History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: rc
Ademollo, Francesco. 2015. "Names, Verbs and Sentences in Ancient Greek Philosophy." In Linguistic Content: New Essays on the History of Philosophy of Language , edited by Cameron, Margaret and Stainton, Robert J., 33-54. New York: Oxford University Press.
"My purpose here is to investigate some ancient conceptions of the composition and structure of sentences, focusing on Plato and Aristotle, with short forays into other authors and ages. I shall concern myself mainly with two mutually connected issues.
First, both Plato and Aristotle hold that a minimal simple sentence consists of two expressions of different kinds, which they call onoma and rhema; I shall try to make clear the nature and purport of this distinction, which is controversial. Secondly (but partly at the same time), I shall try to trace the emergence and early development, from Plato to the Stoics, of the idea that a simple declarative sentence has a signification of its own over and above the signification of its parts. Most individual details of what I am going to say are, I am afraid, not new; but perhaps the story as a whole deserves to be told. (1) As so often with stories about ancient matters, telling it will require some detailed discussion and a modicum of philological excavation." (p. 33)
(1) For partly comparable and very valuable surveys, from which I have learnt much, see Nuchelmans (1973: 13-44) and Barnes (1996).
Barnes, J. (1996). 'Grammar on Aristotle's Terms', in M. Frede and G. Striker (eds), Rationality in Greek Thought . Oxford: Oxford University Press, 175-202; repr. in Barnes (2012: 147-71).
Barnes, J. (2012). Logical Matters: Essays in Ancient Philosophy II. Oxford: Oxford University Press.
Nuchelmans, G. (1973). Theories of the Proposition: Ancient and Medieval Conceptions of the Bearers of Truth and Falsity . Amsterdam and London: North-Holland.
Allen, James. 2007. "Rhetoric and Logic." In A Companion to Greek Rhetoric , edited by Worthington, Ian, 350-364. Malden: Blackwell.
"Logic was the property of the philosophers, and it is to those philosophers who also interested themselves in rhetorical argument that one must turn in order to explore the relations between logic and rhetoric in Greek antiquity. Though it has roots in Plato and Aristotle, the division of philosophy into logic, physics and ethics seems first to have been made explicitly in the second half of the fourth century, after which time it became standard (Sextus Empiricus, Against the Mathematicians 7.16). In the Stoic version of the division, which was especially influential, the logical part of philosophy was further divided into rhetoric and dialectic, and some Stoics also made a place for a separate part concerned with definition and another concerned with canons and criteria, i.e., epistemology (Diog. Laert. 7.41). The connecting thread is a common concern with logos, and the variety of items encompassed by the ancient discipline of logic reflects the range of the term logos, which can mean a word, a proposition, a definition, speech, a speech in the sense of an oration, an argument or the faculty of reason. These were seen to form a unity because speech and thought were regarded as two aspects of logos. Speech is external logos, thought internal logos, according to the Stoics, who are in accord with older views like that of Plato, who defined thought as internal speech (Sextus Empiricus, Against the Mathematicians 8.275; Pl. Sophist 263e)." (p. 350)
Asmus, Conrad, and Restall, Greg. 2012. "A History of C:onsequenc:e Relation." In Logic: A History of Its Central Concepts , edited by Gabbay, Dov M., Pelletier, Francis Jeffrey and Woods, John, 11-61. Amsterdam: North-Holland.
Volume 11 of the Handbok of te History of Logic .
"Consequence is a, if not the , core subject matter of logic. Aristotle’s study of the syllogism instigated the task of categorising arguments into the logically good and the logically bad; the task remains an essential element of the study of logic. In a logically good argument, the conclusion follows validly from the premises; thus, the study of consequence and the study of validity are the same.
In what follows, we will engage with a variety of approaches to consequence.
The following neutral framework will enhance the discussion of this wide range of approaches. Consequences are conclusions of valid arguments. Arguments have two parts: a conclusion and a collection of premises. The conclusion and the premises are all entities of the same sort. We will call the conclusion and premises of an argument the argument’s components and will refer to anything that can be an argument component as a proposition . The class of propositions is defined functionally (they are the entities which play the functional role of argument components); thus, the label should be interpreted as metaphysically neutral. Given the platonistic baggage often associated with the label “proposition”, this may seem a strange choice but the label is already used for the argument components of many of the approaches below (discussions of Aristotlean and Medieval logic are two examples). A consequence relation is a relation between collections of premises and conclusions; a collection of premises is related to a conclusion if and
only if the latter is a consequence of the former."
Bailey, D. T. J. 2008. "Excavating Dissoi Logoi 4." Oxford Studies in Ancient Philosophy no. 35:249-264.
"i begin with a necessary apology for the extreme obscurity of the text I shall discuss. The Dissoi Logoi , whose fourth chapter is the subject of this paper, is perhaps unique among texts in the history of philosophy for its murkiness. It is an anonymously authored philosophical work appearing to argue, among other things, for the sameness and then the difference of properties such as good and bad, just and unjust, true and false. Almost every aspect of it likely to interest scholars is monstrously undetermined. Thus:
(1) Its date is unknown. Many suppose it to be a Sophistic moot book or the like from around the late fifth/early fourth century b.C.(1)
Others take the location of its only manuscripts, always in the works of Sextus Empiricus, to indicate a dating anything up to six hundred years later. One scholar has suggested that it might have been written as late as the medieval end of the Byzantine era.(2)
(2) Its original dialect is unknown. It is largely composed in Doric, but with numerous Atticisms and dashes of Ionic. (...)
(3) Partly because of its content, and partly because of (1) and (2), its purpose is unknown. (...)
Given (1), (2), and (3), it is almost impossible to say anything about the Dissoi Logoi that goes beyond mere conjecture. But it would be a pity to let caution silence all contributions to the understanding of this most mysterious text. In what follows, I discuss two issues—the meaning of the word logos3 in 4. 1–5, and the argument of 4. 6—with a view to assessing just how Sophistic this chapter is, and asking what there is about it that might have aroused interest in later Sceptical traditions. I shall not count the exercise a failure if all I can achieve is to make this text even more intriguing than it has seemed beforehand."
(1) For a detailed discussion of one disagreement, even among those who view the text as belonging to the early Sophistic movement, see T.M. Robinson, Contrasting Arguments: An Edition of the Dissoi Logoi (Salem, NH, 1979), 34–41. I rely on this magnificent work of scholarship throughout.
(2) T.M. Conley, ‘Dating the So-Called Dissoi Logoi: A Cautionary Note’, Ancient Philosophy , 5 (1985), 59–65.
Baltussen, Han. 1992. "Peripatetic dialectic in the De sensibus ." In Theophrastus: His Psychological, Doxographical and Scientific Writings , edited by Fortenbaugh, William W. and Gutas, Dimitri, 1-19. New Brunswick (N. J.): Transaction Publishers.
"Once attention is directed towards Theophrastus’ argumentation, the choice of Peripatetic dialectic as a normative model (or heuristic device), being a general theory of argumentation, seems obvious. But there are more specific reasons. Since the fundamental study of E. Weil(7) the picture of the function and content of the dialectical method has undergone considerable adjustment. Dialectic was rehabilitated against the dominant role of analytics and freed from sophistic qualifications which were undeservedly attached to it.(8) This caused a new interest in the Topics, the treatise in which Aristotle expounded his theory of dialectical reasoning.
Although today no overall agreement exists upon details of interpretation, it is still possible to summarize the main elements of the results so far. I have attempted to incorporate the various results into one description which will enable us to gain a new understanding of the dialectical procedure. I shall first focus on the goal of dialectic, passing on to its more specific function in ‘doxographic’ contexts. It may seem a small detour at the moment, but I hope it will prove to be a reculer pour mieux sauter ." (p. 3, note 9 omitted)
(7) E. Weil, ‘La place de la logique dans la pensée aristotélicienne’, RMM 56 (1951), 283-315 [= ‘The Place of Logic in Aristotle’s Thought’, repr. in J. Barnes et al. (edd.), Articles on Aristotle, 1. Science (London, Duckworth 1975), pp. 88-112]. I shall quote from the English translation. An earlier instance of a study that investigated the role of the search for principles in Aristotle’s Physics is J.M. LeBlond, Logique et Méthode chez Aristote, Paris 1939. But the earliest (and least quoted) instance is H.D.P. Lee, 'Geometrical method and Aristotle’s account of first principles’, CIQ , 29 (1935), 113-24. The most recent contributions on the subject are by T.H. Irwin, Aristotle’s First Principles (Oxford, Clarendon Press 1988) and A. Beriger, Die aristotelische Dialektik. Ihre Darstellung in der Topik’ und in den ’Sophistischen Widerlegungen und ihre Anwendung in der 'Metaphysik' M 1-3 (Heidelberg / Carl Winter 1989).
(8) As Weil (pp. cit. p. 89) summarized it: “... both [analytics and dialectic] are equally formal, both apply a method that is independent of the content, both use the syllogism as their principal tool”.
Barnes, Jonathan. 1982. "Medicine, Experience and Logic." In Science and Speculation: Studies in Hellenistic Theory and Practice , edited by Barnes, Jonathan, Brunschwig, Jacques, Burnyeat, Myles F. and Schofield, Malcolm, 24-68. Cambridge: Cambridge University Press.
Reprinted in J. Barnes, Logical Matters: Essays in Ancient Philosophy II , New York: Oxford University Press 2012, pp. 538-581.
"The concept of ‘experience’ has a long history, going back through Aristotle to the Presocratic philosophers.3 I shall not attempt to write that history, nor to give an account of the precise way or ways in which the concept was understood by the Empirical doctors who took their sobriquet from it. I assume that an experience is a piece of general knowledge (‘Pomegranates cure diarrhoea’), based upon a series of particular observations (‘Pomegranates were good for Dio when he had diarrhoea’); and I assume, further, that in the eyes of the Empiricists the general knowledge was justified by its observational basis. In effect, then, the Empirical doctors were committed to the acceptability of certain inductive inferences; and the soritical argument—or the sorites, as it is now customarily called—was used by the Dogmatists to cast doubt upon induction." (p. 540, notes omitted)
"What is fundamentally at issue here is a question about the nature of logic: is logic in a way prior to science and to experience, is it something which gives shape to experience and which cannot be modified by experience? or is logic rather parasitical upon science, constrained by the observed facts and open to modification in the light of empirical discovery? Those questions still exercise us — quantum physics gave them new life not so long ago. I think that they are at the bottom of the dispute between Galen’s two doctors. (p. 578, a note omitted)
———. 1986. "Peripatetic negations." Oxford Studies in Ancient Philosophy no. 4:201-214.
Reprinted in J. Barnes, Logical Matters: Essays in Ancient Philosophy II , New York: Oxford University Press 2012, pp. 172-186.
"Ancient logicians did not question the Aristotelian view that ‘for every affirmation there is an opposite negation, and for every negation an opposite affirmation’ (int 17a32–33); nor did they doubt that ‘a single affirmation has a single negation’ (17b37): every affirmation, P, has one and only one negation neg:P. Moreover, it was taken to be constitutive of the notion of negation that P and neg:P cannot both be true and cannot both be false. And it was supposed that a negation, neg:P, will normally be constructed from its affirmative twin, P, together with a negative operator.
Those common notions form the background to a short essay on negation which Alexander of Aphrodisias inserted into his commentary on Aristotle’s Prior Analytics . Alexander defends an Aristotelian account of negation and argues against a rival account.(3) The rival account is generally supposed to be Stoic or even Chrysippean; and it contains indisputably Stoic elements.
But Alexander does not name his opponents, nor does he offer any information about the history of the dispute." (pp. 172-173, notes omitted)
(3) in APr 402.1–405.16.
———. 1990. "Logical Form and Logical Matter." In Logica, mente e persona. Studi sulla filosofia antica , edited by Alberti, Antonina, 7-119. Firenze: Olschki.
Reprinted in J. Barnes, Logical Matters. Essays in Ancient Philosophy II , Oxford: Clarendon Press 2012, pp. 43-146.
"The first theorem of the first Book of Euclid’s Elements is this:
On a given finite straight line, there can be constructed an equilateral triangle." (p. 43)
"At the heart of the proof lies an argument which I shall call the Euclidean Argument. It can be set out as follows:
(1) Things equal to the same thing are equal to one another.
(2) CA is equal to AB.
(3) CB is equal to AB.
Therefore: (4) CA is equal to CB.
The argument is utterly clear and utterly simple. It might stand as a paradigm of deductive inference.
The first premiss of the Euclidean Argument is the first of Euclid’s ‘common notions’; that is to say, it is one of the axioms of Euclid’s geometry.
If we omit the axiom, we are left with the following argument:
(1) CA is equal to AB.
(2) CB is equal to AB.
Therefore: (3) CA is equal to CB.
This argument, which I shall call the Truncated Argument, is also utterly simple and utterly clear. It too might be regarded as a paradigm of deductive inference.
It is plain that both the Euclidean Argument and the Truncated Argument are deductively valid. Their conclusions follow from their premisses.
It is plain, moreover, that the Euclidean Argument is, so to speak, one member of a large family of arguments, each of which is valid." (p. 44, notes omitted)
"!If the Euclidean Argument and the Truncated Argument are valid, and yet are neither hypothetical nor categorical syllogisms, then it will be tempting to infer that there must be a third kind of syllogism in addition to the two kinds commonly recognized by the ancient logicians.
At least one ancient logician drew exactly that inference. My phrase ‘a third kind of syllogism’ is taken from Galen. In his Institutio Logica Galen presents elementary and unoriginal expositions both of categorical and of hypothetical syllogistic; and then he turns to the novelty— to his third kind of syllogism (xvi 1)." (p. 50, notes omitted)
———. 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.
"Stoic logicians attended to words rather than to things: so claimed Galen, a dozen times or more; and so claimed Alexander of Aphrodisias. Galen and Alexander meant the claim as an accusation and a criticism: it was because they thought not of things, but of words, that the Stoics made fundamental errors in their logic.
Nineteenth-century historians of logic echoed the ancient claim, and they too thought that Stoic logic was ruined by its passion for words. Twentieth-century historians of logic also echoed the ancient claim. But for them it was not a criticism. On the contrary, it was a sign that the Stoic logicians were ‘formalists’ — and it is good thing for a logician to be a formalist.
But whether it is bad or good to attend to words rather than to things can scarcely be decided until we know what it means to attend to words rather than to things. In the following pages I shall discuss one or two aspects of the ancient claim and one or two of the texts pertinent to it. The texts concern complex propositions — conditionals, conjunctions, disjunctions. Such items form the foundations of Stoic logic. According to Galen and Alexander, the Stoics made fundamental errors about those fundamental items: they did so because they attended to words rather than to things, because their misdirected gaze encouraged them to misclassify compound propositions." (p. 512)
———. 2007. Truth, etc.: Six Lectures on Ancient Logic . Oxford: Clarendon Press.
Contents: 1 Truth 1; 2 Predicates and Subjects 93; 3 What is a Connector? 168; 4 Forms of Argument 264; 5 The Science of Logic 360; 6 When is a Syllogism not a Syllogism? 448; Onomasticon 529: Index of Passages 533; General Index 543-551.
"The book is about ancient logic. Antiquity is the antiquity of Greece and Rome—which here starts in the fourth century BC and continues, discontinuously, to the sixth century AD. As for logic, the table of Contents indicates what sort of thing is on or under the carpet.
Ancient logic lacks sex appeal.
Most contemporary logicians have little interest in the history—or at least in the ancient history—of their subject. No doubt they suppose that their long-dead colleagues have little or nothing to teach them, and perhaps they prefer the present and the future to the past. If that is so, then it must be confessed that their supposition is quite true: no logician has anything to learn from a study of Aristotle; and the pages of this book make no contribution to logic or to philosophy. As for preferences, I myself rate the past way above the future. But de gustibus .
Most students of the ancient world have little interest in logic. Some indeed despise it, or affect to despise it; and some fear it, or affect to fear it. Such attitudes—which were sometimes assumed in antiquity—are lamentable, and they are vexing. But there is nothing much I or anyone else can do about them.
Nonetheless, on my own pink official form there is written: ‘I like my work.’ And I hope that a few discerning readers will find parts of the book engaging—and even entertaining." (Preface, pp. VII-VIII)
———. 2007. "Peripatetic Logic: 100 BC - AD 200." In Greek and Roman Philosophy 100 BC - 200 AD. Vol. II , edited by Sharples, Robert W. and Sorabji, Richard, 531-546. London: Institute of Classical Studies.
"Andronicus wrote commentaries; his successors wrote commentaries; the writing of commentaries was the philosophical activity of the imperial epoch. What was once philosophy had become philology. For although commentary is an honest activity and a useful activity, it is not an exciting activity and it is not an innovative activity. Commentators are essentially conservative beings: they are concerned to preserve and transmit the thought of the past, not to discover or invent the thought of the future. Such conservatism is likely to be even more marked in logic than in other areas of philosophy. After all, Aristotle had perfected - had he not? - the art of logic. That being so, we should not expect too much in the way of novelty from Andronicus and his Peripatetic successors." (p. 533)
———. 2012. Logical Matters . New York: Oxford University Press.
Contents: Acknowledgements VII; Preface XI; 1. Galen, Christians, logic 1; 2. Cicero on logic 22; 3. Logical form and logical matter 43; 4. Grammar on Aristotle’s terms 147; 5. Peripatetic negations 172; 6. Aristotle’s Categories and Aristotle’s ‘categories’ 187; 7. Syllogistic and the classification of predicates 266; 8. Speusippus and Aristotle on homonymy 284; 9. Property in Aristotle’s Topics 312; 10. ‘Sheep have four legs’ 346; 11. The law of contradiction 353; 12. Proofs and the syllogistic figures 364; 13. Aristotle and Stoic logic 382; 14. Theophrastus and Stoic logic 413; 15. Terms and sentences 433; 16. Logic and the dialecticians 479; 17. The Logical Investigations of Chrysippus 485; 18. Πιτανα συνημμένα 499; 19. What is a disjunction? 512; 20. Medicine, experience, and logic 538; 21. Meaning, saying, and thinking 582; 22. Epicurus: meaning and thinking 602; 23. Ammonius and adverbs 621; 24. Priscian and connectors 639; 25. Late Greek syllogistic 659; 26. Boethius and the study of logic 666; 27. Syllogistic in the anon Heiberg 683; Bibliography 729; Index of Passages 751; General Index 775-796.
———. 2014. "Boethus and Finished Syllogisms." In Strategies of Argument: Essays in Ancient Ethics, Epistemology, and Logic , edited by Lee, Mi-Kyoung, 175-198. New York: Oxford University Press.
"According to Aristotle, the four canonical syllogisms of the first figure—Barbara, Celarent, Darii, Ferio—are τέλειοι or finished (APr A 26b28–30). The four canonical syllogisms of the second figure, and the six of the third, are all ἀτελεῖς or unfinished (28a4–7, 15–16).(1) And “all the unfinished syllogisms are finished by way of the first figure” (29a30–31).(2)" (p. 175)
"And yet Ammonius took himself to be rehearsing a generally accepted view—a view which had been championed by Boethus, who “proved that all the syllogisms in the second and third figures are finished,” and by Porphyry and Iamblichus and Maximus. Themistius defended Aristotle against Maximus, and the disputants asked the emperor Julian to arbitrate.
Julian decided for Maximus; and Syrianus and Proclus and Hermias later took the same line. What is more, “it appears that Theophrastus, Aristotle’s pupil, held the opinion contrary to his on the matter.” (See Ammonius, in APr 31.11–15.)
It is a striking story.(5) And puzzling, for two reasons. First, it is hard to believe that Theophrastus and Boethus and all those later lights wasted their breath on such a silly business. Secondly, Alexander breathes no word of the “contrary opinion” in his commentary on the Analytics —neither does Philoponus, and neither does Boethius. The silence is strange.(6) As for Theophrastus, Porphyry, Iamblichus, Syrianus, Proclus, and
Hermias, no other text supports Ammonius—and in the case of Theophrastus, scholars have doubted his claim. But Ammonius did not invent the story." (p. 177, a note omitted)
(1) As for the non-canonical syllogisms of the first figure (Baralipton, Barbari, and the rest), Aristotle does not expressly say whether they are finished or unfinished; but he was taken, no doubt rightly, to have thought them to be unfinished (see e.g. Alexander, in APr 69.26–29; Boethius, syll cat 823A).
(2) On the finishing of syllogisms see Striker, “Perfection”; cf. Patzig, Aristotle’s Theory, pp.43–87; Barnes, Truth, etc ., pp.378–386.
(5) Parts of it are also told in an Aristotelian scholium, 156b43–47, and by David, in APr xi 1. According to the Suda, Julian wrote About the three figures (s.v. Ἰουλιανός): his written judgement on the dispute?
(6) Lee, Syllogistik in der Spätantike , p.132, suggests, implausibly, that it would have been out of place to discuss the question in a commentary on Aristotle.
Barnes, J., Truth, etc. (Oxford, 2007)
Lee, T.-S. Die griechische Tradition der aristotelischen Syllogistik in der Spätantike , Hypomnemata 79 (Göttingen, 1984)
Patzig, G. Aristotle’s Theory of the Syllogism (Dordrecht, 1968)
Striker, G. “Perfection and reduction in Aristotle’s Prior Analytics, ” in M. Frede and G. Striker (edd), Rationality in Greek Thought (Oxford, 1996), pp.203–19
Barnes, Jonathan, Bobzien, Susanne, Mignucci, Mario, and Schenkeveld, Dirk. 1999. "Part II. Logic and Language." In The Cambridge History of Hellenistic Philosophy , edited by Algra, Keimpe, Barnes, Jonathan, Mansfeld, Jaap and Schofield, Malcolm, 65-225. Cambridge: Cambridge University Press.
Chapter 4: Introduction (pp. 65-76) by J. Barnes; Chapter 5: Logic: I. The Peripatetics (pp. 77-83) by J. Barnes; II. The 'Megarics' (pp. 83-92) by S. Bobzien, III. The Stoics §§ 1-7 (pp. 92-157) by S. Bobzien; § 8 (pp. 157-176) by M. Mignucci; Chapter 6: Language (pp. 177-225) by D. Schenkeveld, J. Barnes (pp. 193-213).
"Introduction. 1. A map of logic
The Stoics were the innovative logicians of the Hellenistic period; and the leading logician of the school was its third scholarch, Chrysippus. Most of this section of the History will therefore describe Stoic ideas and Stoic theories.
Its hero will be Chrysippus.
Logic is the study of inference, and hence of the items upon which inference depends – of propositional structure (or ‘grammar’), of meaning and reference. That part of their subject which the Hellenistic philosophers called λογική (logiké ) was a larger discipline;(1) for logiké –was the science which studies λόγος in all its manifestations,(2) and logic is included in logiké as a part. Indeed as a part of a part. For the Stoics divided logiké into two subparts, rhetoric and dialectic; and logic is a part of dialectic.(3)
(1) On the parts of philosophy see the Preface pp. xiii–xvi; see also Hadot 1979, Ierodiakonou 1993b and Dörrie and Baltes 1996, 205–31.
(2) See e.g. [Plu.] Plac. 874e. (But note Hülser 1987–8, lxxxii.)
(3) D.L. vii.41 (ενιοι ); Sen. Ep. 139.17. Other divisions of λογική are recorded: D.L. vii.41; cf. Hülser 1987–88, lxxix–xc.
Dörrie, H. & Baltes, M. (1996) Der Platonismus in der Antike IV (Stuttgart/Bad Cannstatt)
Hadot, P. (1979) ‘Les divisions des parties de la philosophie dans l’antiquité’, Museum Helveticum 36, 201–23
Hülser, K.-H. (1987–8) Die Fragmente zur Dialektik der Stoiker. 4 vols. (Stuttgart/Bad Cannstatt)
Ierodiakonou, K. (1993b) ‘The Stoic division of philosophy’, Phronesis 38, 57–74
Barnouw, Jeffrey. 2002. Propositional Perception. Phantasia, Predication, and Sign in Plato, Aristotle, and the Stoics . Lanham: University Press of America.
Contents: Preface I; Introduction 1; Chapter 1. Phantasia , Judgment and Statement in Plato 9; Chapter 2. Phantasia in Aristotle 49; Chapter 3. Predication and Sign in Aristotle 97; Chapter 4. Phantasia and Sign in Stoic Philosophy 149; Chapter 5. Recalling Sign and Revealing Sign. Part I. Sceptics and Stoics 215 Chapter 5. Recalling Sign and Revealing Sign. Part II. The Debates of the Hellenistic Medical Sects 245; Chapter 6. Predication, Proposition, Sign and Proof in Stoic Logic 275; Appendix 1. Declarative Predication vs. Kahn’s Veridical Be 327; Appendix 2. Peirce, the Epicureans and the Stoics 341; Bibliography 369; Indices 279-383.
"There has been considerable growth in the understanding and estimation of Stoic logic 'in the last thirty years, yet an important dimension of this Stoic achievement has not been grasped. Stoic logic was broadly conceived to include their theories of knowledge and perception, and the theory of perception provides the starting point and foundation of their logic. It is essential to the structure and unity of that logic that the Stoics take perception to be propositional. Starting from a new interpretation of the Stoic conception of phantasia as propositional perception, this study offers a view of Stoic logic that brings out the continuity linking perception, predication, inferential signs and proof." (p. 1)
Bénatouil, Thomas, and Ierodiakonou, Katerina, eds. 2018. Dialectic after Plato and Aristotle . Cambridge: Cambridge University Press.
Proceedings of the 13th Symposium Hellenisticum.
Contents: List of Contributors VII; Preface IX; List of Abbreviations X; Thomas Bénatouïl: Introduction: Dialectics in Dialogue 1; James Allen: Megara and Dialectic 17; Paolo Crivelli: Dialectic in the Early Peripatos 47; David Sedley: Epicurus on Dialectic 82; Katerina Ierodiakonou: Dialectic as a Subpart of Stoic Philosophy 114; Jean-Baptiste Gourinat: Stoic Dialectic and Its Objects 134; Luca Castagnoli: Dialectic in the Hellenistic Academy 168; Tobias Reinhardt: Pithana and probabilia 218; Sophie Aubert-Baillot: Terminology and Practice of Dialectic in Cicero’s Letters 254; Benjamin Morison: The Sceptic’s Modes of Argumentation 283; Riccardo Chiaradonna: Galen and Middle Platonists on Dialectic and Knowledge 320; Bibliography 350; Index of Names 371; Index of Passages 376-391.
Bobzien, Susanne. 2000. "Wholly Hypothetical Syllogisms." Phronesis.A Journal for Ancient Philosophy :87-137.
Abstract: "In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the 'mixed hypothetical syllogisms'. The other type is the one to which the present paper is devoted. These arguments went by the name of 'wholly hypothetical syllogisms'. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For instance, we find 'If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C'. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is 'is', where it occurs, predicative, existential, or veridical? That is, should 'A esti ' be translated as 'it is an A', 'A exists', 'As exist' or 'It is true/the case that A'? If A, B, C are term letters, and 'is' is predicative, are the conditionals quanti ed propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded."
———. 2000. "Why the Order of the Figures of the Hypothetical Syllogisms Was Changed." Classical Quarterly no. 50:247-251.
"In chapter 6 of Alcinous' Handbook of Platonism we find a discussion of categorical, hypothetical, and mixed syllogisms. Alcinous distinguishes three figures of the hypothetical syllogism, and illustrates each figure with a syllogism based on an argument from Plato. Here he remarks in passing that most people called the second hypothetical figure the third and that some called the third figure the second.(1) We may assume that those who called the third figure the second and those who called the second the third were the same. In a parallel passage, Alexander of Aphrodisias advocates the same ordering of figures of hypothetical syllogisms as Alcinous, and reports that Theophrastus, in the first book of his Analytics , had the second and third figure in reverse order.(2) Combining these passages, we can infer that at the turn of the second century A.D. there existed two different views on the ordering of the figures of the hypothetical syllogisms, of which one goes back to Theophrastus, whereas the other presumably was the result of a later change. This curious fact has so far not received a satisfactory explanation. In the following pages I seek to show what prompted this reversal of the order of figures." (p. 247, notes omitted)
(1) (...) Alc. Didasc. 159.14-15 and 20 (...)
(1) (...) Alex. An. Pr. 328.2-5, (...)
———. 2000. "How to give someone Horns. Paradoxes of Presupposition in Antiquity." Logical Analysis and History of Philosophy no. 15:159-184.
Abstract: "This paper discusses ancient versions of paradoxes today classified as paradoxes of presupposition and how their ancient solutions compare with contemporary ones. Sections 1-4 air ancient evidence for the Fallacy of Complex Question and suggested solutions, introduce the Horn Paradox, consider its authorship and contemporary solutions. Section 5 reconstructs the Stoic solution, suggesting the Stoics produced a Russellian-type solution based on a hidden scope ambiguity of negation.
The difference to Russell's explanation of defmite descriptions is that in the Horn Paradox the Stoics uncovered a hidden conjunction rather than existential sentence. Sections 6 and 7 investigate hidden ambiguities in "to have" and "to lose" and ambiguities of quantification based on substitution of indefinite plural expressions for indefmite or anaphoric pronouns, and Stoic awareness of these. Section 8 considers metaphorical readings and allusions that add further spice to the paradox."
———. 2002. "The Development of Modus Ponens in Antiquity: From Aristotle to 2nd Century AD." Phronesis.A Journal for Ancient Philosophy no. 47:359-394.
Abstract: "Aristotelian logic , as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens , modus (tollendo) tollens , modus ponendo tollens , and modus tollendo ponens . In late antiquity, arguments of these forms were generally classified as 'hypothetical syllogisms'. However, Aristotle did not discuss such arguments, nor did he call any arguments 'hypothetical syllogisms'. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them 'hypothetical syllogisms'; nor did they describe them as ponendo ponens , etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle's logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called 'hypothetical syllogisms'? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle's dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle's logic as preserved in his Topics and Prior Analytics ; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories."
———. 2002. "Some elements of propositional logic in Ammonius." In Interpretation und Argument , edited by Linneeweber-Lammerskitten, Helmut and Mohr, Georg, 103-119. Würzburg: Königshausen & Neumann.
"In his recent research, Gerhard Seel has demonstrated that Ammonius' semantics of assertoric sentences and propositions deserves far more attention than it has hitherto received.(3) In acknowledging this fact,
I shall in the present paper attempt to show that Ammonius' theory of compound assertoric sentences and of hypothetical propositions can provide us with some insight into the specifically Peripatetic-Platonist understanding of the .syntax, semantics, and function of molecular propositions in their logic; and in particular that it is mistaken to treat Ammonius where he remarks on issues of 'propositional logic'(4) as nothing but a muddled late witness of Stoic logic. The relevant main text passages are the Preface and Chapter 5 of Ammonius' De lnterpretatione commentary (Int .), some short, passages from Ammonius' Prior Analytics commentary (APr .) and the section on hypothetical syllogisms in [Ammonius] On Aristotle's Prior Analytics ([Amm.] APr .), which very closely follows what we know from Ammonius directly elsewhere.
Following Aristotle's footsteps, Ammonius builds his logic on a distinction between two ontological levels: the level of things (πράγματα) and the level of linguistic items. The latter comprises as sub-levels thoughts, the spoken word, and the written word (Int. 18.23-19.1). Only (compound) linguistic items are admitted as truth-bearers in a straightforward sense.(5)
Their truth-value depends on their relation to the things that make up the first level. I shall focus in the main on Ammonius' treatment of the spoken word, and its relation to the things. This is the sub-level of linguistic items Ammonius appears to be concerned with most of the time. The spoken word is caused by thought, whereas the written word serves to preserve the memory of the spoken word." (pp. 103-104)
(3) 'Ammonius' Semantics of the Asseri:oric Sentence', in Seel 2000.
(4) I use '.scare quotes' as a reminder thad use the e;xpression 'propositional logic' in a loose sense.
(5) Cf. Int. 21.21-4; 22.1-2.
Seel, Gerhard (ed.), 2000, Ammonius and the Sea-battle, Berlin, New York
Bochenski, Joseph. 1951. Ancient Formal Logic . Amsterdam: North-Holland.
Contents: I. Prolegomena 1; II. The Forerunners 14; III. Aristotle 19; IV. The Old Peripateticians 72; V. The Stoic-Megaric School 77; VI. The last period 103; Bibliography 110; Index of Greek terms 118; Index of names 121.
"The present book is intended to supply mathematical logicians with a synthetic outline of the main aspects of ancient formal logic which are known in the present state of research. In order to avoid misunderstandings, each of the above terms has to be explained.
The reader is supposed to be a mathematical logician, i.e., to know both the symbolisms and the (English) language of contemporary mathematical logic; those who are not acquainted with it must be warned that several terms used in that language have a particular meaning, different from the meaning attributed to the terms of the same form in other contexts.
The subject of the book is formal Logic; by this we understand a science such as was developed by Aristotle in his Prior Analytics , i.e., essentially the theory of syllogisms as defined in An. Pr. A 1, 24b 18-20. Along with the syllogisms proper, the structure of the sentences and semiotics will be studied; contrariwise, not only all ontological, psychological and epistemological problems, but even methodological topics will be omitted in so far as possible. This is perhaps regrettable; but there are several good books on those subjects while there is none on ancient formal logic as a whole - and the limitation of space forced us to omit everything which was not strictly formal.
By ancient formal logic, Greek logic from the beginning of Greek Philosophy until the end of Antiquity is meant. We have, it is true, some Latin textbooks of formal logic - but they all seem based on, or even copied from, Greek sources. It is perhaps worthwhile mentioning that there is also an ancient Indian Logic; this lies, however, outside our present scope.
What is offered here is an outline, moreover a very fragmentary one. A complete account of ancient formal logic cannot be written at the present date because of the lack of scientific monographs on individual logicians and topics. The initial aim of the author was to limit himself to a reassumption of monographs already published; in the course of the work he was compelled, however, to use some of his own unpublished researches on Aristotle and had the exceptional fortune of reading the manuscript of Dr Benson Mates' book on Stoic logic. He also collected some new data on other topics. In spite of this, considerable parts of ancient logic have hardly been touched upon - e.g. the logic of the Commentators - while others, Aristotle included, have been treated in a way which is far from being complete. On the whole, what the book contains may be considered as a kind of starting point for future research. Yet, it is hoped that even this will supply logicians with some information difficult to be found elsewhere and give a general idea of what the ancient logic was and how it developed." (pp. 1-2)
———. 1961. A History of Formal Logic . Notre Dame: Indiana University Press.
Translated from the German edition "Formale Logik " (1956) by Ivo Thomas; eeprinted New York, Chelsea Publishing Co., 1970.
"§4. Method and Plan.
A. Hisotry of Problems, and Documentation
Conformably to the directions of the series Orbis Academicus this work will present a documented history of problems.
We are not, therefore, presenting a material history of logic dealing with everything that has any historical importance, but a delineation of the history of the problematic together with the complex of essential ideas and methods that are closely connected with it. We only take into account those periods which have made an essential contribution to the problematic, and among logicians those who seem to us to rank as specially good representatives of their period. In this connection some thinkers of outstanding importance, Aristotle above all, Frege too, will receive much fuller treatment than would be permissible in a material history.
The story will be told with the help of texts, and those originally written in a foreign language have been translated into English.
This procedure, unusual in a scientific work, is justified by the consideration that only a few readers could understand all the texts if they were adduced in their original language. For even those readers with some competence in Greek are not automatically able to understand with ease a text of formal logic in that tongue. But the specialist logician will easiliy be able to find the original text by reference to the sources.
The passages quoted will be fairly thoroughly commented where this seems useful, for without some commentary many of them would not be readily intelligible." (p. 18)
Bonevac, Daniel. 2012. "A History of Quantification." In Logic: A History of Its Central Concepts , edited by Gabbay, Dov M., Pelletier, Francis Jeffrey and Woods, John, 63-126. Amsterdam: North-Holland.
Volume 11 of the Handbok of te History of Logic .
"Aristotle (384–322 BC), the founder of the discipline of logic, also founded the study of quantification. Normally, Aristotle begins a topic by reviewing the common opinions, including the opinions of his chief predecessors. In logic, however, he could not adopt the same strategy; before him, he reports, “there was nothing at all” (Sophistical Refutations 183b34–36). Aristotle’s theory dominated logical approaches to quantification until the nineteenth century.
That is not to say that others did not make important contributions. Medieval logicians elaborated Aristotle’s theory, structuring it in the form familiar to us today. They also contemplated a series of problems the theory generated, devising increasingly complex theories of semantic relations to account for them. Textbook treatments of quantification in the seventeenth and nineteenth centuries made important contributions while also advancing some peculiar theories based on medieval contributions." (p. 63)
Bonevac, Daniel, and Dever, Josh. 2012. "A History of the Connectives." In Logic: A History of Its Central Concepts , edited by Gabbay, Dov M., Pelletier, Francis Jeffrey and Woods, John, 175-233. Amsterdam: North-Holland.
Volume 11 of the Handbok of te History of Logic .
"Contemporary students of logic tend to think of the logic of the connectives as the most basic area of the subject, which can then be extended with a logic of quantifiers. Historically, however, the logic of the quantifiers, in the form of the Aristotelian theory of the syllogism, came first. Truth conditions for negation, conjunction, and disjunction were well understood in ancient times, though not until Leibniz did anyone appreciate the algebraic features of these connectives. Approaches to the conditional, meanwhile, depended on drawing an analogy between conditionals and universal affirmative propositions. That remained true throughout the ancient, medieval, and early modern periods, and extended well into the nineteenth century, when Boole constructed an algebraic theory designed to handle sentential and quantificational phenomena in one go. The strength of the analogy, moreover, undercuts a common and otherwise appealing picture of the history of logic, according to which sentential and quantificational threads developed largely independently and, sometimes, in opposition to each other, until Frege wove them together in what we now consider classical logic. Frege did contribute greatly to our understanding of the connectives as well as the quantifiers. But his contribution consists in something other than unifying them into a single theory" (p. 175)
Brunschwig, Jacques. 1994. "Remarks on the classification of simple propositions in Hellenistic logics." In Papers in Hellenistic Philosophy , 57-71. Cambridge: Cambridge University Press.
"The first and chief difference among propositions (αξιώματα), the dialecticians say, is that between simple (απλα) and non-simple (οὐχ απλα)' These are the words of Sextus Empiricus (M VIII.93) and nobody would challenge the importance of that distinction. The declaration introduces a long passage (93-129) which sets out the subdivisions within this fundamental division. It is a passage which historians of logic tend to use as one of the sources that provide us with information on the Stoic classification of propositions, despite the fact that the Stoics are not specifically named, for it is generally accepted that Sextus does refer to them as 'the dialecticians'. The task that faces us, then, is to compare his text with the classification transmitted to us by Diogenes Laertius (VII. 68-76), who possibly bases his remarks on Diocles of Magnesia, - a classification which, for its part, is explicitly ascribed to Chrysippus and a number of his successors." (p. 57)
"What I propose to do is study the formal characteristics of the classification of simple propositions, as it is set out by SE and by DL. My principal questionwill be whether or not this division is a true partition, that is to say whether it is of such a kind that every simple proposition necessarily belongs to one, and only one, of the classes that the division comprises. But in considering that question, I shall also be addressing myself to another: that of the criteria of the simplicity of a proposition. The two questions are clearly linked, insofar as they respectively concern the extension and the comprehension of the concept of propositional simplicity. That is why I think it a good idea to start off by saying a word or two about the division of propositions into sim le and nonsimple, before moving on to the subdivision of simple propositions." (p. 58)
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.
"The notion of sign itself is of course virtually as old as the Greeks’ habit of giving grounds or evidence for their assertions.
The term ‘sëmeion may be found in tragedy, in the orators, in the historians, in the medical writers, in the philosophers.
Given this background, we naturally assume, when first Aristotle and then later the Stoics propose an analysis of sign, that it will be a technical analysis of a notion in common use, not the stipulation of a technical concept. We expect no restriction on the range of things that can serve as a sign or evidence of something, for existing usage displays none. It is not even correct to say that a sign is what we would call empirical evidence for something.
Often this is so, but in the Elcatic tradition, when Parmenides’ ‘signposts’ (sëmata , fr. 8,2) became Melissus’ signs (sëmeia , fr. 8,1), they were intended to give demonstrative proof of an inescapable conclusion. Likewise in Sextus Empiricus it is regularly reported that demonstrative proof is one species of sign (PH II 96, I22, 131, 134; M VIII 140, 180, 278, 289, 299). If so, if ‘sign’ covers any kind of ground, evidence, or reason for believing something, including demonstrative evidence, we might expect that a rough, general first sketch of the notion as it functions in everyday discourse could take the following simple form: For X to be a sign or evidence of Y requires (i) that X should be evident or manifest to us in some appropriate way, (ii) that it should be evidence of something else in that Y can be inferred from it. The task of the technical analysis would then be to explain the relationship between X and Y which sustains and justifies the inferring of the second from the first.
Let us see how far Aristotle fulfils these expectations." (pp. 193-194)
Castagnoli, Luca. 2010. Ancient Self-Refutation: The Logic and History of the Self-refutation Argument from Democritus to Augustine . Cambridge: Cambridge University Press.
"I suggest that the various forms of self-contradiction and inconsistency which I have sketchily outlined should be carefully kept distinct from self-refutation, while recognising that the edges between all these notions are not always as sharp as we might desire. Independently of its theoretical merits, I hope that my rough via negativa to self-refutation will serve its contingent purpose of conveying some preliminary idea (and warning) of what the reader should not expect to find in the pages of this book. Standard reductio ad impossibile arguments, which on my account are located in the sphere of self-contradiction, will not be on our menu (although some of my contentions concerning the logic of ancient self-refutation might have consequences for some forms of ancient reductio as well). The elenchus (Socratic, Aristotelian or otherwise) will also lie beyond the scope of my analysis, since its gist seems to remain, through all its varieties, intended aims and interpretations, that of unmasking hidden inconsistencies between sets of beliefs, concessions, theses; for the same reason, Plutarch, with the material sedulously collected in his De Stoicorum Repugnantiis (On the Contradictions of the Stoics ), will not be a hero of our story. The charge of pragmatic inconsistency was a favourite weapon in ancient philosophical controversy: while its history would certainly deserve a comprehensive investigation analogous to the one I am undertaking here for self-refutation, my tentative map of various types of refutation has banned it from the ground covered in this book. Also the notorious Liar Paradox, for reasons to be explained in chapter 1, will make only a cursory appearance on· the stage, to be quickly dismissed." (pp. 7-8, notes omitted)
———. 2018. "Dialectic in the Hellenistic Academy." In Dialectic after Plato and Aristotle , edited by Bénatouil, Thomas and Ierodiakonou, Katerina, 168-217. Cambridge: Cambridge University Press.
"To begin with, what do we mean, exactly, when we say, for example, that X’s argument Y in passage Z is dialectical, or that X’s defence Y against the charge W as reported in Z was dialectical? Did our source, the author of Z, clearly speak, or conceive, of that argument or defence as ‘dialectical’? And is there any sign that X himself thought that, by proposing Y, he was engaging in some form of dialectic? If so, what form precisely?
This chapter aims to show how a nuanced approach to these questions can provide firmer foundations for the debate concerning the ‘dialectical nature’ of the philosophy of Arcesilaus and Carneades. I will begin, in section 1, by reconstructing their attitudes towards what they, and their contemporaries, called ‘διαλεκτική’. In Section 2, I will examine some key ancient testimonies on their philosophical method and ask whether, and in what sense exactly, it can be characterised, on the basis of those testimonies, as ‘dialectical’. In Section 3, I will examine the broad structure of Arcesilaus’ and Carneades’ ‘core argument’ for suspension of judgement (section 3.1) and then survey some other more specific types of Academic arguments (section 3.2), asking in what sense, if any, all these arguments were ‘dialectical’.
Finally, in section 4, I will consider whether any exegetical and logical space is left to interpret the philosophy of Arcesilaus and Carneades as an exercise in ‘pure dialectic’, as proposed by Pierre Couissin in his influential article on ‘The Stoicism of the New Academy’ (Coussin 1929/1983)." (p. 169)
Couissin, P. (1983) ‘The Stoicism of the New Academy’, in The Skeptical Tradition , ed. M. Burnyeat. Berkeley and Los Angeles: 31-63. First published as Couissin, P. (1929) ‘Le Stoïcisme de la Nouvelle Académie’,
Revue d’histoire de la philosophie 3, 241-276.
Castagnoli, Luca, and Fait, Paolo, eds. 2023. The Cambridge Companion to Ancient Logic . Cambridge: Cambridge University Press.
Contents: List of Contributors VII; Luca Castagnoli and Paolo Fait: Introduction 1;
I The Development of Logic in Antiquity 19
1 NIcholas Denyer: The Prehistory of Logic 21; 2 Paolo Fait: Aristotle and Theophrastus 37; 3 Karlheinz Hülser: Megarians and Stoics 57; Benjamin Morison: 4 Late Antiquity 82;
II Key Themes 107
5 Walter Cavini: Truth as a Logical Property and the Laws of Being True 109; 6 Michael Ferejohn: Definition 128; 7 Paolo Crivelli: Terms and Propositions 147; 8 Luca Castagnoli and Paolo Fait:: Validity and Syllogism 167; 9 Alexander Bown: Demonstration 199: 10 Mark Malink: Modalities and Modal Logic 216; 11 Luca Castagnoli: Fallacies and Paradoxes 236; 12 Christof Rapp: Logic in Ancient Rhetoric 263; 13 Rviel Netz: Ancient Logic and Ancient Mathematics 283;
III The Legacy of Ancient Logic 299
14 John Marenbon: Ancient Logic in the Middle Ages 301; 15 Mirella Capozzi and Leila Haaparanta: Ancient Logic from the Renaissance to the Birth of Mathematical Logic 319; 16 John Woods: Ancient Logic Today 345;
Bibliography 364; List of Abbreviations 407; Index of Passages 411; General Index 424-432.
"Unlike contemporary logic, which is as well a mathematical discipline, ancient logic was squarely under the purview of philosophy. Not surprisingly, then, as historiographical disciplines developed during the first half of the nineteenth century, ancient logic was studied by general historians of philosophy and was not felt to require some special methodology. This rapidly changed near the end of the century, when the revolution that was radically transforming logic also changed the perception of its past, making a lasting impact on the way the history of the subject would be studied and written ever since. Several leading figures of the logical renaissance cast a curious eye on the history of their subject: Peirce, Couturat, Russell, perhaps even Frege, but the logician who more than anyone else cultivated historical studies, and the one who introduced a new way of reading ancient logical texts, was certainly Jan Lukasiewicz, the Polish logician best known as the father of multi-valued logics (Chapter 15 - Capozzi and Haaparanta). (p. 16)
Charles, David, ed. 2010. Definition in Greek Philosophy . Oxford: Oxford University Press.
Contents: Notes on Contributors IX; Introduction 1;
Part I. Plato on Definition
1 Lindsay Judson: Carried Away in the Euthyphro 31; 2 Vasilis Politis: Explanation and Essence in Plato’s Phaedo 62; 3 David Charles:The Paradox in the Meno and Aristotle’s Attempts to Resolve It 115; 4 Lesley Brown: Definition and Division in Plato’s Sophist 151; 5 Mary Louise Gill: Division and Definition in Plato’s Sophist and Statesman 172;
Part II. Aristotle on Definition
6 Kei Chiba: Aristotle on Essence and Defining-Phrase in his Dialectic 203; 7 Deborah Modrak: Nominal Definition in Aristotle 252; 8 David Charles: Definition and Explanation in the Posterior Analytics and Metaphysics 286; 9 James G. Lennox: Bios and Explanatory Unity in Aristotle’s Biology 329;
Part III. Post-Aristotelian Writers on Definition
10 Paolo Crivelli: The Stoics on Definition 359; 11 Richard Sorabji: The Ancient Commentators on Concept Formation 424; 12 Jane Hood: Galen’s Aristotelian Definitions 450; 13 Annamaria Schiaparelli: Essence and Cause in Plotinus’ Ennead VI. 7  2: An Outline of Some Problems 467; 14 Gail Fine: Sceptical Enquiry 493;
Index Locorum 527; Index Nominum 546; General Index 552-556.
"Definition was a central topic in Greek philosophy. Socrates’ most significant philosophical innovation, in Aristotle’s view, was to focus on the search for definitions, raising and attempting to answer his famous ‘What is it?’ question (Metaphysics 1078b22ff.). In many of Plato’s dialogues, Socrates asks such questions as ‘What is virtue?’, ‘What is knowledge?’, ‘What is justice?’ and hunts, often unsuccessfully, for an adequate answer. Aristotle, in the Topics , Analytics , and Metaphysics , devoted considerable time and effort to determining what counts as a good definition. Later philosophers pursued these issues further, developing their own accounts of the nature and role of definition. The topic remained, from Socrates onwards, an important concern in Greek philosophy." (p. 1)
Corcoran, John. 1972. "Conceptual Structure of Classical Logic." Philosophy and Phenomenological Research no. 33:25-47.
"Among other things logic is concerned with the correctness of arguments. An examination of the kinds of things pronounced correct and incorrect in logic reveals two distinct kinds of arguments, each with its own characteristic kind of correctness. Indeed, each kind of correctness is so distinctively related to its corresponding kind of argument that nonsense generally results from predicating one kind of correctness (and/or incorrectness) of the other kind of argument.
Indeed, it appears that the set of arguments of one sort is the range of applicability of the corresponding kind of correctness. Similarly for the other."
"One purpose of this paper is to discuss the two kinds of argument(2) so that it will be clear how consideration of the kinds of "correctness" appropriate to each leads to distinct logical problems and to distinct philosophical problems. The problem, in logic, of determining the conditions under which the truth of a set of sentences "guarantees" the truth of another sentence contrasts with the problem of deter- mining "norms of correct reasoning." In philosophy, questions con- cerning the nature of the relationship which obtains between a set of sentences and each of its consequences are to be contrasted with questions concerning the nature of deductive reasoning." (pp. 25-26)
(2) This phrase is not intended to suggest one overarching genus "argument" subsuming two species.
———, ed. 1974. Ancient Logic and its Modern Interpretations . Dordrecht: Reidel.
Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972.
Contents: John Corcoran: Preface IX; Part One: Ancient semantics; Norman Kretzmann: Aristotle on spoken sound significant by convention 3; Ronald Zirin: Inarticulate noises 23; Newton Garver: Notes for a linguistic reading of the Categories 27; Part Two: Modern research in ancient logic; Ian Mueller: Greek mathematics and Greek logic 35; John Mulhern: Modern notations and ancient logic 71; Part Three: Aristotle's logic; John Corcoran: Aristotle's natural deduction system 85; Mary Mulhern: Corcoran on Aristotle's logical theory 133; Part Four: Stoic logic; Josiah Gould: Deduction in Stoic logic 151; John Corcoran: Remarks on Stoic deduction 169; Part Five: Final session of the Symposium; John Corcoran: Future research on ancient theories of communication and reasoning 185; A panel discussion on future research in ancient logical theory 189; Index of names 209-211.
"During the last half century there has been revolutionary progress in logic and in logic-related areas such as linguistics. Historical knowledge of the origins of these subjects has also increased significantly. Thus, it would seem that the problem of determining the extent to which ancient logical and linguistic theories admit of accurate interpretation in modern terms is now ripe for investigation.
The purpose of the symposium was to gather logicians, philosophers, linguists, mathematicians and philologists to present research results bearing on the above problem with emphasis on logic. Presentations and discussions at the symposium focused themselves into five areas : ancient semantics, modern research in ancient logic, Aristotle's logic, Stoic logic, and directions for future research in ancient logic and logic-related areas.
Seven of the papers which appear below were originally presented at the symposium. In every case, discussion at the symposium led to revisions, in some cases to extensive revisions. The editor suggested still further revisions, but in every case the author was the final judge of the work that appears under his name.
In addition to the seven presented papers, there are four other items included here. Two of them are papers which originated in discussions following presentations. Zirin's contribution is based on comments he made following Kretzmann's presentation. My 'Remarks on Stoic Deduction' is based on the discussion which followed Gould's paper. A third item contains remarks that I prepared in advance and read at the opening of the panel discussion which was held at the end of the symposium. The panel discussion was tape-recorded and the transcript proved of sufficient quality to merit inclusion in these proceedings with a minimum of editing." (From the Preface )
———. 2006. "Schemata: The Concept of Schema in the History of Logic." Bulletin of Symbolic Logic no. 12:219-240.
Abstract: "Schemata have played important roles in logic since Aristotle's Prior Analytics . The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper . Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski's 1933 Convention T . Mathematical logicians recognize the role of schemata in first-order number theory where Peano's second-order Induction Axiom is approximated by Herbrand's Induction-Axiom Schema . Similarly, in first-order set theory, Zermelo's second-order Separation Axiom is approximated by Fraenkel's first-order Separation Schema . In some of several closely related senses, a schema is a complex system having multiple components one of which is a template-text or scheme-template , a syntactic string composed of one or more "blanks" and also possibly significant words and/or symbols. In accordance with a side condition the template-text of a schema is used as a "template" to specify a multitude, often infinite, of linguistic expressions such as phrases, sentences, or argument-texts, called instances of the schema. The side condition is a second component. The collection of instances may but need not be regarded as a third component. The instances are almost always considered to come from a previously identified language (whether formal or natural), which is often considered to be another component. This article reviews the often-conflicting uses of the expressions 'schema' and 'scheme' in the literature of logic. It discusses the different definitions presupposed by those uses. And it examines the ontological and epistemic presuppositions circumvented or mooted by the use of schemata, as well as the ontological and epistemic presuppositions engendered by their use. In short, this paper is an introduction to the history and philosophy of schemata."
 Abraham Fraenkel - Part I. Historical introduction - to Paul Bernays - Axiomatic set theory (1958) - Reprint Dover 1991 pp. 3-35.
 Jacques Herbrand, Logical Writings , (W. Goldfarb, Tr. Goldfarb, and van J. Heijenoort, editors), Harvard University Press, Cambridge, MA, 1971.
 Johann von Neumann, Zur Hilbertschen Beweistheorie , Mathematische Zeitschrift , vol. 26 (1927), pp. 1-46.
 Adam Tarski, The concept of truth in the languages of the deductive sciences , Prace Towarzystwa Naukowego Warszawskiego, Wydzial III Nauk Matematyczno-Fizycznych , vol. 34 (1933), reprinted in , pp. 13-172; expanded English translation in , pp. 152-278.
 Adam Tarski, Logic, Semantics, Metamathematics, papers from 1923 to 1938 , 2nd ed., Hackett, Indianapolis, 1983, edited with introduction and analytic index by J. Corcoran (first edition 1956).
 Jan Zygmunt (editor), Alfred Tarski, Pisma Logiczno-Filozoficzne, 1 Prawda , Wydawnictwo Naukowe PWN, Warsaw, 1995.
Crivelli, Paolo. 2018. "Dialectic in the Early Peripatos." In Dialectic after Plato and Aristotle , edited by Bénatouil, Thomas and Ierodiakonou, Katerina, 47-81. Cambridge: Cambridge University Press.
"Before plunging into the examination of the early Peripatetics’ views about dialectic, a methodological issue must be addressed. It concerns the noun ‘dialectic’. This noun has been and is used differently by different authors, in antiquity as well as in modern times.
In consideration of these different uses, one wonders precisely what task one is setting up for oneself when one refers to the subject of one’s inquiry as ‘the early Peripatetics’ views about dialectic’.
There are several reasonable answers to this question. According to the one adopted in this chapter, the subject referred to as ‘the early Peripatetics’ views about dialectic’ is that of the early Peripatetics’ views about the discipline that they themselves called ‘dialectic’. This project, however, also faces a difficulty because there are regrettably few occurrences of the noun ‘dialectic’ or cognate expressions in the fragments of Aristotle’s immediate followers. A plausible solution to this further problem is to assume that the early Peripatetics’ use of ‘dialectic’ is roughly the same as Aristotle’s, namely that they employed ‘dialectic’ to denote an art of arguing on the basis of reputable views, an art codified mainly in the Topics, (1) the work to which Aristotle himself refers as ‘the treatise concerning dialectic’.(2) My own use of the noun ‘dialectic’ in this study will be in line with this assumption: I shall use ‘dialectic’ to denote the art of arguing on the basis of reputable views codified mainly in Aristotle’s Topics . My aim is to reconstruct and evaluate the early Peripatetics’ views about this discipline.
The available data enable us to reconstruct a substantial amount of the theses concerning dialectic put forward by Theophrastus and a small number of the views of Eudemus and Strato. Accordingly, the first of this chapter’s sections (section 1) will be concerned with Theophrastus, while the second and the third shorter ones (sections 2 and 3) will be dedicated, respectively, to Eudemus and Strato." (pp. 47-48)
(1) Some corroboration of this hypothesis will be offered in the subsections to notes 77 and 79.
(2) APr 1.30.46a29-30, cf. Rhet. 2.22.1396b26, 24-1401a2.
Dumitriu, Anton. 1977. History of Logic: Volume I . Tunbridge Wells: Abacus Press.
Revised, updated, and enlarged translation from the Roumanian of the second edition of "Istoria logicii ".
Contents: Foreword IX; Historical note on works on the history of logic XIII-XVI;
Part I: Logic in Non-European Cultures
Chapter I. The logical structure of primitive mentality 3; Chapter II. Logic in ancient China 12; Chapter III. Indian logic 39;
Part II: Logic in ancient Greece
Chapter IV: The beginning of Greek logic 69; Chapter V: The sophists 95; Chapter VI: Socrates' reaction. Plato 103; Chapter VII: The lesser Socratics 128; Chapter VIII: Aristotle's logic 141; Chapter IX: The Peripatetic School 207; Chapter X: The logic of the Stoics 216; Chapter XI: The Epicurean School. Scepticism and the New Academy 284;
Part III: Rhetors and commentators
Chapter XII: Logic and rhetoric in rome 273; Chapter XIII: Commentaries and commentators 261;
Index of names 323; Index of subjects 335-342.
"The potential author of a history of logic should not depend on any preconceived point of view. The formalistic option, for example, requires logic to be treated in a purely symbolic way, as a logical syntax of meaningless signs; obviously the historian who adopts such a view, hoping to achieve an absolute objectivity by eliminating any philosophical hypothesis, will be bound by it.
Such a logic is a logic without any philosophical content, and surely its history will have to adopt the same line. But is it possible to deal with logic without having any philosophical point of view? It is evident that such an intention is not realistic, and even in the formalistic point of view a certain philosophy is understood. Aristotle's statement "he who philosophizes, philosophizes, and he who does not philosophize, philosophizes too, so everybody philosophizes" is very significant.
A history of logic based on such a view would have to leave out of the list of logicians names like Thomas Aquinas, Kant, Hegel, Husserl, and many others. Is it possible to explain the development of logic without commenting on thinkers of great influence, who actually moulded the whole frame of human thought in their time? Obviously such a point of view is inadmissible.
A history of logic without philosophical references leads to very important consequences, to wide mutations and alterations of the very concept of logic and philosophy. After two and a half millennia, logic is taken from philosophy, and belongs henceforth to another domain, that of mathematics. In this way, logic has escaped from the jurisdiction of philosophy, but philosophy has remained independent of logic. In the past logic was, on the contrary, closely connected to philosophy, whether it was conceived as a part of philosophy, or an introduction to it, or as an organon, or even as the philosophy itself." (Foreword, pp. IX-X)
Everson, Stephen, ed. 1994. Language . Cambridge: Cambridge University Press.
Contents: 1 Introduction 1; 2 V: Plato on understanding language 10; 3 Bernard Williams: Cratylus’ theory of names and its refutation 28; David Charles: Aristotle on names and their signification 37; Stephen Everson: Epicurus on mind and language 74; Michael Frede: The Stoic notion of a lekton 109; David K. Glidden,: Parrots, Pyrrhonists and native speakers 129; David Blank: Analogy, anomaly and Apollonius Dyscolus 149; R. J. Hankinson: Usage and abusage: Galen on language 166; Christopher Kirwan: Augustine on the nature of speech 188; Lesley Brown: The verb ‘to be’ in Greek philosophy: some remarks 212; Bibliography 237; Index of names 264; Index of passages discussed 269; Index of subjects 277-280.
"Ancient philosophers, then, like their modern successors, were concerned to answer various sorts of question in their study of language. At the most basic level, they attempted to provide an analysis of the structure of language - to distinguish between subjects and predicates, nouns and sentences, and so on28 - and to clarify the meaning of individual expres¬ sions. Secondly, they set out to give accounts of how it is that sounds and marks can be meaningful. Thirdly, they dealt with the question of how a speaker can come to understand a language. In answering all of these, the study of language could not be dissociated from questions to do with the nature of the mind and the world. Even if the ancients did not share the presuppositions of the contemporary analytical philosopher, neither their interests in the explanation of language nor their methods of general philosophical enquiry will prove alien to those brought up to take those presuppositions almost for granted." (Introduction , p. 9)
28 David Blank, in ch. 8, describes the relation between philosophy and grammar in the Hellenistic period.
Fink, Jakob L., ed. 2012. The Development of Dialectic from Plato to Aristotle . Cambridge: Cambridge University Press.
Contents: List of contributors VII; Jakob L. Fink: Introduction 1;
Part I. dialectic as interpersonal activity
1. Luca Castagnoli: Self-refutation and dialectic in Plato and Aristotle 27; 2. Marja Liisa Kakkuri Knuuttila: The role of the respondent in Plato and Aristotle 62; 3. Hallvard Fossheim: Division as a method in Plato 91;
Part II. Form and content in the philosophical dialogue
4. Morten S. Thaning: Dialectic and dialogue in the Lysis 115; 5. Holger Thesleff: The Laches and ‘joint search dialectic’ 138; 6. Charles H. Kahn: The philosophical importance of the dialogue form for Plato 158; 7. Jakob L. Fink: How did Aristotle read a Platonic dialogue? 174;
Part III. Dialectical methodology
8. Vasilis Politis: What is behind the ti esti question? 199; 9. Hayden W. Ausland: Socratic induction in Plato and Aristotle 224; 10. Louis André Dorion: Aristotle’s definition of elenchus in the light of Plato’s Sophist 251; 11. Robert Bolton: The Aristotelian elenchus 270; 12. Wolfgang Kullmann: Aristotle’s gradual turn from dialectic 296;
Bibliography 316; Index rerum 332; Index locorum 338; Index nominum 352-355.
"Concerning dialectic, Plato and Aristotle might be thought to stand on each side of a very wide gap. To Plato, dialectic is the best means available to philosophy for reaching truth, whereas Aristotle seems to grant dialectic little more than the function of testing propositions and thus denies a direct access to philosophical insight through dialectic. However, even if this were an adequate description of Platonic and Aristotelian dialectic (and it hardly is), one question would remain: what happened in between, or in other words, how did the concept of dialectic develop from Plato to Aristotle? The present volume aims at giving some answers to this question." (p. 1)