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History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: rc@ontology.co

 

Annotated Bibliography on the Ancient Stoic Dialectic (First Part: A - G)

Bibliography

  1. Acerbi, Fabio. 2003. "On the Shoulders of Hipparchus: A Reappraisal of Ancient Greek Combinatorics." Archiv for History of Exact Sciences no. 57:465-502

    "My interest here is to reconstruct the way Hipparchus’ numbers were arrived at, trying en passant to convince the reader that time has come for a reappraisal of ancient Greek combinatorics. I shall provide only a resumé of the striking (to modern eyes) interpretation of the numbers in terms of Stoic logic, leaving a wider discussion of the logico-philosophical background for a separate study.The present work is organized as follows. The rationale beyond the identification of 103049 as the tenth Schröder number is briefly summarized in Sect. 2. Section 3 presents a short discussion of the Plutarchean passage, focussing on the technical lexicon employed, and an outline of the interpretation in terms of Stoic logic. Section 4 contains a discussion of combinatorial results in ancient Greek sources, with additional evidence with respect to the one usually adduced, the data being organized in such a way as to follow Hipparchus’ probable calculations. Section 5 offers some provisional conclusions." (p. 467)

  2. Achard, Martin. 2001. "Logos Endiathetos et théorie des Lekta chez les Stoiciens." Laval Théologique et Philosophique no. 57:225-233

    "En guise de préliminaire à ce type d'exploration théorique, et en guise aussi de réponse, bien modeste il va sans dire, aux voeux exprimés par Panaccio dans l'introduction de son ouvrage(11), nous voudrons dans le présent article formuler quelques remarques sur deux des hypothèses interprétatives avancées par notre auteur au sujet de la conception stoïcienne du logos endiathetos, et répondre, comme par avance, à certaines objections qui pourraient être soulevées contre celles-ci. Nos développements nous permettront de signaler, en conclusion, un fait assez intéressant concernant l'histoire de l'élaboration des catégories grammaticales traditionnelles et le rapport pouvant exister entre celles-ci et les catégories de la pensée conceptuelle." (p. 225)(11) « J'espère seulement que le travail accompli [dans mon livre] paraîtra, comme je le crois, suffisamment fécond pour qu'on veuille bien se donner la peine de le compléter ou de le corriger là où il demande à l'être » {Paris, Seuil 1999, p. 14).

  3. Alessandrelli, Michele. 2013. Il problema del 'lekton' nello Stoicismo antico. Origine e statuto di una nozione controversa. Firenze: Olschki

    "According to Michael Frede’s interpretation, the notion oflekton was developed in the context of the Stoic theory of causality, and conceived as a metaphysical entity. The author of the book challenges this developmental explanation, upholding the linguistic origin of the notion oflekton, that would have been always conceived by the Stoics as a purely semantic entity – that is, as the incorporeal meaning of a corporeal linguistic voice."

  4. Allen, James. 2001. Inference from Signs. Ancient Debates About the Nature of Evidence. New York: Oxford University Press

    Contents: Abbreviations XI; Introduction 1; Study I: Aristotle on Sign-inference and Related Forms of Argument 13; Study II: Rationalism, Empiricism, and Scepticism: Sextus Empiricus’ Treatment of Sign inference 87; Study III: The Stoics on Sign-inference and Demonstration 147; Study IV: Epicurean Sign-inference in Philodemus 194; Conclusion 242; Bibliography 255; Index Locorum 265; General Index 276-279."...Study II has three tasks: first, to free the philosophical views that Sextus reports, especially the Stoic position, from the framework he used to classify them; second, to examine the debate about the nature of sign-inference between partisans of commemorative and indicative signification that was carried on in medicine; and last, to examine the sceptical credentials of the commemorative sign which Sextus embraces on behalf of Pyrrhonism.""Study III examines the Stoic theory of signs, now freed from the distorting influence of Sextus’ framework. There I argue that, contrary to the expectations created by Sextus, it belongs among low views of signification and has more affinities with commemorative than indicative signification. But while the medical Empiricists distinguish a higher form of inference, indicative signification, only to repudiate it, the Stoics, like Aristotle, recognize superior forms of inference that they classify under the head of ‘demonstration’. The Stoic distinction between signs and demonstrations takes a different form from Aristotle’s, however, in a way that reflects some fundamental epistemological differences between Aristotle and the Stoa.And we shall see, as others have noticed before, that there was room within the Stoic position for disagreement and development: there were in fact a number of related Stoic positions, which seem to have differed mainly over whether and how demonstrations enter intoscientific explanation." (pp. 9-10)

  5. Annas, Julia. 1980. "Truth and Knowledge." In Doubt and Dogmatism. Studies in Hellenistic Epistemology, edited by Barnes, Jonathan, Burnyeat, Myles and Schofield, Malcolm, 84-104. Oxford: Clarendon Press

    "In the debate on the question, 'What is the criterion of truth ?'(1) the answer provided by the Stoics was, in the main,(2) katalepsis or kataleptike phantasia. l shall translate these as 'apprehension' and 'apprehensible presentation'. (3) These are problematic concepts, asdifficult as the much-debated question of 'the criterion of truth' itself. This discussion tries to bring out some ways in which the debates were clouded by the Stoic failure to distinguish clearly between questions about what we can know and questions about what is the case, and to realize that truth is a metaphysical notion, not an epistemological one." (p. 84)(1) Graeser [75], 68 (cf. Hartmann [47], 4) holds that the question of a criterion of truth was not one the Stoics faced until forced to do so by the challenge of their opponents in the sceptical Academy. But this cannot be right; Zeno was forced by Arcesilaus' criticisms to modify his definition of the apprehensible presentation (e.g. Acad. II 77, Numen. apud Eus. PE XIV 5-6, esp. 732 a and 733 a-c), so he already defended a theory of apprehensible presentations as the criterion. (Possibly he was attacking the Epicurean view that all presentations (not just all perceptions) were true; see SVF II 78, and Striker [133].)(2) DL VII 54 offers what look like various alternative criteria, but these are not rivals to the apprehensible presentation (see Rist [33], 133-4, Long [69]). The word 'criterion' itself did not imply that what was put forward was a guarantee of truth, rather than just a means or way of judging (see Striker [21]); but the Stoics did think of a criterion as a guarantee (see above n. 1).(3) I do not want here to go into the vexed question of whether the word καταλεπτικε had a suggestion of activity (as in 'apprehensive') or of passivity (as in 'apprehensible'). On this see Sandbach [121], 14-15, Graeser [75], 45-50.References[ 21] Striker, G. Kriterion tes Aletheias (Gottingen, 1974); Nachrichten der Akademie der Wissenschaften in Gifttingen, Phil.-hist. klasse, 1974, Nr. 2, 47-110.[37] Rist, J. Epicurus, An Introduction (Cambridge, 1972).[47] Hartmann, H. Gewissheit und Wahrheit: der Streit zwischen Stoa und akademischen Skepsis (Halle, 1927).[69[ 'Sextus Empiricus on the Criterion of Truth', Bulletin of the Institute of Classical Studies 25 (1978), 35-49.[ 75] Graeser, A. Zenon von Kition, Positionen und Probleme (Berlin, 1975).[121] Sandbach, F. H., 'Phantasia Kataleptike', in Long, A. A., ed. Problems in Stoicism (London, 1971), 9-21.[133] Striker, G. 'Epicurus on the Truth of Sense-Impressions', Archiv fiir Geschichte der Philosophie 59 (1977), 125-42.

  6. Aubert, Sophie. 2008. "Cicéron et la parole stoïcienne : polémique autour de la dialectique." Revue de Métaphysique et de Morale:61-91

    Résumé: "Sous la République, la parole stoïcienne fit l’objet, de la part de Cicéron, d’analyses aussi nombreuses et précises que polémiques. La coexistence d’un style syllogistique et d’un autre plus ample au sein d’un même discours conduisit l’Arpinate à discréditer la rhétorique des Stoïciens au point de ne plus reconnaître à ces philosophes qu’un seul mode d’expression – le mode dialectique, dont il conteste la validité tant sous l’angle de la pratique philosophique, jugée inefficace, que du point de vue de l’éloquence, celle-ci étant foncièrement inappropriée à tous les auditeurs. Dans le De Oratore, Crassus analyse le mode d’expression philosophique des Stoïciens sous un angle oratoire, alors qu’il étudie l’éloquence philosophique des Académiciens et des Péripatéticiens sans chercher à examiner si elle conviendrait à un orateur. Dans le Brutus, le personnage éponyme insiste quant à lui sur le caractère prétendument unitaire d’une éloquence stoïcienne censée être identique à Rome et à Athènes, au cours d’entretiens philosophiques ou de discours oratoires. La description du style de Diogène de Babylonie par Antoine confirme pour finir la réduction du style des Stoïciens à la dialectique ainsi que son incapacité à charmer, émouvoir ou même enseigner, sa sécheresse, son obscurité (due à un constant décalage entre le fond et la forme du discours), son inutilité dans le cadre de l’invention et de la topique, et surtout sa propension à l’autodestruction. Pour autant, la dialectique du Portique était bien dotée d’une fonction heuristique, et non uniquement défensive ou agonistique."

  7. Baldassarri, Mariano. 1993. "Un trattatello Plutarcheo di dialettica stoica: De E Delphico Cap. VI." In Studi di filosofia antica. Vol. II, 43-65. Como: Libreria Noseda

    Prima edizione in tedesco in: Klaus Döring, Theodor Ebert (hersg.), Dialektiker und Stoiker. Zur Logik der Stoa und ihrer Vorläufer, (1993), pp. 33-46."Del passo plutarcheo or ora presentato in traduzione [*] vediamo di effettuare un inquadramento rapido nel contesto dell’opuscolo e, soprattutto, una accurata analisi in vista di alcune conclusioni significative (i).Il dialogo s’imposta, come è noto, sul significato da dare alla E di grandi dimensioni sospesa come dono votivo al di sotto del frontone del tempio di Apollo in Delfi tra le colonne del pronao." (p. 43)(...)"Questo capitolo sesto si presenta dunque come un trattatello di dialettica stoica. Compito primo della dialettica è la soluzione delle ambiguità (e dei sofismi) ossia la ricerca ed il conseguimento della verità: il rettamente discutere in vista del rettamente intendere. La dialettica ha come unità elementari non gli enunciabili completi non assertorii bensì le proposizioni logiche (semplici o non semplici); e delle non semplici la proposizione più caratteristicamente deduttiva è la proposizione condizionale, la quale si imposta sulla congiunzione caratteristicamente connettiva ‘se’: mentre le bestie hanno conoscenza dei fatti, soltanto l’uomo (che è fornito di ragione) conosce e giudica la connessione necessaria di un fatto con un altro fatto, il conseguire di un fatto ad un altro fatto, ossia il rapporto — positivo o negativo — del conseguente (del secondo) con l’antecedente (col primo) sia per presenza implicita del conseguente nell’antecedente sia per coerenza del conseguente con l’antecedente. Sorge così il primo anapodittico: aggiungendo alla proposizione condizionale, che pone la connessione e costituisce la premessa maggiore, l’affermazione dell’effettivo darsi dell’antecedente mediante la premessa minore, si afferma nella conclusione l’effettivo darsi del conseguente (o si ottiene il secondo anapodittico: negando nella minore il darsi del conseguente, si nega nella conclusione il darsi dell’antecedente). Per questa via (ma anche per la via della proposizione congiuntiva e della proposizione disgiuntiva, ossia mediante gli anapodittici terzo, quarto e quinto) si può realizzare la dimostrazione, che è verità (e sapere organizzato o scienza). E la dimostrazione è conoscenza, attraverso ciò che presentemente è, di ciò che in passato fu, in quanto causa appunto del presente, e di ciò che in futuro sarà, in quanto effetto appunto del presente: la ragione è ricerca della causa, e la sillogistica (innanzitutto la sillogistica della dialettica mantica) ha il suo fondamento nel principio ontologico di causa (nella serie eterna delle cause)." (p. 56)[*] De E Delphico 6, pp. 386D-387D; tr. it. Plutarco, L'E di Delfi, a cura di Claudio Moreschini, Napoli, D'Auria, 1998.

  8. ———. 1993. "Il Simposio di Bamberg sulla logica degli Stoici e dei suoi precursori." In Studi di filosofia antica. Vol. II, 67-107. Como: Libreria Noseda

    Note sul Symposion zur Logik der Stoiker und ihrer Vorläufer (Bamberg, 2-6 September 1991).

  9. ———. 1993. "Una rilevante disciplina antica documentata in modo nuovo (Discussione)." In Studi di filosofia antica. Vol. II, 109-123. Como: Libreria Noseda

    A proposito del libro di Karlheinz Hülser, Die Fragmente zur Dialektik der Stoiker, Stuttgart: Frommann Holzboorg 1986-1987.

  10. ———. 1993. "Osservazioni sull'interpretazione Prantliana della logica Stoica." In Studi di filosofia antica. Vol. II, 125-138. Como: Libreria Noseda.

  11. ———. 1993. "Ein kleiner Traktat Plutarchs über stoische Logik." In Dialektiker und Stoiker. Zur Logik der Stoa und ihrer Vorläufer, edited by Döring, Klaus and Ebert, Theodor, 33-46. Stuttgart: Franz Steiner.

  12. Barnes, Jonathan. 1980. "Proof Destroyed." In Doubt and Dogmatism. Studies in Hellenistic Epistemology, edited by Barnes, Jonathan, Burnyeat, Myles and Schofield, Malcolm, 161-181. Oxford: Clarendon Press

    Reprinted in: J. Barnes, Proof, Knowledge, and Scepticism: Essays in Ancient Philosophy III, edited by Maddalena Bonelli, Oxford: Clarendon Press 2014.

  13. ———. 1982. "Medicine, Experience and Logic." In Science and Speculation. Studies in Hellenistic Theory and Practice, edited by Barnes, Jonathan, Brunschwig, Jacques, Burnyeat, Myles and Schofield, Malcolm, 24-68. Cambridge: Cambridge University Press

    Reprinted in: J. Barnes, Logical Matters. Essays in Ancient Philosophy II, edited by Maddalena Bonelli, Oxford: Clarendon Press 2012, pp. 538-581.Translated in French as "Médécine, expérience et logique", in Revue de Métaphysique et de Morale, 1989, 94, pp. 437-481.

  14. ———. 1985. "Theophrastus and Stoic Logic." In Aristoteles. Werk Und Wirkung, Paul Moraux Gewidmet, I: Aristoteles Und Seine Schule, edited by Wiesner, Jürgen, 557-576. Berlin: Walter de Gruyter

    Reprinted in: J. Barnes, Logical Matters. Essays in Ancient Philosophy II, edited by Maddalena Bonelli, Oxford: Clarendon Press 2012, pp. 413-432.

  15. ———. 1997. Logic and the Imperial Stoa. Leiden: Brill

    Contents: Preface IX-XI; Chapter One: The Decline of Logic 1; Chapter Two: Seneca 12; Chapter Three: Epictetus 24; Chapter Four: Conclusion 126; Appendix: Epictetus, diss I vii 129; Bibliography 147; Indexes: Passages 155; Persons 159: Topics 162-165.

  16. ———. 1999. "Aristotle and Stoic Logic." In Topics in Stoic Philosophy, edited by Ierodiakonou, Katerina, 23-53. Oxford: Clarendon Press

    Reprinted in: J. Barnes, Logical Matters: Essays in Ancient Philosophy II, Oxford: Clarendon Press, 2012, pp. 382-412."Were Aristotle's logical writings known to the early Stoic logicians, and did Aristotle's logical ideas have any influence on the development of Stoic logic? The evidence which bears on this question is perplexing: there are numerous pertinent texts which favour an affirmative answer; yet as we approach them they seem, like so many will-o'-the-wisps, to retreat -- and we are stumbling in a treacherous marsh.But the question is not without its fascination, in as much as it concerns the historical relations between two magnificent monuments to Greek philosophical acumen; and it may stand some discussion. Section I presents some general ruminations. Section II deals with the preliminary question of whether the Stoics could in principle have read Aristotle. Section III assembles a sample of the evidence which suggests that the Stoics did in fact read and study their Aristotle. And the remaining sections try to assess the value of this evidence.The question is a historical one, and it invites consideration of a certain type of historical explanation. It is not merely a matter of whether the Stoics were aware of the Peripatetic achievement in logic: it is a matter of whether this awareness influenced their own logical thoughts and caused them to think in this way rather than in that." (p. 23)

  17. ———. 2005. "What Is a disjunction?" In Language and Learning: Philosophy of Language in the Hellenistic Age. Proceedings of the Ninth Symposium Hellenisticum, edited by Frede, Dorothea and Inwood, Brad, 274-298. Cambridge: Cambridge University Press

    Reprinted in J. Barnes, Logical Matters. Essays in Ancient Philosophy II, Oxford: Clarendon Press 2012, pp. 512-537."That the Stoics were the instigators of the emphasis put on linguistic observations in ancient philosophy is uncontested. To what degree they are rightly accused of paying more attention to expressions rather than to things is quite another matter, despite the fact that this reproach was voiced repeatedly in antiquity by authorities such as Galen and Alexander of Aphrodisias and has lasted through the nineteenth century AD. If the Stoics have enjoyed a better press since the twentieth century it is because they were taken to be logicians for logic's sake, committed formalists who stopped just short of inventing the appropriate type of artificial language. That this picture needs revision is argued by Jonathan Barnes (What is a disjunction?') in a painstaking investigation of the treatment of connectives in Apollonius Dyscolus' essay with that title and Galen'sInstitutio logica. Barnes shows that Apollonius' text is coherent and thereby undermines a long-standing prejudice about the Stoic impact on the development of traditional grammar: contrary to what has been assumed (via an unwarranted textual emendation in a crucial passage of Apollonius Dyscolus) Apollonius does not criticise the Stoics' meddling with grammar, but rather their insufficient interest in some of its finer points. Far from adopting a purely formalistic stance, the Stoics distinguished between natural and non-natural disjunctions and colligations. They used these considerations not only to distinguish between natural and occasional disjunctions, but also between grammatical and semantical nonsense. Since no other text besides Apollonius' attributes the conception of 'natural disjunctions' to the Stoics it is a question whether it actually is of Stoic origin rather than derived from the Peripatetics or an invention by certain grammarians. As Barnes shows, the interconnections and boundaries between natural language and formal logic did not only play a crucial role in the treatment of disjunctions by Apollonius Dyscolus. They are also the basis of Galen's criticism of Stoic logic on the differentiation between complete and incomplete conflict and implication, whose intent was to show what is and what is not a legitimate use of conjunctions. If that distinction is at stake, then Galen's view on disjunctions and conjunctions turns out to be coherent, despite initial appearances to the contrary. The differing parties accused each other of not having paid sufficient attention to thepragmata; however, their complaint is not that the facts in the world have been ignored, but rather that the meaning of the terms has not received sufficient attention." From the Introduction by Dorothea Frede and Brad Inwood (pp. 11-12).

  18. ———. 2009. "Grammaire, rhétorique, épistémologie, et dialectique." In Lire les stoïciens, edited by Gourinat, Jean-Baptiste and Barnes, Jonathan, 135-149. Paris: Presses Universitaires de France.

  19. ———. 2011. "Reading the Hypotheticals." In Argument from Hypothesis in Ancient Philosophy, edited by Longo, Angela, 187-280. Napoli: Bibliopolis.

  20. Becker, Oskar. 1957. Zwei Untersuchungen Zur Antiken Logik. Wiesbaden: Otto Harrassowitz

    Inhalt: Zum Problem der platonischen Idealzahlen (Eine Retraktation) 1; Miszellen zu mathematisch-philosophischen Texten 23; Über die vier Themata der stoischen Logik 27; Miszellen zur stoische Logik 50-55.

  21. Berrettoni, Pierangiolo. 1997. "L'άξίωμα διασαφου̂ν τό μα̂λλον nella logica stoica." In Grammatica e ideologia nella storia della linguistica, edited by Berrettoni, Pierangiolo and Lorenzi, Franco, 1-34. Perugia: Margiacchi - Galeno.

  22. Bobzien, Suzanne. 1986. Die Stoische Modallogik. Würzburg: Kõnighausen-Neumann

    Inhalverzeichnis: Einleitung 4;I. Der Axioma-Begriff der Stoiker 11;1. Die stoische Definition des Axioma-Begriffes 11; 2. Vorläufige Bestimmung der Wahrheitskriterien des stoischen Axioms 14; 3. Der gleiche Satz bezeichnet verschiedene Axiomata: das definite Axioma 17; 4. Axiomata vergehen 18; 5. Axiomata, die ihren Wahrheitswert wechseln:meta - piptonta 21; 6. Das Bestehen des dem Axioma korrespondierenden Sachverhalts wird durch das Axiome je nur für den Zeitpunkt der Behauptung dieses Axioma behauptet 23; 7. Zeitbezogene Axiomata 26; 8. Wahrheitsbedingungen der zeitbezogenen Axiomata 28; 9. Wahrheitswertwechsel der zeitbezogenen Axiomata 26; 9. Axiomata mit Pseudodaten 31; 11. Nichtzeitbezogene Axiomata 34; 12. Zusammenfassung 36;II. Die stoische Modallogik 40;1.Die Definitionen der stoischen Modalbegriffe 40; a) Interpretation und Rekonstruktionsversuche vor Frede 40; b) Fredes Rekonstruktion der stoischen Modalbegriffe 45; 2.Korrelation der stoischen Axioma- und Sachverhaltsmodi 50; 3. Die Sachverhaltsmodi und ihre überlieferten Bestimmungen 51;4. Kontingente Axiomata und Sachverhalte 56; 5. Der Ausdruck 'epidektikon aletés / pseudos einai 60; 6. Die Modalitäten der nichtzeitbezogenen Axiomata 63; 7. Der Ausdruck 'äussere Umstände hindern...' 67; 8. Die Modalitäten der zeitbezogenen Axiomata 72; a) Die Modalitäten der Axiomata über die Gegenwart 73; b) Die Modalitäten der Axiomata über die Vergangenheit 76; c) Die Modalitäten der Axiomata über die Zukunft 91; 9. Zusammenfassung und Schlussfolgerung bzgl. der Art der Modalitäten der zeitbezogenen Axiomata 98; 10. Modalitätenwechsel 103; 11. Aus Möglichem folgt Unmögliches 105; 12. Die Rekonstruktion des stoischen Modalsystems von Mignucci und Vuillemin 113; 13. Zusammenfassung 118; Anmerkungen 121; Symbol- und Abkürzungsverzeichnis 142; Literaturverzeichnis 143-147.English Abstract: "Part I 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 II 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 I see "Stoic Logic", in K. Algra et al. (eds), The Cambridge History of Hellenistic Philosophy, Cambridge: Cambridge University Press 1999, pp. 92-157.For a shorter, updated, English version of Part II see "Chrysippus' Modal Logic and its Relation to Philo and Diodorus", in K. Döring, Th. Ebert (eds.), Dialektiker und Stoiker, Stuttgart: Franz Steiner1993, pp. 63-84.

  23. ———. 1996. "Stoic Syllogistic." Oxford Studies in Ancient Philosophy no. 14:133-192

    "For the Stoics, a syllogism is a formally valid argument, and the primary function of their syllogistic is to establish the formal validity of arguments. Stoic syllogistic can be understood as a system of formal logic that relies on two types of argumental rules:' first, five rules (the accounts of the indemonstrables) which were used to determine whether any given argument is an indemonstrable argument (anapodeiktos logos), i.e. an elementary syllogism the validity of which is not in need of further demonstration (D.L. 7.79), since its validity is evident in itself (Sextus,M. 2. 223);2 second, one unary and three presumably binary argumental rules, called themata, which allow one to establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (D.L. 7. 78). The function of these rules is not to generate non indemonstrable syllogisms from indemonstrable ones, but rather to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed. The Stoic system may hence be called an 'argumental reductive system of deduction'.In the following I present a reconstruction of this system of logic. The rules or accounts used for establishing that an argument is indemonstrable have all survived, and the indemonstrables are among the best-known elements of Stoic logic. However, their exact role and logical status in Stoic syllogistic are usually neglected. I expound how they are integrated in the system of deduction. The state of evidence for thethemata is dismal -- although perhaps not hopeless. I suggest a reconstruction of thethemata, based on a fresh look at some of the sources, and then offer a reconstruction of the general method of reduction of arguments and some general remarks on Stoic syllogistic as a whole and on the question of its completeness (much of which will not depend on the particular formulation of thethemata I propose, but on more general considerations for a reconstruction).Stoic logic is a propositional logic, and Stoic negation and conjunction are truth-functional. This has, naturally, led to comparisons with the 'classical' propositional calculus (as e.g. presented inPrincipia Mathematica), including repeated examinations of Stoic syllogistic on completeness in the modern sense. The Stoic theory of deduction invariably comes out as deficient, inferior, or simply outlandish in such comparisons, which has evoked adjusting additions and modifications -- tacit or explicit -- in previous reconstructions of the system. I suggest that this is the wrong approach; that the classical propositional calculus is the wrong paradigm; that Stoic logic has to be considered first of all in its own light; and that, if one looks for comparisons with contemporary logic, one can find some rather more interesting parallels when turning one's attention to non-truth-functional propositional logics." (pp. 133-134)(1) By an argumental rule I mean a rule that produces arguments from (zero or more) arguments, as opposed to a rule that produces propositions from (zero or more) propositions.(2) The accounts of the indemonstrables, when interpreted as rules, are nullary argumental rules.

  24. ———. 1997. "The Stoics on Hypotheses and Hypothetical Arguments." Phronesis.A Journal for Ancient Philosophy no. 42:299-312

    "In the list of Chrysippus' logical writings in Diogenes Laertius, in its fourth section of works on arguments(λογοι), e find ten books on hypothetical arguments (υποθετικόι λογοι, D. L. VII 196). The questionI shall follow up in this paper is: what were these Stoic hypothetical arguments about which Chrysippus had so much to say? Little has been written on this issue, the situation of the sources being not exactly favourable. No example of an hypothetical argument assigned to Chrysippus or any other early Stoic has survived, nor do we have any Stoic definition.One way of approaching the issue is to look and see what arguments were called "hypothetical arguments" or "hypothetical syllogisms" after Chiysippus, and to examine whether these are the same kind of arguments Chrysippus wrote about." (p. 299)

  25. ———. 1999. "Logic. III. The Stoics." In The Cambridge History of Hellenistic Philosophy, edited by Algra, Keimpe, Barnes, Jonathan, Mansfeld, Jaap and Schofield, Malcolm, 92-176. Cambridge: Cambridge University Press

    §§ 1-7 (pp. 92-157) by Susanne Bobzien; § 8 (pp. 157-176) by Mario Mignucci.

  26. ———. 2002. "Pre-Stoics Hypothetical Syllogistic in Galen's Institutio Logica." In The Unknown Galen, edited by Nutton, Vivian, 57-72. London: Institute of Classical Studies, University of London

    "The text of the Institutio Logica (IL) or Introduction to Logic is not found in Kuhn [*] because its sole surviving manuscript was first published, not long after its discovery, in 1844, and thus too late for inclusion in Kuhn. Moreover, some have thought the work to be spurious.(1)The reasons given for this assumption were on the whole unconvincing. I take it for granted that the Institutio Logica is by Galen.In this paper I trace the evidence in the Institutio for a hypothetical syllogistic which predates Stoic propositional logic. It will emerge that Galen is one of our main witnesses for such a theory. In the Institutio, Galen draws from a number of different sources and theories.There are the so-called ancient philosophers (οι παλαιοι των Φιλοσοφων); there is the Stoic Chrysippus, whose logic Galen studied in his youth.(2) There are the ‘more recent philosophers’ (οι νεωτεροι), post-Chrysippean Stoics or logicians of other schools who adopted Stoic terminology and theory.(3) There are from the 1st century BC the Stoic Posidonius and the Peripatetic Boethus, both of whom Galen may have counted among the ‘more recent philosophers’. Again, in some passages Galen seems to draw from contemporary logicaltheories of non-Stoic make, presumably of Peripatetic or Platonist origin; and in others he explicitly introduces his own ideas.(4) But apart from Plato, who is generously credited by Galen with the use of the later so-called second hypothetical syllogism, the only promisingcandidates for pre-Stoic proponents of a hypothetical syllogistic are the above-mentioned 'ancient philosophers'. In the following I concentrate on their theory."[* Karl Gottlob Kühn, Claudii Galeni Opera Omnia. Leipzig: C. Cnobloch, 1821-1833, 19 volumes, reprinted Hildesheim: Georg Olms,1964-1997].(1) E.g. C. Prantl, Die Geschichte der Logik im Abendlande vol. I (Leipzig 1855) 591-92.(2) Cf. Galen, On my own books, 43 (Kühn XIX).(3) Cf. L S. Kieffer, Galen's Institutio Logica (Baltimore 1964) 130-32; J. Bames, ‘Form and Matter’, in A. Alberti, ed., Logica, Mente e Persona (Florence 1990) 7-119, at 71-23.(4) E.g. in chapters 16-17 of the Institutio.

  27. ———. 2003. "Stoic Epistemology." In The Cambridge Companion to Stoics, edited by Inwood, Brad, 59-84. Cambridge: Cambridge University Press.

  28. ———. 2005. "The Stoics on Fallacies of Equivocation." In Language and Learning. Philosophy of Language in the Hellenistic Age. Proceedings of the Ninth Symposium Hellenisticum, edited by Frede, Dorothea and Inwood, Brad, 239-273. Cambridge: Cambridge University Press

    "As Susanne Bobzien shows, the Stoics had philosophical reasons for the development of strategies to handle `lexical' ambiguities, because they regarded fallacies of ambiguity as complexes of propositions and sentences that straddle the realm of linguistic expression (the domain of language) and the realm of meaning (the domain of logic); moreover, there is also a pragmatic component because being deceived is a psychological disposition that can be reduced neither to language nor to meaning. Not all arguments are, after all, as transparently fallacious as is the example that exploits the ambiguity of 'for men/manly' and concludes that a 'garment for men' must be courageous because manliness is courage. Bobzien provides a detailed analysis of the relevant passages, lays bare textual and interpretative difficulties, and explores what the Stoic view on the matter implies for their theory of language. She points up that the Stoics believe that the premisses of the fallacies, when uttered, have only one meaning and are true, and thus should be conceded; hence no mental process of disambiguation is needed, while Aristotle, by contrast, assumes that the premisses contain several meanings, and recommends that the listeners explicitly disambiguate them. Bobzien proffers two readings of the Stoic advice that we 'be silent' when confronted with fallacies of ambiguity, and explicates how each leads to an overall consistent interpretation of the textual evidence. Finally, she demonstrates that the method advocated by the Stoics works for all fallacies of lexical ambiguity." (From the Introduction by Dorothea Frede and Brad Inwood, (pp. 10-11)

  29. ———. 2011. "The Combinatorics of Stoic Conjunction: Hipparchus Refuted, Chrysippus Vindicated." Oxford Studies in Ancient Philosophy no. 40:157-188.

  30. ———. 2019. "Stoic Sequent Logic and Proof Theory." History and Philosophy of Logic no. 40:234-265

    Abstract: "This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. "

  31. Bobzien, Suzanne, and Dychoff, Roy. 2019. "Analyticity, Balance and Non-admissibility of Cut in Stoic Logic." Studia Logica no. 107:375-397

    Abstract: "This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), extended by a classical rule T1 (from the Stoics) and using certain axioms (also from the Stoics), all derivations are analytic: every cut formula occurs as a subformula in thecut’s conclusion. Since the Stoic cut rules are instances of Gentzen’s Cut rule of 1933, [*] from this we infer the decidability of the propositional logic of the Stoics. We infer the correctness for this logic of a “relevance criterion” and of two “balance criteria”, and hence(in contrast to one of Gentzen’s 1933 results) that a particular derivable sequent has no derivation that is “normal” in the sense that the first premiss of each cut is cut-free. We also infer that Cut is not admissible in the Stoic system, based on the standard Stoicaxioms, the T1 rule and the instances of Cut with just two antecedent formulae in the first premiss." [*] Gentzen, G., ¨Uber die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen, Mathematische Annalen 107:329–350, 1933.

  32. Bobzien, Suzanne, and Mignucci, Mario. 2003. "Logic." In The Cambridge Companion to Stoics, edited by Inwood, Brad, 85-123. Cambridge: Cambridge University Press

    §§ 1-7 (pp. 92-157) by S. Bobzien; § 8 (pp. 157-176) by M. Mignucci.

  33. Bochenski, Joseph. 1951. Ancient Formal Logic. Amsterdam: North-Holland

    Chapter V. The Stoic-Megaric School, pp. 77-102.

  34. ———. 1961. A History of Formal Logic. Notre Dame: Indiana University Press

    Translated from the German edition "Formale Logik" (1956) by Ivo Thomas.Reprinted New York, Chelsea Publishing Co., 1970.On the Stoics see Part III. The Megarian-Stoic School, pp. 105-251.

  35. Boersma, Gerald P. 2014. "The Logic of the Logos: A Note on Stoic Logic in Adversus Praxean 10." Journal of Early Christian Studies no. 22:485-498

    "Tertullian sees logic as inhering in language, and he takes this notion from the Stoic tradition. I will argue that it is this Stoic link between logic and language that enables Tertullian to make sense of the scriptural language that distinguishes between the divine persons. After briefly considering the nature of Stoic dialectic, I will analyze the presence of Stoic dialectic in Adversus Praxean 10, and conclude by remarking on the theological significance of Stoic dialectic in this passage. Studies on the place of Stoic thought in Tertullian have tended to focus on his appropriation of this philosophical tradition in his ethics and anthropology. There remains a lacuna in any real engagement with the place of Stoic dialectic in his thought." (p. 486)

  36. Brancacci, Aldo. 2005. "Antisthène et le stoïcisme: la logique." In Les Stoïciens, edited by Romeyer, Dherbey Gilbert and Gourinat, Jean-Baptiste, 55-73. paris: Vrin.

  37. Brittain, Charles. 2005. "Common Sense: Concepts, Definition and Meaning in and out of the Stoa." In Language and Learning: Philosophy of Language in the Hellenistic Age. Proceedings of the Ninth Symposium Hellenisticum, edited by Frede, Dorothea and Inwood, Brad, 164-209. Cambridge: Cambridge University Press

    "Charles Brittain also focuses on an important aspect of the philosophical analysis of language: its relation to reality and to the conceptual apparatus in the human mind, which on most theories connects reality to language. To the naive mind, a concept like 'common sense' would not seem to be in need of development since it must have been in place since the dawn of human reasoning. Nor is that the issue of Brittain's paper. Instead, he focuses on the development of atheory of common sense that is based on the connection between a stock of rational conceptions that is the common possession of all humans and the words which map naturally onto those conceptions and so give expression to them. The Stoics themselves did not maintain that everyone can acquire conceptions that successfully capture the essence of things; such success presupposes the uncorrupted mind of the wise; so these normative concepts do not seem to be an obvious source for a theory of common conceptions that are open to all. As Brittain contends, it would nevertheless be wrong to attribute such a theory to the later Platonists despite the fact that they advocated the existence of universally acceptable word-meanings that are open to every human being's grasp. For Platonists regarded these meanings as mere accidental features of the thing in question. What was needed to establish a theory of common sense was a combination of the two theories: the 'preliminary definition' of a term with universal acceptance that lays claim to at least a partial grasp of the thing's essence. En route to this solution Brittain offers,inter alia, a reconstruction of the mechanism at work in the formation of common concepts with abstract and general contents and seeks to solve the conundrum of how definitions of the words corresponding to the concepts are formed. He does so by carefully sifting through different sources that employ Stoic vocabulary (such as 'preconceptions' or 'common conceptions') but that differ significantly from the Stoic view that all humans have at least a partial grasp of a thing's essential properties, rather than mere accidental properties. This assumption paves the way towards a theory of 'common sense' that establishes a direct connection between the concepts and the objects of the world and explains how ordinary language-speakers have at least an outline understanding of the world. Such a theory, so Brittain argues, is the upshot of Cicero's treatment of preconceptions, in the basis of definitions. The rendering of 'preconception'(prolepsis) as shared by all - bycommunis mens and finally bycommunis sensus - justifies the attribution to Cicero of at least 'a fragment of a theory of common sense' in civic and political matters that everyone in principle can understand. This was a theory that deeply influenced the later rhetorical tradition and thereby became a lasting asset in cultural history." (From the Introduction by Dorothea Frede and Brad Inwood, (pp. 8-9)

  38. ———. 2014. "The compulsions of Stoic assent." In Strategies of Argument: Essays in Ancient Ethics, Epistemology, and Logic, edited by Lee, Mi-Kyoung, 332-355. New York: Oxford University Press.

  39. Brochard, Victor. 1892. "La logique des Stoïciens." Archiv für Geschichte der Philosophie no. 5:449-468

    Repris dans: V. Brochard, Études de philosophie ancienne et de philosophie moderne: XI. La logique des Stoïciens (Première étude, pp. 220-238); XII. La logique des Stoïciens (Deuxième étude, pp. 239-251), Paris: Vrin, 1954.

  40. Bronowski, Ada. 2014. "La structure logique du langage ordinaire chez les Stoiciens." In Philosophie et langage ordinaire de l'Antiquité à la Renaissance, edited by Counet, Jean-Michel, 83-96. Edition Peeters.

  41. ———. 2019. The Stoics on Lekta: All There Is to Say. New York: Oxford University Press.

  42. Brunschwig, Jacques. 1980. "Proof Defined." In Doubt and Dogmatism. Studies in Hellenistic Epistemology, edited by Barnes, Jonathan, Burnyeat, Myles and Schofield, Malcolm, 125-160. Oxford: Clarendon Press.

  43. ———, ed. 2006. Les Stoïciens et leur logique. Paris: Vrin

    Actes du Colloque de Chantilly 18-22 septembre 1976.Première édition 1978; deuxième édition, revue, augmentée et mise à jour (reproduit la pagination de l'édition originale).Table des matières: Avant propos de la deuxième édition 7; Avant propos de la première édition 11; John M. Rist: Zeno and the Origins of Stoic Logic (non revu par l'auteur) 13; Ian G. Kidd: Posidonius and Logic (revu par l'auteur) 29; Victor Goldschmidt: Remarques sur l'origine épicurienne de la "prénotion" (revu par Pierre-Marie Morel) 41; Anthony A. Long: The Stoic Distinction Between Truth (me alétheia) and the True (to alethés) (revu par l'auteur) 61; Claude Imbert: Théorie de la représentation et doctrine logique dans le stoïcisme ancien (revu par l'auteur) 79; George Kerferd: The Problem of syntakatathesis and katalepsis in Stoic Doctrine (revu par Thomas Bénatouïl) 109; Urs Egli: Stoic Syntax and Semantics (revu par l'auteur) 131; Pierre Pachet: l'imperatif stoïcien (revu par l'auteur) 149; Françoise Caujolle-Zaslawsky: Le style stoïcien et la paremphasis (revu par l'auteur) 165; Richard Goulet: La classification stoïcienne des propositions simples selon Diogène Laërce, VII 69-70 (revu par l'auteur) 191; Anthony C. Lloyd: Definite Propositions and the Concept of Reference (revu par Jean-Baptiste Gourinat) 223; Jacques Brunschwig: Le modèle conjonctif (revu par l'auteur) 235; Gérard Verbeke: La philosophie du signe chez les stoïciens (revu par Danielle Lories) 261; Hervé Barreau: Cléanthe et Chrysippe face au maître-argument de Diodore (revu par l'auteur) 283; Mario Mignucci: Sur la logique modale des stoïciens (revu par Paolo Crivelli) 303; Pasquale Pasquino: Le statut ontologique des incorporels dans l'ancien stoïcisme (revu par l'auteur) 333; Andreas Graeser: The Stoic Categories (revu par l'auteur) 347; Janine Bertier: Une hénadologie liée au stoïcisme tardif dans le commentaire d'Alexandre d'Aphrodise à laMétaphysique d'Aristote (990 b 9) (non revu par l'auteur) 369; Jean-Paul Dumont: Mos geometricus, mos physicus (revu par Pierre-Marie Michel) 389; Joseph Moreau: Immutabilité du vrai, nécessité logique et lien causal (revu par Valéry Laurand) 405; Jonathan Barnes: La doctrine du retour éternel (revu par l'auteur) 421; Maria Daraki: Les fonctions psychologiques dulogos dans le stoïcisme ancien (non revu par l'auteur) 441; Bibliographie complémentaire 475; Index locorum 485-509.

  44. Burnyeat, Myles. 2005. "The origins of non-deductive inference." In Science and Speculation. Studies in Hellenistic Theory and Practice, edited by Barnes, Jonathan, Brunschwig, Jacques, Burnyeat, Myles and Schofield, Malcolm, 193-238. Cambridge: Cambridge University Press

    Reprinted in M. Burnyeat, Explorations in Ancient and Modern philosophy, Volume 1, Cambridge: Cambridge University Press 2012 pp. 112-151.

  45. Cameron, Margaret. 2015. "On What is Said: The Stoics and Peter Abelard." In Linguistic Content: New Essays on the History of Philosophy of Language, edited by Cameron, Margaret and Stainton, Robert, 55-73. Oxford: Oxford University Press

    "A novel kind of meaning shows up, apparently independently, in the philosophy of the Stoics and of Peter Abelard (1079–1142). For the Stoics it is the lekton, or ‘sayable’ (or, more precisely, the axioma, or‘assertible’, which is one type of lekton), and for Abelard it is the dictum. The extent of similarity between their doctrines is surprising, especially because there is no evidence of a historical connection between them: as far as we know, Abelard did not have access to any Stoic writings, or reports of Stoic views, on the topic of linguistic content. (1) The similarity is more surprising still, given that Abelard was working within the context of Aristotle’s logic, which contains no comparable doctrine. Historians of philosophy have noticed this similarity.(2) When the comparison is drawn it is with reference to the fact of their shared recognition of this new type of content—propositional content. But there are other remarkable points of similarity in their views. First, both seem to have been motivated, at least in part, by the need to disambiguate the notion of‘predication in the ancient philosophical tradition. Second, both the Stoics (at least beginning with Chrysippus, the third head of the school) and Abelard were driven by a commitment to anti-realism, and by the need to present an anti-realist, or at least deflationary, metaphysics. After a brief outline of each of their doctrines, I will compare their views on the points mentioned here." (p. 55)(1) While Augustine’s De dialectica contains some version of the Stoic doctrine, his treatise does not appear to have circulated until the thirteenth century. Another possible source might have been Cicero, but I know of no evidence to support such a transmission. (2) Martin (2004), who cites Nuchelmans (1973) and Schenkeveld (1984). See also Jacobi (1983) and Lenz (2005). But see Nuchelmans (1973: 152): it is hardly necessary to add that the Abelardian term dictum has nothing to do with the Stoic term lekton.’"Conclusion. In conclusion, what happens to this new type of linguistic content after Abelard? Theories of propositional content emerge, disappear, and re-emerge throughout the medieval and scholastic periods. The interest is preserved in the continuation of the logical tradition, still rooted in Aristotelian logic, beginning in the twelfth century. Some theorists seemed to have been entirely unconcerned with the ontological implications and underpinnings of these sorts of linguistic content. For example, the author(s) of a thirteenth-century logical textbook called the Ars Burana explain(s) that it is best considered to be an extrapredicamental thing (that is, not countenanced in what exists in an Aristotelian ontology of substances and accidents): Note that whether it is called a dictum propositionis or the significatum propositionis or the enuntiabile, it is the same. The enuntiable is that which is signified by the proposition . . . If you inquire what kind of thing it is, whether it is a substance or an accident, it must be said regarding the enuntiable, just as regarding the predicable, that it is neither a substance nor an accident nor is it of any other category. For it has its own per se mode of existing. And it is called ‘extrapredicamental’, not for the reason that it does not belong to any category, but because it does not belong to any of the ten categories that Aristotle distinguished. It is therefore of a certain category which can be called the ‘enuntiable category’. (53) Later, some philosophers attempted to defend a view that took the opposite tack— that is, to defend a view of propositional realism, only to encounter some of the same sorts of anti-realist challenges.(54)" (p. 71)(53) Ars Burana (1967: 208). See De Libera (1981); Martin (2004). (54) The best study of this topic is Cesalli (2007).ReferencesArs Burana (1967). Anon., Ars Burana, in L. M. de Rijk (ed.), Logica modernorum: A Contribution to the History of Terminist Logic. Assen: Van Gorcum, 175–213. Cesalli, L. (2007). Le Réalisme propositionnel: Sémantique et ontologie des propositions chez Jean Duns Scot, Gauthier Burley, Richard Brinkley, et Jean Wyclif. Paris: J. Vrin. De Libera, A. (1981) ‘Abélard et le dictisme’, Cahiers de la revue de théologie et de philosophie, 6: 59–92. Jacobi, K. (1983).‘Abelard and Frege: The Semantics of Words and Propositions’, in Atti del convegno internazionale di storia della logica, ed. V. M. Abrusci (San Gimignano: CLUEB), 81–96. Lenz, M. (2005).‘Peculiar Perfection: Peter Abelard on Propositional Attitudes’, Journal of the History of Philosophy, 43/4: 377–86. Martin, C. (2004).‘Propositionality and Logic in the Ars Meliduna’, in A. Maierù and L. Valente (eds), Medieval Theories on Assertive and Non-Assertive Language. Florence: Olschki, 111–28. Nuchelmans, G. (1973). Theories of the Proposition: Ancient and Medieval Conceptions of the Bearers of Truth and Falsity. Dordrecht: North-Holland. Schenkeveld, D. M. (1984).‘Stoic and Peripatetic Kinds of Speech Act and the Distinction of Grammatical Moods’, Mnemosyne, 37: 291–351.

  46. Casari, Ettore. 1958. "Sulla disgiunzione nella logica megarico-stoica." In Actes du VIII Congrès Internationale d'Histoire des Sciences. Florence-Milan, 3-9 Septembre 1956. Vol. III, 1217-1224. Paris: Hermann et C.ie.

  47. ———. 2018. La logica stoica. Pisa: Edizioni ETS

    A cura di Enrico Moriconi.

  48. Castagnoli, Luca. 2010. "How Dialectical Was Stoic Dialectic?" In Ancient Models of Mind: Studies in Human and Divine Rationality, edited by Nightingale, Andrea Wilson and Sedley, David, 153-179. Cambridge: Cambridge University Press.

  49. Cavini, Walter. 1983. "La teoria stoica della negazione." In Atti del Convegno internazione di storia della logica, edited by Abrusci, Michele, Casari, Ettore and Mugnai, Massimo, 229-234. Bologna: CLUEB.

  50. ———. 1985. "Il papiro Parigino 2. Testo, traduzione e commento." In Studi su Papiri Greci di logica e medicina, edited by Cavini, Walter, Donnini Macciò, Maria Cristina, Funghi, Maria Serena and Manetti, Daniela, 85-126. Firenze: Olschki.

  51. ———. 1985. "La negazione di frase nella logica greca." In Studi su Papiri Greci di logica e medicina, edited by Cavini, Walter, Donnini Macciò, Maria Cristina, Funghi, Maria Serena and Manetti, Daniela, 85-126. Firenze: Olschki

    Indice dei Contenuti: Nota liminare 9;LA NEGAZIONE ARISTOTELICA1. La sintesi dichiarativa: supplemento di frase e contenuto descrittivo 11; 2. Negazione semplice e affermazione trasposta 17; 3. Le asserzioni indeterminate: trasformazione predicativa ed equivocità composta 26; 4. Portata esistenziale dell'affermazione 36; 5. Negative categoriche 41;LA NEGAZIONE STOICA1. Frammenti e testimonianze 47; 2. La teoria stoica degliaxiomata 48; 3. Negazione semplice e composta 51; 4. Opposti contraddittòri 57; 5. Ambiguità della negazione ordinaria 67;APPENDICE - IL PAPIRO PARIGINO 2Testo e traduzione 86; Commento 107; Bibliografia 122-126.

  52. ———. 1996. "Essere ed essere vero. Sull'uso assoluto di Hyparcho nella logica stoica." In Odoi Dizesios = Le Vie Della Ricerca. Studi in Onore Di Francesco Adorno, edited by Funghi, Maria Serena, 141-145. Firenze: Olschki.

  53. Celluprica, Vincenza. 1980. "La logica stoica in alcune recenti interpretazioni." Elenchos.Rivista di Studi sul Pensiero Antico no. 1:123-150.

  54. ———. 1989. "Diocle di Magnesia come fonte della dossografia stoica in Diogene Laerzio." Orpheus.Rivista di Umanità Classica e Cristiana no. 10:58-79.

  55. Chiesa, Curzio. 1991. "Le problème du langage intérieur chez les Stoiciens." Revue Internationale de Philosophie no. 45:301-321.

  56. Colish, Marcia L. 1979. "The Stoic Hypothetical Syllogisms and Their Transmission in the Latin West through the Early Middle Ages." Res Publica Litterarum no. 2:19-26

    Reprinted in M. L. Colish, The Fathers and Beyond: Church Fathers between Ancient and Medieval Thought, Aldershot: Ashgate 2008, Essay XIV.

  57. Corcoran, John. 1974. "Remarks on Stoic Deduction." In Ancient Logic and Its Modern Interpretations. Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972, edited by Corcoran, John, 169-181. Dordrecht: Reidel

    "The purpose of this note is to raise and clarify certain questions concerning deduction in Stoic logic. Despite the fact that the extant corpus of relevant texts is limited, it may nevertheless be possible to answer some of these questions with a considerable degree of certainty. Moreover, with the answers obtained one might be able to narrow the range of possible solutions to other problems concerning Stoic theories of meaning and inference.The content of this note goes somewhat beyond the comments I made during the discussion of Professor Gould's paper 'Deduction in Stoic Logic', in the symposium. I am grateful to Professors Gould and Kretzmann for pointing out the implications of those comments as well as for encouraging me to prepare them for this volume.One of the obstacles to a careful discussion of Stoic logic is obscurity of terminology. Clarification of terminology may catalyze recognition of important historical facts. For example, in 1956 a modern logician suggested (incorrectly) in a historical note [Alonzo Church, Introduction to mathematical logic, Princeton. 1956, fn. 529] that the distinction between implication and deduction could not have been made before the work of Tarski and Carnap. But once historians had clarified their own terminology it became obvious that this distinction played an important role in logic from the very beginning. Aristotle's distinction between imperfect and perfect syllogisms is a variant of the implication-deduction distinction and Gould 'Deduction in Stoic Logic' suggests the existence of a parallel distinction in Stoic logic." (p. 169)

  58. Crivelli, Paolo. 1994. "Indefinite Propositions and Anaphora in Stoic Logic." Phronesis.A Journal for Ancient Philosophy no. 39:187-206

    "If I utter in succession the sentences 'Someone is ringing at the door' and 'He is looking for you', my utterance of the pronoun 'he' is anaphoric on my utterance of the indefinite description 'someone', and the proposition expressed by my utterance of 'He is looking for you' is anaphoric on the indefinite proposition expressed by my utterance of 'Someone is ringing at the door'. Propositions anaphoric on indefinite propositions are very important in Stoic logic because they can be parts of indefinite conditionals and indefinite conjunctions, which are 'universal' and 'particular' propositions.In this paper I aim at establishing two main results concerning the Stoic conception of indefinite propositions and propositions anaphoric on them: the verb υοταττειν belongs to the jargon of Stoic logic and expresses the operation of subordination, which yields the definite propositions that are relevant to the truth or falsity of a given indefinite proposition; the standard ('sentential') truth conditions of conditionals and conjunctions yield the expected ('quantificational') truth conditions of indefinite conditionals and conjunctions, i.e. truth conditions suitable for 'universal' and 'particular' propositions." (p. 187)

  59. ———. 1994. "The Stoic Analysis of Tense and of Plural Propositions in Sextus Empiricus, Adversus Mathematicos X 99." Classical Quarterly no. 44:490-499

    "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.M. X 99 occurs within the report of a debate on motion and time between Diodorus and some unnamed opponents. The passage is probably corrupt (as was already noticed by Heintz) [*] and contains some observations on plural propositions and tense which have not yet been satisfactorily explained. In this paper I argue that Diodorus' critics are Stoics, propose a new emendation of the text, and attempt a plausible account of the remarks on plural propositions and tense. Thereby some light is shed on a hitherto unexplored region of Stoic logic." (p. 490)[* Werner Heintz, Studien zu Sextus Empiricus, Halle, 1932.]

  60. ———. 2009. "La dialectique." In Lire les Stoïciens, edited by Gourinat, Jean-Baptiste and Barnes, Jonathan, 41-61. Paris: Presses univeristaires de France.

  61. ———. 2010. "The Stoics on Definitions." In Definition in Greek Philosophy, edited by Charles, David, 359-423. New York: Oxford University Press

    "The present study is a reconstruction of the Stoic theory of definition. The topic is vast and the sources are scarce. My focus is on the epistemological and semantic aspects of the Stoic theory of definition.The study's first section explains how important definitions were for the Stoics. The second section expounds the different locations of the study of definitions within the Stoic system of philosophical disciplines. The third section discusses the epistemological side of the theory of definitions on which one of these locations relies. In particular, it addresses two roles played by definitions: sharpening our conceptions in such a way that they are more successfully applied to or withheld from entities, and endowing our conceptions with a systematic structure that makes them suitable for instruction. The fourth section discusses the link between definition and essence: it argues that the Stoics do not think that definitions reveal the essence of what is defined. The fifth section discusses the position of definitions within Stoic philosophy of language: definitions are not linguistic expressions, but sayables of a special kind (distinct from statables)." (p. 359)

  62. Croissant, Jeanne. 1984. "Autour de la quatrième formule d'implication dans Sextus Empiricus, Hyp. Pyrrh. II, 112. Essai de mise au point." Revue de Philosophie Ancienne no. 2:73-120

    Repris dans: J. Croissant, Études de philosophie ancienne, Bruxelles: Ousia 1986, pp. 297-345."Le chemin que nous avons suivi nous a conduits à interpréter la quatrième formule de Sextus comme l'expression d'un lien causal entre l'antécédent et le conséquent, avec cette précision supplémentaire, qui fait corps avec le texte de Galien, que la proposition ypothétique dans laquelle s'exprime l'endeixis procède à partir de l'effet pour découvrir la cause. Nous débouchons donc sur une présence du lien causal dans la proposition hypothétique qui est à l'opposé de l'interprétation de J. Moreau (126) qui voit dans l'emphasis l'inclusion dynamique de l'effet dans la cause, disons plutôt de l'ultérieur dans l'antérieur. Alors que mes réflexions m'ont orientée vers le domaine médical, J. Moreau a cherché à retrouver dans la logique stoïcienne la trace et la mise en forme de la conception stoïcienne de l'ordre du monde et des raisons séminales qui président à son déroulement. Les deux positions impliquent en outre une métaphorisation d'emphasis, un peu différente de part et d'autre, sous l'identité du "περιεχεται δυναμει". C'est aux lecteurs qu'il appartiendra de juger." (pp. 116-117)(126) [Joseph Moreau, "Immutabilité du vrai, nécessité logique et lien causal", Les Stoïciens et leur logique (Actes du Colloque de Chantilly, septembre 1976), Paris, Vrin, 1978, pp. 347-360] Cf. p. 84.

  63. Detel, Wolfgang, Hülsen, Reinhard, Κrüger, Gerhard, and Lorenz, Wolfgang. 1980. "λεκτὰ ἐλλιπῆ in der Stoischen Sprachphilosophie." Archiv für Geschichte der Philosophie no. 62:276-288.

  64. Dorandi, Tiziano. 2005. "La tradition papyrologique des Stoïciens." In Les Stoïciens, edited by Romeyer, Dherbey Gilbert and Gourinat, Jean-Baptiste, 29-52. Paris: Vrin

    "J'ai organisé ma contribution en cinq sections: 1. Noms de philosophes stoïciens et de leurs oeuvres dans les papyrus (d'Égypte et d'Herculanum). 2. Histoire de la Stoa de Philodème de Gadara. 3. Textes stoïciens en tradition directe (livres ou fragments de philosophes stoïciens transmis par les papyrus d'Égypte ou d'Herculanum). Je considère d'abord les textes dont l'attribution à un philosophe défini est certaine ou présumée telle: Chrysippe, Hiéroclès, Musonius Rufus; ensuite, je m'arrête sur le papyrus Parisinus 2 dont l'attribution à Chrysippe a été contestée; enfin, j'examine des cas de fausses attributions. 4. Textes stoïciens en tradition indirecte (les extraits de la Politeia de Zénon de Citium cités par Philodème; ceux tirés des œuvres d'Ariston de Chios, d'Antipatros de Tarse et de Diogène de Séleucie). 5. Pour terminer, je dresserai une liste de papyrus où se trouve une référence à la Stoa, aux stoïciens, ou des allusions à des doctrines stoïciennes." (p. 30)Les pages 35-37 sont sur les Recherches logiques (Logika zêtêmata) (fragmenta, P. Herc. 307) de Chrysippe.

  65. Döring, Klaus, and Ebert, Theodor, eds. 1993. Dialektiker und Stoiker. Zur Logik der Stoa und ihrer Vorläufer. Stuttgart: Franz Steiner

    Inhaltsverzeichnis: Vorwort 7; Abkürzungsverzeichnis 8; Teilnehmerverzeichnis 9; Wolfram Ax: Der Einfluss des Peripatos auf die Sprachtheorie der Stoa 11; Mariano Baldassarri: Ein kleiner Traktat Plutarchs über stoische Logik 33; Jonathan Barnes: Meaning, Saying and Thinking 47; Susanne Bobzien: Chrysippus' Modal Logic and Its Relation to Philo and Diodorus 63; Walter Cavini: Chrysippus on Speaking Truly and the Liar 85; Theodor Ebert: Dialecticians and Stoics on the Classification of Propositions 111; Urs Egli: Neue Elemente im Bild der stoischen Logik 129; Michael Frede: The Stoic Doctrine of the Tenses of the Verb 141; Gabriele Giannantoni: Die Philosophenschule der Megariker und Aristoteles 155; Karheinz Hülser: Zur dialektischen und stoischen Einteilung der Fehlschlüsse 167; Katerina Ieorodiakonou: The Stoic Indemonstrables in the Later Tradition 187; Fritz Jürss: Zum Semiotik Modell der Stoiker und ihrer Vorläufer 201; Mario Mignucci: The StoicThemata 217; Luciano Montoneri: Platon, die Ältere Akademie und die stoische Dialektik 239; Luciana Repici: The Stoics and the Elenchos 253; Andreas Schubert: Die stoischen Vorstellungen 271; Gerhard Seel: Zur Geschichte und Logik destherizön logos 291; Hermann Weeidemann: Zeit und Wahrheit bei Diodor 319; Literaturverzeichnis 331; Register 343-361.

  66. Drozdek, Adam. 2002. "Λεκτόν. Stoic Logic and Ontology." Acta Antiqua. Academiae Scientiarum Hungaricae no. 42:93-104

    Summary: "For the Stoics, the lekton is as an intermediary between the thought and the object. They do not exist independently of the mind, but, at the same time, the mind does not create them. Due to this status, they guarantee intersubjectivity of the rational discourse. They are incorporeals that do not exist, but subsist and the Stoic Logos-God guarantees their permanent subsistence. The Iekta are semantico-syntactic entities. Their role is analogous to the role of an interlingua used as a tool for automated translation of languages."

  67. Dumitriu, Anton. 1977. History of Logic. Tunbridge Wells: Abacus Press

    Revised, updated, and enlarged translation from the Roumanian of the second edition of "Istoria logicii" (1969, 4 volumes).On the Stoics see: Vol. I, pp. 216-253.

  68. Ebert, Theodor. 1987. "The Origin of the Stoic Theory of Signs in Sextus Empiricus." Oxford Studies in Ancient Philosophy no. 5:83-126.

  69. ———. 1991. Dialektiker und frühe Stoiker bei Sextus Empiricus. Untersuchungen zur Entstehung der Aussagenlogik. Göttingen: Vandenhoeck & Ruprecht

    Inhalt: Einleitung 13; I. Teil: Der Ursprung der stoischen Theorie des Zeichens. Erstes Kapitel: Die stoische Theorie des Zeichens bei Sextus Empiricus 29; Zweites Kapitel: Die stoische Theorie des Zeichens vor dem Hintergrund der Berichte bei Diogenes Laertius 54; Drittes Kapitel: Dialektiker und frühe Stoiker zur Theorie des Zeichens 66; II. Teil: Die Dialektiker bei Sextus Empiricus. Viertes Kapitel: Die Dialektische Klassifikation der Aussagen bei Sextus Empiricus 83; Fünftes Kapitel: Die Dialektische Klassifikation der Aussagen als Vorstufe der stoischen 108; Sechstes Kapitel: Die Dialektische und die stoische Klassifikation der Fehlschlüsse bei Sextus Empiricus 131; Siebtes Kapitel: Die Dialektiker über Trugschlüsse und ihre Auflösung 176; Anhang I zum II. Teil: Diodor und die 'Dialektiker' in AM 10.111 209; Anhang II zum II. Teil: Dialektiker und Stoiker bei Apuleius 213; III. Teil: Der Ursprung der stoischen Theorie des Beweis. Achtes Kapitel: Der frühstoische Charakter der Theorie des Beweises bei Sextus Empiricus 219; Neuntes Kapitel: Ubereinstimmungen und Unterschiede in den Referaten des Sextus zur stoischen Beweistheorie und das genetische Verhältnis ihrer Quellen 232; Zehntes Kapitel: Von den Dialektikern zu Chrysipp -- der Weg einer Theorie in der Alten Stoa 287; Schlussbemerkung 303; Anhang: Texte aus Sextus Empiricus zu den Dialektikern und den Stoikern 311; Literaturverzeichnis 326; Register 337-346.English translation of the first part in: T. Ebert, The Origin of the Stoic Theory of Signs in Sextus Empiricus (1987).

  70. ———. 1993. "Dialecticians and Stoics on the Classification of Propositions." In Dialektiker und Stoiker. Zur Logik der Stoa und ihrer Vorläufer, edited by Döring, Klaus and Ebert, Theodor, 111-127. Stuttgart: Franz Steiner

    "In his discussion and refutation of the logical theories of dogmatist philosophers in Adversus Mathematicos (M.) 8, Sextus Empiricus treats us, among other things, to an account of a classification of propositions (M. 8.93-129). The doctrine reported on here is usually taken to form part of Stoic logic.(1) Together with its apparent counterpart in Diogenes Laertius (D.L.) 7.68-76, this Sextian report is used to reconstruct a theory supposedly held by Stoic philosophers. In what follows I shall try to refute this view and I shall argue that Sextus’ report encapsulates a doctrine worked out not by the Stoic, but by the Dialectical school whose most prominent members seem to have been Diodorus Cronus and Philo.(2)First I shall try to show that the two reports by Sextus and by Diogenes resp. are quite different indeed as to their systematic content and that, therefore, both reports must be drawn from different sources. In a second step it is then argued that Sextus’ account is based on Dialectical material. Finally, I shall compare the Dialectical classification to be found in Sextus to the Stoic one in Diogenes with an eye to exploring these two divisions as different phases within the development of propositional logic." (p. 111)(1) Cp. Mates (1953) 30f, 54, Kneale (1962) 146, 148f., Mignucci (1965) 131, Egli (1967) 37f., Mueller (1969) 185, Frede (1974a) 49-62 passim, Brunschwig (1984) 9ff.; already v. Arnim put this text, omitting some parts, among the logical fragments of Chrysippus: SVF fr. 205, 211, 216.(2) Cp. D. Sedley (1977). ReferencesH. v. Arnim, Stoicorum Veterum Fragmenta. 3 Bde. Leipzig 1903-1905; Bd. 4: Indices v. M. Adler. Leipzig 1924Brunschwig, J. (1984). Remarques sur la théorie stoïcienne du nom propre. In: Histoire, Épistémologie, Langage 6 (1984) 3-19Egli, U. (1967). Zur stoischen Dialektik. Diss. Basel 1967Frede, M. (1974a), Die stoische Logik. Göttingen 1974Kneale, M./Kneale, W. (1962). The development of logic. Oxford 1962, '1978Mates, B. (1953). Stoic logic. Berkeley 1953,21961Mignucci, Μ. (1965). Il significato della logica stoica. Bologna 1965, 19672Mueller, I. (1969). Stoic logic and Peripatetic logic. In: Archiv für Geschichte der Philosophie 51 (1969) 173-187Sedley, D. N. (1977). Diodorus Cronus and Hellenistic philosophy. In: Proceedings of the Cambridge Philological Society 203 (N.S. 23) (1977) 74-120

  71. Egli, Urs. 1967. Zur Stoischen Dialektik. Basel: Sandoz

    Inauguraldissertation (Universität Bern).Inhaltsverzeichnis: 1. Allgemeines zur Rekonstruktion der stoischen Dialektik 2; 2. Diokles bei Diogenes Laertios 7.49-82 8; 3. Quellengeschichtliche Nebenergebnisse zu Diogenes und Sextos 59; 4. Nebenergebnisse zu Galens Einführung in die Logik 74; Zusammenfassung und Ausblick 87; Erklärung der wichstigsten Abkürzungen 106; Bibliographie 107-113.

  72. ———. 1983. "The Stoic Theory of Arguments." In Meaning, Use, and Interpretation of Language, edited by Bäuerle, Rainer, Schwarze, Christoph and von Stechow, Arnim, 79-96. Berlin: Walter de Gruyter

    Contents: 1. Relevance of the topic; 2. Concepts involved; 2.1 Arguments; 2.2 Simple and logical concepts; 2.3 A hypothesis on Stoic deduction theory; 3. A commentary on Sextus' passage on invalidity [Adv. Math. 8, 292-294]; 3.1 The context; 3.2 The passage; 4. Deductions; 5. Completeness; 6. Conclusion; Appendix: Possible existence of cut free systems; Bibliography."1. Relevance of the TopicThe Stoic theory of arguments to my mind illustrates one point: If certain ancient doctrines had been properly understood, the corresponding modern theories would have been developed sooner. We would have had a propositional logic by 1800, we would have had a serious syntax long before transformational grammar. Stoics, in addition, had already something like a speech act theory. In one or two cases modern theories have directly been elaborations of Stoico-Megarian developments: First, Prior's tense logic was influenced by reflections on Diodorus. Second, Kripke's semantics for modal logic was directly influenced by Prior's exposition of the theory of modality of Diodorus Kronos. Compare his truth definition of modal statements with that of Kripke:p is possible now iff p is true now or will be true later (Diodorus).p is possible in our world iff p is true in a world accessible from ours (Kripke).Kripke replaced points of time by possible worlds and the relation "to be now or later" by the accessibility relation. It is not impossible that further study of Stoic theories will contribute in a similar way to modern discussions.It has been proved by Lukasìewìcz and Mates that the Stoic theory of what they called syllogisms contained something we might call propositional logic in modern terms. Mates also brought up the problem of deciding whether1) Stoics contended that their propositional logic was complete; and whether2) Stoic logic actually was complete according to modern criteria (Mates 1961, 81-82).As to the first question, the evidence that Mates adduces is not wholly conclusive, for the passages are little more than consequences of the definition of syllogisms (= valid arguments): According to this definition a syllogism is either a basic syllogism (anapodeiktos) or derived from basic syllogisms by the deductive rules(themata) (DL 7.78). From this definition follows that every syllogism (which is not basic) is derived from the basic ones -- the passages adduced by Mates say just that. If it is not clear whether the Stoics actually held that their propositional logic was complete, Becker's attempt toprove the completeness of Stoic logic by reconstructing the missing pieces of the deductive apparatus may seem futile. He has also been severely criticised by Mueller, Frede and others because it is not clear(a) whether the Stoic conditional signei is to be taken as a truth-functional connective or not,(b) how the Chrysippean exclusion of arguments with but one premise can be reconciled with Becker's full use of such arguments in his proofs of semantic completeness,(c) whether the completeness extended from the part of the system involving only conjunction and negation to other connectives.I now want to reopen the question by arguing that a kind of completeness is indeed to be found in Stoic passages (though not in those Mates adduced) and that an examination of the sources renders some plausibility to the thesis that the Stoics had a system of deduction rules which can be proved adequate according to modern criteria." (pp. 79-80)

  73. ———. 1986. "Stoic Syntax and Semantics." In The History of Linguistics in the Classical Period, edited by Taylor, Daniel J., 281-306

    Also published in: Historiographia Linguistica, 13, 1986 and in J. Brunschwig (ed.), Les Stoiciens et leur logique, Paris, Vrin, 1986, pp. 135-147 (2nd edition 2006, pp. 131-148)."Let me now summarize the main points of my exposition of Stoic syntax:1. Stoic loquia (lekta) are designated by expressions of a normalized Greek. They have the same structure as these Greek expressions. Thus in most technical uses they serve approximately the same purpose as "semantic structures" or "semantic representations" in modem linguistics and philosophy of language.2. There is an infinity of loquia derived by a finite number of recursive rules of four types, lexical, inclusion, combination and transformation rules. Semantic categories like statement, predicate and subject are used in the formulation of these rules which enable us to build complex loquia of the various categories from atomar ones (asuntheta). The structure of a compound loquium may be revealed by using Chomsky or Montague analysis trees.3. This infinity of loquia is related with real things by an analogue of modern model theory. General terms are said to denote individuals according to a variant of multiple denotation theory. Deictic subjects are assigned values, like their modern analogues: individual variables by an assignment (deixis). Statements are either true or false. Complex expressions are valuated in function of their syntactic composition and the values of their parts.4. Denotations of Greek expressions are determined indirectly. E.g. appellatives signify appellative subjects, which refer to individuals. Thus appellatives indirectly denote these individuals too.5. All this would have to be refined by taking into account tense.6. By neglecting tense, plural and subjectivization, Stoic loquium theory becomes an analogue of modern first order predicate logic bya) the introduction of n place predicates with arbitrary n,b) the introduction of a means to handle relative clausesStoic syntax and related model theory thus proves interesting and comparable to modern treatments." (from Les Stoiciens et leur logique, 2nd edition 2006, pp. 144-145)

  74. ———. 1993. "Neue Elemente im Bild der stoischen Logik." In Dialektiker und Stoiker. Zur Logik der Stoa und ihrer Vorläufer, edited by Döring, Klaus and Ebert, Theodor, 129-139. Stuttgart: Franz Steiner.

  75. Evans, John David Gemmill. 2011. "The Old Stoa ont the Truth-Value of Oaths." Cambridge Classical Journal no. 20:44-47

    "Recent works on Stoic logic report that among complete λεκτα only a sub-class was regarded as capable of being true or false: by contrast with statements (αξιωματα), such other sentences as questions, orders and oaths do not bear a truth-value.(1) But the situation is a good deal more complicated than that, at least in the case of oaths, which I propose to examine.In characterising all such utterances as 'sentences' I do not wish to beg questions which will be discussed below. Surface grammar, with its distinctions of indicative, imperative, interrogative and optative, can mislead us as to the real force of an utterance. In the case of oaths there seems to be no preferred form of expression; and it is a matter for deeper philosophical probing to determine their true relation to other speech-acts.The standard view derives its best support from a passage in Diogenes Laertius, which expressly denies truth-value to non-statements.(2) But a similar report in Sextus Empiricus is not so clear. After giving a scheme of complete λεκτα which sets the declarative (αποφαντικον) co-ordinate with the questioning, cursing etc. types, he says that only some of them - namely αξιωματα - were regarded as bearing truth-values.(3) Although the passage may suggest that the declarative λεκτα are identical with the αξιωματα, it does not actually say this, and thus leaves it unclear which types of complete λεκτα do not bear a truth-value. Ammonius' report of the topic says that the non-statement types 'are all bearers of falsity and truth and might be subsumed under the declarative';(4) but the grammar of his sentence makes it uncertain whether this is his or the Stoic view." (p. 44)(1) See Benson Mates, Stoic logic (Berkeley, 1961), pp. 18-19; W. and M. Kneale, The development of logic (Oxford, 1962), pp. 144-5.(2) Stoicorum Veterum Fragmenta, ed. J. von Arnim (photoreprint, Stuttgart, 1964), vol. 11. 186 [henceforth, SVF II etc.].(3) SVF II. 187. (4) SVF II 188.

  76. Frede, Michael. 1974. Die Stoische Logik. Göttingen: Vandenhoeck & Ruprecht

    Inhaltverzeichnis: (I) Einleitung 9; A.Der Gegenstand dieser Arbeit 9; Die äussere Geschichte der stoischen Logik 12; (II) Die Aussage 32; A. Der stoische Begriff der Aussage 32; 1. Die stoischen Bestimmungen der Aussage 32; 2. Aussagen ändern ihren Wahrheitswert 44; 3. Die Vergänglichkeit von Aussagen 48; B. Die Arten von Aussagen 49; 1. Die Unterscheidung von einfachen und nichteinfachen Aussagen 49; 2. Dier Arten von einfachen Aussagen 51; 3. Die Arten von nicht-einfachen Aussagen 73; 4. Logisch wahre Aussagen 105; C. Die Modalität von Aussagen 107; (III) Der Schluss 118; A. Die gültigen Schlüsse 118; 1. Die stoische Definition des Schlusses 118; B. Die Syllogistik 124; 1. Der stoische Begriff des Syllogismus 124; 2. Die elementaren Syllogismen 127; 3. Die nicht-elementaren Syllogismen 167; (iv) Arten von Schlüssen, welche mit Hilfe des 2. Themas analysiert werden 181; 4. Die Vollständigkeit der stoischen Syllogistik 196; 5. Der Formalismus der stoischen Syllogistik 198; Indices 202; (I) Literaturverzeichnis 202; Sachregister 208; Verzeichnis griechischer Termini 209; Verzeichnis lateinischer Termini 210; Bemerkungen zum Text 210; Stellenregister 211-224.Reviews (in English): Robert Edlow, Mnemosyne, 29, 1976, pp. 199-200; A. C. Lloyd, Mind, 86, 1977, pp. 286-289; Ian Mueller, The Philosophical Review, 86, 1977, pp. 226-229.

  77. ———. 1974. "Stoic vs. Aristotelian Syllogistic." Archiv für Geschichte der Philosophie no. 56:1-32

    Reprinted in: M. Frede, Essays in Ancient Philosophy, Minneapolis: University of Minnesota Press 1987 pp. 99-124.

  78. ———. 2009. "The Stoic Notion of a Lekton." In Language: Companions to Ancient Thought. Vol. 3, edited by Everson, Stephen, 109-128. Cambridge: Cambridge University Press.

  79. Gabriel, Gottfried, Hulser, Karlheinz, and Schlotter, Sven. 2009. "Zur Miete bei Frege – Rudolf Hirzel und die Rezeption der stoischen Logik und Semantik in Jena." History and Philosophy of Logic no. 30:369-388

    Abstract: "It has been noted before in the history of logic that some of Frege’s logical and semantic views were anticipated in Stoicism. In particular, there seems to be a parallel between Frege’s Gedanke (thought) and Stoic lekton; and the distinction between complete and incomplete lekta has an equivalent in Frege’s logic.However, nobody has so far claimed that Frege was actually influenced by Stoic logic; and there has until now been no indication of such a causal connection. In this essay, we attempt, for the first time, to provide detailed evidence for the existence of this connection. In the course of our argumentation, further analogies between the positions of Frege and the Stoics will be revealed. The classical philologist Rudolf Hirzel will be brought into play as the one who links Frege with Stoicism. The renowned expert on Stoic philosophy was Frege’s tenant and lived in the same house as the logician for many years."

  80. Gardies, Jean-Louis. 1985. "Sur le διεζενγμενον de la logique stoïcienne." Logique et Analyse no. 28:385-394.

  81. Gaskin, Richard. 1997. "The Stoics on Cases, Predicates and the Unity of the Proposition." In Aristotle and After, edited by Sorabji, Richard, 91-108. London: Institute of Classical Studies.

  82. Giavatto, Angelo. 2012. "Logic and the Meditations." In A Companion to Marcus Aurelius, edited by van Ackeren, Marcel, 408-419. Malden: Wiley-Blackwell.

  83. Gould, Josiah. 1974. "Deduction in Stoic Logic." In Ancient Logic and Its Modern Interpretations. Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972, edited by Corcoran, John, 151-168. Dordrecht: Reidel

    "In their logical theory Stoic philosophers made use of a simple but important distinction alleged to hold among valid arguments, a distinction to which Aristotle had first called attention.(1) They distinguished those arguments whose validity is evident from those whose validity is not evident and so needs to be demonstrated. The Stoics, having supposed that the distinction obtains, raise and answer the question, how does one demonstrate the validity of those arguments whose validity is not plain? The Stoics appear to have set forth both a discursive method of demonstration and a test for validity. In this paper I examine these two facets of Stoic logic.(2)The paper is in three parts. The first is essentially terminological and taxonomic. There I record Stoic definitions of logical terms and I give three Stoic classifications of arguments, appending samples from the writings of Sextus Empiricus.(3) This provides and puts on exhibit an array of typically Stoic arguments to which I refer in the second part of the paper. There I examine Sextus' contention that the disagreement among the Stoics over the criterion of truth for a conditional proposition renders inefficacious the test that had been set forth as sufficient for judging the validity of an argument, and I argue that Sextus' charge has to be qualified. Even if an unqualified form of Sextus' accusation could be established, its importance, I maintain, would be diminished by the fact that the Stoics didn't make extensive use of this test anyhow. As I show in the third part of the paper, the Stoics ordinarily claim to prove the validity of all valid arguments(4) not by means of a test but by means of a calculus of propositions(5) having its base in a theory of deduction, which includes a language consisting of connectives and variables, axiomatic inference schemata, and rules of derivability. I conclude with a statement about the Stoic theory of deduction in relation to systems of logic developed in the 19th and 20th centuries and to Aristotelian syllogistic." (p. 151)(1) Prior Analytics I.24b22-26, 27a16-18. The distinction between plainly valid syllogisms and non-evidently valid syllogisms is for Aristotle the distinction between 'perfect' syllogisms, on the one hand, and 'imperfect' syllogisms, on the other. A perfect syllogism is one in which, as Aristotle frequently puts it, the necessity (of the conclusion if the premises be assumed) is evident. That the Stoics presupposed this distinction is made clear in Part III of this paper.(2) I wish to thank my colleagues, James A. Thomas and Harold Morick, for helpful critical remarks on an earlier draft of this paper. I am also enormously indebted to John Corcoran for many incisive remarks and helpful suggestions on two later versions of the paper.(3) Sextus is the richest source we have for a knowledge of Stoic logic. Being a Sceptic he is extremely critical of the Stoics. He also tends to be tediously repetitious. He appears to have quoted and paraphrased with care, though there aren't always non-circular ways of checking this. As Mates has observed (Stoic logic (1961), p. 9), "any parts of Stoic logic which he found either too difficult or too good to refute will be absent from his account", but even so there is enough material in Sextus to extract a fairly good account of the elements of Stoic logic.(4) Mates refers in several places (pp. 4, 58, 82) to and gives evidence for the Stoics' claim that their propositional logic was complete.(5) The Stoics didn't call their logic a calculus of propositions (Diogenes Laertius groups Chrysippus' books dealing with the subject under the heading 'Logic in Relation to Arguments and Moods', Vitae VII. 193); but Stoic logic shares so many similarities with modern propositional logic, calling their logic 'a calculus of propositions' while anachronistic is at least not baneful, and it is, in fact, in my view illuminating to use this expression to refer to Stoic logic.

  84. Gourinat, Jean-Baptiste. 1999. "La définition et les propriétés de la proposition dans le Stoïcisme ancien." In Théories de la phrase et de la proposition de Platon à Averroès, edited by Büttgen, Philippe, Dieble, Stéphane and Marwan, Rashed, 133-150. Paris: Éditions rue d'Ulm.

  85. ———. 2000. La dialectique des stoïciens. Paris: Vrin.

  86. ———. 2019. "Stoic dialectic and its objects." In Dialectic after Plato and Aristotle, edited by Bénatouil, Thomas and Ierodiakonou, Katerina, 134-167. Cambridge: Cambridge University Press.

  87. Graeser, Andres. 1978. "The Stoic Theory of Meaning." In The Stoics, edited by Rist, John M., 77-100. Berkeley:: University of California Press

    Reprinted in: A. Graeser, Issues in the Philosophy of Language Past and Present, Bern: Peter Lang, 1999, pp. 121-144."Whether or not the Stoics conceived of any "science" corresponding in scope and methods to formal semantics in the sense described, for example, by J. Moravcsik (1) seems hard to determine. Evidence regarding this issue is scanty, particularly in view of the fact that some of the isolated testimonies relating to the Stoic theory of meaning are extremely difficult to assess and still require good deal of extensive analysis. From the meager reports concerning the bare essentials of this theory as incorporated into later manuals and elsewhere, it would appear, however, that in the course of their school's history the Stoics developed a fairly detailed semantic theory. It is a theory of meaning that has invited comparison with modern theories and obviously stood it well. In fact, it is generally agreed that the Stoic account of semantics is superior to and more sophisticated than the more influential one offered by Aristotle in theDe Interpretatione (16a3-18).(2) It is also considered to figure among the very few definitely modern-minded contributions to the systematic study of philosophical problems carried out by ancient Greek thinkers.Semantics in general, according to Stoic philosophers, seems to be an integral part of what they called "Logic" or "Dialectic" respectively, that is, the study of the utterance and the study of the utterance as meaningful. It is integral inasmuch as the Stoic conception of logic is one that depends again on their theory of meaning. In the analysis of meaning three components seem to been distinguished. The components or aspects under consideration are: first, the sign (sèmainon, i.e., that which signifies) which is a phoneme or grapheme; second, the significate (sémainomenon, i.e., that which is signified) which is expressed by the sound which we apprehend as it arises in our mind; and third, the external object referred to." pp. 77-78(1) Understanding Language (The Hague, 1975) 21.(2) On this most influential text in the history of semantics, see N. Kretzman, "Aristotle on Spoken Sound," in J. Corcoran, ed., Ancient Logic and its Modern Interpretations (Dordrecht and Boston, 1974) 3-21.