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Selected Bibliography on the Logic of Eudemus of Rhodes and Theophrastus of Eresus

Critical edition of the Fragments of Eudemus of Rhodes

  1. Wehrli, Fritz, ed. 1955. Eudemos von Rhodos. Basel: B. Schwabe & C.

    The standard collection of Fragments, abbreviated W. in the citations; second edition 1969.

Selected bibliography on Eudemus' logic

  1. Alexander, of Aphrodisias. 1999. On Aristotle Prior Analytics 1.8-13 (with 1.1736b35 - 37a31), Ancient Commentators on Aristotle. London: Duckworth.

    Translated by Ian Mueller with Josiah Gould.

    On the modal logic of Eudemus of Rhodes see pp. 59ff. with notes on Alexander 124.11 ff.

  2. Bodnár, István, and Fortenbaugh, William W., eds. 2002. Eudemus of Rhodes. New Brunswick: Transaction Publishers.

    Contents: Preface VII; Contributors IX; 1. Dimitri Gutas: Eudemus in the Arabic tradition 1; 2. Hans B. Gottschalk: Eudemus and the Peripatos 25; 3. Tiziano Dorandi: Qualche aspetto controverso della biografia di Eudemo di Rodi 39; 4. William W. Fortenbaugh: Eudemus' work On Expression 59; 5. Pamela M. Huby: Did Aristotle reply to Eudemus and Theophrastus on some logical Issues? 85; 6. Robert W. Sharples: Eudemus' physics: change, place and time 107; 7. Han Baltussen: Wehrli's edition of Eudemus of Rhodes: the physical fragments from Simplicius' commentary On Aristotle's Physics 127; 8. Sylvia Berryman: Continuity and coherence in early Peripatetic texts 157; 9. István Bodnár: Eudemus' Unmoved Movers: fragments 121-123b Wehrli 171; 10.Deborah K. W. Modrak: Phantasia, thought and science in Eudemus 191; 11. Stephen A. White: Eudemus the naturalist 207; 12. Jørgen Mejer: Eudemus and the history of science 243; 13: Leonid Zhmud: Eudemus' history of mathematics 263; 14. Alan C. Bowen: Eudemus' history of early Greek astronomy: two hypotheses 307; 15. Dmitri Panchenko: Eudemus fr. 145 Wehrli and the ancient theories of lunar light 323; 16. Gábor Betegh: On Eudemus fr. 150 (Wehrli) 337; Index of ancients sources 359-383.

    "This volume of Rutgers University Studies in Classical Humanities, no. XI in the series, is the third devoted to Theophrastus' colleagues, pupils and successors, i.e., those Peripatetic philosophers, whom Fritz Wehrli brought together under the label die Schule des Aristoteles. Volume IX focuses on Demetrius of Phalerum, who was Theophrastus' pupil and for ten years the ruler of Athens. Volume X has Dicaearchus of Messana, Theophrastus' fellow-pupil within the Aristotelian Peripatos, as its subject. The present Volume, no. XI, concentrates on Eudemus of Rhodes, who, like Dicaearchus, studied under Aristotle and alongside Theophrastus. This concern with die Schule des Aristoteles will continue with the next two volumes: Lyco of Troas and Ieronymus of Rhodes will be the subjects of Volume XII, and Aristo of Ceos will be featured in Volume XIII. All three belong to the post-Theophrastean Peripatos. Like Volumes IX and X, so Volumes XII and XIII will present the ancient sources with translation as well as discussion by various scholars. Volume XI is different in that it is entirely composed of articles which discuss Eudemus from differing points of view." (from the Preface by the Editors)

  3. Fortenbaugh, William W. 2002. "Eudemus' work On Expression." In Eudemus of Rhodes, edited by Bodnár, István and Fortenbaugh, William W., 59-83. New Brunswick: Transaction Publishers.

    "Eudemus of Rhodes wrote a work entitled On Expression, Peri lexeos. It was at least two books or rolls long and was the subject of a lost treatise by Galen. Apparently the work was not only substantial but also full of interesting material. It is therefore regrettable that we have only a few fragments from which to judge the content of the work. Five fragments, nos. 25-9, are assigned to the work by Wehrli, but that may be too generous. In what follows, I intend first to consider Wehrli's five fragments and then to ask what we can conclude concerning the content of On Expression." (p. 59)

  4. Gottschalk, Hans B. 2002. "Eudemus and the Peripatos." In Eudemus of Rhodes, edited by Bodnár, István and Fortenbaugh, William W., 25-37. New Brunswick: Transaction Publishers.

  5. Gutas, Dimitri. 2002. "Eudemus in the Arabic Tradition." In Eudemus of Rhodes, edited by Bodnár, István and Fortenbaugh, William W., 1-23. New Brunswick: Transaction Publishers.

    Reprinted as Chapter VIII in D. Gutas, Greek Philosophers in the Arabic Tradition, Aldershot: Ashgate, 2000. see IV. Logic pp. 9-11.

    "The information on Eudemus of Rhodes that can be recovered in Arabic sources falls into three categories: there is a full collection of sayings (Section II below and Appendix), some incidental biographical notices that mainly state his relation to Aristotle and Theophrastus (Section III), and a number of references to his views on logic which lie held in common with Theophrastus (Section IV). No work of his is reported to have been translated into Arabic or is known to be extant. Apart from the sayings, therefore, Eudemus has no independent persona or presence in Arabic but rides on the coattails primarily of Theophrastus. This is hardly surprising, given the little information on Eudemus that was available even in Greek at the time of the rise of Islam." p. 1

  6. Huby, Pamela M. 2002. "Did Aristotle reply to Eudemus and Theophrastus on some logical issues?" In Eudemus of Rhodes, edited by Bodnár, István and Fortenbaugh, William W., 85-106. New Brunswick: Transaction Publishers.

  7. Steiger, Kornél. 2000. "Eudemos von Rhodos und der Peripatos." Acta Antiqua. Academiae Scientiarum Hungaricae no. 40:449-451.

    "Von Eudemos berichtet die Kommentarliteratur, vor allem im Zusammenhang mit Andronikos, dass er zu den bedeutendsten ἑταῖροι des Aristoteles gehört und wichtige und seiner Zeit weit vorauseilende philosophische Erkenntnisse gewonnen habe. Trotzdem gibt es von ihm keine Vita, Diogenes Laertios, Suda und Cicero kennen ihn nicht. Man darf wohl annehmen, dass der Rhodier Andronikos einen ganz und gar unauffälligen Aristotelesschüler aus Rhodos zum bedeutenden Philosophen hochstilisiert hat, um an eine alte peripatetische Tradition auf der Insel glauben zu machen."

Selected bibliography on Theophrastus' logic

  1. Barnes, Jonathan. 1983. "Terms and Sentences: Theophrastus on Hypothetical Syllogisms." Proceedings of the British Academy no. 69:279-326.

    "One of the topics which Theophrastus certainly treated was that of ‘wholly hypothetical’ syllogisms. Our main source for that treatment is a long passage in Alexander’s commentary on Aristotle’s Prior Analytics in which he draws on the first book of Theophrastus’ Prior Analytics (1). The passage is not a quotation from Theophrastus, nor indeed does it purport simply to document Theophrastus’ views. None the less, we can extract his views from Alexander’s commentary with reasonable confidence." (p. 286)

    (...)

    "A generous, but not wholly implausible, reconstruction of Theophrastus’ account of hypothetical syllogisms would thus ascribe the following discoveries to him. He investigated inferences of the form (H**) (^). He arranged them into three figures. Within each figure he discussed, systematically, the possible moods, singling out those which were valid. He asserted, if he did not prove, certain metatheorems about hypothetical syllogistic. He showed that the second- and third-figure moods could be derived from the first figure. He produced some derivations within the figures. He may perhaps have said something about compound syllogisms.

    Modern logicians will not perhaps regard that achievement as particularly remarkable. Yet in its day it represented a definite extension of logical science beyond anything that is found in Aristotle’s Organon.(2) At the same time, it is clear that Theophrastus was relying upon his master’s work: Aristotle’s treatment of categorical syllogistic gave him a model and a pattern for his own treatment of wholly hypothetical syllogisms." (p. 307)

    (1) In A.Pr. 325. 31-328. 7: text and translation in the Appendix, below [for another translation see Alexander of Aphrodisias, On Aristotle Prior Analytics 1.23-31, London: Duckworth 2006, pp. 116-119]. Most of the passage appears as Theophrastus, F 30 G, frags. 34a and 34b R. See also Philoponus, in A.Pr. 302. 6-23, which is, however, a highly condensed and somewhat inaccurate version of Alexander’s account.

    (2) Wholly hypothetical syllogistic does not comprise the sum of Theophrastus’ achievement in non-categorical logic: see Barnes, op. cit. (p. 285 n. 4), for further details (and for a brief argument against the tempting conclusion that Theophrastus the Peripatetic invented Stoic logic).

    (^) Let us use ‘M’ to designate the middle hypothesis, ‘E’ and ‘E*’ to designate the extremes. And let ‘IF [X, Y]’ be ambiguous between ‘If X, then Y’ and ‘If Y, then X’. Then Theophrastus’ wholly hypothetical syllogisms are arguments of the specific form:

    (H**) IF [±E, ±M]

    IF [±E*, ±M]

    _____________

    IF [±E, ±E*] (p. 296)

  2. ———. 1985. "Theophrastus and Hypothetical Syllogistic." In Aristoteles. Werk und Wirkung, Paul Moraux gewidmet, I: Aristoteles und seine Schule, edited by Wiesner, Jürgen, 557-576. Berlin: de Gruyter.

    Reprinted in: W. W. Fortenbaugh, P.M. Huby, A. A. Long (eds.), Theophrastus of Eresus. On His Life and Work, New Brunswick, Transaction Books, 1985, pp. 125-141 and with the title Theophrastus and Stoic Logic in: J. Barnes, Logical Matters: Essays in Ancient Philosophy II, Oxford: Clarendon Press, 2012. pp. 413-432.

    "In APr 1.44 Aristotle considers "arguments on the basis of a hypothesis." He deals first with arguments that are "agreed to by way of a compact," and then with those that "reach their conclusion by way of the impossible." The chapter ends with a promise: "Many other arguments reach their conclusion on the basis of a hypothesis. We should consider them and mark them out clearly. We shall say later what varieties of them there are and in how many ways arguments can rest on a hypothesis" (APr 50 a 39-b2).

    Alexander of Aphrodisias (In APr 389, 31-390.9) (1) comments on that passage as follows:

    Having talked about arguments on the basis of an agreement and arguments by reductio ad impossible, he says that "many others reach their conclusion on the basis of a hypothesis." He postpones discussion of them, as though intending to deal with them more carefully; but no book of his on the subject is in circulation. Theophrastus, however, refers to them in his own Analytics -- and so do Eudemus and some others of Aristotle's associates.

    Aristotle presumably has in mind those arguments which proceed by way of a continuous proposition (or a connected proposition, as it is also called) together with the additional assumption, and those which proceed by way of a separative or disjunctive proposition -- and perhaps also those which proceed by way of a negated conjunction, if they are indeed different from the ones already mentioned. (2)

    In addition to those we have mentioned, there will also be arguments on the basis of proportion and those which they call "qualitative" (i.e., arguments from what is more so or less so or equally so) and whatever other varieties of arguments based on a hypothesis (3) there are (they have been discussed elsewhere).

    In addition to those we have mentioned, there will also be arguments on the basis of proportion and those which they call "qualitative" (i.e., arguments from what is more so or less so or equally so) and whatever other varieties of arguments basal on a hypothesis' there are (they have been discussed elsewhere).

    Those paragraphs are of some importance for the history of logic: the present paper is a commentary on them."

    1. The passage is F 29 in A. Graeser, Die logischen Fragmente des Theophrast (Berlin / New York 1973), and frag. 33c in L. Repici, La logica di Teofrasto (Bologna 1977).

    2. Wallies, in the CIAG edition, punctuates so as to begin a new sentence with the clause "if they-already mentioned." The result is ungainly and obscure. In my translation I gratefully adopt a suggestion made by David Sedley: his punctuation gives perfect sense and makes better Greek. (It leaves an unpleasant asyndeton. Perhaps we should insert a particle and begin the new sentence at 390.6 with para de tous.)

    3. I excise protaseon (390.9): the phrase "propositions based on a hypothesis" is strange, and even if it may be allowed as a variant on "hypothetical proposition," it is out of place; Alexander is enumerating types of hypothetical arguments, not types of hypothetical propositions.

  3. Bobzien, Susanne. 2000. "Wholly hypothetical syllogisms." Phronesis.A Journal for Ancient Philosophy:87-137.

    "Traces the history in Aristotelian commentators of the type of syllogisms called "wholly hypothetical" -- that is, those consisting in two conditionals as premisses, with a third as the conclusion -- and sets forth the deductive system on which the logic of this syllogism was grounded. There was no unique prevalent understanding of the logical form of these arguments, but rather a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. The roles of Theophrastus, Alexander of Aphrodisias, and Porphyry (via Boethius) in the transmission and transformation of this problematic are investigated."

  4. ———. 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. 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. 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."

  5. ———. 2002. "Pre-Stoics hypothetical syllogistic in Galen's Institutio logica." In The Unknown Galen, edited by Nutton, Vivian. London: Institute of Classical Studies, University of London.

    ρόλο"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; there is the Stoic Chrysippus, whose logic Galen studied in his youth.(2) There are the ‘more recent philosophers’, 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 logical theories 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 promising candidates for pre-Stoic proponents of a hypothetical syllogistic are the above-mentioned ‘ancient philosophers’." (p. 57)

    (...)

    "I now turn to the question who the ancient philosophers were. In the present section, I consider the passages in the Institutio and in other Galenic writings. In the Institutio the ancients are contrasted in ch. 14 with the Stoics and in ch. 3 with ‘the more recent philo

    sophers’, who use Stoic terminology. We can infer that the ancient philosophers (i) were not Stoics, (ii) were older than those Stoics, (iii) were older than those more recent philosophers.

    Furthermore, we have some good reasons for assuming that the ancient philosophers were Peripatetics: first, the terminology they use is Peripatetic: e.g. πρότασις, ‘hypothetical premiss’, ‘hypothetical syllogism’;(26) second, the account of the hypothetical premisses in terms of things (πράγματα) is Peripatetic;(27) third, the predicate of holding (ὑπάρχειν) is used not of the truth-bearers (as the Stoics would do), but of those things;(28) fourth, the two things that are related in a hypothetical premiss must differ from each other, whereas for the Stoics they could be the same;(29) fifth, at IL 7.7 the ancient philosophers are said to distinguish three figures of categorical syllogisms, and these syllogisms and their classification are without doubt Peripatetic.

    In addition, everything suggests that the ancient philosophers were early Peripatetics, i.e. Aristotle, Theophrastus, Eudemus, and their contemporaries.(30) And in the case of hypothetical syllogistic, since as far as we know Aristotle did not have such a thing,(31) the ancients could only have been Theophrastus and Eudemus and their contemporaries." (p. 64)

    (1) E.g. C. Prantl, Die Geschichte der Logik im Abendlande vol. I (Leipzig 1855) 591-592.

    (2) 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.

    (26) Cf. Philop. APr. 242.24-243.10, and my ‘Stoic Hypotheses and Hypothetical Argument’, Phronesis 1997, 299-312.

    The expressions άπόφα[ν]σις at IL 3.1, and πρόβλημα, at IL 14.2 also suggest a Peripatetic origin.

    (27) Cf. Philop. APr. 242.27-8 (= F (Fortenbaugh) 111B), where, after having mentioned Theophrastus and Eudemus in the previous paragraph, Philoponus states that the Peripatetics call the things (πράγματα) things (πράγματα); cf. also [Amm.] APr 68.4-5.

    (28) Cf. Alex. APr. 156.29-157.2 (= F 100B) for the use of ὑπάρχειν by Theophrastus.

    (29) See above, pp. 61-62.

    (30) Theophrastus and Eudemus wrote books entitled Περi ερμηνέιας. and Αναλυτικά (Philop. Cat. 7.20-22), and in particular Theophrastus wrote many more books on logic (Diog. Laert. 5.42 and 50). Of their contemporaries, we know that Phaenias of Eresus and Strato of Lampsacus wrote on logic. The first seems to have written works entitled Κατηγοριαι, and Αναλυτικά (Philop. Cat. 7.20-22, Wehrli frg. 8), the second wrote, among other things, an introduction to the Topics and a treatise Περi του μαλλον καi ηττον (Diog. Laert. 5.59-60).

    [* Karl Gottlob Kühn, Claudii Galeni Opera Omnia. Leipzig: C. Cnobloch, 1821-1833, 19 volumes, reprinted Hildesheim, Georg Olms,1964-1997].

  6. Bochenski, Joseph. 1947. La logique de Théophraste. Fribourg en Suisse: Librairie de l'Université.

    Table des matières: Préface 5; Abréviations de titres des œuvres les plus fréquemment citées 7; Introduction 9; I. Les sources 15; II. Les œuvres logiques 27; 1. Liste des œuvres logiques 27; 2. « De l’affirmation » 32; 3. « Premiers Analytiques » 35; 4. Topiques 36;

    5. Les autres travaux; conclusions 37; III. Les fragments du traité « De l'affirmation » 39; IV. La syllogistique assertorique 54; 1. Conversion des propositions universelles négatives 54; 2. Les nouveaux modes 56; V. La logique de la modalité 67; 1. La logique de la modalité chez Aristote 67; 2. Les notions du nécessaire et du possible 73; 3. La règle du « peiorem » 79; 4. La « conséquence des modales » 87; 5. Reconstruction du système 91; 6. Théophraste et Aristote 95; VI. Les syllogismes hypothétiques 103; 1. Les syllogismes hypothétiques chez Aristote et les Stoïciens 103; 2. Les propositions et les syllogismes hypothétiques en général 107; 3. Les syllogismes « totalement hypothétiques » 111; 4. Les autres catégories des syllogismes hypothétiques 116; VII. Les fragments des autres écrits 121; VIII. Conclusions 125; Index 132; 1. Index des noms 132; 2. Index des textes 133; 3. Index des termes techniques grecs 136; 4. Index des thèses logiques 137-138.

    "Le présent travail fut écrit en 1937 pour les Collectanea Logica dirigèes par M. J. Lukasiewicz, professeur à l'univerité de Varsovie." (Préface, p. 5)

    "Appréciation générale. On voit donc que l'importance historique de la logique théophrastienne est vraiment grande: la préparation du Stoïcisme, la formation de la plupart des thèses « classiques », la découverte de quelques théories « modernes ». Au point de vue systématique, il en va autrement: il semble que les doctrines de Théophraste, viciées par un formalisme mal compris et par plusieurs thèses incompatibles, formaient un ensemble peu cohérent. Il serait naturellement déplacé de vouloir juger sa valeur en le comparant à nos systèmes modernes et il ne faut pas demander aux anciens ce que nous possédons aujourd’hui, grâce à l'effort de tant de siècles. Cependant, même comparé au système d’Aristote, celui de Théophraste reste inférieur. Théophraste n’est pas un logicien de premier ordre, tel que furent Aristote et Chrysippe chez nous, Dinnaga en logique indienne. Mais quand on le compare à la plupart des auteurs qui composèrent des logiques aux temps modernes — du XVIe au XIXe siècle — il semble leur être de beaucoup supérieur. Sans être un des génies de la logique formelle il peut être classé parmi les grands logiciens." (p. 138)

  7. Brunschwig, Jacques. 1982. ""Indeterminé" et "Indefini" dans la logique de Théophraste." Revue Philosophique de la France et de l'Étranger no. 172:359-370.

  8. Clark, Joseph T. 1952. "Theophrastus and Hypothetical Syllogisms." Philosophical Studies of the American Catholic Philosophical Association no. 3:22-23.

  9. ———. 1952. "Theophrastus on Quantification." Philosophical Studies of the American Catholic Philosophical Association no. 3:19-22.

  10. Fortenbaugh, William W. 1991. "Theophrastus, fr. 65 Wimmer: Is it important for understanding Peripatetic rhetoric?" American Journal of Philology no. 111:152-156.

    Revised reprint in: W. W. Fortenbaugh, Theophrastean Studies, Wiesbaden: Franz Steiner, 2003, I Section: Logic: pp. 15-21.

  11. ———. 1995. "Theophrastus, no. 84 FHS&G: nothing new here!" In The Passionate Intellect: Essays on the Transformation of Classical Traditions, edited by Lewis, Ayres, 161-176. New Brunswick: Transaction Publishers.

    Revised reprint in: W. W. Fortenbaugh, Theophrastean Studies, I Section: Logic, pp. 22-34, with the subtitle: Did Theophrastus oppose Aristotle and accept quantification of the predicate?.

  12. ———. 1995. "Theophrastus of Eresus: Rhetorical Argument and Hypothetical Syllogistic." In Theophstean Studies, 22-34. Stuttgart: Franz Steiner Verlag.

    Originally published in Italian as "Teofrasto di Efeso: Argomentazione retorica e sillogistica ipotetica".

  13. ———. 1998. "Cicero: On Invention 1.51-77: Hypothetical Syllogistic and the Early Peripatetics." Rhetoric no. 16:25-46.

    Revised reprint in: W. W. Fortenbaugh, Theophrastean Studies, I Section: Logic: 51-67.

  14. ———. 2000. "Teofrasto di Ereso: argomentazione retorica e sillogistica ipotetica." Aevum no. 74:89-103.

    Versione inglese riveduta in: W. W. Fortenbaugh, Theophrastean Studies, I Section: Logic: pp. 35-50 col titolo: Theophrastus of Eresus: Rhetorical Argument and Hypothetical Syllogistic.

  15. ———. 2005. "Cicero as a reporter of Aristotelian and Theophrastean rhetorical doctrine." Rhetorica no. 23:37-64.

  16. Gottschalk, Hans B. 1987. "Did Theophrastus write a Categories?" Philologus no. 131:245-253.

  17. ———. 1992. "An Errant Fragment of Theophrastus." Classical Quarterly no. 42:529-533.

    "There are a number of fragments attributed to Theophrastus, as well as titles in Diogenes Laertius' catalogue of his writings, of which it is uncertain whether they should be placed among his logical or rhetorical works. In this note I want to give my reasons for excluding one of them from my forthcoming edition of his logical fragments. It is not my intention here to discuss all the questions it raises; I hope to come back to them in a later volume of my commentary."

    [This fragment of Theophrastus is found in two versions:

    1) Ammonius, De interpr. 17 a 5, p. 65, 31 Busse = fr. 65 Wimmer

    2) Anon., De interpr. p. 94 a 96 sq. Brandis = fr. 64 W.]

  18. Huby, Pamela M. 1977. "Apuleius and Theophrastus' fifth "indemonstrable" mood." Liverpool Classical Monthly no. 2:147-148.

    An interpretation of Apuleius Peri hermeneias chapter 13.

  19. ———. 1979. "A neglected fragment of Peripatetic logic." Liverpool Classical Monthly no. 4:207-210.

    "Discussion of an account of hypothetical syllogisms appended in an 11th cent. ms. (Laurentianus 72.5) to Aristotle's Posterior Analytics. The account may represent the views of Theophrastus."

  20. ———. 1989. "Theophrastus and the Criterion." In The Criterion of Truth. Essays Written in Honour of George Kerferd, Together with a Text and Translation (with Annotations) of Ptolemy's On the kriterion and hegemonikon, edited by Huby, Pamela M. and Neal, Gordon, 107-122. Liverpool: Liverpool Univrsity Press.

  21. ———. 2002. "Did Aristotle reply to Eudemus and Theophrastus on some logical issues?" In Eudemus of Rhodes, edited by Bodnár, István and Fortenbaugh, William W., 85-106. New Brunswick: Transaction Publishers.

  22. Kneale, William, and Kneale, Martha. 1972. "Prosleptic Propositions and Arguments." In Islamic Philosophy and the Classical Tradition. Essays Presented by His Friends and Pupils to Richard Walzer on His Seventieth Birthday, edited by Stern, S.M., Hourani, Albert and Brown, Vivian, 189-207. London: Bruno Cassirer.

    "In some ancient writers on logic we find mention of propositions and syllogisms κατά πρόσληφιν. We shall attempt in this paper to determine I lie nature and logical relations of these propositions and arguments, which we call for brevity prosleptic." (p. 189)

  23. Lejewski, Czeslaw. 1961. "On prosleptic syllogisms." Notre Dame Journal of Formal Logic no. 2:158-176.

    "As a rule modern textbooks of traditional logic distinguish only two kinds of syllogism: the categorical syllogism, which has originated with Aristotle, and the hypothetical syllogism, which goes back to the early Peripatetics and to the Stoics. Rarely, if ever, is mention made of the third kind of syllogism namely the prosleptic syllogism. Yet, the prosleptic syllogism, for which we seem to be indebted to Theophrastus, appears to have been regarded at least by some logicians in later ages of antiquity as a legitimate part of logical theory.

    Like the expressions 'categorical' and 'hypothetical' the expression 'prosleptic' is a technical term and its full significance can only emerge at a later stage of our enquiry. At this stage suffice it to say that 'prosleptic' is meant to render the Greek expression kata proslepsin in its adjectival use.

    Although the prosleptic syllogism has not played as important a role in the development of logic as the other two kinds of syllogism, it deserves our attention particularly for the following two reasons. First, the validity of prosleptic syllogisms is based, as we shall see, on certain logical notions which in modern logic find their expression in the use of the universal quantifier. Secondly, the theory of prosleptic syllogism bears witness to the resourcefulness of Theophrastus as a logician.

    In what follows I propose to reconstruct the theory of prosleptic syllogisms to the extent to which the scarcity of textual evidence permits, and to examine it from the point of view of modern logic." (p. 158)

    (...)

    "Following our anonymous authority we can repeat that prosleptic premisses were called so because each of them contained an indefinite term, or a bound variable as we would say. Once this term has been made definite, i.e., once a constant noun expression has been substituted for the bound variable, the prosleptic premiss becomes an implication, which, granted its antecedent, yields its consequent as the conclusion in a valid inference of the modus ponens type.

    Inferences which originated from prosleptic premisses in this way were called prosleptic syllogisms." (p. 170)

  24. ———. 1976. "On prosleptic premisses." Notre Dame Journal of Formal Logic no. 17:1-18.

    "Galen claimed that prosleptic premisses, used for the first time by Aristotle and treated systematically by Theophrastus, were equivalent to appropriate categorical premises. This claim can only be sustained with substantial qualifications. The paper carries out a detailed examination of equivalence relationship between the two kinds of premisses within the framework of axiomatized Aristotelian syllogistic, which had to be suitably extended for the purpose by additional assumptions. The results of the enquiry differ from those obtained by William and Martha Kneale in their paper on "Prosleptic propositions and arguments" in "Islamic philosophy and the Classical tradition", edited by S. M. Stern and others, Cassirer 1972."

    (...)

    "Within the limits of the present paper our analysis of prosleptic premisses with reference to traditional syllogistic must now be concluded. We have found, as the Kneales have done, that prosleptic premisses conveniently fall into four groups. The prosleptic premisses of the first two groups, which are the same as those distinguished by the Kneales, are each equivalent to a categorical proposition. However, in order to prove this for the prosleptic premisses of the second group we have extended traditional syllogistic by including among its presuppositions the principle of ecthesis.

    In this way we have avoided using inadmissible terms. We have had no recourse to inadmissible terms in connection with the analysis of the remaining prosleptic premisses. And this is why our results differ from those arrived at by the Kneales. Traditional syllogistic, which allows for the use of negated terms but does not admit terms that are empty or universal, appears to provide an appropriate framework for investigating the meaning of prosleptic premisses even though that framework has to be extended. This does not mean that it would be wrong to analyse the meaning of prosleptic premisses within the framework of a system whose language favours different restrictions as regards the range of substituends for the variables.

    Thus, for instance, one could examine the logical import of prosleptic premisses within the framework of a system whose language allows for the use of universal terms but does not admit empty terms or negated terms.

    Alternatively, one could relate one's enquiry to a system which, like that of Lesniewski's, has no inadmissible terms. Whichever strategy is adopted, the need for specifying one's presuppositions cannot be overemphasised." (p. 16)

  25. Lorenzen, Paul. 1969. "Theophrastische Modallogik." Archiv für mathematische Logik und Grundlagenforschung no. 12:72-75.

  26. Malink, Marko. 2012. "Figures of prosleptic syllogisms in Prior Analytics 2.7." Classical Quarterly no. 62:163-178.

    "In chaps. 2, 5-7 of his Prior analytics, Aristotle is concerned with circular proof. He gives an account of circular proofs within the framework of his syllogistic theory and discusses how they come about in the three figures of categorical syllogisms. The results of this discussion are summarized at the end of this section, at APr. 59 A 32-41. The summary contains several statements to the effect that certain circular proofs come about in the third figure. Some of these statements are problematic because the circular proofs in question are actually not in the third figure of categorical syllogisms ; in fact, these proofs are not categorical syllogisms at all, but what Theophrastus called prosleptic syllogisms (Aristotle, Sch. Σ 190 A 1-4 Brandis). Hence, the statements are incorrect if they are understood to refer to the third figure of Aristotle's categorical syllogisms. The passage can, however, be shown not to be spurious: the problematic statements in it refer not to the third figure of categorical syllogisms, but to the third figure of prosleptic syllogisms. On this interpretation, the statements can be regarded as genuine. They show that Aristotle was aware of a classification of prosleptic syllogisms into three figures, even though such a classification does not occur elsewhere in his writings. Thus, the passage appears to be the earliest evidence we have of figures of prosleptic syllogisms."

  27. Maróth, Miklos. 1979. "Die hypothetischen Syllogismen." Acta Antiqua Academiae Scientiae Hungaricae no. 27:407-436.

  28. Mignucci, Mario. 1965. "Per una nuova interpretazione della logica modale di Teofrasto." Vichiana:227-277.

  29. ———. 1998. "Theophrastus' Logic." In Theophrastus. Reappraising the Sources, edited by Ophuijsen, Johannes Van and Raalte, Marlein Van, 39-66. New Brunswick: Transaction Publishers.

  30. ———. 1999. "La critica di Teofrasto alla logica aristotelica." In Antiaristotelismo, edited by Natali, Carlo and Maso, Stefano, 21-39. Amsterdam: Adolf M. Hakkert.

  31. Repici, Luciana. 1977. La logica di Teofrasto. Studio critico e raccolta dei frammenti e delle testimonianze. Bologna: Il Mulino.

    Indice: Parte prima. Gli studi moderni sulla logica di Teofrasto 9; Parte seconda. Le opere logiche di Teofrasto. I. I problemi della ricostruzione della logica di Teofrasto 33; II. Dell'affermazione e della negazione 45; III. Analitici Priori 81; IV. Analitici Secondi 159; V. Topici 167; Vi. Le altre opere logiche 179; Parte terza. Testimonianze e frammenti 193; Bibliografia 227; Indici delle fonti 235; Tavola di raffronto dei Frammenti [con l'edizione di Andreas Graeser - Die logischen Fragmente des Theophrast - Berlin, 1973] 241-243; Indice dei nomi 245-247.

  32. Rose, Lynn. 1968. Aristotle's Syllogistic. Springfield: Charles C. Thomas.

    Contents: I. Plato's dialectic and Aristotle's syllogistic 3; II. The varieties of predication 13; III: The three figures 16; IV. The non-use of rules 27; V. Validation by reduction 34; VI. Invalidation by counterexample 37; VII. The syllogistic system 53; VIII. The Fourth Figure and the indirect proof 57; IX. Subalternation 80; X. Premise order 81; Appendix. I. The square of opposition 99; II. The mnemonic lines 102; III: The perfection of Aristotle' First Figure 104; IV. Theophrastus and the indirect moods 109; V. The diagrams of the three figures 133; VI. John Locke's criticisms of Aristotle and the syllogism 137; Bibliography 144; Index 147-149.

    "Traditional "Aristotelian" logic recognizes four figures of the syllogism, including five "indirect" moods of the first figure.

    The usual account of the origin of these is that Aristotle himself developed the first, second, and third figures, that Theophrastus added the indirect moods of the first figure, (2) and that the fourth figure was added later on by someone else, probably Galen. (3)

    I shall attempt to show that the five argument forms added to the first figure by Theophrastus were in fact not the indirect moods of the first figure that became part of the traditional "Aristotelian" logic. They were, rather, argument forms corresponding both to the later indirect first and to the later fourth figure moods, but not recognizing any distinction between the two. From the modern (i.e., traditional) point of view, it is just as accurate, and just as wrong, to say that Theophrastus added the fourth figure as to say that he added the indirect first. In a sense he did both; in a sense he did neither. For in the later logic the indirect first moods are carefully distinguished from the fourth figure moods. But Aristotle and Theophrastus had no formal basis for distinguishing the indirect first form the fourth. They attached no significance to premise order. (4)" (pp. 109-110)

    (2) The main evidence for this is the statement of Alexander, Alexandri in Aristotelis Analyticorum Priorum Librum I Commentarium, CAG, edited by Maximilian Wallies. Berlin, 1883, vol. II, part I, pp. 69.26-70.21 and 109.29-110.21. See also Boetii De Syllogismo categorico libri duo. In Patrologiae Cursus Completus, Series Latina, edited by J.-P. Migne. Paris, Bibliothecae Cleri universae, 1891, vol. LXIV, 814C-816C.

    (3) The best known source for this is Averroes. Two recent and full treatments of the history of the fourth figure and of reports about it are in A. I. Sabra: A twelfth-century defence of the fourth figure of the syllogism. Journal of the Warburg and Courtauld Institutes. XXVIII: 14-28, 1965, and Nicholas Rescher: New light from Arabic sources on Galen and the fourth figure of the syllogism. Journal of the History of Philosophy, III: 27-41, 1965.

    (4) For Aristotle on premise order, see Chapter X above. We shall see in this Appendix that there seems to be no reason to suppose that Theophrastus had nay conventions regarding premise order either.