani, Logica modale e metafisica. Saggi aristotelici, Pisa: Edizioni ETS 2018, pp. 319-330.

    Abstract: "Come risulta chiaro già dal titolo, il libro di Gaskin è diviso in due parti: la prima, che comprende i capitoli 1-14, tratta del famoso e famigerato argomento fatalista di De Interpretatione 9, mentre la seconda, che comprende i capitoli 15-25, è dedicata al quasi altrettanto famoso e dibattuto "Argomento Dominatore" di Diodoro Crono, nonché alle sue possibili relazioni con la "Battaglia navale" aristotelica. Seguono poi tre appendici, la prima dedicata ad alcune interpretazioni arabe e medievali di De Interpretatione 9, le altre due al tema della prescienza e della contingenza in Alessandro di Afrodisia. Si tratta – è già chiaro da questo sommario – di un libro ricco e stimolante, la cui disamina approfondita richiederebbe molto più spazio di quanto ne ho a disposizione. Mi limiterò dunque a discutere innanzitutto la sua interpretazione della "Battaglia navale", e in secondo luogo il rapporto che la sua ricostruzione dell’"Argomento Dominatore" stabilisce tra Diodoro e Aristotele."

  53. Massie, Pascal. 2016. "Diodorus Cronos and the logic of time." The Review of Metaphysics no. 70:279-309.

  54. McKirahan, Richard. 1979. "Diodorus and Prior and the Master Argument." Synthese no. 42:225-253.

  55. Meixner, Uwe, and Newen, Albert, eds. 1999. Antike Philosophie mit einem Schwerpunkt zum Meisterargument = Ancient philosophy with a focus on the Master Argument. Paderborn: Mentis.

    Philosophiegeschichte und logische Analyse, Vol. 2.

    Inhalt / Contents: Einleitung 1; Uwe Meixner: Die Zentralität der analytischen Methode für die Philosophie, insbesondere die der Antike 25; Fernando Ferreira: On the Parmenidean misconception 37; Erwin Tegtmeier: Parmenides' problem of becoming and its solution 51; Theodor Ebert: Der fragende Sokrates : Überlegungen zur Interpretation platonischer Dialoge am Beispiel des Menon 67; Katarzyna Paprzycka: Socrates meets Carnap : explication in the Theaetetus 87; Burkhard Hafemann: Indefinite Aussagen und das kontingent Zukünftige 109; Fernando Inciarte: Aristotle and Aquinas 139; Nicholas White: Intrinsically valued parts of happiness: Aristotle, Butler, and Mill 149; Verity Harte, Meilssa Lane: Pyrrhonism and Protagoreanism : catching Sextus out? 157; Christian Schäfer: Proklos' Argument aus De malorum subsistentia 31, 5-21 in der modernen Interpretation 173; Hermann Weidemann: «Aus etwas Möglichem folgt nichts Unmögliches»: zum Verständnis der zweiten Prämisse von Diodors Meisterargument 189; Richard Gaskin, Richard: Tense logic and the Master Argument 203; Michael J. White: The lessons of Prior's Master Argument 225; Nicholas Denyer: The Master Argument of Diodorus Cronus 239-252.

  56. Michael, Frederick S. 1976. "What is the Master Argument of Diodorus Cronos?" American Philosophical Quarterly no. 13:229-235.

  57. Mignucci, Mario. 1966. "L'argomento dominatore e la teoria dell'implicazione in Diodoro Crono." Vichiana no. 3:3-28.

  58. ———. 1987. " Über eine neue Interpretation des Meisterschlusses." Grazer Philosophische Studien no. 30:161-172.

  59. Mortensen, Chris. 2015. "The Master Argument of Diodorus Cronus as an Alternative Account of Modality." In Reading, Interpreting, Experiencing: an inter-cultural journey into Greek letters, 15-22. Parkville, Victoria: Modern Greek Studies Association of New Zealand.

  60. Muller, Robert. 1984. "Signification historique et philosophique de l'argument Souverain de Diodore." Revue de Philosophie Ancienne no. 2:3-37.

  61. Nasti de Vincentis, Mauro. 2018. "Chrysippus’ counterargument against the Master Argument: a reappraisal." SATS. Northern European Journal of Philosophy.

  62. Øhrstrøm, Peter. 1980. "A New Reconstruction of the Master Argument of Diodorus Cronus." International Logic Review no. 21:60-65.

  63. Øhrstrøm, Peter, and Hasle, Per F. V. 1995. Temporal Logic: From Ancient Ideas to Artificial Intelligence. Dordrecht: Kluwer.

    Part 1: Time and Logic; 1.2. The Master Argument of Diodorus Cronus, pp. 15-32.

  64. Picolet, Françoise. 1977. "A propos d'une reconstitution recente du Maître Argument de Diodore Cronus." Cahiers Fundamenta Scientiae no. 72:1-12.

    Sur Barreau (1975).

  65. Prior, Arthur Norman. 1955. "Diodoran Modalities." The Philosophical Quarterly no. 5:205-213.

  66. Purtill, Richard L. 1973. "The Master Argument." Apeiron no. 7:31-36.

  67. Quevedo, Amalia. 1989. "Posibilidad e indeterminación. Aristóteles frente a Diodoro Crono." Thémata. Revista de filosofía no. 6:125-136.

  68. Rescher, Nicholas. 1966. "A Version of the 'Master Argument' of Diodorus." Journal of Philosophy no. 63:438-445.

    Revised version as a Section of: Truth and Necessity in Temporal Perspective, in: N. Rescher, Essays in Philosophical Analysis, Pittsburgh: University of Pittsburg Press, 1969, pp. 271-302 (see note 36, p. 296).

  69. Schotch, Peter M., and Payette, Gillman. 2011. "Worlds and times: NS and the master argument." Synthese no. 181:295-315.

  70. Schuhl, Pierre-Maxime. 1960. Le dominateur et les possibles. Paris: Presses Universitaires de France.

  71. Sedley, David. 1977. "Diodorus Cronus and Hellenistic Philosophy." Proceedings of the Cambridge Philological Society no. 23:74-120.

    Reprinted in: Terence Irwin (ed.), Hellenistic Philosophy (Classical Philosophy Collected Papers vol. 8), New York: Routledge, 1995, pp. 270-315.

    On the Master Argument see § 6, pp. 96-102.

  72. Seel, Gerhard. 1982. "Diodore domine-t-il Aristote? En hommage à J. Vuillemin." Revue de Métaphysique et de Morale no. 87:293-313.

    Errata: Revue de Métaphysique et de Morale, 89, 1984. p. 143.

  73. ———. 2018. "The Puzzles of the 'Master Argument' and their Solutions." International Philosophical Inquiry no. 41:81-93.

  74. Shain, Ralph. 2011. "A Defence of Aristotle's 'Sea-Battle' Argument." Pli. The Warwick Journal of Philosophy no. 22:124-137.

  75. Slama, Paul. 2016. "Nécessité, contingence, et possibilité. Heidegger, Vuillemin et l’argument Dominateur." Klesis no. 36:59-90.

  76. Stahl, Gérold. 1963. "Une formalisation du « dominateur »." Revue Philosophique de la France et de l'Étranger no. 153:239-243.

  77. ———. 1979. "Le Dominateur et ses problèmes." Logique et Analyse no. 22:121-131.

  78. Sutula, John. 1976. "Diodorus and the "Master Argument"." Southern Journal of Philosophy no. 14:323-344.

  79. Thomas, Janice. 2006. "The Solipsism Trap, the So-Called Master Argument, and the Pleasant Mistake." History of Philosophy Quarterly no. 23:339-355.

  80. Trzęsicki, Kazimierz. 1987. "Is Discreteness of Time Necessary for Diodorean Master Argument." Bulletin of the Section of Logic no. 16:125-131.

  81. Vidal-Rosset, Joseph. 2009. Les paradoxes de la liberté. Paris: Ellipses.

    Chapitre 2: L’argument de Diodore Kronos 7; 2.1 L’argument rapporté par Epictète 8; 2.2 L’argument du pseudo-Diodore (1965) 8; 2.2.1 Exposé de l’argument 8; 2.2.2 Analyse de l’argument 10; 2.3 Retour à l’argument de Diodore (350 av. J.-C.) 14-16.

    "L’« argument dominateur » de Diodore est plus souvent qualifié d’« aporie(1) » que de « paradoxe ». Cela peut s’expliquer par le fait que la prétendue contradiction produite par la conjonction des trois énoncés n’est en rien intuitive. En effet, Vuillemin, après d’autres, s’est efforcé de donner une démonstration formelle de la contradiction, démonstration qu’il corrigée par la suite(2). Pour des raisons de simplicité, je ne reprendrai pas ici les arguments que Vuillemin donne en faveur de sa reconstruction formelle qu’il veut à la fois fidèle à l’histoire et à la philosophie de Diodore. Les reconstructions formelles de l’argument qui ont été données n’entrent pas dans le cadre de cet ouvrage et je ne ferai donc que les mentionner à l’attention du lecteur qui souhaiterait approfondir la question.

    Mon intention est de donner une explication rigoureuse mais intuitive de l’argument de Diodore (appelé « argument dominateur ».) La section qui suit est un « détour » qui devrait permettre de rendre plus transparent et plus aisé le sens réel de l’argument, présenté d’une façon plus simple. On reviendra à la présentation axiomatique dans la section suivante." (p. 8)

    (1) On nomme « aporie » (en grec aporia, absence de passage, difficulté, embarras) une difficulté à résoudre un problème. Les premiers dialogues de Platon sont dits « aporétiques » parce qu’ils s’achèvent sur une absence de réponse au problème dont il est question dans le dialogue. Ce n’est que par extension de la signification originelle de ce terme que l’on désigne souvent aujourd’hui par « aporie » une problème insoluble et inévitable.

    (2) J. Vuillemin : Necessity or Contingency - The Master Argument. Numéro Lecture Notes N°56. CSLI Publications, Stanford, 1996.

    J. Vuillemin : « Nouvelles réflexions sur l’argument dominateur : une double référence au temps dans la seconde prémisse ». Philosophie, (55): 14-30, sept 1997.

  82. ———. 2011. "Une preuve intuitionniste de l’argument de Diodore-Prior." Travaux de logique no. 20:103-122.

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  84. von Wright, Georg Henrik. 1979. "The 'Master Argument' of Diodorus." In Essays in Honour of Jaakko Hintikka. On the Occasion of His Fiftieth Birthday on January 12, 1979, edited by Saarinen, Esa, Hilpinen, Risto, Niiniluoto, Ilkka and Hintikka, Merill Provence, 297-307. Dordrecht: Reidel.

  85. ———. 1991. "Possibility, plenitude and determinism (with some comments on ancient authors)." In Peter Geach: Philosophical Encounters, edited by Lewis, Harry A., 83-96. Dordrecht: Reidel.

  86. Vuillemin, Jules. 1979. "L'argument dominateur." Revue de Métaphysique et de Morale no. 84:225-257.

  87. ———. 1984. Nécessité ou contingence : L'aporie de Diodore et les systèmes philosophiques. Paris: Éditions du Minuit.

    Nouvelle édition augmentée, 2018.

  88. ———. 1984. "Un système de fatalisme logique: Diodore Kronos." Revue de Philosophie Ancienne no. 3:39-72.

    Repris comme Chapitre III dans: J. Vuillemin, Nécessité ou contingence. L'aporie de Diodore et les systèmes philosophiques, Paris: Éditions de Minuit, 1984.

  89. ———. 1985. "Sur deux cas d’application de l’axiomatique à la philosophie : l’analyse du mouvement par Zénon d’Élée et l’analyse de la liberté par Diodore Kronos." Fundamenta Scientiæ no. 6:209-219.

  90. ———. 1985. "Die Aporie des Meisterschlusses von Diodoros Kronos und ihre Lösungen.

    Ein Beispiel für die Anwendung der axiomatischen Methode auf die Philosophie." Allgemeine Zeitschrift für Philosophie:1-19.

  91. ———. 1986. "Zur Rekonstruktion des Meisterschlusses: Antwort an Helmut Angstl." Allgemeine Zeitschrift für Philosophie no. 11:83-87.

  92. ———. 1991. "Replies." In Causality, Method and Modality: Essay in Honor of Jules Vuillemin, edited by Brittan Jr., Gordon G., 207-224. Dordrecht: Kluwer.

    "This third section responds to a version of Wiggin's article which has been slightly altered. But since the causes of our disagreements have not changed, I did not think it necessary to change my response.

    The first of these disagreements concerns the economy of Diodorus' axioms; it results in part from a misunderstanding, my critique not having taken account of my retractio (see note 2). The second disagreement concerns the original axiom E, for which Wiggins substitutes the forms E' and E", without having reflected on the clauses of external hindrance assumed by the Ancients in the notion of the possible. The third, fundamental disagreement is of a philosophical kind: in order to found the analysis, one of us reverts to the suggestions of natural language, the other of us criticizes them in the name of scientific language."

    (2) For the old, faulty version, see J. Vuillemin, Necessité et Contingence (Les Editions de Minuit, 1984), chapter 2, pp. 27-57. For the new version, see J. Vuillemin, "Zur Rekonstruktion des Meisterschlusses, Antwort an Helmut Angstl. " Allgemeine Zeitschrift fur Philosophie, Frommann Holzboog, 113, 1986.

  93. ———. 1996. Necessity or Contingency. The Master Argument. Stanford: Center for the Study of Language and Information.

  94. ———. 1997. "Nouvelles réflexions sur l'Argument Dominateur: une double référence au temps dans la seconde prémisse." Philosophie no. 55:14-30.

    Repris comme Addedum dans la nouvelle édition augmentée de Nécessité ou contingence. L’aporie de Diodore et les systèmes philosophiques (2018).

    "Révision de l'interprétation modale de la seconde prémisse de l'argument dominateur d'Epictète, selon laquelle l'impossible ne suit pas logiquement du possible, développée par l'Auteur dans son ouvrage intitulé Nécessité ou contingence: l'aporie de Diodore et les systèmes philosophiques (1984). L'Auteur reconstruit son analyse de l'argument aristotélicien du De Coelo et aménage le système chrysippéen à la lumière des principes aristotéliciens de la nécessité conditionnelle et de la contraction synchronique de la possibilité."

  95. Weidemann, Hermann. 1987. "Das sogenannte Meisterargument des Diodoros Kronos und der Aristotelische Möglichkeitsbegriff." Archiv für Geschichte der Philosophie no. 69:18-53.

  96. ———. 1999. "„Aus etwas Möglichem folgt nichts Unmögliches“. Zum Verständnis der zweiten Prämisse von Diodors Meisterargument." Philosophiegeschichte und logische Analyse / Logical Analysis and History of Philosophy no. 2:189-202.

  97. ———. 2008. "Aristotle, the Megarics, and Diodorus Cronus on the Notion of Possibility." American Philosophical Quarterly no. 45:131-148.

  98. ———. 2013. "Die Seeschlacht und das Meisterargument." In Klassische Argumentationen der Philosophie, edited by Puster, Rolf W., 73-89. Münster: Mentis.

  99. White, Michael J. 1980. "Diodorus' "Master" Argument: A Semantic Interpretation." Erkenntnis no. 15:65-72.

  100. ———. 1984. "The Necessity of the Past and Modal-Tense Logic Incompleteness." Notre Dame Journal of Formal Logic no. 25:59-71.

  101. ———. 1985. Agency and Integrality. Philosophical Themes in the Ancient Discussions of Determinism and Responsibility. Dordrecht: Reidel.

  102. ———. 1999. "The Lessons of Prior's Master Argument." Philosophiegeschichte und logische Analyse no. 2:225-238.

    Abstract: "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 ("every past truth is necessary"). 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."

  103. Wiggins, David. 1991. "Temporal Necessity, Time and Ability: a philosophical commentary on Diodorus Cronus' Master Argument as given in the interpretation of Jules Vuillemin." In Causality, Method and Modality: Essay in Honor of Jules Vuillemin, edited by Brittan Jr., Gordon G., 185-206. Dordrecht: Kluwer.

  104. Zeller, Eduard. 1882. "Über Den Kurieuon des Megarikers Diodorus." Sitzungberichte der Preussischen Akademie der Wissenschaften:151-159.

    Reprinted in E. Zeller, Kleine Schriften, Band I, edited by Otto Leuze, Berlin: Reimer, 1910, pp. 252-262.

Related pages

Ancient Stoicism: The Collection of Fragments

The Dialectical (Megarian) School and the Origins of Propositional Logic (under construction)

Bibliography on The Dialectical (Megarian) School

Ancient Stoicism. Editions of the Texts:

Critical Editions and Translations of the Fragments and Testimonia

Stoic Logic:

Stoic Logic: The Dialectic from Zeno to Chrysippus

The Stoic Doctrine of Lekta (Sayables)

Stoic Philosophy of Language and Grammar (under construction)

Annotated Bibliographies on Ancient Stoicism:

Stoic Logic. First Part: A - E

Stoic Logic. Second Part: F - Z

Early Stoic Logicians: Zeno of Citium, Cleanthes, Chrysippus

Philosophy of Language, Grammar and Rhetoric