Summulae de demonstrationibus (Artistarium) 9070419416, 9789070419417

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ARTISTARIUM ----10-8----

JOHANNES BURIDANUS

SUMMULAE DE DEMONSTRATIONIBUS

introduction, critical edition and indexes by

L.M. DE RIJK

Groningen - Haren

2001

To my grandson Bart Blom

ISBN 90 70419 41 6 Copyright 2001 by lngenium Publishers, P.O. Box 131, NL-9750 AC, Haren, The Netherlands. All rights reserved. No part of this book may be reproduced or translated in any form, by print, photoprint, microfilm, microfiche or any other means without written permission from the publisher. PRINTED by Krips REPRO MEPPEL, THE NETHERLANDS.

TABLE OF CONTENTS

I ACKNOWLEDGEMENTS

vii

II INTRODUCTION II.1 The editorial project II.2 John Buridan and his Summulae II.2.1 Introductory II.2.2 On the texts commented upon by Buridan II.2.3 On the composition and structure of the Summulae II.2.4 Its date II.3 Treatise VIII, De demonstrationibus: on its general structure and contents II.3.1 The general structure of De demonstrationibus II.3.2 Buridan as a commentator of Aristotle and Boethius II.3.3 A summary of its contents II.4 List of manuscripts hitherto known II.5 Description of the manuscripts used II.5.1 Text witness E II.5.2 Text witness T II.5.3 Text witness V II.5.4 Text witness K II.5.5 The codices raro adhibiti, G and B II.5.6 Evaluation of the Manuscripts II.6 Stemma codicum II.7 Editorial principles II.8 The critical apparatus II.9 Orthography. Punctuation II.10 Headings II.11 Apparatus of quotations II.12 Bibliography

ix xi xi xi xiv xvi xvii xxi xxi xxii xxiii xxxi xxxii xxxm xxxvii xli xiv xlviii

III TEXT AND APPARATUS III.1 Index capitulorum et partium III. 2 Sigla codicum; signa in apparatu critico adhibita III. 3 Textus et apparatus

1 3 6 7

IV INDEXES IV.1 Index of quotations IV.2 Index of names and terms.

243 245 249

Iii Iii liv Iv lvi lvii lviii

I. ACKNOWLEDGEMENTS

The editor of the present fascicle has taken great adYantage of the preliminary transcription of Buridan's Summulae which our colleague Professor Hubert Hubien (Liege) has put at the disposal of the Buridan Society, for which we ov:e him sincere thanks. The Buridan Society would also like to express its gratitude to Professor M. Markowski (Cracow), Dr. Friis-Jensen (Copenhagen) and Dr. L. Valente (Heidelberg) for their help with the description and identification of part of the manuscripts. The initiator and president of the Buridan Society, Professor Sten Ebbesen (Copenhagen) most kindly read through the present fascicle, offering as usual both valuable comments and general agreement. To Professor Gyala Klima (Notre Dame, Indiana), who is preparing a complete English translation of the Summulae, I am grateful for some useful suggestions. My Leyden colleague and former pupil and team-mate, Dr. E.P. Bos, deserves my heartfelt gratitude for his typographical assistance, especially when it came to the laborious task of inserting the critical apparatus.

II. INTRODUCTION

II.I The editorial project The present fascicle is number eight of the first complete edition of Buridan's Summulae, which contains eight treatises, supplemented with a new edition of his Sophismata. The plan is being realised by an international team composed of scholars from Belgium, Denmark and the Netherlands. A first and too optimistic version of the project was discussed in 1975 at the Third European Symposium on Medieval Logic and Semantics, which was devoted to the logic of John Buridan. In 1986 The Buridan Society was formed with the explicit purpose to produce an edition of the Summulae, and guidelines for the work were laid down. The following scholars initially joined the Society: E.P. Bos, H.A.G. Braakhuis, S. Ebbesen, H. Hubien, R. van det Lecq, F. Pironet, L.M. de Rijk, J.M.M.H. Thijssen. l To make the task manageable, it was decided to aim only at an edition based on a handful of manuscripts carefully selected on the advice of H. Hubien, who had made pilot studies of the tradition. Also, considering that all the participants in the project were scholars with many other obligations and hence likely to be distracted from the work on Buridan at unpredictable times, it was decided to publish each fascicle of the work as soon as it was finished, without regard to regular intervals or an orderly progression from fascicle 1 to fascicle 9.

II.2 John Buridan and his Summulae II.2.1 Introductory John Buridan - Johannes Buridanus - was one of the most influential philosophers of the Late Middle Ages. A native of the Southern Netherlands, he was probably born somewhere in the diocese of Atrecht2 (nowadays, An-as, France), in Buridan's days part of the County of Flanders3, at an unknown date, perhaps as early as in the 1290s, 1 De introductionibus will be edited by R. Yan der Lecq, De syllogismis by J. Spruyt, De locis by H.A.G. Braakhuis, Defallaciis by J. Rustenburg. 2 In papal letters dating from 1329, August, 30 (Pope John XXII) and 1342, June, 19 (Clemens VI) Buridan is called 'clericus atrebatensis diocesis, magister in artibus, naturales, metaphysicales et morales libros, ut asseritur, parisius legens'. 3 Atrecht has had an eventful history. Part of Artois, it became part of the County of Flanders in 987, and at the end of the 12th century part of the County of Artois, of which it became the capital in

John Buridan, Summulae, De Dernonstrationibus

but not later than 1304/5. While there is hardly any evidence to support the common assumption that he was born in Bethune, 4 there may be a clue in our best manuscript (Vatican Library, Pal. lat. 994, our E) of the tract De fallaciis, in which Buridan's comments on one of the lemmas are introduced by the phrase 'sequitur glosa Jo. Audr.' (only the first three letters of which are perfectly clear), in which the topographical indication may be taken to stand for 'Johannis Audomarensis', i.e. 'by John of Sint-Omaars' (in Buridan's life-time, a Flemish town; nowadays, SaintOmer, France). Like Atrecht, Sint-Omaars is situated in the region that in Buridan's life-time was part of the County of Flanders.5 He was active as a master of arts at the University of Paris from about the 1320s till his death, 1361 being the terminus ante quem, if not the very year of his death, because at that date John's benefice in Saint-Pol-sur-Ternoise went to somebody else. 6 His philosophical production is closely connected to his work as a university teacher and consists primarily of commentaries on Aristotle, some of which have been edited in recent years, 7 as has also his treatise on consequences. 8 And then there

1237. In 1384, about twenty years after Buridan's death, Atrecht accrued to Burgundy, and in 1477 to France. In 1479 its inhabitants were driven away to make room for a French population. In 1492 it was reconquered by Maximilian of Austria. Since 1640, it has been permanently part of France. 4 B. Michael, Johannes Buridan: Studien zu seinem Leben, seinen Werken ... etc. (Berlin 1985) rightly rejects (I, 81-83) Johannes Dullaert's 'testimony' ('natione picardus, ex bethunia oppido oriundus, dyocesis attrebatensis'), which is found in his 1509 edition of Buridan's Quaestiones in Physicam. In a letter to the Parisian theologians (Epist. 89, October 28, 1498), the Parisian humanist Robert Gaguin, who was himself a native of Artois (born 1433 in Calonne-sur-la-Lys, near Bethune), writes 'Itaque fuit Joannes Buridanus ex Arthesio oriundus; cuius nascentie locum nemo est qui tradat, aut parentes eius meminerit'. See Michael, op. cit., 82, n. 6. In section 8.7.8 our Wertheim copy of the Summulae text has presumably preserved the original reading 'Johannes Martini attrabatensis diocesis'. 5 Sint-Omaars, named after the founder of the Saint Bertin Abbey, Saint Audomarus (about 662). Like Atrecht, it became (987) part of Flanders, and in 1384 of Burgundy. By the Treaty of Nijmegen, after the Dutch War (1672-78), King Louis XIV acquired, at the cost of Spain, a number of border towns and cities in the Spanish Netherlands, among which Sint-Omaars. 6 See B. Michael, Johannes Buridan, I, 401-402. 7 On logic: M.E. Reina, 'Giovanni Buridano: Tractatus de suppositionibus', in Rivista critica di storia della.filoso.fia 12 (1957), pp. 175-208 and 323-352. S. Ebbesen, 'The Summulae, Tractatus VII, De fallaciis' (excerpts), in The Logic of John Buridan. Acts of the Third European Symposium of Medieval Logic and Semantics, ed. J. Pinborg. Copenhagen 1976, pp. 139-160. NJ. Green-Pedersen, 'The Summulae of John Buridan, Tractatus VI, De locis' (excerpts), in ibidem, pp. 121-138. J. Pinborg, 'The Summulae, Tractatus I, De introductionibus' (excerpts), in ibidem, pp. 71-90. S. Ebbesen, 'Can Equivocation be Eliminated?', in Studia Mediewistyczne 18/2 (1977), pp. 103-124 (appendix:

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Introduction

is his Summulae or Summa Logica( e ), undeservedly neglected by historians of logic because it has never been printed. To be sure, there are printed books Jating from the 16th, 17th and 18th centuries purporting to contain the work, but in fact they do not, despite their frequently going under Buridan's name. This, however, does not alter the fact that a fair number of preserved manuscripts (eighteen known to us so far) testify to the popularity of the Summulae during the late 14th century and well into the 15th, especially at the Central European studia (Erfurt, Prague, Vienna, Cracow); cf. our section II. 4, below. Later Buridan' s work could only exercise its influence indirectly through John Dorp's commentary on it; it itself was never printed. The extent, however, of its direct and indirect influence still awaits exploration. The Summulae consists of the following eight treatises: I. On Introductory Items, also called On Propositions9 IL On Predicables III. On Categories -------------·····---

Quaestiones super Sophisticos Elenchos, qu. 8, de termino aequivoco). Johannes Buridanus, Sophisnzata. Critical edition with an introduction by T.K. Scott, Stuttgart-Bad Cannstatt 1977. R. van der Lecq, 'Buridan on modal propositions' (appendix: Questiones longe in Perihermeneias, liber II, questio 7), in English Logic and Semantics: from the End of the 12th Century to the Time of Ockham and Burley, Acts of the 4th European Symposium on Mediaeval Logic and Semantics, ed. H.A.G. Braakhuis, C.H. Kneepkens, L.M. de Rijk, Nijmegen 1981, pp. 441-442 (Artistarium, Supplementa 1). Johannes Buridanus, Quaestiones in Praedicamenta, ed. by J. Schneider, Mtinchen 1983. Johannes Buridanus, Questiones longe super librwn Perihermeneias, edited with an introduction by R. van der Lecq, Nijmegen 1984 (Artistarium, Supplementa 4, Ph. D. Thesis, University of Utrecht 1983). Jan Buridan: Komentarz do Isagogi Porfiriusza, ed. R. Tatarzynski, in Przeglad Tomistyczny II (1986), pp. 121-195. F. Pironet, 'Le paradoxe du Menteur dans la logique medievale ( ... )'. Memoire presente en vue de l'obtention du grade de Licenciee en philosophie. Universite de Liege, 1987. Jan Buridan: Tractatus de differentia universalis ad individuum, ed. S. Szyller, in Przeglad Tomistyczny, III (1987), pp. 137-178. Johannes Buridanus, Summulae III: In Praedicamenta Introduction, Critical Edition and Appendices by E.P. Bos, Nijmegen 1994 (Artistarium 10-3). Johannes Buridanus, Questiones Elencorum, ed. by R. van der Lecq and H.A.G. Braakhuis, Nijmegen 1994 (Artistarium 9). Johannes Buridanus, Summulae II: De praedicabilibus. Introduction, critical edition and indexes by L.M. de Rijk, Nijmegen 1995 (Artistarium 10-2). Johannes Buridanus, Summulae IV: De suppositionibus .. Introduction, critical edition and indexes by Ria van der Lecq, Nijmegen 1998 (Artostarium 10-4) For a bibliography of editions and translations of Buridan's works on logic and other subjects, I refer to R. Schonberger and B. Kible (eds.), Repertorium ediener Texte des Mittelalters aus dem Bereich der Philosophie und angrenzender Gebiete, Berlin 1994, nrs. 14378-14429. 8 Johannis Buridani Tractatus de consequentiis, ed. H. Hubien, Edition critique, Louvain/Paris 1976. 9 'Introductiones' covers a broader field than just propositions, though the latter are predominant. Cf. Peter of Spain, Tractatus (... ),ed. L.M. de Rijk, pp. lxxxix-xci.

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John Buridan, Summulae, De Demonstrationibus

IV. On Suppositions V. On Syllogisms VI. On Topics VII. On Fallacies VIII. On Definitions, Divisions, and Demonstrations. Buridan himself at one time regarded his Sophismata as treatise IX, as is clear from our version of the Summulae text. 10 However, there is no genuine connection between treatise IX and the rest, which are organized quite differently. I I

ll.2.2 On the texts commented upon by Buridan Buridan's basic idea was to 'read', i.e. comment upon, basic introductory texts. For Tracts I-VII, the basic text was taken from a contemporaneous interpolated version of Peter of Spain's thirteenth-century handy introduction to logic, the Tractatus or Summulae logicales. Bmidan himself added a special tract to deal with demonstrative knowledge, which he prefaced with two short expositions on division and definition, subjects that Peter and the writers of the adapted texts had neglected, as had other authors of thirteenth-century handbooks of logic. When dealing with the introductory texts commented upon by Buridan in his Summulae, one has to distinguish between the Tracts I-VII and the present Tract VIII. [a] As for Summulae I-VII, it is clear throughout the work that Buridan had a text at his elbow that had already been considerably altered in the course of transmission, and which he himself may have subjected to further changes, and time and again major ones at that. Buridan' s introductory text is as a rule indicated by him as 'auctor'. Peter's work originally contained twel\'e treatises.12 The 'auctor' had fused Peter's Tracts 8-12 (on relatives, ampliation, appellation, restriction, and distribution) with his own version of the tract on supposition (treatise IV). That left

IO See the opening lines of the Summulae quoted in our section ll.2.3 below.

11 Joel Biard has made a French translation based upon the critical edition, to be published soon by Dr. Fabienne Pironet: Buridan, Sophismes. Introduction, traduction et notes par J. Biard, Paris 1993. 12 See Peter of Spain, Tractatus, called afterwards Summule logicales. First Critical Edition from the Manuscripts with an Introduction by L.M. de Rijk, Assen 1972, § 6 of the introduction. It should be noted, incidentally, that there are convincing arguments to identify the author of the famous textbook with a Spanish Black Friar rather than with the Portugese Pope John XXL See Angel d'Ors, 'Petrus Hispanus 0.P., Auctor Summularum', in Vivarium 35 (1997), 21-71.

xiv

Introduction

seven treatises. Thus Buridan's additional tract De demonstrationibus became

Summulae VIII. Buridan' s text of tracts I-VII consists of the lemmata of the Summulae proper, i.e. a brief presentation of standard lore, as found in the adapted and interpolated version of Peter's text, where the material is presented in such a way as to be easily memorized. As Pinborg13 pointed out, the way Buridan speaks about his choice of Peter's work permits the conclusion that 'using Peter of Spain's manual was not the obvious thing to do', and Pinborg may well have been right in his conjecture that Buridan was the first to introduce Peter's manual as a textbook at university level in Paris, where earlier it had been used only at less exalted levels of education ('pro iunioribus'; see also our section Il.2.4, and note 21 below). Buridan might have made his choice out of the different versions available at the time, but seems to have considered it unnecessary to make a complete version of his own, as may appear from his frequently criticizing that auctor' s text quoted in the lemmata.14 Buridan commented very extensively on the standard material, which he often re-interprets in ways its authors could scarcely have imagined. He certainly makes no secret of his intentions, as can be gathered from the general introduction prefaced to the whole work: Summulac I, De introductionibus, l.O (ed. Van der Lecq, forthcoming): 'Propter quod de logica tota volens sine nimis exquisita perscrutatione disserere quaedam communia, elegi specialiter descendere ad ilium logicae tractatum brevem quern vcnerandus doctor magister Petrus Hispanus dudum composuit, exponendum et supplendum, immo etiam et aliter aliquando quam ipse dixerit et scripserit dicendum et scribendum, prout mihi videbitur opportunum.'

In the Renaissance edition of what was issued as Buridan's Summulae, it is John Dorp'sl5 comments that have taken the place of Buridan's and thus the reader had no

13 J. Pinborg, 'The Summulae, Tractatus I, De introductionibus', in J. Pinborg (ed.),The Logic of John Buridan. Acts of the Third European Symposium of Medieval Logic and Semantics, Copenhagen 1976, p. 72. 14 Sten Ebbesen may be right in saying that 'Buridan's philosophy and his attitude to auctores ( ... ) represent a real break with scholastic tradition'. See his contribution on Summulae VII in Jan Pinborg, The Logic of John Buridan referred to in the previous note, p. 139. 15 The oldest manuscript copy of John Dorp's Summulae seems to be Torino (Italy), Biblioteca Nazionale, cod. G III 12, ff. lra-167ra, dating from as early as 1411. (I owe this information to Dr. E.P. Bos, Leiden). The author must be the Johannes Dorp who came from Voorhout near Leiden (Netherlands), and became bachelor in the Faculty of the artes and magister artium in Paris in 1393, and magister medicinae in 1404. In 1405 he left Paris for Cologne. In 1417 he appears in the Cartulaire des Comtes de Hinaut as the court physician of Jacoba of Bavaria.

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John Buridan, Summulae, De Demonstrationibus

means of seeing how original Buridan was. 16 This much is certain, as Buridan went on commenting upon the 'auctor', he seems to have grown increasingly irritated with the text at his elbow, and sometimes simply dispensed with it, composing instead an alternative text to comment on (thus IV and VII). [b] The basic text underlying Buridan' s eighth treatise is still more difficult to identify. It is not found in any interpolated text of Peter's Summulae, and cannot be identified with e.g. Walter Burley's short tract De probationibus.17 Although it is not possible so far to state with all due certainty that, as it stands, all the lemmata commented upon in tract VIII are from Buridan's own hand, he might be the author of those of the 'prima and secunda materia' (on division and definition).18 The first major survey of logic to include a chapter on demonstration was William of Ock:ham's Summa Logicae, which may be only about ten years older than Buridan' s treatise VIII, as is also the_ case with the third tract (De principiis scientiarum) of the Logica written by another Franciscan master, Giraldus Odonis, which extensively deals with 'the two first and most common principles of demonstrative knowledge' .19 However, it is most unlikely that Buridan, or his

exemplar, was inspired by people as Burley, Ockham or Odonis. Anyway, by adding treatise VIII Buridan produced a book covering all the main subjects of Aristotle's Organon as well as such medieval additions to logic as the doetrine of the properties of terms. As for the tracts on division and definition prefaced by Buridan to the tract De demonstrationibus proper, their origin is not easy to identify either.20 11.2.3 Composition and structure of Buridan's Summulae

16 Walsh is completely wrong in putting ('Some Relationships between Gerald Odo's and John Buridan's Commentaries on Aristotle's Ethics ( ... )', in Franciscan Studies 35 (1975) p. 272) Buridan's using Peter of Spain's Summulae logicales on a par with his dependence upon Girald Odonis's Ethics. 17 It is found in Erfurt, Wissenschaftliche Allgemeinbibliothek, cod. Amp/on. Q 276 (written between 1295-1333), ff. 6r-2lv. 18 See our section I/.3.1 and 2 below. 19 An edition of Girald's Logica is found in: Giraldus Odonis O.F.M., Opera philosophica. Vol. I : Logica. Critical Edition From The Manuscripts edited by L.M. de Rijk, Leiden etc. 1997 (Studien und Texte zur Geistesgeschichte des Mittelalters hrsg. von Dr. Jan Aertsen. Band LX.). 20 Buridan's tract on division and definition can hardly be compared to Burley's short tract De diffinitione sive de modo diffiniendi found a.o. in London, Lambeth Palace (s. XIV), fol. l 19va-vb. For other manuscripts of Burley's tract, see James A. Weisheipl, 0.P. ,'Repertorium Mertonense' in Mediaeval Studies 31 (1969) [173-224], p. 194.

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Introduction

Buridan's Summulae is a highly structured work. At first glance it presents itself as alternating pieces (partes) of basic text and commentary, but those partes are but the smallest independent units in a strictly hierarchical division of the basic text carried out and presented according to the conventions of literal commentaries ( expositiones). When commenting on the first lemma of the work, Buridan announces which treatises the basic text ('auctor'), and the introductory texts on division, definition and demonstration for treatise VIII will contain: Summulae I, De introductionibus 1.1.1: Istum librum dividemus in novem tractatus. Quorum primus erit de propositionibus et earum partibus et passionibus, secundus de praedicabilibus, tertius de praedicamentis, quartus de suppositionibus, quintus de syllogismis, sextus de locis dialecticis, septimus de fallaciis. Octavus apponetur de divisionibus, definitionibus et demonstrationibus, de quibus auctor noster in hoc suo libro non tractavit. Nonus erit de practica sophismatum, sed in hac lectura istum ultimum tractatum ego non exsequar cum lectura aliorum octo tractatuum.

As a standard procedure, the commentary on the first pars of each treatise informs the reader about which chapters the treatise under discussion contains; the commentary on the first pars of each chapter announces the partes of that chapter, and, finally, the commentary usually divides each single pars into particulae or clausulae. Buridan numbers his treatises ('tractatus'), chapters ('capitula'), parts ('partes'), and this numbering can be used for purposes of reference. We indicate this by means of such headings as '8.1.3' ='Treatise 8, chapter 1, part 3', and recommend its use for references (it is a much more durable system than, e.g., referring to our page numbers).

Il.2.4 Its date Whereas there can be no doubt that the Summulae as a whole was composed for didactic purpose at the Arts Faculty in Paris, the date of composition is harder to ascertain. None of our sources simply dates the work in absolute terms. A relative chronology in Buridan's total production is also difficult to establish, not only because many works remain as yet unedited, but also as it is known that he 'read' the same authoritative texts several times during his long career, and each 'reading', i.e. teaching course, is likely to have produced its own written version of the lectures. Hence cross-references are of dubious value for establishing the relative chronology. It is perfectly possible for some version of work A to refer to work B while some

version of work B refers to work A.

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John Buridan, Summulae, De Demonstrationibus

Buridan 'read' the Summulae several times and it seems that none of our manuscripts reflects the first 'reading', since as far as we know at present all manuscripts contain the editorial remark at L 1.1 quoted in the previous section. Apart from the fact that Buridan worked with successive versions of the Summulae text, there is also one clear piece of evidence that at least some of the tracts that make up the present text of the Summulae may have previously existed as separate tracts. The main part of Summulae VIII (called 'tertia materia' in the present version) must have been in existence as a separate tract entitled De demonstrationibus before it was incorporated as 'tertia materia' into Summulae VIIJ.21 Another possible clue is found in the tract De fallaciis. In its colophon as handed down in most of our manuscripts, it is said to have been read by Buridan 'pro iunioribus' .22 We should not exclude the possibility that at an earlier stage of Buridan's career as a teacher (perhaps during the period he (possibly) taught at the cathedral school of Atrecht23), he lectured and wrote ('dixerit et scripserit' to paraphrase his words of the proemium) on the fallacies.24 A terminus a quo for either the first or the last version of the work is not really available as we do not know when Buridan started to teach (in Paris, or possibly earlier at Atrecht), but any date earlier than the 1320s seems rather unrealistic. As for a terminus ante quem, the situation is rather complicated. In his introduction to the edition of the tract on the Categories, E.P. Bos has given some arguments for 1335 as a terminus ante quem. 25 H. Hubien has made a strong case for dating Buridan's De

21 See our section ll.3.2 below. 22 'Haec igitur dicta de fallaciis [secundam opinionem Buridanicam add. VJ sufficiant pro iunioribus' (ETVKB); only G has 'et quae igitur dicta sunt de fallaciis dicta sufficiant' . --- For that matter, Braakhuis has provided firm proofs for the view that course-books on logic were not part of the official curriculum of the Faculty of Arts (at the University of Paris and elsewhere as well) but rather of preparatory training. These courses were given by uni,·ersity masters outside the university and were not subjected to the official regulations of the faculty. See Braakhuis, 'Logica Modernorum as a Discipline ... etc.', pp. 138-42. 23 This school is reported as early as in 1095, when an 'Achardus, magister scholarum' is mentioned to have been in the company of bishop Lambert of Atrecht making his way to the Council of Clermont. See Emile Lesne, Les ecoles de la fin du Ville siecle ii la fin du xne (Histoire de la propriete ecclesiastique en France, tome V) Lille 1940, p. 327. 24 Separate lectures and writings on the fallacies were not uncommon. For example, Thomas Aquinas wrote a separate tract Defallaciis ad nobiles artistas. For this genre and its specific role in the development of medieval logic and the curriculum of logic, see LM. de Rijk, Logica modernorwn (3 vols. Assen 1962-67), passim. 25 See Johannes Buridanus, Summulae III: In Praedicamenta, ed. Bos, p. xvl.

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Introduction

consequentiis to 1335.26 Now, if this date holds, and if certain ideas of the Summulae are on their way to the stage of development evidenced by De consequentiis,27 we have 1335 as a terminus ante quem. There is a possible clue to a date around 1336 in the present tract, De demonstrationibus. There Buridan clearly refers to the epistemological position held by Nicholas of Autrecourt cum suis concerning the supposedly unique role of the principle of non-contradiction, and especially Autrecourt' s thesis that from the existence of A one cannot infer that of B with proper evidence. Buridan ascribes this erroneous position ('error quornndam') to sheer ignorance of logic: 8.5.2 (ad fin.): 'Et ex istis dictis manifestus est error quorundam nunc legentium qui dicunt nullam posse esse evidentem probationem secundum quam concludimus per aliquid esse aliud esse, ut si per motum esse volumus probare motorem esse vel per domum esse parietem esse. Dicunt enim non posse evidentem probationem esse nisi sit reducibilis ad primum principium complexum. ( ... ) Isti ergo supponunt falsum, puta quad illud solum principium sit evidens et quod omne aliud principium possit et indigeat probari per illud. Et haec sunt absurda et dicta ex ignorantia logicae'.

The phrase 'nunc legentium' is very likely to refer to the activities of Nicholas of Autrecourt and his adherents at the university of Paris around 1336.28 Convincing as these arguments may seem, the conclusion cannot hold for the Summulae as a whole. Anyhow, the version of De suppositionibus which we have at our disposal, is clearly of a later date. In 4.5.3 Buridan explicitly proposes a revision of an opinion he had advocated in the Sophismata on the topic of verbs signifying cognitive acts. He explicitly refers to the sixth sophism of chapter four (De appellationibus) of the Sophismata.29 The reference itself is not conclusive, but the refuted opinion is. De suppositionibus contains various references to the Sophismata, some of which contain parts of the work that are unknown to us: for all we know they may never have been written. So the conclusion may be justified that Buridan had finished the part of the Sophismata that is known to us before he made the final 26 See Johannis Buridani Tractatus de consequentiis, ed. Hubien, ( ... ). Louvain!Paris 1976, p. 9. 27 See J. Pinborg, 'The Summulae. Tractatus I. De introductionibus', p. 73. 2S For the date (c. 1336) of this Parisian controversy at the Sorbonne, see Zenon Kaluza, 'Nicolas d'Autrecourt. Un amide la verite', in Histoire litteraire de la France (t. XLII, fasc. l; Paris 1995), 54-74, and L.M. de Rijk, Nicholas of Autrecourt. His Correspondence with Master Giles and Bernard of Arezzo ( ... ),Leiden 1994, p. 5 and 121. 29 4.5.3, ed. Van der Lecq, p. 8619- 23. Verum est tamen, prout mihi videtur, quod illud corrigendum est quod ego dixi quantum ad sextum sophisma, scilicet quad ego vidi Petrum et Robertum, vel etiam quad videbo vel possum videre omne astrum, nam istae propositiones forte non sunt concedendae, propter appellationem rationis, eo quod 'videre' significat actum animae cognoscitivae.

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version of De suppositionibus, and that he had the intention to finish the Sophismata sooner or later. In the fifth sophism of chapter one Buridan criticises the theory of the complexe significabile. Michael has argued that this theory was not known in Paris before 1342, which would make a terminus post quern for the Sophismata.30 But even if Michael's arguments were not to hold,31 there is strong evidence for a date not much earlier than 1340, the year of the Statute against the Ockhamists. Since Michalski various scholars have confirmed that there are some doctrinal and verbal parallels between the text of the Statute and certain passages in De suppositionibus.32 Notably in 4.3.2 of that text Buridan defends the position advocated in the Statute, namely that propositions should be taken as they are meant by their author, although he adds the important qualification that in the proper sense (secundum propriam locutionem) such a proposition may be false. As a logician Buridan defends a position that is more sophisticated than the one advocated in the Statute. Nevertheless it is quite possible that he had no serious problem with the content of the Statute. With our present state of knowledge it is impossible to decide whether Buridan has written the Statute himself copying his text of De suppositionibus, or that he has used the text of the Statute writing the passage in De suppositionibus, but, anyhow, it is likely that De suppositionibus as it has been handed down to us, should be dated not much earlier or later than 1340. With the great uncertainty surrounding Buridan's production, we must confess that we are still not able to date any version of the Summulae as a whole with any precision. They all must fall within the approximate limits of 1325 and 1360, and it is likely that the first version, or part of the work at least, was made in the 1320s or early 1330s, and was composed of separate tracts that previously were in existence, as 30 See B. Michael, op. cit., pp. 272-272 and 527. 31 Michael argues that Buridan's criticism concerns Gregory of Rimini' s version of the theory of

the cornplexe significabile rather than Adam Wodeham's. Recently, Jack Zupko has defended the same view with different arguments. See: B. Michael, op. cit., p. 272, and J. Zupko, 'How it played in the RUE DE FOUARRE. The Reception of Adam Wodeham's Theory of the COMPLEXE SIGNIFICABILE in the Arts Faculty in Paris in the Mid-Fourteenth Century' in Franciscan Studies 54 (1994-7), pp. 211-225. 32 K. Michalski, 'Les courants philosophiques a Oxford et a Paris pendant le XIVe siecle' in Bulletin international de l'Acadernie des sciences de Cracovie, 1920. Cf. M.E. Reina, II Problema def Linguaggio in Buridano. Vicenza 1959, esp. pp. 93-107 (also in Rivista critica di storia della Filosofia 15 (1960), pp. 251 .. 264) and Z. Kaluza, ·Les sciences et leurs languages. Note sur le statut de 29 decembre 1340 et le pretendu statut perdu contre Ockham', in L. Bianchi, Filosofia e Teologia nel Trecento. Textes et Etudes du moyen il.ge I, Louvain-la-Neuve 1994, esp. pp. 235-9. See also the discussion in the Introduction to Johannes Buridanus, Questiones Elencorurn, ed. by R. van der Lecq and H.A.G. Braakhuis, Nijmegen 1994 (Artistarium 9), esp. pp. xix-xxx. xx

Introduction

has been remarked before. It is also probable that later editions were partly identical with the first one. But at the same time it should not be ruled out that such changes as were introduced with each subsequent version may have been of high theoretical importance. We are still not in a position now to see the development of Buridan's thought via the different versions of the Summulae. The present edition may help clear the path for relevant research, as far as Buridan' s most extensive treatise on demonstration is concerned.

ll.3 Treatise VIII. De demonstrationibus: on its general structure and contents The present edition contains the eighth tract, De demonstrationibus, by far the greater part of which deals with demonstrative argument, and for the sake of this prefaces it with a discussion of the standard lore concerning division and definition.

II.3.1 The general structure of De demonstrationibus The main division of the work clearly appears from the opening lines (1.1 in the present edition), in which Buridan proposes to deal with demonstration, but thinks it indispensable to discuss first the doctrine of division and definition which lies at the bottom of that concerning demonstrative argument, despite the fact that 'auctor noster' did not pay any attention to this important part of logic ('pars logicae magis nobilis et final is'). The author next remarks that the present tract is the eighth one according to what was said in the general introduction to the whole work ('secundum dicta a principio'). It strikes the reader firstly that our author does not say 'octavus et ultimus tractatus', and, for that matter, in doing so, is quite in line with what he had outlined before in his general division of his Summulae (section 1.1.1 of the planned edition), notwithstanding the fact that in all the extant manuscript versions of the work the author lets us know that in the present 'lectura' he does not intend to read on the ninth and conclusive treatise on sophisms. The other noticeable thing is that in this passage, each treatise is announced with the phrase 'it will be about' ('erit de') the respective subject matter, with the exception of the present treatise on demonstration, of which it is said that it 'will be added' ('octavus apponetur'): Summulae I, De introductionibus, I. I. I: Primus erit de propositionibus et earum partibus et passionibus, secundus de praedicabilibus (... ), octavus apponetur de divisionibus,

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definitionibus et demonstrationibus, de quibus auctor noster in hoc suo libro non tractavit. Nonus erit de practica sophismatum; sed in hac lectura istum ultimum tractatum ego non exsequar cum lectura aliorum octo tractatuum

Our treatise quite understandably consists of three main parts ('tres materiae principales'), one about division, one about definition, the third about the proper subject matter, demonstration. There are good reasons for assuming that in an earlier version, the two parts on division and definition were not yet integral parts of the eighth treatise. As a matter of fact, unlike all other manuscripts, our two most reliable manuscripts, E and T start a fresh numeration for the ten chapters of the 'tertia materia de demonstrationibus', whereas the others continue the initial numbering of the preceding parts on division and definition, counting the ten chapters on demonstration as 'capitulum quartum, quintum, sextum', and so on. Thus, in its final version, the work is divided into twelve chapters, so that the two first parts ('materiae) in fact are the two first chapters of the work. Each chapter is divided into 'partes' and the latter are subdivided into 'clausulae' in the usual way.

Il.3.2 Buridan as a commentator of Aristotle and Boethius Although from the doctrinal point of view, the 'tertia materia' on demonstration heavily depends on Aristotle's Posterior Analytics, including the common lore found in medieval commentators, particularly Robert Lincoln, Buridan's discussion of the matter testifies to the same original and creative spirit one finds in the other parts of the Summulae and in his Quaestiones-commentaries on Aristotle as well. As for the two first chapters ('materiae') on division and definition, they are likely to have made use of Boethius' works of the same name. HoweYer, his being tributary to Boethius is not explicitly recognized by the author; in point of fact, he only twice explicitly refers to Boethius' De divisionibus. Unlike the lemmata of tracts I-VII, those preceding Buridan's expositions in the present treatise are never ascribed to 'auctor'. The word 'auctor' is used only once in the singular, viz. in the opening lines of the work (at 8.1 of the present edition), to refer to the 'auctor' commented upon in the previous treatises. The plural 'auctores' occurs once at 8.1.7, referring to teachers of the common doctrine on division whose dictum, as it stands, is not taken from Boethius - , and once (at 8.4.3) in a vague reference to the ways in which authoritative writers interpret the notions 'scientia' and 'opinio'. It must strike the reader that Buridan once (in section 8.4.3)

xx ii

Introduction

qualifies what is said in the lemma of the introductory text, when he discusses its fourth clause: 8.4.3: Quarta clausula ponit omnem scientiam vel opinionem esse actus vel habitus intellectuales. Et cum nomina sint ad placitum, ego hanc clausulam non probo, nisi per hoc quod auctores nomina 'scientiae' et 'opinionis' negant de re esse extendi ad notitias vel iudicia sensus, licet multis eorum acquiescamus et secundum ea multa agamus.33

Elsewhere he makes a complaint about the obscurity of the introductory text he has to comment upon: 8.3.3: Verba huius tertiae partis et sententia habent obscuritatem et summam difficultatem. (... ) Sed tamen plus dicitur in ista clausula, quia dicitur quod quaestio 'propter quid' non solum quaerit medium 'propter quid', sed etiam medium 'quid est'. Et hoc est dubitabile. Ideo ad hoc probandum ponuntur aliae duae clausulae, quae sunt duae rationes hoc probantes.

8.9.3: Dico ergo quod haec verba sunt satis obseura et fecerunt dubitare et multos errare. Sed videtur mihi quod debeant exponi concorditer his praedictis.

We cannot know for sure, however, if in these cases Buridan is merely criticizing the unnecessary obscurity of the text he has to explain, or only points out - for didactical purposes, perhaps the obscure Aristotelian doctrine as found in Posterior Analytics. All in all, one may say that the lemmata occurring in the present treatise are much more sophisticated than those found in treatises I-VII. Especially the lemmata of the third 'materia' including 'dubitationes'3 4 themselves even testify to a more mature doctrinal level than is usually found in the more basic lemmata of treatises IVII. No doubt, the identification of the basic texts read by Buridan requires still much research. For the time being, the present editor is inclined to think that the basic texts underlying the first two main parts ('materiae') on division and definition are, as they stand, from Buridan's own hand. The third materia may have been somehow available before he undertook the Summulae project as a whole.

Il.3.3 A summary of its contents

33 Compare the proviso made by Buridan at 8.9.5: 'Ista quinta pars ponit unum modum circulationis demonstrationum, quern puto quodammodo concessibilem'. 34 See 8.8.! and 8.8. 2; 8.12.1and8.12.3. xxiii

John Buridan, Summulae, De Demonstrationibus

The following sketch of the contents of the three main parts ('materiae') may be given. PRIMA MATERIA: De divisionibus 8.1 contains the general introduction to the whole treatise, and explains its design, especially the addition of the two preambulary tracts on division and definition. 8.1.l presents its division and the subdivision of the tract on division, and next it defines the notions 'division' and 'composition'. 8.1.2 explains what is understood by 'componere' and 'dividere'. 8.1.3 discusses the notions 'totum' and 'pars'. 8.1.4 deals with the various divisions of 'totum' and the corresponding kinds of composition and division. 8.1.5 discusses 'tota praedicabilia' and their parts, 8.1.6 is about perfect and imperfect division. Two problematic questions ('dubitationes') are raised, one concerning the division of some genera into their species, the other about why in such cases the genus can be regarded as the totum of its species, rather than the other way round, and how a species is a subjective part of its genus. 8.1.7 discusses the remaining, less common kinds of division.

SECUNDA MATERIA: De definitionibus 8. 2 The eight common properties of definitions and things defined are enumerated. 8.2.1 The chapter is divided into seven parts, the first of which deals with the eight properties: (a) definitio (i.e. definiens) and definitum are said reciprocally, i.e. they have converse relationships as every definiens is the definiens of its definition, and vice versa; (b) definiens and definitum are mutually convertible; (c) every definiens notifies the definitum in an explicit way; (d) every definiens is a phrase ('oratio'), while every definitum is an incomposite term, or at least less complex than the definiens; (e) neither the definiens nor the definitum are singular terms; (f) nor are they a proposition; (g) no definiens has a parabolic or metaphoric sense; (h) no definiens should suffer from superfluity or deficiency. 8.2.2 Definitions ('definientia') are divided into nominal, quiditative, causal, and descriptive ones. 8.2.3 Nominal definition is defined and discussed.

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8.2.4 Quiditative definition is defined, and its properties are dealt with. In a lengthy digression three questions of semantical interest are raised and extensively answered: (a) whether phrases such as 'nasus simus' are nugatory; (b) whether definitions such as 'simum est nasus cavus' is nominal; (c) whether a subject's property should be defined by including its subject in the definition. 8.2.5 Causal definition is defined and explained, including the di verse kinds of cause (formal, material, efficient, and final cause). 8.2.6 Description is defined, and its use is clarified. 8.2.7 discusses complex definitions and their use in demonstrative arguments. TERTIA MATERIA: De demonstrationibus 8.3 General division of this tract into ten chapters. 8.3.1 The first chapter deals with the 'quaestio scibilis' and pre-existent cognition required for acquiring demonstrative knowledge is divided into seven parts. 8.3.2 The four so-called 'quaestiones scibiles', questions, that is, that are appropriate to demonstrative argument ('si est', 'quid est', 'quia est', 'propter quid est') are discussed, including their number and mutual differences. 8.3.3 explains that every question involved in a demonstrative procedure is a 'quaestio medii'. The subject matter of this section is said to be very obscure and difficult. 8.3.4 distinguishes the integral components of demonstrative argument. 8.3.5 discusses pre-existing knowledge being needed in order to acquire demonstrative knowledge. 8.3.6 is about the unity and universal character of specific sciences, such as geometry consisting of partial pieces of knowledge, viz. geometrical theses ('conclusiones'). Several false opinions are rejected. 8.3.7 shows in what way we have pre-existent knowledge of premisses; Plato's (putative) opposite position is rebuked. An important 'dubitatio' is raised: If an effect necessarily follows from sufficient causes, it might be concluded that whoever knows the principles of geometry, immediately or very soon at least, knows all geometrical theses, even without being taught by a teacher. 8.4 The next chapter deals with similarities and dissimilarities between demonstrative and dialectical argument, and the distinction between true knowledge ('scientia') and opinion. 8.4.1 The chapter is divided into four parts, in the first of which five resemblances between demonstrative and dialectical argument are dealt with.

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8.4.2 The six main differences between them are enumerated and extensively discussed. In this context, the constitutive properties of demonstration are explained: necessary and formal inference, syllogistic form, its premisses being really known, being true, primary and immediate. 8.4.3 discusses the five resemblances between demonstrative knowledge and opinion: (a) they are the assent given to a proposition, rather than this proposition itself; (b) sometimes they are actual, sometimes only virtual; (c) just as opinion is about an opinable proposition, so 'scientia' is about a 'propositio scibilis'; (d) both are intellectual; (e) they are also alike in that no opinion is acquired by dialectical argument, and no 'scientia' by demonstration. 8.4.4 deals with the three main differences between them: (a) unlike opinion, demonstrative knowledge should be both certain and evident; the notions of certitude and evidence are extensively discussed; (b) demonstrative knowledge is always about a true proposition, opinion can be about false propositions; (c) there can be opinion about first principles, not demonstrative knowledge, because they are by nature indemonstrable. 8.5 This chapter discusses first and indemonstrable principles. 8.5.1 divides the chapter into four parts, the first of which clarifies the existence of such principles. 8.5.2 argues that there are more than just one first and indemonstrable principle, innumerable in fact, because there is an infinite number of possible theses. The discussion includes an assessment of the famous first principle of Metaph. IV 3, 1005bl9-22, the law of non-contradiction. The manifest error of people like Nicholas of Autrecourt is severely criticized.35 8.5.3 is about necessary and contingent, and evident and inevident first principles. 8.5.4 explains how first principles are evident to us. They are not innate nor known to us as a result of teaching, but owing to the natural inclination of our intellect to assent them. The assent is accomplished either owing to a sensorial act only, or to such an act together with memory, or together with memory and experience. The principles are either singular or universal propositions. Finally the role of induction and example is discussed. 8.6 This chapter deals with the notions 'de omni', 'per se', and 'secundum quod ipsum'. 35 See for Nicholas' thesis of the uniqueness of the law of non-contradiction L.M. de Rijk, Nicholas of Autrecourt ( ... ).Leiden etc. 1994, esp. Epist. II, 4sqq., ibid., 48 sqq. and 119sqq. xx vi

Introduction

8.6.1 It is divided into four parts, the first of which deals with 'de omni'. The question of whether propositions that are about non-permanent subjects, such as the eclipse of the moon, may be regarded as 'de omni'. 8.6.2 is about the three modes of 'per se' involved in the demonstrative procedure, including a discussion of accidental modes of predicating and of being, as well as of substantial and connotative terms and of essential and accidental causes. 8.6.3 subdivides the first mode of 'per se' into two special modes, viz. those concerning quiditative and denominative propositions, respectively. The 'perseitas' of a great many propositions is questioned. 8.6.4 discusses the important notion of 'universale' or 'secundum quod ipsum' and 'dici primo de subiecto'. The author explains the different senses of 'primo' and 'secundum quod ipsum' .36 8.7 The next chapter is about the division of 'demonstratio'. 8.7.1 The chapter is divided into ten parts according to the ten distinctions to be made. The first part is about the definition of 'demonstratio' in its largest sense, and the three different senses of 'scientia' (viz. 'cornmuniter, proprie, propriissime dicta') are discussed. There follows a 'dubitatio' whether the definiens 'syllogismus faciens scire conclusionem' should apply to any demonstration. 8.7 .2 is about demonstration in the most common sense and explains it by its division into categorical and hypothetical demonstrative argument. 8.7.3 is about the division into ostensive demonstration and 'demonstratio ad impossibile'. 8.7.4 is about affirmative and negative demonstration. 8.7.5 divides common demonstration into universal, particular or indefinite, and singular demonstrations, and questions the existence of singular ones. 8.7 .6 is about 'universal' and 'particular' demonstration, whereby the term 'universale' is taken in the sense of 'primo' and 'secundum quod ipsum'. 8.7.7 discusses the division of demonstration according their having necessary or contingent conclusions. 8.7.8 is about demonstrations about the present, past, or future, and about the division into demonstration 'de inesse' and modal demonstration.

36 For the decisive role of 'secundum quod ipsum' in Aristotle's view of demonstrative (or 'epistemonic') cognition see L.M. de Rijk, 'Ockham as the Commentator of His Aristotle etc.' Steenbrugge etc. 1995, 78-102, esp. 98-101, and the same, ARISTOTLE. Semantics and Ontology (forthcoming).

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8.7.9 is about demonstration in the proper sense, and 'demonstratio mansiva' and 'demonstratio doctrinalis'. In this context, there is an interesting discussion about the 'singular' character of legal argumentation. 8.7.10 is about Aristotle's division into 'propter quid' and 'quia' demonstrations. 8.8 This chapter deals with the 'demonstratio propter quid', about which many difficulties ('dubitationes') can be raised, as has already been observed in the introductory text. 8.8.1 It is divided into six parts and contains five dubia and a corollary. The first problem running 'why should there be a cause assigned in a demonstration 'propter quid' rather than in a demonstration 'quia' ?' is extensively discussed. 8.8.2 The second is whether Aristotle's well-known definition of 'scire' presented in Posterior Analytics, 7lb9-ll ('being aware both that the explanation because of which the state of affairs obtains is its explanation, and that it is not possible for it to be otherwise') really applies to the demonstration 'propter quid'. 8.8.3 Three corollaries are drawn from the foregoing observations. 8.8.4 The third difficult problem concerns Aristotle's alternative definition of 'scire' presented ibid., 71b20-22 ('demonstrative understanding depends on states of affairs that are true and primitive and immediate and more familiar than, and prior to, and explanatory of the conclusion'). 8.8.5 The fourth is whether any kind of cause meets the requirements of the demonstration 'propter quid'. The answer is in the affirmative. 8.8.6 The fifth is whether mathematical demonstrations are rightly regarded by Aristotle as being 'propter quid'. Buridan agrees with the suggestion made in the text that, properly speaking, this is not true. The sixth and final problem is about whether mathematical demonstrations are accomplished 'per causam formalem'; it is answered in a similar way. 8.9 This chapter extensively discusses the demonstration 'quia'. 8.9.1 It is divided into five main parts, the first of which, dealing with the diverse modes of demonstration 'quia', is discussed. Three modes are distinguished and subdivided. 8.9.2 It is asked whether a demonstration 'quia' and one 'propter quid' concern the same or different pieces of knowledge. The different positions in this respect of subalternant and subalternate sciences are discussed. 8.9.3 is about what is called 'circulatio demonstrationum inter quia et propter quid'. The author explains in what way these demonstrative procedures are

xx viii

Introduction

convertible. A big problem ('fortis dubitatio') is put forward concerning the remark found in the second clause of the lemma to the effect that in a sense a cause is better known than its effect, and in another the other way round. 8.9.4 discusses the mutual circulations of different demonstrations 'propter quid'. 8.9.5 presents a kind of circulation which to Buridan's mind, can be admitted in some way. The author clarifies his position. 8.10 This chapter deals with some special kinds of demonstration which were not considered before in much detail. 8.10.1 divides this chapter into six parts. 8.10.2 discusses the 'demonstratio ad impossibile'. It is defined as a demonstrative argument consisting of four inferences, which are described. 8.10.3 is about negative demonstration. The doubts that might be raised about its validity are dealt with. 8.10.4 discusses another dubium on this score. 8.10.5 is about demonstrative argument having a contingent conclusion. 8.10.6 discusses those containing conclusions about the past or the future. 8 .11 This chapter deals with the comparison of the diverse demonstrative arguments. 8.11.1 divides this chapter into seven parts. The intricate question of whether the premisses should be better known than the conclusion is discussed. 8.11.2 claims that any demonstration taken in the proper sense has a necessary conclusion, whereby its being necessary is defined thus: whenever the conclusion, or its equivalent, is propounded it is true and cannot be false, as long as its meaning and those of its terms are maintained. 8.11.3 compares the demonstration 'propter quid' to the other demonstrations, and the former each to the others. A dubium is raised about whether a demonstration 'secundum quod ipsum' is possible in the second or third syllogistic figure. The purport of the 'secundum quod ipsum' requirement is explained. 8.11.4 is about the demonstrations in the first syllogistic figure, and those accomplished in its first mode in particular. 8.11.5 claims that, ceteris paribus, universal demonstrationes are more powerful and more generative of true knowledge than particular ones. This claim is extensively argued for. 8.11.6 The same claim is made and defended with regard to affirmative demonstrations when compared to negative ones.

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8.1L7 claims that ostensive demonstrations are more powerful than those 'ad impossibile'. 8.12 The concluding chapter deals with the diverse ways in which the questions that are appropriate to demonstrative argument ('quaestiones scibiles') can, and should be, brought to a satisfactory conclusion ('terminari'), and what knowledge precisely is intended by the demonstrator ('quae quaeruntur sciri'). 8.12.1 The chapter is divided into six parts. The author explains that any demonstrative question contains an element known to the demonstrator and a dubium; well, the question is properly answered once the dubium has been removed. 8.12.2 discusses a sequel following from the foregoing, to the effect that any demonstrative question can only be solved by a determinate answer ('responsio determinata'); the latter should be a proposition that either is knowable qua demonstrative principle which is itself indemonstrable, or a conclusion that is knowable qua conclusion of a demonstrative procedure. 8.12.3 is about the question 'quid est' and its proper subject matter, viz. the definition of the thing under consideration. 8.12.4 explains how a question 'quid est' is properly answered. The procedure is desc1ibed in much detail. Each step of it is stated, the appropriate use of division in particular. 8.12.5 discusses the procedure of the 'propter quid' argument, what is asked in it and what is presupposed. Special attention is paid to the invention of the middle ('medium') and the 'terminus causalis'. 8.12.6 is about the questions 'quia est' and 'si est'. This matter is only briefly discussed here, because it was already dealt with in more detail elsewhere in the present treatise, as well as in the treatise De syllogismis. The present chapter, as the entire treatise, winds up with the intricate discussion about the question 'si est', viz. of whether existential propositions, such as 'God exists' or 'the void does not exist' are demonstrable. One answer is that they are demonstrable, once they are framed as hypotheticals. E.g. 'if there exists some first and uncreated cause, God exists; well, such a cause does exist; therefore God exists'. Another way out of the problem is to exploit the possibility of inferring existential propositions from predicative ones, this way: if you know that a mover is eternal (i.e. an eternal one), then there exists an eternal mover. Like the treatises I-VII the present one, too, consists of elementary exegesis as well as extensive objections and dubitationes in which specific questions are dealt with,

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mostly in an original fashion and always along the lines of thought found in Buridan's numerous commentaries on Aristotle.37 11.4 List of manuscripts hitherto known

The editors are aware of the following manuscripts of Buridan's Summulae with the author's own commentary. Read the dates as follows: 15.0 = 15th c.; 14.2 =second half of the 14th c.; 15.1 =first halfofthe 15th c.; 14.2/15.1=either14.2 or 15.1.

37 The conspicuous coherence in Buridan's thought coming to the fore throughout his various works is rightly highlighted by Sten Ebbesen, 'Proofs and its Limits according to Buridan, Summulae 8', in Z. Kaluza-P. Vignaux 'Preuve et raisons ... etc., Paris 1984, p. 97: 'John Buridan was( ... ) remarkably consistent. He almost invariably says the same about the same things, and what he says about one subject is usually consistent with what he says about any other somehow related subject. His work abounds in cross-references, from one part of a work to another, and from one work to another. He obviously wanted his readers to think of his philosophical works as one coherent corpus presenting one coherent philosophy.'

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John Buridan, Summulae, De Demonstrationibus

Erfurt, Amp!., 2° 302

Date

Summulae

Sophismata

Siglum

14.2115. l

lr-155ra

15Srbl91 vb

F G

Erfurt, Amp!., 20 305

1378

lr-97v

98r-va (fr.)

Krakow, B. Jag., 662

14.2

lra-126rb

126val56vb

Krakow, B. Jag., 703

14.2

2ra-l 70ra

l 70rb-181 va

J

Krakow, B. Inst. Teo!. Ksiezy Misjon., 171

1371

3ra-182vb

183ra-219ra

K

Miinchen, CLM 7708

14.0/15.0

68r95r(syl)

missing

H

Oxford, Magdalen, 88

15.0

lr-139

missing

M

Praha, St. Kn., Osek 39

14.2

lra-160ra

missing

0

Torino, BN, D III 27 (462)

1372

lra-98ra

98ra-l l 7rb

T

Uppsala, BU, C 609

1374

3r-l 12va

missing

u

Vaticano, Pal. lat., 994

14.2/15. l

2r-119v

120ra-137vb

E

Vaticano, Vat. lat., 3020

1384

lr-104ra

missing

D

Warszawa, BN, akc. 1819

1375

lr-96v

97ra-l 15rb

w

chenbibl., 157

1363vel 1384

2ra-135vb

missing

v

Wien, ONB, lat. 5365

14.2

lra-126ra

126val48vb

A

Wien, 0NB, lat. 5420

14.2

lra-128ra

l 28ra- l 62rb

B

Wien, ONB, lat. 5466

15.0

lra-140ra

l 40rb- l 68ra

c

Wertheim, Evangelische Kir-

The Buridan Society intends to publish detailed descriptions of the manuscripts on a later occasion. For the manuscripts used in this fascicle, see the next paragraph.

1/.5 Description of the manuscripts used The Vatican library owns two copies of our tract. One is our best manuscript, Pal. lat. 994 (our E), the other is Vat. lat. 3020 (our D), which is among the copies of minor importance, but contains a beautiful, coloured picture of the so-called 'Arbor porphyriana'. The only other copy of the Summulae found in Italy is Torino, Biblioteca Nazionale D III 27 (our T), which is most useful for the constitution of the text. The Osterreichische Nationalbibliothek in Vienna possesses three copies, viz. lat. 5365, 5420 and 5466, of which only cod. 5420 (our B) is of interest, because of

xx xii

Introduction

the others' frequent erroneous readings and various interpolations. The Bayerische Staatsbibliothek in Munich has only one copy (of minor use), viz. CLM 7708. Another copy is found in the Evangelische Kirchenbibliothek at Wertheim (BadenWtirttemberg, Germany), cod. 157. The University Library of Uppsala has a fourteenth-century copy (C 609), which does not rank among our valuable sources. So much for the libraries of Western Europe. In the Central European manuscript collections a remarkably large number of manuscripts contain Buridan's Summulae, viz. four in Poland, two in Erfurt, one in Prague. One of the Polish manuscripts belongs to the Biblioteka Narodowa (cod. 1819) in Warsaw. The three others are found in Cracow, two of them in the Biblioteka Jagiellonska (B.J. 662 and 703), one in the Biblioteka Instytutu Teologicznego Ksiezy Misjonarzy, cod. 171 (olim 627, antea 827), which, going now under the label 'Stradom MS', is among the manuscripts used for the present edition (our K). The two copies from the Wissenschaftliche Allgemeinbibliothek in Erfurt are Amplon.2° 302 and 2° 305 (our G). The Prague manuscript is cod. Osek 39 of the Statni Knihovna. It is of minor use. The edition of this fascicle is based on manuscripts ETVKBG, the last two of which are taken as codices in apparatu critico raro adhibendi. 11.5.1 Text witness E

E = Citta del Vaticano, Biblioteca Apostolica Vaticana, Pal. lat. 994, a paper and vellum codex (saec. 14.2/15.1), measuring 300x225 mm, ff. V + 160, contains our tract on ff. 96va-1l9va, in one hand, which also wrote the other tracts of the Summulae. The (relatively few) corrections are all in the same handwriting. We owe the codicological informat10n to Dr. K. Friis-Jensen. In section 8.7.9, Buridan presents a juristical example concerning a 'Johannes Martini, parisiensis diocesis'. The most likely correct topographical indication ('Paris) is only found in K, while in all the other manuscripts the scribe took the liberty of adapting it at his own discretion. E reads 'Trevirensis diocesis'. Sometimes - much less frequently than e.g. in the tract De praedicabilibus38 - E has what may be taken as the better reading, where all other MSS have erroneous or less acceptable readings. Here are some specimina: At 8.2.2: 'alii et alii' E; alii TVK. At 8.2.4 (discussion of first clause): 'notificandum' E; 'notandum' T; 'demonstrandum' V; 'denotandum' K. Ibid. (third

38 See my introduction to the edition of that tract, XXIII-XXIV.

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John Buridan, Summulae, De Demonstrationibus

clause): E correctly reads (together with B, for that matter) 'circumscribendo', where T, instead of the gerund reads the finite form of the verb 'circumscribo', which was corrected by rcvc into 'si circumscribo', and by K into 'si circumscripta'. Ibid. (sixth clause): E does not suffer of an omission of five lines that is found in TVK. Ibid. (right before the first dubium): 'provenit' E; 'probatur' TVK. Ibid. (in the third dubium), only E rightly omits an addition ('in propositione categorica') found in the other Mss. At 8.3.6: 'quorumcumque' E; 'quarum habet' TV; 'quarum quandoque' K. At 8.4.1. all Mss except for E omit the word 'illatio'. At 8.6.3. 'tamen' E; 'ergo' TVKG. On the other hand, E has a great many obviously erroneous readings, among them a few omissions and interpolations. Here are some examples: At 8.1.3: 'resolvitur' TVK; 'separatur' E. At 8.1.5: 'concipientes' TVK; 'considerantes' E. At 8.1.6: 'explicatio' TV; 'exemplificatio' EK. At 8.1.7 'circa' TK; 'contra' EV. At 8.2.3: 'in mente' TVK; 'immediate' E, and 'omnino' TVK; 'idea' E. At 8.2.4 (in the third clause): 'intendimus' TVK; 'intelligimus' E. Ibid. (in the reply to the first dubium): 'substantivum' K; 'subiectum' E; 'substantiam' TV. At 8.2.5 'materialiter integratur' TVK; 'materia insequitur' E. Ibid.: 'construendo' TVK; 'concludo' E. At 8.2.6: 'naturis' TVK; 'substantiis' E. !bid.: 'concipiendo' TV; 'considerando' EK. Ibid. : 'cygnum' TVK; 'ignem' E. Ibid. (adfin.): 'inquisivero' TK; 'in considerando' E; 'in communi modo' V. At 8.3.2: 'nominavit' TVK; 'notavit' E. Ibid. : 'differenter quaerunt' TVK; 'differunt' E. At 8.3.4: 'distinctione' TVK; 'demonstratione' E. At 8.3.5 (ad fin.): 'disputare' TV; 'despicere et non supponere sed' E. At 8.3.6: 'resolvuntur' TVK; 'componuntur' E, and: 'commensurabiles' V; 'commutabiles' ET; 'convertibiles' K. Ibid.: 'restat' TVK; 'resultat' E. At 8.3.7: 'addentes' TVK; 'additam' E. Ibid. : 'determinatus' TVK; 'inclinatus' E. Ibid. : 'praemissis earn concludentibus' V; 'praemissas eas concludentes' EK; 'praemissas earn concludentes' T. At 8.4.2: 'exemplariter' TVK; 'exemplificatur' E. Ibid. : 'adductam' TVK; 'adiectam' E. Ibid., ad fin. : 'nomina' TVK; 'omnia' E. At 8.4.3: 'assentimus' V; 'assensus' ETK. At 8.5.1: 'reversio' TVK; 'responsio' E. At 8.5.2 ad fin. : 'ineruditio' TVG; 'in eo iudicio' E; 'in eruditione' K. At 8.5.3: 'recipere' TVK; 'retinere' E. Ibid. : 'assentiendo' TVK; 'asserendo' E. Ibid. : 'suppositis' TVK; 'oppositis' E. Ibid. : 'inferre' TVK; 'informare' E. Ibid. : 'naturali' KG; 'doctrinali' ETV. At 8.5.4: 'nostras' TVK; 'notitias' E. At 8.6.1: 'subdistinguit' TVK; 'subiungit' E, and 'obstante' TVK; 'absolute' E. Ibid. : 'dicendi' TVK; 'sciendi' E. At 8.6.2:

'attributae his' TVK; 'attributis his' E. At 8.6.3: 'implicatur' 1YK; 'multiplicatur' E. At 8.7.7: 'suspicamur' TVK; 'speculamur' E. Ibid.: 'manifeste de scientia et

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demonstratione propter quid in effectu TVK; de demonstratione manifeste et scientia in effectu propter quid in' E. At 8.7.8: 'tycius' TVKGB; 'tullius' sic semper E. At 8.8.1: 'negativam' TVK; 'necessariam' E. At 8.9.2: 'principalitatem' VK; 'principia' E; 'paucitatem' T. At 8.10.4: 'propositiones' TVKGB; 'demonstrationes' E. At 8.10.5: 'ut per' TVK; 'propter' E. At 8.11.1: 'assertive' TVK; 'sensitive' sic saepius E. In the lemma of 8.11.2, E reads 'concedendum' instead of 'commune'. At 8 .11.3 (right before the second dubium): 'consideratum' TVK; 'quaesitum' E. At 8.11.4: 'specialiter quae' TVKGB; 'quae specialiter' E. Ibid. : 'mathematicas' TVKGB; 'metaphysicas' E. At 8.11.5: 'minus' TVK; 'communius' E, and 'inaniores' TVKGB; 'a rebus' E, and 'perfectior' TVK; 'prior' E. Ibid. : 'scientiam' VKGB; 'evidentiam' ET. Ibid. : 'inaniores' TV; 'manifestiores' E; 'maiores' K, and 'veriores' TV; 'universaliores' E; 'notiores' K. At 8.12.3: 'donec assignata' TVK; 'nisi scita' E. At 8.12.4: 'excedunt' TVK; 'extendunt' E. At 8.12.6: 'reduci' TVK; 'illud duci' E. In E, there are far more corrections in the present tract than in previous parts of the Summulae, e.g. in De praedicabilibus. Sometimes these 'corrections' are wrong, e.g. at 8.12.6: 'demonstrativa' T; 'demonstratione' E; 'demonstranda' EC (with VK). Ibid. : 'motor aetemus est' ETVK; 'motus aetemus est' EC. E also has more omissions in our tract than in the previous ones, among which some major ones. E.g. at 8.2.4 three lines; ibid. ad fin. E when omitting about twenty five lines reads 'quod hie deficit reperitur in parvo folio', but such a leaf is missing. At 8.3.3 about twelve lines omitted by E have been filled up by EC. At 8.4.2 E omits four lines. At 8.7.6, the two final sentences of the lemma are found in the inverse order in E, which could point to a gauche adjustment of an omission. At 8.12 E omits (together with 1) three lines. At 8.12.3 there is another omission of three lines. Sometimes E inserts, wrongly, it seems, some words. E.g. at 8.1.5 the presumably superfluous words have been interpolated 'et haec est divisio animalium in homines et bruta', where Vadds 'et haec est divisio in homines et bruta' and K 'et haec est divisio animalis in homines et bruta', whereas T has nothing added. In the first lemma of De definitionibus (8.2), E has a huge interpolation (in common with T). At 8.2.4 (right in the beginning of the first dubium) E has an unsuitable addition, which is found in all other manuscripts, for that matter. Some lines further on, E solely adds the words 'quare etiam erat prius tamquam implicita'; ibid. (in the third dubium) E rather inappropriately adds the remark 'ideo etiam rationabile est quod concretum definiatur per cavitatem (!) ut dicebatur', which does not fit very well the opening lines of the next paragraph 'Ideo etiam rationabile est ut concretum definiatur per concretum'. At 8.2.5 (ad fin.) E unnecessarily adds 'sicut definitum

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John Buridan, Summulae. De Denwnstrationibus

differt ab aliis per genus et suas differentias'. At 8.2.6 E (together with VK) has the rather odd addition, which rightly is missing in T: 'ut subiectum definiatur per passionem'. At 8.3.6 E has (together with K) the explanatory interpolation: 'cuiusmodi dicimus scientiam unius [unitatem! K] esse conclusionis demonstratae'. At 8.4.2 the words 'si non adducatur auctoritas poetae', which are part of a quotation from Aristotle, are extended by EVKG with the phrase 'aut [EC om. E !] alterius doctoris' [huiusmodi ! V], which conspicuously is missing not only in the good manuscript T, but in the rather mediocre copy G as well. At 8.4.2, by adding a marginal gloss ('quae post dicentur') to 'demonstrationem dialecticam', the scribe of E 's exemplar has caused a later copyist to replace 'dialecticam' with this gloss. In the second dubium of 8.11.3, E reads 'subaltematio' instead of 'sub altero'. At 8.11.3 ad fin.Eis the only one to have a somewhat disturbing remark inserted ('quae non sunt scibiles aut demonstrabiles similiter(!) perfecte ideo nee dicentur illae demonstrationes propter quid'). Sometimes E does not know how to choose between two alternative possible readings, e.g. at 8.2.4 (second dubium): 'sensationem sive intellectionem' instead of 'intellectionem' (TVKGB), or at 8.3.2 (second clause): 'effective vel efficienter' (E), 'efficienter' (TV), 'effective (K). Likewise, at 8.4.2 (versus finem); 'creditae' TVK; 'credulitatem vel creditae' E; at 8.4.3: 'opus' TV; 'opus vel usus' E; 'origo' K. E shows three diverse relationships, two of which are rather conspicuous: one to T, another to K; see our discussions of these two manuscripts, below (sections II.5.2

and Il.5.4, respectively). This does not mean, however, that there are no remarkable common readings in E and V against all others. To begin with their common misbehaviour, at 8.1.8 both E and V read 'aliquibus aut pro pluribus' whereas all the others, including the less reliable codex G, have the correct reading 'pluribus'.39 That the former reading does not suit the context is clear (italics mine): 8.1.8: Et est notandum quod iste modus divisionis est valde communis, quia omnis terminus supponens pro pluribus hoc modo divisionis dividi potest per quemcumque alium terminum supponentem pro aliquo vel aliquibus illorum plurium, non tamen pro ill is omnibus .... etc.

A conspiracy of E and V against the sound reading occurs in 8.2.4 (right before the sixth clause), where EV have 'unum praedicatum' instead of 'verumtamen'. On the other hand, EV also frequently conspire against the others in providing the correct reading, as will be seen in the critical apparatus.

39 Codex B here has one of its huge omissions; see below.

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Finally, a peculiar feature of E (which it shares with T, for that matter) should be highlighted. As we have remarked before, the proper tract De demonstrationibus is prefaced by Buridan by two short tracts on division and on definition, respectively, which, as prima and secunda materia, have been incorporated as two introductory chapters in tract VIII, De demonstrationibus, as it is handed down in all the extant manuscripts of the work,40 with the result indeed that the ten chapters of the 'tertia materia', De demonstrationibus, are to be regarded as chapters 3-12 of the whole tract. However, in E and T there is an unmistakeble trace of the previous independence of the two additional tracts, because E, and T as well,41 have consistently maintained the earlier numbering of the 'tertia materia', making a fresh start at the beginning of the 'tertia materia', and sticking to it throughout the work. All other manuscripts count the ten chapters of the 'tertia materia' as 'capitulum 3um, 4um, 5um, and so on.42

II.5.2 Text witness T T = Torino, Biblioteca Nazionale D III 27 (462), anno 1372. We have no codicological description of this manuscript. It contains our tract on ff. 73ra-98rb written in one hand, the same that also copied the remaining tracts and the greater part of the (relatively few) corrections made to our text.43 The juristical example used by Buridan in section 8.7.9. here reading 'Trajectensis diocesis' seems to point to the Low Countries as the place of its (or its exemplar's) scribe's origin. Throughout the Summulae, T proves to be one of our better copies. In some passages it is the only manuscript to provide what may be considered the correct reading. Here are some of the multitude of examples. Tis the only copy in which an obvious addition (occurring at the end of 8.1.5; see above, in our discussion of E) is missing; at 8.4.2 a similar case is found, in which T shares the omission of the interpolated text only with B; see ibid. 40 See also the opening lines of the first tract of the Summulae, quoted above, section II.3.1. 4 1 T even quite unequivocally reads at the end of the second 'materia': 'SEQUITUR CAPITULUM PRINCIPALE'. 4 2 With only two exceptions: at 8.5.l and 8.8.l, K shares the indication 'tertium capitulum' ('sexto capitulo', respectively) with ET, and at 8.12.1, E, too, has the later numbering and reads 'istud duodecimum capitulum et ultimum huius tractatus', whereas T continues with the original numbering and has 'istud decimum et ultimum capitulum huius tractatus'. Notice that unlike EVKGB, Tmeans by 'huius tractatus' only the 'tertia materia, De demonstrationibus', rather than the entire tract VIII. 43 For a number of extensive additions to the tract De praedicamentis see the critical edition by E.P. Bos, Appendix,§ IV.l.

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At 8.1.6, only T succeeds in escaping a tempting pitfall: 'terminus communis respectu sui ipsius sumptus (T; sumpti EVK) cum accidentali determinatione'. At 8.1.7 (in the reply to the first dubium), only T has the most probable reading in the example of the incorrect division of 'magnitudo'; ibid., at the end of this reply: 'digressionem' T; 'disgregationem' E; 'distinctionem' VK,; ibid., in the beginning of the second dubium Thas 'et subiectio'; 'subiective' E; 'in subiecto' VK. At 8.2.1: 'modificare' T; 'moderare' EVK. At 8.2.3, in the lemma, T correctly reads 'exprimens', whereas EVK have 'explicans' .; ibid., in discussion of the second clause, only T has the grammatically correct reading 'puer (T; puero EVK) docetur'; two lines further on, it shares the better reading with VK : 'infans (infanti E) doeetur'. At 8.2.4 (init.), T correctly has 'totalis', which is missing in EVK; some lines further on, in the third clause, Treads 'indieat', whereas EVK have the less probable reading 'significat'; ibid., in the opening passage of the second dubium: 'nomini' T; 'terrnino' EVK. At 8.4.2, only T presents the correct quotation from Aristotle, Metaph. II 3, 995a3-6; ibid., in the second clause T correctly reads 'consequentiam. aut', whereas EVKGB all have the odd reading 'consequentia autem'; ibid., (ad fin.): 'demonstrat' T; 'determinat' wrongly EVK. At 8.4.3 (in the fourth clause), where EVKGB have the odd reading 'debere', T rightly reads 'de re'. However, T certainly does not qualify for canonization, because it also presents a great number of mistaken, or less probable readings. At 8.2.1, Thas the clumsy reading 'cognitio' instead of 'congregatio' (EVKGB). At 8.2.3, in the lemma, T incorrectly reads 'significatis' instead of 'definitis' found in EVK. In the second dubium of 8.2.4, T has 'substantia' instead of 'subiecto' (EVK); ibid., some lines further on, T reads 'simpliciter' instead of 'singulariter' (EK; 'universaliter' V). At 8.2.5 T has 'demonstrationes' instead of 'definitiones' (EVK). At 8.2.6, T reads 'substantialis' ('subiecti substantialis' V) instead of 'subiecti specialis' (EK). At 8.3.2 (init.), T has 'notitia et' instead of 'numero et de' EV, which words are omitted in K; ibid., some lines further on, Treads 'rationem' instead of 'orationem'. At 8.3.3 (first clause), T has 'econverso quod' instead 'eo modo quo'; ibid. (ad fin.), Treads 'subiectum' instead of 'definitum' (EV; 'definitionem' K). At 8.3.5, T clumsily reads 'cognitio' instead of 'cum ergo' EVK). At 8.4.2 T has 'demonstrationis' instead of 'conclusionis'; ibid., 'false' instead of 'intense', and 'opinantem' instead of 'opinandam'; ibid., 'dubitatione' instead of 'demonstratione'. At 8.4.3 (lemma), T has 'propositioni adaequatus' instead of 'propositioni additus'; ibid.,

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Introduction

'quando' instead of 'quin'; ibid. (ad fin.) Treads 'negare' instead of 'notare'. At 8.4.4, instead of 'expetenda' (found in EKG) Treads 'expedienda' ('expectanda' V; 'competenda' B). At 8.5.4, T has 'ampliatione' instead of 'multitudine' (EK; 'multiplicatione' V), and 'statibus' instead of 'stabitur'. At 8.5.3, T has 'potentia' instead of 'ponitur'; ibid., 'correspondentes' instead of 'contingentes', and 'precise' instead of 'praemissae'; ibid. (end of the discussion of the fourth clause), T always reads 'levis' instead of 'laesivus'; ibid. (ad fin.), T has 'complexum' instead of 'exemplum'. At 8.6.2, T has 'patet' instead of 'passio', and 'videns' instead of 'vadens'. At 8.6.5, Treads 'superioris' instead of 'suppositionis'. In the lemma of 8.6.4, T has 'in idem videtur incedere' instead of 'idem videtur [sc. Aristotle] intendere'; in Buridan's comments, T has 'pertinentem ad' instead of 'tenentem per'. At 8.8.1, T has 'penes' instead of 'ponens'. At 8.8.1, T has 'demonstrant' instead of 'differant'. At 8.9.2 (lemma) Treads 'scientiam' instead of 'differentiam'; ibid. (ad fin.), T has 'conclusiones' instead of 'contractiones', and 'sanitatem' instead of 'sanationem'. At 8.9.3 (init.), T has 'demonstratio' instead of 'circulatio'. At 8.10.6 (ad fin.), Treads 'movetur' instead of 'morietur'. At 8.11.5 (init.), T has 'media'

instead of 'memoria'; ibid., 'sciens cognita' instead of 'scientia congregata'. At 8.12, T has 'homo' instead of 'quaestio'. At 8.12.3, Treads 'quoniam' instead of 'quin', and 'connotativum' instead of 'quiditativum'. At 8.12.5, T has 'vel proprietatem' instead of 'appropriate'. The manus corrigens TC is more than once active, e.g at 8.2.5, where it corrects an omission of two lines (found in T and VK). At 8.2.4 (in the reply to the first dubium), T makes an attempt to fill up the omission (committed in its exemplar owing to haplography) of 'sed idem diversimode significant, scilicet albedinem, nam' by inserting 'nisi quod iste terminus'. On top of that, there are quite a lot of omissions in T. Here are some examples of the major ones. At 8.1.6 (ad fin.), as in 8.2.5, three lines are missing. At 8.1.7 (in the dubium), four lines are missing. At 8.2.6 (ad fin.), two lines have been omitted, as in 8.3.3. At 8.4.1, the 27 lines concluding this section are missing. At 8.4.3 (adfin.), four lines have been omitted. At 8.5.2 (in the discussion of the second clause), there is an apparent haplography, as in 8.5.4 and 8.6.4. At 8.5.3, three lines are missing. At 8.12.4 (ad fin.), a entire notandum of seven lines is missing. In the first part of Buridan's comments on each main section, T often replaces the enumeration of the opening words of the lemmata with the phrase 'partes patebunt'. As in the tract De praedicabilibus, T sometimes has alternative readings that seem quite acceptable by themselves, though not shared by any of the other Mss.,

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but without the pedantic didacticism we have come across in that tract. In the present tract, you find harmless alternative readings such as 'apparet' for 'patet', but also slight discrepancies such as 'notum' for 'manifestum' or 'sequitur' for 'infertur' (8.4.2, in the discussion of the second clause); ibid. (ad fin.), T does not choose between 'intentum' and 'propositum'. At 8.9.2 (ad fin.), T has 'curantur' instead of the common 'sanantur'. At 8.12.5 (in the discussion of the fourth clause), Treads 'interveniente', the other Mss. having 'impediente'. There are also a few interpolations in T. At 8.3.4 (ad fin.), T adds to 'demonstratione' the words 'in mente vel propositione'. At 8.4.2 (right before the discussion of the third clause), it inserts the words 'quod dictum est in proemio tractatus'. At 8.6.2 (in the discussion of the fourth clause), it inserts another example before the phrase 'et sic de multis aliis', which is found in all Mss including T. As for T' s relationships to the other Mss., two different connections should be recognized, as is patently clear from our critical apparatus: one with our basic codex, E, the other with V. First, E and Tvery often have the correct reading against all other Mss., as is clear from our critical apparatus. To mention only an important one, at 8.1.8 (in the discussion of the first kind of division), ET twice have the correct 'esse non' instead of 'non esse' found in VKGB. On the other hand, they have also a lot of errors in common which are not found in VK. In the lemma 8.2, ET (together with K, for that matter) oddly add a ninth clause, of which there is no trace in their texts of Buridan's comments upon the lemma. At 8.2.l (in the discussion of the fourth clause), they wrongly have 'hominis' instead of 'animalis'; ibid. (ad fin.), they omit the indispensable word 'quasi'. At 8.3.6 (in the discussion of the fourth clause), they read the odd 'commutabiles' instead of 'commensurabiles' (V; 'convertibiles' K). At 8.4.4, they share two omissions in the lemma; in the comments to the first clause, they both omit the indispensable indication 'in Symbolo', as they also share in mistaking the next explicative phrase ('in fine') for the verb 'inferre'; ibid., they both read 'incertis' instead of 'non scitis', 'quiescere' instead of 'quietare', 'numerum' instead of 'materiam' and 'talis' instead of 'naturalis'; ibid. (at the end of the discussion of the first clause), they share with K the odd reading 'assensu' instead of 'a sensu' found in V. At 8.8.1 (in the discussion of the fourth clause), they both have the unacceptable reading 'ex vi istorum modorum' instead of 'ex vi vocabulorum'. At 8.8.6 (at the end of the discussion of the first 'dubitatio' raised in the lemma), E and T have 'posterioritate' instead of 'causalitate'. At 8.11.3 (first dubium, in the paragraph opening with the words 'Et si scio quod figura'), they both fill up an apparent

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omission brought about by haplography in an inappropriate way. Sometimes E and T do not present the correct reading, but two different own readings. E.g. at 8.11 (last sentence of the lemma), E reads 'utrumque' and T 'utrorumque' instead of the correct reading found in VK 'unicuique'. At 8.11.5, ET incorrectly read 'evidentiam' instead of 'scientiam' (VK), and 'demonstrationem' instead of 'scire' (VK). In the lemma 8.12, ET have the omission of the fourth clause in common, the discussion of which, however, is not missing in ET. With respect to the close relationship between E and T, their common (old) numbering of sections 8.3-8.12 (discussed earlier, sub Il.5.1, end) should also be taken into consideration. The relationship between T and V will be discussed in the next section. 11.5.3 Text witness V

V

= Wertheim (Germany),

Evangelische Kirchenbibliothek (or: Historische Bibli-

othek in der Stiftskirche) 157 (anno 1362 vel 1384) a paper manuscript of 139 folios

measuring 280x215 mm., contains a copy of our tract on ff. 96rb-135vb. We owe this codicological information to Dr. L. Valente. The couleur locale of the juristical example found in section 8. 7 .9 here reading 'Attrabatensis diocesis' refers us again to the Southern Netherlands (the diocese of Atrecht, nowadays Arras, France); it should be taken into consideration that in 1328, Buridan was a member of the clergy ('clericus') of this diocese and in 1342 as a canon member of the Chapter. Another clue for its whereabouts may be found in the (rather odd) addition of the southern Dutch word 'calfstert' (= 'calf-tail') to the final sentence of section 8.8.5, which runs as follows: 'ergo omne grave vel !eve est corruptibile propter generationem alterius etc.', where the 'etcetera' stands for the phrase 'formae vel substantiae'. This manuscript is not of the same rank, it seems, as ET, but nonetheless often useful for the constitution of the text. In more than one case it testifies to the correct or more plausible reading, against all other Mss. Thus, in the first lemma of the present tract (8.1), it reads 'praesupponunt' instead of the less probable reading 'supponunt' found in the other Mss. In the lemma of 8.2, it does not suffer (with GB, for that matter) from an odd interpolation found in ETK. At 8.2.4 (in the reply to the first dubium), only V has the correct reading 'neque etiam iste terminus', against 'neque etiam' (£), 'neque iste terminus' (T), and 'ut iste terminus' (K). Ibid. (second dubium), only V does not suffer from an omission caused by haplography ('hoc esse

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et iudicat' after 'iudicat'). At 8.3.5 (in the discussion of the second clause), V correctly reads 'sint numeraliter', whereas ET unfittingly have 'sic numerantur', and K: 'sit numerus'. At 8.3.6 (in the discussion of the fourth clause), V has the correct 'in postassumendo', but E 'in posterius assumendo', T 'in postassignando', and K 'per posterius assumendo'; ibid., only V has the correct reading 'commensurabiles' ('commutabiles' ET; 'convertibiles' K). At 8.3.7, V has the correct reading 'ante novit', against 'cognovit' in ETKGB. At 8.4.2, V correctly reads 'vel demonstrata', rather than 'vel determinata' found in TK (om. E). At 8.5.2 (end of the discussion of the first clause): 'prioris' V (together with G); 'aliorum' E; 'primorum' T; 'poni' (!) K. At 8.5.4 (lemma), V reads (together with G) 'cum ministerio tamen praevio sensus', while the others have incorrect or less probable readings. At 8.6.2 (end of the discussion of the first clause), V has the suitable reading 'tractans', whereas EKG have 'tractatus', and T 'capituli'; ibid. (ad fin.) V correctly has 'quinto', the others the incorrect 'secundo'. At the end of 8.11.2, only V does not share in an omission brought about by haplography; likewise, some lines further on; ibid. (at the end of the discussion of the third clause), V reads the correct 'excedit' ('concedit' ETK). Many times, however, it presents erroneous or less probable readings, partly sharing them with other Mss. (mainly from the KGB group). Here are some examples of wrong readings that only occur in V. In lemma 8.1, V reads 'principalis' instead of 'praedicabilis'. At 8.1.4, it has 'composito naturali' instead of 'conceptu numerali', and 'unione' instead of 'unitate'. At 8.1.5, 'continuationem' instead of 'discontinuationem'. At 8.1.6 (init.), 'in voce' instead of 'univoce'. At 8.2.1, 'modum' instead of 'nomen'. At 8.1.7 (init.), a gloss ('subiectum et praedicatum') that crept into the text seems to have dispelled the original reading 'nomen et verbum'. At 8.2.3, V has 'explicante interpretante' (!) instead of 'interpretatae'; ibid.: 'amatur' (!) instead of 'a matre', and 'assign at' instead of 'ostendit'. At 8.2.4 (in the discussion of the first clause), 'sensibilis' instead of 'sensitiva'; ibid. (fourth clause), 'praedicatur' instead of 'praesciatur'; ibid. (second dubium), 'immediate' instead of 'in mente', and 'quia' instead of 'quare'; ibid. (reply to the second dubium), 'significatione' instead of 'sensatione'; ibid. (end of reply to second dubium), 'eligendo' instead of 'eliciendo'. At 8.2.5, 'genus' instead of 'syllogismus'; ibid. in the third clause), 'casualis' instead of 'causalis'; ibid. (in the discussion of the sixth clause), 'auferunt' instead of 'conferunt'. At 8.2.6, 'verissimum' instead of 'levissimum'; ibid. (in the discussion of the third clause), V reads 'definitio' instead of 'intelligi', and 'simplicem' instead of 'complexum'.

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At 8.3.2 (in the discussion of the second clause), 'ignorantiae' instead of 'inhaerentiae'. At 8.3.3 (right before the discussion of the second clause), 'indubitabiles' instead of 'indemonstrabiles', and 'indistincte' instead of 'in mente'. At 8.3.5 (end of the discussion of the second clause), 'manifestando' instead of 'magnitudo', 'manifestationem' instead of 'magnitudinem'. At 8.3.6 (end of the discussion of the fourth clause), 'posteriorum' instead of 'physicorum'. At 8.3.7 (in the dubium), 'ad hoc deficientes' instead of 'adhuc sufficientes', 'voluptas' instead of 'voluntas', and 'additione' instead of adtaediatione'; ibid. (in the discussion of the third clause), 'sciendi' instead of 'faciendi'. At 8.4.4 (init.), 'falsa' instead of 'certa'; ibid., 'oculo' instead of 'obiecto'; ibid. (end of first clause), 'effectum' instead of 'defectum'. At 8.5.2 (end of first clause), 'subintellectio' instead of 'solutio autem'. At 8.6.1 (dubium), V has 'terrae' instead of 'lunae'. At 8.7.2, 'probatur' instead of 'proponatur'. At 8.7 .8, V has 'scientiam definitivam' instead of 'sententiam'. At 8.8.1, 'conclusionis' instead of 'materialis'. At 8.9.2 (discussion of second clause), V has 'ruminantur' ('they are ruminated'!) instead of 'reuniuntur' ('sanantur' T); ibid., 'senarius' instead of 'sonorus'. At 8.10.6, 'naturam' instead of 'evidentiam' ('indigentiam' E). At 8.11.4, the common confusion between 'intendo' (V) and 'intelligo' (ETK) is found; that between 'esse' and 'omne' is committed more than once, e.g. at 8.2.4 (in the discussion of the fifth clause). At 8.11.5, V reads 'calore' ('colore' K) instead of 'cholerae'. Several omissions can be pointed out in V. At 8.1.7 (init.) eight words and ibid. (in the first dubium) two words, and in the second dubium even three lines have been omitted. Likewise, there are omissions at 8.2.4 (second dubium), and ad fin. At 8.2.6 (in the discussion of the third clause). At 8.3.2 (lemma). At section 8.3.6 (end of third clause), and in the fourth clause, as at 8.4.4 (ad fin.) several lines have been omitted. At 8.3.7 (right before the dubium). At 8.5.3 (first clause), three lines have been omitted owing to haplography. At 8.6.2 (init.), one line is missing in V. At 8.1.7 (in the beginning of the second dubium), V has an omission of five words, which it inserts at the wrong place, two lines further on. Also a few interpolations can be shown. E.g. at 8.2.4 (third dubium), where V needlessly adds another example, and similarly at 8.2.5 (in the discussion of the fourth clause). At 8.3.6 (in the discussion of the fourth clause), where an addition such as the words 'in medio circuli' to 'centrum' seems superfluous. V has a strikingly close relationship to one of our two best manuscripts, T, as is clear from our apparatus at first glance. I shall confine myself to highlighting some conspicuous examples. In the opening lemma of the work (8.1), only TV have the

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preferable reading 'nobilis' instead 'notabilis' (EKGB). At 8.1.3, they correctly read 'unaquaeque', whereas the others (EKGB) have the less suitable reading 'utraque'. In the lemma of 8.4, TV omit about six lines, which are found in EKGB. At 8.1.4, their 'accipitur' should surely be preferred to the others' 'attenditur'. At 8.5.4 (ad.fin., in a quotation from Aristotle), TV read (with G, for that matter) 'ineruditio', where E has the odd reading 'in eo iudicio', and K 'in eruditione'; as a matter of fact, the entire section is missing in B. The close relationship between T and V is also evidenced by some common misreadings. E.g. right in the first lemma (8.1), 'inveniendas' instead of 'investigandas', and at 8.3.6 (in the discussion of the fourth clause), 'conclusiones' instead of 'demonstrationes'. At 8.5.2 (at the end of the discussion of the second clause), they have the incorrect reading 'argumentatione' (instead of 'augmentatione') in common. Besides, TV share some omissions. E.g. at 8.2.4 (before the discussion of the seventh clause), TV have (together with K, for that matter) an omission of about five lines owing to haplography. In the discussion of the fourth clause of 8.3.6, they have a rather disturbing omission of four words, brought about by haplography. At 8.11.5 (init.), they omit the indispensable qualification ('quantum ad omnes modos') which is found in the other Mss. At 8.12.3, they both omit the verb 'addit'. Finally, in the lemma of 8.12.4, TV omit the indispensable phrase 'secundum quod homo est'. However, T's huge omission of 27 lines at the end of 8.4.2 does not occur in V. It is worthwhile to signal hints found in 8.2.4 for the possibility that V goes back

to the T tradition after the latter had been corrected by F. In the discussion of the third clause, V has (together with TC) the attempted 'correction' of the incorrect reading 'circumscribo' by supplying 'si' (instead of the correct reading of EB), whereas the grammatically inadequate 'circumscribo' is found in T. Likewise, in the lemma of 8.3.3, V shares the reading 'quaeritur' with F, in a passage, for that matter, which is missing in T. 44 This chronology seems to fit in well with the fact that V must date from a later stage of the manuscript tradition than ET, as is clear from the fact that the old numbering of the ten chapters 8.3-8.12 occurring in ET differs from that in VKGB; see our section II.5.1 (end). Besides, as we have seen, it is, quite a few times, the only one to share readings with our best manuscript E; see our section Il.5.1. Moreover, notably as far as wrong 44 Of course, this relationship between V and Tc does not rule out cases in which TVc have readings in common against EVK; see e.g. at 8.3.7 (right before the dubium): 'scientiae conclusionis' (TVc) against 'conclusionis scientiae' (EVK). Cfr. ibid. (discussion of the third clause): 'quad' (rvc).

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readings are concerned, V shows a clear affinity with our second rank Mss., KGB, more often indeed than is clear from our apparatus. Il.5.4 Text witness K K =Krakow, Biblioteka lnstytutu Teologicznego Ksiezy Misjonarzy 171 (olim 627, antea 827; labelled 'Stradom Ms.', after the district where the Institute is situated) is a paper manuscript of 220 folios (measuring 297x215 mm) written in two columns, (saec. 14.2/15.1). It contains our tract on ff. 145ra-182vb in one handwriting. There are many corrections, partly in what seems to be a different hand from the manus principalis. A 15th-century Ex-libris on the inside of the front cover reads: 'Iste liber est Canonicorum Regularium Monasterii Corporis Christi in Cazimiria'. This means that the Ms. was already at that time in Krakow, where it probably stayed, until K. Michalski acquired it for the library where it is now kept. We owe this information to Professor S. Ebbesen. Its previous location in uncertain. K 's reading of the juristical example of 8.7.9. ('parisiensis diocesis') could be Buridan's, but the reading found in V ('Attrabatensis diocesis') is perhaps more plausible, at least as far as an earlier version of the Summulae is concerned, but the reading 'parisiensis' could hint, although not necessarily, at K's origin in Paris. K certainly belongs to the manuscripts of lower rank. It contains a great number of errors, many of which are conspicuous for their stupidity. Here are a few of them. At 8.1.2, 'distincta' instead of 'describenda', and 'collectio' instead of 'compositio'. At 8.1.3, you meet with 'toti omnes' instead of 'locutiones', and at 8.1.4, 'diffinitur' is found instead of 'distinguitur'. At 8.1.5, K has 'nomen' instead of 'nullum', and 'meretur' (!) instead of 'desinunt'. At 8.1.6, 'reduplicabiles' instead of 'reducibiles'. At 8.1.7 (ad fin.), K reads 'dicunt' instead of 'differunt'. At 8.2.4, 'coniunctio' instead of 'congregatio', and continually 'curvum' instead of 'cavum'. At 8.2.5 (init.), 'propria definitio' instead of 'proprium definito'. At 8.3.3 (discussion of second clause), 'concederemus' instead of 'consideremus'. At 8 .3 .4 (lemma), 'praecognoscentibus' instead of 'praecognoscendis', and at 8.3.6 (lemma), 'veritas' instead of 'dignitas'. Other odd errors are: 'posse ea' instead of 'bursa mea', and 'materialiter' instead of 'naturaliter' (8.3.7), and 'nescire' instead of 'me scire' (ibid., ad fin.); 'expositione' instead of 'experientia', and 'per te positae' instead of 'partis oppositae' (8.4.2); 'origo' instead of 'opus' (lemma of 8.4.3); 'innate ut' instead of

'in arte et', and 'aristoteles' instead of 'ars', and (8.4.3, ad fin.); at 8.4.4, 'narrandi' instead of 'errandi'. At 8.5.4 (discussion of the second clause), K reads 'monstrata'

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John Buridan, Summulae, De Demonstrationibus

instead of 'ministrata', and ibid., ad fin., 'considerat' instead of 'consurgit'; ibid. (third clause), K reads the odd 'inculpat' instead of 'in quolibet'. At 8.6.3 (in the beginning of the dubium), K has 'differentias' instead of 'directas', and 'non tamen notat' instead of 'connotat', and in the dubium of 8.7 .5, 'ignorantibus' instead of 'in moralibus'. At 8.7.8, K reads 'instantias' instead of 'iniustitias'. At 8.8.1 (discussion of first clause), 'res gestare' instead of 'restare'; ibid. (fourth clause), K reads 'quod est conclusio' instead of 'quam econverso'. In the lemma of 8.9.1, K reads 'circumlocutionis' instead of the technical term 'circulationis', and omits the words 'de circulatione in demonstrationibus'. At 8.11.2, one finds 'communiter' instead of 'consequenter'. At 8.11.3 (right before the second dubium), K reads 'cognatum' instead of 'quantum', and 'demonstrantem' instead of 'descendentem', and ibid, ad fin., 'sequitur' instead of 'scitur'. At 8.11.5, 'inferiores' instead of 'veriores ', and 'fortiores' instead of 'pauciores'. At 8.11.7, the phrase 'secundum quod ipsum' is found instead of 'secundum quid', and at 8.12.1, the word 'restat' instead of 'cessat'. On top of all that, K frequently reads 'et etiam' instead of the abbreviation 'etc.'. A peculiar error found in 8.7 .8 ('sciat' instead of 'si ad') suggests that the text was being read to the scribe (of Kor its exemplar). At 8.9.5, the scribe takes the phrase 'considerans de a' for 'consideranda'. K suffers from a lot of omissions (e.g. one of about 8 lines in section 8.9.5), sometimes together with other Mss., e.g. at 8. 1.5 there is one due haplography found in EK. As a matter of fact, there are some errors found only in EK, e.g. at 8.1.6, 'exemplificatio' instead of 'explicatio', and 'possibilitate' instead of 'perseitate' at 8.6.3. The manus corrigens of K is far less active in our tract than e.g. in the tract De praedicabilibus, and its laziness is conspicuous.

However, K is surely not completely useless. Many times, especially in the second half of our tract, it is the only one to present what may be regarded as the correct or most plausible reading. Here are some examples. At 8.1.4, it reads 'ordinatione', the others 'ordine'. At 8.1.7 it has the correct reading 'tertias', the others reading 'ternarius'. At 8.1.8 (adfin.), only K has 'huius termini entis'. At 8.2.1, K reads 'nisi ratione', whereas EV have the odd reading 'nisi oratio' and T presents something of its own invention in writing 'sed solum'. At 8.2.3 (discussion of second clause), K cmrectly reads 'extraneae' instead of 'extrinsecae (ETV); ibid., (end fifth clause) K has 'plane', but ETV the useless 'probare'; ibid. (reply to first dubium): 'substantivum' (K), 'subiectum' (E), 'substantiam' (TV); ibid. (reply to

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second dubium), K has 'discemit' against 'distinguit' in ETV. At 8.2.4 (reply to first dubium), KGB have 'verbo' which is wrongly omitted by ET. At 8.3.2 unlike K, ETV omit 'praedicamenti'. At 8.3.6 (end of fourth clause), K correctly reads 'illi totali', whereas E has 'illius', T 'talis', and V 'totalis'. At 8.3.7 (init.), it correctly reads 'demonstrandam' against the others ('demonstrativam' E;

'demonstratam' TV). At 8.6.2 (right before the fourth clause), only K has the suitable reading 'semper connotationem super significationem subiecti', whereas E has 'connotationem super subiectum', E c 'connotationem super et significationem subiecti', T 'super connotationem seu significationem subiecti, V 'semper super connotationem et significatum subiecti, and G 'super connotationem super significationem subiecti'. At 8.8.4 (ad fin.), K correctly reads 'mansivitatem', whereas TVG have 'mansitatem' and Ethe odd reading 'mansuetatem'. At 8.10.2, K has 'incompossibilibus', while ETV read 'compossibilibus non'. At 8.12.2 all Mss. except for K read 'propter quid' instead of 'per quid'. Frequently, K shares the correct reading with only our better manuscript E. Sometimes, however, with one of our codices deteriores (GB), against ETV. E.g. at 8.2.4 (fourth clause), KGB read the indispensable letter 'A' (used to indicate a random example), which is omitted by our better manuscripts ETV. 8.5.4 (end fifth clause), 'naturali' (KG) against 'doctrinali' (ETV), and at 8.4.4 (first clause), K correctly reads (with B) 'metaphysicas', and E 'mechaniles'(!) and TVG 'mathematicas'. In the lemma of 8.8.4, only K has the presumably correct reading 'causisque', while T has 'causis quam' and V reading in two words 'causis que' takes 'que' for the relative pronoun 'quae'; E has the possible and unequivocal reading 'et causis'. All in all, it is mainly because of its stupid readings that K qualifies for the second rank.

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11.5.5 The codices raro adhibiti, G and B

G = Erfurt, Wissenschaftliche Allgemeinbibliothek, 2° 305, a paper manuscript (ff. I+ 98), dating from 1373 and measuring 294x224 mm, contains our tract on ff. 72ra97vb, all written in one hand. The date (June to August, 1373) is given in the colophon, f. 97vb: 'Explicit loyca reverendi magistri Byridani reportata Prage per manus Luce de Wienna. Incepta in vigilia Petri et Pauli et finita in crastino Bartholomei. Anno domini millesimo cccm0 septuagesimo tercio'. The codicological information about this Ms. derives from Prof. S. Ebbesen. The juristical example of 8.7.9 as reported by G reading (89rb) 'pragensis diocesis' seems to confirm the Prague origine. G seems to be the least reliable of the manuscripts used. The scribe of G, or of its exemplar, is time and again rather careless, In a great many cases, its readings are simply erroneous. As in the tract De praedicabilibus, it comes rather close to K (and B as well, though to a somewhat lesser extent, it would seem). Negative evidence for the relation between Kand G can be gathered from an alternative reading 'tentum' only found in K (in the reply to the first dubium of 8.2.4), which obviously is the fruit of an initiative taken by its exemplar's scribe in order to emend the omission (only occurring in G) of 'sumptum', which is the reading found in all others (ETVB). On the other hand, G several times provides the correct reading against (nearly) all our other Mss. E.g. in 8.4.4 (discussion of first clause), where our best manuscripts ET read 'in is tis', G has the more plausible reading 'in sanctis', which is supported by KB rather oddly reading 'in scientiis'. In 8.5.3 (ad fin.), G correctly reads 'evidentem contradictionis repugnantiam', whereas E has 'evidentiam contradictionis vel repugnantiam', T 'evidentiam contradictionis evidentem vel repugnantiam', V 'evidentem contradictionis evidentiam vel repugnantiam', and K 'evidentiam vel'. At times, G shares its correct reading with only part of the other Mss. E.g. in 8.2.4 (reply to first dubium): 'verbo' KGB, omitted by ET, and at 8.4.4 (discussion first clause): 'expetenda' EKG; 'expedienda' T; 'expectanda' V; 'competenda' B. In 8.5.2 (ad fin.), TVG have the correct 'ineruditio' against 'in eo iudicio' (E), and 'in eruditione' (K). In 8.5.4 (end fifth clause): 'naturali' KG; 'doctrinali' ETV. In the lemma of 8.5.4, VG present the more probable reading of the phrase 'cum ministerio tamen praevio sensu' against ETK. In the lemma of 8.12.2, GB read 'ex dictis', whereas ETVK have 'ex his' (for 'ex his dictis'?). In 8.12.3 (second clause), TG have the correct reading 'non quaeritur proprie quod praesupponitur' where the others (EECVKB) have less probable or incorrect readings. In 8.12.4, EG have the correct reading, against various

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Introduction

wrong ones occurring in TVK. For correct readings found in KGB as against ETV, see our previous section. B = Vienna, Osterrcichische Nationalbibliothek, Vindobonensis palatinus latinus 5420, saec. 14.2 (ante 1395), chart., mm. 290x210. An ex-libris says: 'Emi hanc summam uno floreno aureo ungarico anno Domini 1395' .4 5 The Ms. contains our tract on ff. 95va-128ra (new numbering 96va-13lra), written by one hand. However, B has huge omissions between (using the old numerotation) fols 96v and 97r (our section 8.1.6, first clause, after 'prout alibi dictum fuit' up to the last lines of 8.1.7 'sicut dictum est de propositione'), as well as between l lOv and 11 lr, where two entire quires seem to be missing, which may have contained the text of section 8.4.4 (concluding passage, after the words 'quantum ad scibile vel opinabile inmediatum') up to about the end of 8.6.4 'ratione totius praedicati scilicet ratione'. In the juristical example of section 8.7.9, B reads (ll4vb; new numbering 116vb) 'pataviensis diocesis', which may point to a scribe (of our copy or its exemplar) of Italian (Padua) or German (Passau) origin. Although B belongs to our secondary sources (and is incomplete at that), it occasionally has what may be regarded as the correct or preferable reading, against all others. E.g. in the lemma of 8.3.2, B has the better reading 'quid est', whereas all the others (ETVKG) have the less suitable 'quaerens de quiditate'. At 8.12.4 (discussion of fifth clause), it has the correct reading 'dato' against 'dico' in ETVKG. At other times, B seems to support the better reading found also elsewhere. E.g. at 8.2.4 (third clause): E shares the correct reading of the gerund 'circumscribendo' only with B. At 8.3.5 (first clause), B shares the correct reading 'ballare' with ET, whereas KG read 'volare'(!), and is (ibid.) the only copy providing the correct reading 'generatur' instead of the inappropriate 'dicitur' occurring in ETVKG. At 8.4.4 (first clause), the correct reading 'metaphysicas' is only found in KB, against various other readings in TVG and E. In 8.12.3, B has the correct reading 'sicut' (TVB) instead of 'sive' in EKG. For correct readings in KGB which are missing in ETV see our section 11.5.5, and above in the discussion of G.

45 Private communication by Professor M. Markowski (Cracow).

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II.5.6 Evaluation of the Manuscripts

The present editor has used complete transcriptions of the manuscripts E, T, V, and K, and, as a rule, their readings are all mentioned in the critical apparatus. The readings of G and B these two having been continually consulted - are only reported in the apparatus if they seem to be of some interest for the constitution of the text or the manuscript tradition. As may be clear from the foregoing discussion of the Mss., none of them is entirely reliable, to say the least. The editor has not only to make a reasonable, rather than a compulsive choice between alternative readings, but is also often compelled to emendate the text as it is handed down to us; see our next section. For the rest, it should be borne in mind that also the existence of different versions of the Summulae may have further complicated the text tradition. From this point of view, you have to take text variants like 'partes patebunt' occurring instead of the complete enumeration of these parts, the use of the abbreviation 'etc.' replacing the completion of a well-known formula, or the addition of still another example after the usual ones; likewise, the use of such words as 'tune' or 'ergo' in apodosi, and, generally speaking, the suppletion or omission of clarifying phrases. In many such cases, the editor cannot help making arbitrary decisions, not to mention modal uses of the verb, such as in 'dicerem' (against 'dico'), when used in the sense of French 'je voudrais dire', as is frequently found with authors active in the French milieu. As is clear at first glance, although being far from perfect, E and Tare our most reliable copies. 4 6 K (and even more GB) are ostentatively of a lower standing, whereas V seems to take a middle position, on the one hand sharing a number of excellent readings with T, but also often being in the bad company of GB. It may be of some interest to recall in this connection that our oldest text witness, G dating from as early as 1373, definitely does not rank among the better manuscripts, as is clear from our analysis in the previous section. In addition to the mutual independence of all our copies, this fact provides some evidence for a respectable circulation of Buridan's Summulae in the second half of the fourteenth century, before it was nearly pushed out in the next century by John Dorp's commentary. The interrelationships between our manuscripts ETVKGB are rather complicated. At the outset, it should be underlined that there is definitely not any strict dependence between them, meaning that one of them should have been copied from ------------

46 It should be stressed, however, that in the present tract, especially in the last part of it, E seems to have lost a bit of its unique value.

Introduction

the other; our previous analysis suffices to rule out that possibility. This does not mean, however, that we should ignore some st1ikingly close relationships between some of them.47 First, as in the tract De praedicabilibus,48 there are some undeniable similarities between E and our second copy of high rank, T, as is patently clear from the foregoing analysis in our section ll.5.2. The same analysis (see ll.5.3) has elucidated the remarkably close affinity between T and V, which, however, is far from including any special affinity between E and V (for some incidental similarities between E and V, see our section ll.5.3). The remarkable (old) numbering of the ten chapters of the 'tertia materia' (i.e. the tract De demonstrationibus proper), which is not found in VGB, and only once in K, should be remembered; see our sections II.3.1. and II.5.1. Besides, as is also the case in De praedicabilibus, there appears to be a rather close relationship between our three copies of lower rank KGB as against ET, as well as a close affinity between V and KG (and to a lesser extent between V and B), as far as incorrect or less probable readings occurring in V are concerned. On the other hand, there are some noticeable similarities between Kand G, which are not shared by B.49 Any mutual dependence between our copies being excluded, the question arises whether the diverse manus corrigentes have possibly had one of the other manuscripts at their disposal. In order to answer this question one should first distinguish three kinds of corrections: [a] corrections of the 'on second inspection' type, i.e. those which are made by the same scribe, or the corrector, and are the result of another, more careful reading of the same exemplar. Thus trivial scribal errors are often corrected by the same hand. [b] corrections of the 'on second thought' type, or 'conjectural emendations', i.e. changes which are made to emend obviously deficient or corrupt passages, without another exemplar being consulted. Thus, e.g., when a manus corrigens emends a deficit by adding 'quam' after 'aliis', instead of the missing preposition 'ab'. Another specimen of such (attempted) emendations may be seen in the vicissitudes of the

47 However, the present editor no longer argues for the distinction of two families (as in the Introduction to De praedicabilibus, xxxiv), as the different interrelations between our copies prove to be too complicated for justifying the use of such a distinction. 48 See the Introduction to my edition of De praedicabilibus, pp. xxxii-xxxiv. 49 For De praedicabilibus see ibid., pp. xxxff.; for the present tract see our previous section, II.5.5.

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corrupt passage of the opening chapter of the tract De praedicabilibus, we have discussed in our Introduction to the edition. 50 [c] corrections of the 'on second opinion' type, i.e. those made after consulting another manuscript. Only the last type is of concern to us, now. In my view, only the manus corrigens of K, which is relatively rather active, although significantly less than in De praedicabilibus, should come into consideration on this score. However, I have found no correction made by Kc that should, or could, be ascribed to its consulting any of our other copies. 11.6 Stemma codicum

Because of the foregoing observations the following stemma codicum may now tentatively be established:

T

E

v KGB

II. 7 Editorial principles. The need for making conjectures

The present edition assumes the correctness of the stemma presented in the previous section. In accordance with the main principle adopted by the members of the Buridan society, the present editor's aim is to give the text of E, which is still taken as our main source. 51 This preference is also supported by the fact that E shares correct readings with alternatively either T, or V, or K (each time against all the others, that 50 See our introduction to the edition of that tract, p. xxxiv. 51 See, however, the qualification made in our note 46 above.

lii

Introduction

is),52 which indeed underlines its basic position. Our preference for E understandably determines our selecting and evaluating the alternative readings occurring in the various Mss. Thus E's readings will be set aside only if they obviously do not make sense, or suffer from minor errors, such as apparent omissions or interpolations. In such cases, the editor being left with the other copies, his first attention will be given to T, since this copy often proves to be remarkably free from errors and mistaken readings that are only due to a scribe's ignorance or negligence, which surely cannot be said of K (let alone GB). However, in several cases in which both E and T are likely to give incorrect or less probable readings, the remaining copies may provide good ones, Vin particular, which anyway reveals its value by sharing many good readings with T (and E). Our codices raro adhibiti G and B are only recorded in the critical apparatus if they present useful readings or seem to augment the reader's insight in rather complicated textual situations. Generally speaking, then, E's reading is accepted unless a) it raises unsurmountable problems regarding sense or consistency, orb) other Mss. reasonably conspire against E in a matter not entirely devoid of interest. More than once, when all readings occurring in our Mss. must be held, or are likely, to be mistaken, the present editor had to resort to conjectural emendation of the text. Thus, for example, the editor felt compelled to intervene in among others the following cases. At 8.1.7 (right before the first dubium): 'dicendo' coni.; 'divisio' E om. TVKGB. At 8.2.4 (fourth clause): 'bene' coni.; all Mss. read the unsuitable 'non'; ibid. (fifth clause): text emended after Aristotle, whereas our Mss. present various unfitting readings; ibid. (first dubium): two lines apparently being a gloss that has crept into the text and is found in all our copies should be cancelled; ibid. (end of the reply to the first dubium): 'simum est turpe' coni.; 'nasus simum [simus K ] est turpis vel turpe' ETVK. At 8.2.5 (first clause): 'subsequuntur' coni.; 'subsequenter' TVKGB; 'consequenter' E. At 8.3.2 (second clause): all Mss. read 'rationem' instead of 'orationem'. 'complexo indistante' coni., ETVKG having various other readings. At 8.3.3 (first clause): 'applicati' coni.; 'applicatio' ETK; 'ampliatio' V. At 8.3.5 (end first clause): 'generatur' coni.; 'dicitur' ETVKGB; ibid. (third clause): 'quod quomodo' coni., where the Mss. have various unfitting readings. At 8.3.6 (third clause), text emended

52 See especially the end of our previous section II.5.1. !iii

John Buridan, Summulae, De Demonstrationibus

after Aristotle. At 8.4.2 (first clause): 'assignari' coni.; 'significare' ETVKGB; ibid. (second clause): 'ideo' coni.; 'immo' ETVKGB. In the lemma f 8.4.3, the first part of the first clause is found in all our Mss. on the wrong place. At 8.4.4 (first clause): 'consequenter' coni.; 'communiter' V om. ETK. At 8.5.2 (second clause): 'quasi' coni.; 'quia' EVTGKB; ibid. (ad fin.): 'legentium' coni., where the common reading 'loquentium' (ETVKG) is unfitting and should be emended either into 'legentium' ('people lecturing') or (less probably) 'loquacium' ('loquacious people'). At 8.6.2 (second clause): 'quae' coni.; 'quia' ETVK. At 8.7.1 (ad fin.): 'dicendum' coni.; 'dictum' ETVK. At 8.8.3: 'obiacens et' coni.; 'opilans(!) et' E om. TVK. At 8.8.6 (ad fin.): 'septimo' coni.; 'secundo' ETVK. At 8.9.3: 'nisi sic ut' coni.; 'nisi sicut' VK; 'et satis' ET. At 8.10.2 (first clause): 'hie [sc. locus] est manifestus' coni.; 'haec est manifesta' E; 'hoc est manifestum' TVK. At 8.10.4: 'physicorum' coni.; 'posteriorum' ETVKGB. At 8.11.3 (first dubium): 'ipso' coni.; 'quo' ETVKG; ibid. (third clause): 'esse' coni.; 'etiam' ETVK; ibid. (sixth clause): 'perfecte' coni.; 'per causas' ETVKGB. In the lemma of 8.11.7, all Mss. wrongly read 'priores' instead of 'potiores'. At 8.12.3 (fourth clause): 'aliquod aliud praedicatum' coni.; various other readings in ETVKGB. At 8.12.4 (fifth clause): 'et definitionibus' coni.; 'et demonstrationibus' EVKGB; definitionibus et demonstrationibus T. At 8.12.5 (fourth clause): 'potest fieri propter' coni.; 'propter' EVKGB; 'potest' T. Frequently, two different readings should be combined, such as at 8.2.4 (right before the answer to the first dubium): 'tune tu' coni.; 'tune' EVK; 'tu' T. Likewise at 8.4.2 (sixth clause): 'aliquas alias' coni.; 'aliquas' T; 'alias' EVK, and 8.5.2 (first clause): 'prima principia' coni.; 'prima' EK; 'principia' TV. 11.8 The critical apparatus The apparatus given in the present edition is intended to provide the reader with plausible alternatives to our text in matters of consequence, and to enable him or her to reconstruct the text, not only as it is read by our basic manuscript, but also as it occurs in the four other manuscripts used for the edition. Of course, insignificant variants, such as 'ergo'/'igitur', 'vel'/'aut' (when interchangeable), 'iste'/'ille', and so on, as well as insignificant changes in word-order will not be taken into consideration. The apparatus is positive: for every reading reported, the manuscripts that have it are listed. A simple entry has this form: 'x TV y E: z K, i.e. manuscripts TV read

!iv

Introduction

'x', E reads 'y' and K reads 'z'. The first reading is always a lemma, i.e. identical with the reading adopted in the text. Each entry is complete in the sense that it informs about the readings of all five manuscripts at the place concerned. Minor variants between a group of manuscripts which agree in the main are sometimes indicated in parenthetical additions with [ ... ], as e.g. 'et sic patet [apparet K] prima pars add. VKG'. The apparatus registers: (1) All cases in which our text deviates from that of E. (2) All cases in which two or more manuscripts carry a different reading from the one adopted. (3) Miscellaneous readings which seem interesting as regards contents or history of the text. Exceptions to (1) and (2) occur: (la) When the rejected reading of Eis an obvious and insignificant slip like an omission to put a line over 'ro' to make it spell 'ratio'. Also, ante correcturam errors (our 'on second inspection' errors; see above, our section 11.7) corrected by the scribe himself are not adopted. (2a) When the variation between the manuscripts concerns matters generally considered of no consequence (such as choice between 'ergo' and 'igitur'; headings, which are not part of the text to be commented on by Buridan; 'sequitur', 'textus', and 'glosa' to announce the authoritative text and Buridan's commentaries, respectively; 'etcetera' when it is apparently used to indicate the wind-up of a section; or between equivalent word-orders), and the text has been established according to the principles described in our section II. 7, above. For the abbreviations used in the apparatus, see our list of the sigla, below, p. 5.

II.9 Orthography. Punctuation In matters of orthography and punctuation we have not followed the manuscripts. The punctuation is our own, and is not based on the manuscripts, which, like all medieval manuscripts, are rather careless in this matter.53 The orthography is classicizing and differs very little from the one used e.g. by the Oxford Latin Dictionary (edited by

53 It should be noted that the colon(:) is also used in the sense of 'therefore, what follows is the case', in order to clarify the syntax of a protasis. E.g. in 8.10.6, 2: 'Sed quia ( ... ) necessario:' = 'Because .. ., therefore: .. .'. Iv

John Buridan, Summulae, De Demonstrationibus

P.G.W. Glare).54 Some of the most salient discrepancies between medieval practice and ours are: We always write 'ae' when classical norm requires it; Buridan always wrote 'e' in such cases. This forces us to decide between adjectival and adverbial interpretation of such ambiguous medieval forms as 'maxime'. The distribution of 'ci' and 'ti' in front of a vowel is regulated according to classical norm, meaning e.g. that we always write 'dictio' whereas medieval practice allows both 'dictio' and 'diccio'; similarly we always write 'condicio' when dealing with the noun derived from 'condico', whereas medieval practice allows both 'condicio' and 'conditio' in this case (as well in the case of the derivative of 'condo', which we would write 'conditio'). Some Greek words appear in forms which were rarely or never used in the Middle Ages. Thus we write 'Aristoteles', 'dia!ectica', 'Coriscus', not 'Aristotiles', 'dialetica', 'Coruscus'. We invariably say 'Socrates' though the Mss. tend to use the short forms 'Sortes' or 'Sor'. As for the medieval word 'quiditas' /'quidditas' we have chosen the spelling with one 'd' since it is, in our experience, the commonest one in medieval manuscripts, and moreover it is etymologically the sounder: quid-itas is modelled on qual(e)-itas and quant(um)-itas. Manuscript abbreviations have been solved, except for those still in use, such as 'etc.' ('and so on'), either in the sense of 'et sic de aliis', or when it refers to the remaining words of a text or formula well known to the medieval reader or hearer, e.g. in 'genus est praedicabile de pluribus etc.', where Porphyry's well-known definition of genus is meant 'genus est praedicabile de pluribus differentibus specie in eo quod quid' .55 Autonymous use of words or phrases is only marked by inverted commas if it is explicitly indicated in the context, e.g. hoc nomen 'homo'. II.JO Headings

Most manuscripts contain clues or marginal headings for indicating new chapters, but not for paragraphing. As a rule, the headings and numbers indicating chapters, parts

54 The present editor has, rather reluctantly, acquiesced to the general editorial arrangement to present not only the text but also the apparatus in classicised form. 55 This use of 'etc.' in the manuscripts should be well distinguished from its use to merely indicate the end of a major part of a tract, where, in fact, it serves as a (very!) full stop. This use is ignored, i.e. not printed in the text nor recorded in the apparatus.

!vi

Introduction

of them, or so-called 'clausulae' are editorial additions, but, at times, they are based on indications found in (some of) our copies. Some of our manuscripts (Tin particular) introduce Buridan's comments on the preceding lemma with the word 'glosa', either in the text or in the margin. I have omitted such indications. The headings are not registered in the apparatus criticus.

II.11 Apparatus of quotations Our apparatus of quotations identifies explicit quotations made by Buridan, and no more. Thus we do not identify tacit quotations or echoes of the logical canon (Aristotle, Porphyry, Boethius or Peter of Spain).

!vii

John Buridan, Summulae, De Demonstrationibus

BIBLIOGRAPHY56 Il.12 Bibliography II.I2.I Primmy literature II.I2.I. I John Buridan Johannes Buridanus: in M.E. Reina, 'Giovanni Buridano: Tractatus de suppositionibus', in Rivista critica di storia dellafilosofia 12 (1957), pp. 175-208 and 323-352. Johannes Buridanus, Summulae III: In Praedicamenta. Introduction, Critical Edition and Appendices by E.P. Bos. Nijmegen 1994 (Artistarium 10-3). Johannes Buridanus, Questiones Elencorum, ed. by R. van der Lecq and H.A.G. Braakhuis. Nijmegen 1994 (Artistarium 9). Johannes Buridanus, Summulae II: De praedicabilibus. Introduction, critical edition and indexes by L.M. de Rijk. Nijmegen 1995 (Artistarium 10-2). Johannes Buridanus, Summulae IV: De suppositionibus. Introduction, Critical Edition and Indexes by R. van der Lecq. Nijmegen 1998 (Artistarium 10-4). Johannis Buridani Tractatus de consequentiis, ed. H. Hubien. Edition critique. Louvain (Publications universitaires)/Paris (Vander-Oyez, S.A.) 1976. ll.12.I.2 Other primary literature Giraldus Odonis O.F.M., Opera philosophica. Vol. I : Logica. Critical Edition From The Manuscripts edited by L.M. de Rijk. Band LX. Leiden /New York/London (Brill) 1997 (Studien und Texte zur Geistesgeschichte des Mittelalters 60, hrsg. von Dr. Jan Aertsen) Nicholas of Autrecourt, His Correspondence with Master Giles and Bernard of Arezza. A Critical Edition from the Two Parisian Manuscripts with an Introduction, English Translation, Explanatory Notes and Indexes, by L.M. de Rijk. Leiden/New York/London (Brill) 1994 (Studien und Texte zur Geistesgeschichte des Mittelalters 42, hrsg. von Dr. Jan Aertsen). Peter of Spain, Tractatus, called afterwards Summule logicales. First Critical Edition from the Manuscripts with an Introduction by L.M. de Rijk. Assen (Van Gorcum) 1972. 56 An extensive bibliography of primary and secondary literature concerning Buridan's work is found in the edition of De suppositionibus (ed. R. van der Lecq) in Artistarium 10-4, pp. xxxv-xxxviii. !viii

Introduction

ll.12.2. Secondary literature Braak.huis, H.A.G., 'Logica Modemorum as a Discipline at the Faculty of Arts of Paris in the Thirteenth Century', in Olga Weijers et Louis Holtz, L'enseignement des disciplines a la Faculte des arts (Paris et Oxford, Xllle-xve siecles). Studia Artistarum. Etudes sur la Faculte des arts dans !es universites medievales, 4. Turnhout (Brepols) 1997, 129-145. Ebbesen, S., 'The Summulae, Tractatus VII: De fallaciis', in J. Pinborg (ed.), The Logic of John Buridan. ( ... ),pp. 139-160. Ebbesen, S., 'Proof and its Limits According to Buridan, Summulae 8', in Z. Kaluza-P. Vignaux (eds.), Preuve et raisons a l'Universite de Paris. Logique, ontologie et theologie au XIVe siecle. Paris 1984, pp. 97-110. Kaluza, Z., 'Les sciences et leurs langages. Note sur le statut du 29 decembre 1340 et le pretendu statut perdu contre Ock.ham', in L. Bianchi (ed.), Filosofia e teologia nel Trecento. Studi in recordo di Eugenio Randi. Louvain-la-Neuve 1994, pp. 197-258 (FIDEM. Textes et Etudes du moyen age 1). Kaluza, Z., 'Nicolas d' Autrecourt. Un ami de la vente', in Histoire litteraire de la France. Tome XLII, fasc. 1, Paris 1995. Lesne, E., Les ecoles de la fin du Vllle siecle a la fin du Xlle (Histoire de la propriete ecclesiastique en France, tome V, Lille 1940. Maieru, A., 'Significatio et connotatio chez Buridan', in J. Pinborg (ed.), The Logic of John Buridan (... ),pp. 101-114. Michael, B., Johannes Buridan: Studien zu seinem Leben, seinen Werken und zur Rezeption seiner Theorien im Europa des spiiten Mittelalters. Berlin 1985. Michalski, K., 'Les courants philosophiques a Oxford et a Paris pendant le XIVe siecle', in Bulletin international de l'Academie des sciences de Cracovie, 1920. d'Ors, Angel, 'Petrus Hispanus O.P., Auctor Summularum', in Vivarium 35 (1997), pp. 21-71. Pinborg, J. (ed.), The Logic of John Buridan. Acts of the Third European Symposium of Medieval Logic and Semantics, Copenhagen 1976. Pinborg, J., 'The Summulae, Tractatus I, De introductionibus', in J. Pinborg (ed.), The Logic of John Buridan. ( ... ) 1976, pp. 71-90. Reina, M.E., ll Problema def Linguaggio in Buridano. Vicenza 1959 (also in Rivista critica di storia delta Filosofia 15 (1960), pp. 251-264) Rijk, L.M. de, 'Ockham as the Commentator of His Aristotle: his Treatment of Posterior Analytics', in Aristotelica et Lulliana magistro doctissimo Charles H. Lohr

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septuagesimum annum feliciter agenti dedicata, ed. F. Dominguez, R. Imbach, T. Pinde et P. Walter, Steenbrugge/The Hagua. 1995, pp. 78-102. Rijk, L.M. de, Aristotle. Semantics and Ontology (forthcoming). Walsh, J. J., 'Some Relationships between Gerald Odo's and John Buridan's Commentaries on Aristotle's 'Ethics'' in Franciscan Studies 35 (1975), pp. 237-275. Zupko, J., 'How it played in the RUE DE FOUARRE. The Reception of Adam Wodeham's Theory of the COMPLEXE SIGNIFICABILE in the Arts Faculty in Paris in the Mid-Fourteenth Century', in Franciscan Studies 54 (1994-7), pp. 211225.

Ix

III. TEXT AND APPARATUS

III. I Index capitulorum et partium IOHANNIS BURIDANI SUMMULARUM TRACT ATUS OCTAVUS DE DEMONSTRATIONIBUS PRIMA MATERIA: DE DIVISIONIBUS 8.1 Prooemium 8.1. l De arte dividendi 8.1.2 De divisione et compositione in communi 8.1.3 Quomodo partes dicantur dividi 8.1.4 De duplici toto et parte 8.1.5 De diversis divisionibus totorum 8.1.6 De totis praedieabilibus et eorum partibus 8.1.7 De divisione perfecta et imperfecta 8.1.8 De divisionibus minus proprie dictis

13 16 22

SECUNDA MATERIA: DE DEFINITIONIBUS 8.2 Introductio 8.2.1 De octo proprietatibus definiti et definitionis 8.2.2 De quattuor modis definitionis 8.2.3 De definitione dicente quid nominis 8.2.4 De definitione quiditativa 8.2.5 De definitione causali 8.2.6 De descriptione 8.2.7 De definitionibus complexis

26 26 27 30 30 34 52 55 60

TERTIA MATERIA: DE DEMONSTRATIONIBUS 8.3 lntroductio 8.3.1 De tota hac materia in generali 8.3.2 De quattuor quaestionibus scibilibus 8.3.3 De quaestionibus medii 8.3.4 De illis ex quibus demonstratio integratur

61 61 62 63 68 71

3

7 7 8 8 9 10 11

Index capitulorum et partium

8.3.5 Quid aut quae oportet de illis praecognoscere 8.3.6 Ex cuius illorum unitate scientia dicatur una 8.3.7 An praemissae sciantur prius tempore quam conclusio

73 80 87

8.4 De comparatione demonstrationis ad argumentationem dialecticam et scientiae ad opinionem 8.4.1 De convenientiis inter demonstrationem et argumentationem dialecticam 8.4.2 De differentiis inter eas 8.4.3 De convenientiis inter scientiam et opinionem 8.4.4 De differentiis inter eas

96 97 106 110

8.5 De principiis demonstrationum primis et indemonstrabilibus 8.5.1 Quod sint aliqua talia principia 8.5.2 De numero seu multitudine eorum 8.5.3 De necessitate et evidentia aliqorum principiorum 8.5.4 Quomodo ilia cognoscantur

116 116 117 123 125

8.6 De dici de omni, de per se et de universali sive secundum quod ipsum 8.6.1 De dici de omni 8.6.2 De tribus modis perseitatis 8.6.3 De primo modo perseitatis 8.6.4 De universali sive secundum quod ipsum

131 132 133 137 145

8.7 De diversis distinctionibus demonstrationis 8.7.1 De demonstratione communiter dicta 8.7.2 De demonstratione categorica et hypothetica 8.7.3 De demonstratione ostensiva et ad impossibile 8.7.4 De demonstratione affirmativa et negativa 8.7.5 De divisione demonstrationis secundum quantitatem 8.7.6 De demonstratione universali et particulari 8.7.7 De demonstratione necessaria et contingenti 8.7.8 De quibusdam aliis divisionibus 8.7.9 De demonstratione mansiva et doctrinali 8.7.10 De distinctione demonstrationis 'propter quid' et 'quia'

148 149 150 151 152 152 156 156 159 159 163

8.8 De demonstratione 'propter quid' 8 .8.1 Quomodo et quae et cuiusmodi debeat esse causa in tali demonstratione 8.8.2 An definitio ipsius scire sit bona definitio scire propter quid 8.8.3 De quibusdam corollariis 8.8.4 De alia definitione demonstrationis 'propter quid'

165 165 171 172 174

4

95

Index capitulorum et partium

8.8.5 An per omne genus causae contingat demonstrare causatum 'propter quid' 8.8.6 De demonstrationibus mathematicis

178

8.9 De demonstratione 'quia' 8.9.1 De diversis modis demonstrationis 'quia' 8.9.2 Quomodo ad eandem scientiam vel ad diversas pertinet de eodem scire 'propter quid' et 'quia' 8.9.3 De circulatione inter 'propter quid' et 'quia' 8.9.4 De circulatione inter plures demonstrationes 'propter quid' 8.9.5 De circulatione inter plures demonstrationes 'quia'

185 185

8 .10 De quibusdam aliis demonstrationibus 8.10.1 De divisione huius capituli 8.10.2 De demonstratione 'ad impossibile' 8.10.3 De demonstratione negativa 8.10.4 De propositione immediata et indemonstrabili 8.10.5 De demonstratione conclusionis contingentis 8.10.6 De demonstratione de praeterito vel de futuro

200 200 200 202 203 204 206

8.11 De comparationibus diversarum demonstrationum 8.11.1 De quattuor proprietatibus communibus 8.11.2 De proprietate demonstrationis proprie dictae 8.11.3 De comparatione demonstrationis 'propter quid' ad alias 8.11.4 De demonstrationibus potioribus 8.11.5 De potestate demonstrationis universalis et particularis 8.11.6 De potestate demonstrationis affirmativae et negativae 8.11.7 De potestate demonstrationis ostensivae et 'ad impossibile'

208 208 21 O 211 219 220 225 226

8.12 Quomodo quaestiones scibiles terminari debeant 8 .12.1 Quod omnis quaestio quaerit praedicatum de subiecto 8.12.2 De diversis speciebus quaestionis scibilis 8.12.3 De quaestione 'quid est' 8.12.4 De terminatione quaestionis 'quid est' 8.12.5 De terminatione quaestionis 'prater quid est' 8.12.6 De quaestione 'quia est' et 'si est'.

227 228 229 230 233 237 239

5

180

187 193 196 197

III.2 Sigla codicum

E = Citta del Vaticano, Biblioteca Apostolica Vaticana, Pal. lat. 994 T =Torino, Biblioteca Nazionale, cod. D III 27 (462) V =Wertheim, Evangelische Kirchenbibliothek (vel Historische Bibliothek in der Stiftskirche), cod. 157 K =Krakow, Biblioteka lnstytutu Teologicznego Ksiezy Misjonarzy, cod. 171 (ohm 627, antea 827) Codices raro adhibiti G = Erfurt, Wissenschaftliche Allgemeinbibliothek, Amplon. 20 305 B =Wien, Oesterreichische Nationalbibliothek, lat. 5420 E c, Tc, V c... etc.= manus quae correxit E, T, V ... etc.

Em, Tm, V m... etc. = manus quae notas marginal es addidit in E, T, V... etc. Signa in apparatu critico adhibita ] = scripsi(t) (scripserunt)

= textus ab editore suppletus add. = addidit (addiderunt) coll.= collato (collatis) coni. = conieci (coniciendo) ex = correctum ex del. = delevit om. = omittit (omittunt) suppl. = supplevi

III. 3 Textus

TRACTATUSOCTAVUS: DE DEMONSTRATIONIBUS PRIMA MATERIA: DE DIVISIONIBUS

5

10

8.1 [PROOEMIUM] [E96va;T73ra; V96rb;K145ra] Nunc restat tractare de demonstrationibus. Et quia praesupponunt definitiones, ideo etiam tractandum est de definitionibus. Ad quas investigandas valet ars dividendi. ldeo etiam tractandum est de divisionibus. De qui bus tamen auctor noster non tractavit, quamvis de eis sit pars logicae magis notabilis et finalis.

gus tractatus in summo margine E INCIPIT TRACTATUS DE DEMONSTRATIONIBUS T EXPLICIT SEPTIMUS TRACTATUS INCIPIT OCTA VUS K INCIPIT TRACTATUS OCT AVUS SC!LICET ISTE G deest titulus in VB 6 nunc] EK om. TV 7 et quia] EKhaec autem TV llpraesupponunt] Vsupponunt ETK II etiam] ETV intercaeteraK 8 investigandas] EKinveniendas TV 9 tamen] E om. TVK IO quamvis] tamenadd. EVK llnobilis] TVnotabilis EKGB

7

Johannes Buridanus, Summulae

5

IO

I5

20

8.1.1 [DE ARTE Dl\'IDENDI] Secundum dicta a principio iste est octavus tractatus huius operis. Qui continet tres materias principales, scilicet primam de divisionibus, secundam de definitionibus et tertiam de demonstrationibus. Prima pars continet unum capitulum, quod est de divisionibus. Et habet octo partes. Prima proponit intentionem huius tractatus; in secunda describit divisionem et compositionem; in tertia ostendit quae dividuntur vel componuntur, et etiam quae dividunt vel componunt; quarta distinguit di versos modos [K145rb] totorum et partium; quinta distinguit diversos modos divisionum; sexta distinguit totum praedicabile; septima assignat omnes virtutes perfectae di visionis; et octava apponit praedictis quosdam alios modos divisionum metaphysice dictos. Secunda incipit ibi "Prout ergo", tertia ibi "Ab his", quarta ibi "Duobus quidem", quinta ibi "Totorum vero", sexta ibi "Multis autem", septima ibi "Divisionum autem", octava ibi "Adhuc quidam". Prima pars est manifesta de se. 8.1.2 [DE DIVISIONE ET COMPOSITIONE IN COMMUN!] Prout ergo magis comrnuniter describenda est divisio et sibi opposita compositio, divisio estmultorumin unumcollectorum separatio, compositio autem est multorum in unum collectio. Et vocatur illud unum 'totum' et illa multa vocantur 'partes' eius. Ista secunda pars describit comrnuniter divisionem et compositionem. Et sunt nomina in descriptionibus posita et nomina descriptorum satis multiplicia, prout in sequentibus apparebit. Et notatur in fine quod divisio est totius in partes et

ad I: GLOSA sic semper T 4 scilicet primam] ETVprima estK II secundam] ETVsecunda K II 5 tertiam] ETVtertiaK //pars] EVparticulaK materia T //primal TVKinprimasic saepius E huius] EVK om. T 7 et] ETV"K aut V 8 et etiam] TVK autE II distinguit] ETV dividit sic saepius K 9 totorum] ETV dictorum totorum K IO omnes virtutes] coni. omnes communitates EVK virtutes omnis T I l praedictis] modis add. ET II divisionum] ETV om. K I2-I4 secunda ... quidam] EVKpartes patebunt T I3 autem] ETV et diversis K IS de se] EK om. TV et sequitur textus sic saepius add. K I7 describenda] ETVdistincta K 18 multorum in unum] ETKplurium compositorum V II compositio] ETV collectio KGB I9 multorum] invicem add. TV 20 multa] ETV om. K 22 descriptionibus] ETV divisione K II descriptorum] ETV scriptorum K

8

De Demonstrationibus

compositio est partium in totum, tamquam in divisione fit processus ab uno, quod vocamus 'totum', velut a termino a quo, ad plura, quae vocamus partes, tamquam ad terminum ad quern; et in compositionc econvcrso.

8.1.3 5

[QUOMODO PAR TES DICANTUR DIVIDI] Ab his autcm nominibus 'compositio' et 'divisio' plura denominantur componi vel dividi, aut etiam componere vel dividere. [V96va] Partes cnim quandoque dicuntur componi quasi simul in unum totum poni, ct sic unaquaeque bene dicitur alteri componi; quandoque etiam dicimus totum

10

componi ex partibus. Et proportionaliter etiam dicimus partes ab invicem dividi, et totum etiam dividi in partes, sed etiam partes quandoque dicimus componere totum, et quandoque partes dividere totum. Haec tertia pars ostendit quae dicuntur componi vel di vi di, aut etiam componere vel

15

dividere; et est textus planus. Sed quamvis huiusmodi locutioncs admittantur, tamen non [E96vb] omnes sunt propriae. Magis enim proprie dictum est quod pars una alteri componitur, idest cum ea ponitur, vel quod partes componuntur, idest simul ponuntur. Et similiter proprie dictum est quod pars a parte dividitur, sivc separatur, vel quod partes ab invicem dividuntur. Cum autem dicimus totum componi ex partibus, hoc significat quod ex compositione partium resultat unum totum; et cum

20

dicirnus totum dividi in partes, hoc significat quod ex divisione partiurn resolvitur totum et cessat esse unum totum, si sit proprie dicta divisio; sicut lignum ante partium abinvicem separationem dicitur totum et unum, et post non dicitur unum

2prius vocamus] Tvocatur EVK II velut] VKscilicet ut T vel E alterum vocamus] ad quern terminum ad quemque vocamus add. K 2-3 partes ... ad quern] EIV om. K 3 econverso] sequitur aliquid add. K 6etdivisio] ETVCK om. V 7 componi vel] ETV om. K //autetiam] TVK om. E 8 quasi] ETKcum VI/in ... poni] ETV om. K 9unaquaeque] TutraqueEVK/lbene] I" om. ETVK II etiam] ETVetsic K etsaepiusadd. T 10 componi] et saepius add. EVK II ex] pluribus add. E 11 in] TKper EV II sed] TVK licet E 14 sed quamvis] TVK quamvis enim E //locutiones] E7Vtoti omnes K 15 una] perseadd. K 16idest] VK etEom. T 17 proprie] ETV om. K II siveseparatur] EVK om. T 18 quod] ETValiquot K 19 ex] Tin EVK 19-20 et cum ... totum] ETV om. K 20 dividi] ETKresolvi V II resolvitur] TV separatur EK

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neque totum. Sed etiam cum dicimus partes componere vel dividere [K145va] totum, non est proprie dicta locutio, immo dornificator est qui componit et ordinat partes domus et eas facit esse unam domum, et etiam homo sec ans vel securis dividit partes ligni abinvicem et facit eas non esse amplius unum totum lignum. Si ergo dicamus partes componere totum, sensus est quod ex compositione partium fit, vel diciturunum totum. Etsi dicamus partes dividere totum, sens us estquodex divisione partium ab invicem ipse cessant esse vel dici unum [T73rb] totum. 8.1.4 [DE DUPLICI TOTO ET PARTE] Duobus quidem modis principalioribus dicuntur 'totum' et 'partes': uno modo dicuntur totum integrale et partes integrales, alio modo totum praedicabile et partes eius subicibiles. Differunt autem, quia omnes partes totius integralis collective sunt unum totum, nulla tamen earum est illud totum; partes autem totius praedicabilis non sunt illud totum, sed de unaquaque illarum vere praedicatur illud totum. Duae enim unitates sunt binarius; sirniliter binarius et temarius non participantes sunt quinarius, et anima et corpus sunt animal. Sed licet nee plures species [V96vb] sint unum genus nee plura singularia sint una species, tamen de unaquaque specierum praedicatur suum genus, et de unoquoque singularium sua species.

In hac quarta parte distinguitur duplex totum, scilicet integrale et praedicabile; et ponitur inter ea manifesta differentia. Sed tamen notandum est quod aliquando totum integrale dicitur proprie unum aut informatione, ut animal, cuius partes sunt corpus et anima, aut continuatione, ut lignum, cuius partes quantitativae sunt ligna

2 immo] ETV ideo K II est qui] TK ille E qui est ille ecv II et ordinal] EVK aut dividit T 5 partium] E~VK om. T 6 dicitur] sic add. E II prius totum] TKunum totumEV 7 abinvicem] ETV om. K II ipse cessant] Tipsa cessantEV cessat K II esse vel dici] TVK esse unum totum vel dici E I 0 principalioribus] ET principalibus VK II partes] unde add. E 13 collective] TVK integraliter collectae EI ltotumnulla] TVKnullumE llearum]EVKeadem T 15 illarum]partiumadd. EVKllverepraedicatur] TVKverificatur E 17 sed licet] coni. licetEV sed TK 18 una] TVunum genus vel unaE om. K llunaquaque] EcTVK quacumque E 17 singularium] predicatur add. EVK 20 distinguitur] ETV definitur K 21 sed tarnen] ETV unde K 23 continuatione] ETV continuative K II quantitativae] ETV om. K II ligna invicem continua] ETV partiales partes ligni continuae K

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invicem continua. Aliquando autem totum integrale nee proprie nee simpliciter dicitur unum nee ens, sedcum additione, ut unus [E97ra] numerus, una domus, unus exercitus, unus populus. Et accipitur ibi unitas vel ex uno conceptu numerali quo plura simul numeraliter numeramus, ut homo, equus et capra simul sunt unus s ternarius, vel ex ordinatione plurium ad invicem et ad unum prim um propter aliquem unum finem, ut dux et multi alii ad ipsum et ad invicem ordinati propter devincere inimicos sunt unus exercitus, vel ex sol a congregatione et ordinatione, ut do mus, vel ex plurium corporum simul aggregatione, ut unus cumulus, vel ex unitate loci 10

communis, ut regni vel civitatis, ut populus; et sic de multis aliis, modis plurimis. Et quia omne totum ab unitate quadam dicitur et partes a quadam multitudine, idcirco terminum unum de multis aliis [Kl45vb] praedicabilem dicimus unum to tum praedicabile, et illos plures de qui bus praedicaturtotum praedicabile vocamus partes eius, et maxime si ille terminus unus significet multa confuse quae illi termini plures significant seorsum et distincte.

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8.1.5 [DE DIVERSIS DIVISIONIBUS TOTORUM] Totorum vero praedictorum diversas dicimus esse divisiones. Quandoque enim totius in suas partes fit divisio per solam animae considerationem, aliquando autem perrealemin ipsis totis vel partibus mutationem. Cum enim dividimus mundum in corpora caelestia et corpora terrestria, in corpora leYia et gravia, aut zodiacum in duodecim signa, nullam facimus in eis mutationem, sed sic haec dividimus secundum rationem, qui a quae prius intelligimus esse unum, consequenter intelligimus ea esse plura.

3 accipitur] Tattenditur EVK II conceptu numerali] ETK composito naturali V 4 numeraliter] E om. TVK II homo ... capra] TVKunus homo unus equus etunacapraE II simul] Tom. EVK 5 ordinatione] Kordine ETV II et ad] Tvel ad EVK II primum] ETprincipium VK 6 unum] EV om. TK II et ad] TV om. EK 7 sunt] ETVfit K II sola] TVK om. E II et. .. vel ex] ETV om. K 8 simul... ut] ETV om. K 9 communis] EK om. TV II ut] K videlicet ET aut V II multis] Vom. ETK II modis] TVK om. E 10 mutate] ETK unione VII quadam] K om. ETV 11 praedicabilem] TVK praedicabile E 11-12 unum ... praedicabile] Ttotum praedicabile VK illos E 12 illos] totos add. K II totum praedicabile] coni. praedicabile E om. TVA. II vocamus] T dicimus EVK 13 unus] TVK om. E II illi] ETK ibi V 18 partes] simul add. K 19 enim] TVK om. E 22 eis] K eius partibus EV illis partibus T 23 prius] Vprimo ET om. K II consequenter] TVK secundo E

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Haec quinta pars manifeste assignat di versos modos divisionis totius in suas partes. Et modus principalis est et proprie dictus qui fit per realem in partibus, vel etiam in aliqua earum, mutationem, secundum quam pars a parte removetur, ita ut partes quae antea [V97ra] dicebantur esse unum totum aliquo modo, non amplius dicantur sic esse illud totum. Et ille modus adhuc habet plures modos speciales. Quorum primus est continui per discontinuationem partium prius in invicem continuatarum, ipsis salvatis, ut si festucam rumpimus vel lignum in plures partes sec am us.

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Secundus modus est compositi ex materia et forma per separationem formae a materia. Et haec mutatio est corruptio compositi et formae, si forma sit materialis, vel est solum desinentia inhaerentiae formae ad materiam, sine eius corruptione, si forma sit immaterialis, ut in morte hominis. Tertius modus est divisio mixti in elementa. Et est mixtum totum non proprie integrale ad elementa, sed virtuale, quia habens virtutes quodammodo similes virtutibus elementorum. Vocatur autem haec divisio 'resolutio mixti in elementa', quae vocamus 'corpora simplicia'. Et fit haec divisio per substantialem mixti corruptionem et elementorum generationem ex eo. Quartus modus est totorum quorum nullum dicitur simpliciter aliquod unum, sed unum aggregatione vel collectione vel ordinatione vel huiusmodi, [T73va] per

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motus locales partium, secundum quos partes desinunt dici taliter unum, ut si de domo auferatur tectum a parietibus, et parietes a fundamento, et ligna et [E97rb] latera abinvicem, aut si ex cumulo lapides dispergantur, aut si ex exercitu unusquisque revertatur ad domum suam. [K146ra]

I di versos ... divisionis] T diversas divisiones EVK 2 partes] \el modos divisionis add. necnon de/. E II et... partibus] ETK om. V 3 aliqua] TVK aliquam E II ita ut] Ti ta quod V ita quod per E igitur quod nee K 4 antea ... arnplius] ETV prius fuerunt proprie dicuntur partes illius totius K 5 sic] Tom. EVK II illud) EVK unum T 6 discontinuationem] ETK continuationem V 8 secarnus ... formae] ETK om. V !Oethaec] ETVet forma haec K II et formae] Eformae Tom. VK 11-12 vel est... hominis] ETVvel (!) inmorte hominis vel asini K 11 desinentia] TV designatio E II si] ETK sicut V 12 sit immaterialis] ETK sicut materia V 14habens]ETVhabetK 15divisio]TKom.EV 16-17etfit... exeo]ETom. VK 18 nullum) ETVnomen K II simpliciter] EV om. TK II aliquod] ETK om. V 19 sed unum) TsedEV vel omni K 20 quos) coni. quas ETVK II desinunt... taliter] EV desinunt dici Tmeretur dici aliquod K 22 latera] TVK!apides E II aut... dispergantur] TV om. EK 23 suam] aut si lapides dispergantur add. K

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Alius autem modus divisionis totius in suas paites est minus proprie dictus. Quae fit per sol am animae considerationem, sicut si haec secundum unumconceptum numeral em dicimus esse sex, et secundum plures alios conceptus numerales dicimus aliqua eorum esse duo et alia esse quattuor, vel aliqua esse tria et alia etiam tria; sic enim dividimus senarium in binarium et quatemarium, vel in duos temarios. Et sic totalem zodiacum considerantes, secundum unum conceptum vocamus ipsum unum circulum, et deinde considerantes seorsum abinvicem duodecim partes aequales, vocamus unamquamque unum 'signum'; et hanc considerationem voco divisionem zodiaci in duodecim signa. Cui tamen considerationi et divisioni correspondent ex parte rei unitas zodiaci et diversitas partium integralium eius abinvicem. Simili autem modo possumus dicere de totis praedicabilibus. Nam plurima animalia uno conceptu concipientes, ea omnia vocamus 'animalia' et quodlibet eorum 'animal'. Duobus autem distinctis conceptibus eadem concipientes, quaedam eorum secundum unum conceptum vocamus 'homines' et alia secundum alium 'bruta'; [V97rb] Sic etiam sine exteriori mutatione dividimus animal in corpus et animam, vel mixtum in quattuor elementa, mundum in gravia et levia, et libros in tractatus, capitula et partes.

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8.1.6 [DE TOTIS PRAEDICABILIBUS ET EORUM PARTIBUS] Multis autem et diversis modis dicuntur tota praedicabilia et partes eorum. Ideo solent assignari multiplices divisiones ipsorum. Est enim unum totum praedicabile quod de suis partibus praedicatur aequivoce, et eius divisionem

2 quae] IVK qui E //haec] hoc IVK !!unum] om. EK 3 numeralem] ETVnaturalemK unumadd. necnondel. E II alios] EV om. TK II numerales] EIV om. K 4 eorum] EVK corpora T II alia] IVK aliqua esse E /Ivel aliqua] coni. et aliquaEV vel alia T sed alia ye aliquaK // etaliaetiam trial TK om. EV 5 senarium] 7VKtemarium sextemarium(!) E II sic] 7Vsicut K om. E 61 totalem] EVKtotaliter T !! ipsum unum] ETipsum K unum V 8 et] E7Vet ad K 8-10 voco ... integraliurn] EIV improprie vocamus divisionem K 8 divisionem] IV considerationern EK 10 abinvicem] et haec sunt exernpla in divisionibus totorurn integralium add. EV 11-12 plurima animalia] T plura animalia £C plura EVK 12 uno conceptu] ETK unum concepturn V 13 distinctis] IVK om. E !! eadem] Tea EVK II concipientes] IVK considerantes E 13-14 quaedam eorum] EIV om. K 15 brutal et haec est dh·isio animaliurn in hornines et bruta add. E et haec est divisio animalis in hornines et bruta add. K et haec est divisio [V97rb] in hornines et brnta add. V 15 sine ... mutatione] TK sine exteriori consideratione E ulteriori consideratione VII dividimus] EIV dicimus dividere consideratione K 16 Inixtum] ETK materiale rnixtum V //levia] et caelestia et terrestriaadd. E et ce!estia add. VK 17 libros] nostros add. EVK II tractatus] Tom. EVK I I partes] animatas add. V(!) 20 autem et diYersis] coni. multis et diversis ETK multis autem V 21 unurn] EVK om. T

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vocamus 'divisionem vocis in significationes'. (2) Et est aliud totum praedicabile de suis partibus univoce, quod est genus vel species; et sic est una divisio generis in suas species per differentias specificas, et alia divisio speciei in sua singularia. (3) Est autem aliud praedicabile de suis partibus denominative; et eius divisio potest vocari 'divisio totius in modo in suas partes', vel reducibilis in huiusmodi divisionem. Sunt autem termini de se invicem praedicabiles denominative, se habentes ad invicem vel sicut subiectum et passio, vel sicut plures passiones eiusdem subiecti, sive dicantur passiones per se si ve per accidens. Et sic Boethius, voe ans passiones 'accidentia', ponit divisionem triplicem [K146rb] totorum denominative de suis partibus praedicabilium, scilicet subiecti in accidentia, accidentis in subiecta, accidentis in accidentia. Ista sex ta pars habet tres clausulas. Quarum prima est de di visione termini aequi voci in suas significationes. Terminus autem aequivocus est terminus significativus vocalis aut scriptus, [E97va] et non terminus mentalis, prout alibi [3.1.2] dictum fuit. Et est terminus vocalis aequivocus cui secundum omnes suas significationes vel omni a significata non correspondet in mente unus conceptus, sed diversi, secundum diversas eius significationes. Et est eius divisio in alios terminos, vel orationes, quorum, vel quarum, unicuique correspondet unus conceptuum illi terrnino aequivoco correspondentium. Et non est aliud haec divisio quam distincta explicatio significationum termini aequivoci per terminos alios vel orationes illis significationibus diversis appropriatos vel appropriatas. Ut si dicamus hoc nomen 'canis' secundum unam eius significationem significare idem quod 'animal latrabile', et secundum aliam idem quod 'sidus caeleste', et secundum tertiam idem quod 'piscis marinus'.

10 De divisionibus, 877813-Cl (ed. Migne). 1 in] suas add. EV sua add. K II totum] TV om. EK 2 univoce] ETK in voce V 3 una] TKbona E om. VII suas] ET om. VK II per] ETV et K 4 est... aliud] Vet est aliud ET est autem alia(!) K 6 reducibilis] ETV reduplicabilis K I /termini] ETValii termini K 7-8 sicut... passio] ETsicut passio vel suum subiectumK sicut subiectum vel passio V 8-9 sive ... passiones] ETVvel K JO denominative] ETV om. K 11 praedicabilium] ETV om. K II subiecti inaccidentia] ETsubiecti K om. V 12 accidentis in] EVaccidentium in T accidentium et K II accidentia] sicut patet add. K 13 clausulas] partes E 14 terminus] TK om. EV 17 unus ... diversi] ETKsed diversis V 18 orationes] illis significationibus diversis add. Tsed del. ye 19 unicuique correspondet] TVKnon(!) E II unus conceptuum] Tunus conceptus EK unius conceptuum V 20 correspondentium] TVK correspondet E II aliud ... quam] Taliud haec quam E adhuc haec divisio nisi V aliud quam K II explicatio] TV exemplificatio EK 21 significationum] Ecr et significatio EVK II aequivoci] ETKunivoci V II illis] ETV vel K 23 unam ... significationem] Tunum eius conceptum EV eius unicam significationem K 24 aliam] eius significationem add. E II tertiam] T aliam EVK 1-2 et... cui] cum sibi T quod K 2 imposita] sibi imposita nisi K II significatio] sed add. K II secundum ...

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Terminorum autem aequivocorum alium vocamus pure aequivocum, et ille est cui non est imposita una significatio secundum aliam et aliam attributionem. Ali um vocamus 'analogum'; cuius est una prima significatio et alia, vel aliae, secundum attributionem ad illam; et tune in rationibus significationum posteriorum semper s includitur ratio primae significationis. 2. Secunda clausula est de divisione [T73vb] termini univoci. Et capio hie 'univocum' prout distinguitur contra 'aequivocum' et 'denominativum', de quibus alias dictum fuit. Sunt autem illi tennini genus et species. Et est uno modo divisio generis in differentias, ut 'animalis' in 'rationale' et 'irrationale' sic: 'animalium alia 10 rationalia, alia irrationalia', vel sic: 'omne animal aut est rationale aut irrationale'. Alio modo est divisio generis in suas species, ut sic: 'omne animal aut est homo aut brutum'. Dicimus au tern genus dividi perdifferentias in species, qui a priorsecundum rationem generis est di visio in differentias quam in species, eo quod differentiae sunt priores secundum rationem speciebus, cum ponantur in definitionibus quiditativis 1s specierum et ipsae, additae generi, constituunt definitiones specierum. Species autem immediate dividuntur in sua singularia, et non per differentias priores essentiales, quiaeiusdem speciei singularia non possunt abinvicem distingui nisi per

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accidentia et extranea, prout videri debet septimo Metaphysicae; et ob hoc etiam, una cum quibusdam aliis causis, dicimus singularia non esse definibilia. 3. Te1iia clausulaest de praedicabili denominative. [K146va] In qua fit mentio de to to in modo. Est autem to tum in modo, sicut alias dictum est, terminus communis respectu sui ipsius sumptus cum accidentali determinatione. Ideo divisio totius in modo in suas partes est ut si dicamus 'equorum alii sunt equi albi, alii equi nigri, alii equi mcdiis coloribus colorati'; vel si dicamus omnem numerum esse numerum parem vel numerum imparem. Quandoque autem in huiusmodi divisionibus terminorum denominative praedicabilium nos iungimus passionem subiecto sine deterrninatione et determinabili. 18 Conferas Buridani Quaestiones in Arist. Metaph. VII, q. !8.

attributionem] V secundum attributionem ad aliam ET sed secundum aliam et ad aliam attributionem K seu similitudinem add. V II alium] EcTVK aliud E 3 vel aliae] EVK om. T 6 est] TVK erit E II de divisione] TK divisio EV II capio] ETcapitur VK 8 et species] VK species etc. E species T 9 sic] TVK sicut E 10 prius auL irrationale] EVK om. T 11 ut] EV sicut T ut quia K 14 cum] ipsae differentiae add. V 15 ipsae] V cum E om. TK II constituunt... specierum] EV constituunt definitionem specierum T differenter constituunt speciem K 17 quia] ETK om. VII eiusdem] ETV eademK II possunt] Kpercipiuntur ET dicuntur V 19 definibilia] ETK definienda V 20 de praedicabili] ET de to to praedicabili V divisio praedicabilis K 22 sumptus] T sumpti EVK II accidentali] ETVactualiK 24alterumnumerurn] Vom. ETK 25numerum] Tom. EVKllhuiusmodi] ThisEVK 26praedicabilium] ETV praedicatorum K II nos iungimus] T non coniungimus EVK II subiecto] ETK substantiae V sed ponimus divisionem add. E sed add. V 27 et] ETV om. K I quos] TVK quas E 2 secundum alii] TVK vel E 2-3 teriium alii .. colorati] TVK etc. E 3 aut] ETV alii K

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Et sic proveniunt tres modi divisionum quos ponit Boethius, scilicet subiecti in passiones seu accidentia, ut 'equorum alii albi, alii nigri, alii mediis coloribus colorati', [E 97vb] vel 'numerorum alii pares, alii impares'; aut accidentis seu passionis in subiecta, ut 'mascu!orum alii homines, alii bruta', vel 'corporum levium alia corpora elementaria, aliaex eis mix ta'; aut accidentis in accidentia, seu passionis in passiones, ut 'gravium alia sicca, alia humida', vel 'humidorum alia calida, alia frigida'. Hae autem denominationes et praedicationes reducuntur ad totum in modo et partes eius. Accidentia enim sunt tarnquam partes in modo suorum subiectorum; est enim aliquid secundum se non quia album vel nigrum, sed non est album nisi quia est aliquid album, nee nigrum nisi quia est aliquid nigrum, prout dicitur septimo Metaphysicae; etetiam primo Posteriorum; reducitenim Aristoteles praedicationem subiecti de accidente vel accidentis de accidente [V97vb] ad praedicationem accidentis de subiecto, tamquam ad priorem et directam. 8.1.7 [DE DIVISIONE PERFECTA ET IMPERFECTA]] Di vision um autem quaedam dicuntur perfectae, aliae imperfectae. Perfecta dicitur quae observat duas proprietates, scilicet quod sit sufficiens et quod non sit superflua; imperfecta autem dicitur si deficiat sibi aliqua dictarum proprietatum. Est autem divisio totius integralis in partes eius sufficiens si illae partes sint ipsum totum, et est deficiens si non sint illud totum. Divisio autem totius praedicabilis est sufficiens in istas partes quae disiunctive praedicantur de ipso toto universaliter sumpto; et si non, non est sufficiens. D1visio au tern dicitur superflua si partes totius in quas fit di visio, participant in aliqua parte illius totius; et si non, non est superflua.

I2 Metaph. VII, I2; Anal. Post. JI 13, 97a23sqq. 4-5 in subiecta ... passionis] EVK om. T 4 corporum] TV corporum graviurn et E gravium et K 5 accidentis] TK accidentium EV II passionis] TK passionum EV 7 frigida] ETVhumida K aut passionis in subiecta ut brutorum alius equus alius asinus etc. add. T 10 aliquid] ETV ad K II non est album] TVKnon album E II quia] TVK prout E I I prout dicitur] Tut dicitur V prout haec dicuntur EK I2 enim] Tom. EVK 13 prius de accidente] TVK om. E 18 duas] conditiones seu add. V I9 si] TVK quae E II sibi] TVKinE 20 sufficiens] ETVsufficientes K 2I illae partes sint] E1V om. K II totum] ETV sunt unum K 22 istas] ET alias VK 24 totius] EV om. TK II fit] TVK est E 25 et... superflua] ET\!" K om. VII alterum non] ETV om. K II est superflua] TVK om. E

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Is ta septima pars manifestabiturper assignationem exemplorum. Sufficiens est ergo divisio huius propositionis 'homo est animal' in subiectum, praedicatum et copulam, quia haec sunt ilia propositio. Sed huius propositionis 'omnis homo est animal' non est sufficiens divisio [K146vb] in subiectum, praedicatum et copulam, quia in assignatione huius divisionis deficit illa pars 'omnis', sine qua illae partes non sunt ill a propositio. Ideo non est sufficiens divisio totius quantitativi in eius duas tertias, sed in tres non participantes. Ita est sufficiens divisio 'animalis' per 'rationale' et 'irrationale', qui a omne animal est rationale vel irrationale; sed non est sufficiens divisio 'animalis' per 'volatile' et 'gressibile', quia non omne animal est volatile vel gressibile. Deinde divisio 'animalis', quamvis non sit superflua per 'rationale' et 'irrationale', tamen esset superflua per 'rationale' et 'mortale', qui a 'mortale' coincidit [T74ra] in aliquibus suppositis cum 'rationali', et in aliquibus cum 'irrationali'. Ita esset divisio superflua gravium et levium in calida et frigida, et humida et sicca, quamvis non esset superflua in calida et frigida, vel in humida et sicca; coincidunt enim 'calidum' et 'frigidum' cum 'humido' et 'sicco'. Similiter de toto integrali dicendo, superflua esset divisio huius propositionis 'homo currit' in nomen et verbum et [E98ra] copulam, quia in verbo implicatur copula. Et esset superflua divisio senarii in tria et quattuor, quia quamvis tam temarius quam quatemarius sint partes senarii, tamen non sunt in senario temarius et quatemarius quin in aliqua unitate participent. Sed non esset superflua divisio senarii in duos temarios, vel in binarium etquatemarium, [V98ra] non participantes. Ita etiam esset superflua divisio lineae in eius medietatem tertiam et quartam, sed non in eius medietatem, sextam et tertiam non participantes. Sic ergo volunt dicere auctores quod bonae divisionis membra dividentia debent evacuare totum ambitum divisi, quantum ad sufficientiam, et non de bent coincidere, quantum ad superfluitatem.

5 sine qua] ETK sive VII illae] ETV aliter K 7 tertias] Ktemarias ETV 9-10 quia ... gressibile] ETK om. V 10 volatile vel gressibile] ETVtale K II sit] K esset ETV 11 prius et] etiarn add. TVK II esset] haec add. V 14-15 quamvis ... sicca] ETK om. V l 5 frigidum cum humido] ETV humidum cum frigido K 16 dicendo] coni. divisio E om. TVKGB 17 nomen et verbum] ETK subiectum et praedicatum V 20 quin] TV sic quin E quando K II unitate] ETV parvitate K 25 coincidere] ETcVK incidere T II superfluitatem] ErcV non superfluitatem TK

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DUBITATUR PRIMO Sed circahaec dicta estmagna dubitatio de divisionibus quorundam generum in suas species, quia omnino videtur quod membra coincidant. Verbi gratia, quantitas dividitur in quantitatem continuam et quantitatem discretam ?, quoniam omnis quantitas continua est numerus; est enim binarius, quia est suae duae medietates; et tamen omnis numerus dicitur quantitas discreta. Item, quomodo magnitudo dividitur in corpus, superficiem et lineam, cum omnis linea et superficies sit corpus? Et quomodo, secundo Ethicorum, dividitur honestum in delectabile et utile, cum omne simpliciter utile vel delectabile [K147ra] sit honestum, et etiam omne utile est delectabile, et econverso? Et sic de multis aliis divisionibus. Respondeo quod, quantum spectat ad propositum, quod ad hoc quod aliqui termini sint diversae species in quas aliquod genus immediate dividitur, non oportet propter hoc quod non supponant pro eisdem rebus, sed sufficit in multis quod sint diversae rationes aquibus illi termini sumuntur contentae sub ratione generali et non una sub alia. Unde quinto Metaphysicae dicitur quod ilia dicuntur unum specie quorum ratio est una; et diversa specie quorum rationes sunt diversae. Isti enim termini 'dulce' et 'album' sunt diversi specie, quamvis pro eodem supponant, ut pro lacte. In talibus igitur non debet poni divisio generis in species per talem modum: 'quantitatum aliae sunt continuae, aliae sunt discretae', vel 'magnitudinum alia linea, aliae superficies, alia corpus'; vel 'bonorum alia delectabilia, alia hones ta, alia utilia'. Sed per talem modum: 'ration um secundum quas aliqua dicunturquantitates, aliae sunt secundum quas dicunturcontinuae, aliae secundumquas dicunturdiscretae'; et 'rationum secundum quas aliqua dicuntur magnitudo, aliae sunt secundum quas

8 Ethica Nicom. II 3, I 104b30-3 l. 15 Metaph. V 6, IOl6a32-34. 2 circa] TK contra EV 3 species] vel differentias add. E" II omnino] EcTVK om. E II videtur quad] ETK om. V 4 quantitas dividitur] ETV quantitatis divisio K 5 est enim] TVK quia enim E 6 dicitur] TK est EV II quomodo] T quando K quantitas EV 7-8 et lineam ... corpus] ETK om. V 7 omnis] EVK om. T 8 quomodo] TV quando EK dividitur add. ET II d1viditur] K om. ETV II honestum in] Vbonum in bonum honestum ET bonum in honestum et K 9-10 cum ... est delectabile] EVK om. T 9 simpliciter] ETV om. K 9-10 etiam ... et] ETK om. V 10 divisionibus] TVKom. E 11 aliqui] ETK diversi V 13 propter hoc] Vpropter Tom. EK II non] EVK om. T II eisdem rebus] EVK rebus diversis T 15 una) ET alia V om. K 16 ratio] ETV res K II rationes ... diversae] EVK ratio est diversa sive rationes sun! diversae T 17 alterum pro] EVKin T 20 vel] magnitudines add. V II magnitudinum] ETV magnitude K 20-21 alia ... corpus] T aliae lineae aliae superficies corpora E aliae sun! lineae aliae sunt corpora aliae superficies V aliae sunt corpus aliae superficies aliae lineae K 22-23 quantitates ... sunt] ETK continuae V 24 aliqua dicuntur] ETV aliquid dicitur K 1624-17 1 magnitude ... dicuntur] EVK om. T

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dicuntur corpus, aliae secundum quas dicuntur linea, aliae secundum quas dicuntur superficies'; et 'rationum secundum quas aliqua dicuntur bona, aliae sunt secundum quas dicuntur honesta, aliae secundum quas dicuntur delectabilia, aliae secundum quas dicunturutilia'; et sic de aliis. Sunt enimin huiusmodi divisionibus separationes sine coincidentia, non rerum a rebus pro quibus termini supponunt, sed rationum a

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rationibus secundum [E98rb] quas nomina diversa pro eisdem rebus supponunt. Et si volumus aliqualiter digressionem facere, manifestum est quod non omne genus est ad quamlibet suarum specierum superius [V98rb] secundum praedicationem, terminis personaliter sumptis, immo omnis quantitas est numerus et omnis numerus est quantitas, et omnis magnitudo est corpus et omne corpus est magnitudo. Tamen verum est quod semper in terminis substantialibus et in terminis non-connotativis genus est superius ~ecundum praedicationem et pro pluribus supponit quam aliqua suarum specierum, et nullae species sive differentiaein tali bus terminis immediate dividentes aliquod genus coincidunt in supponendo pro aliquo eodem vel aliquibus eisdem. Nee enim omne animal est homo, nee omne animal est brutum, nee brutum est homo, vel equus, nee omnis color est albedo nee omnis color est nigredo aut rubedo; [K147rb] nee aliqua albedo est nigredo vel rubedo, nee econverso. Sed non in omnibus generibus et speciebus denominativis oportet sic esse, [T74rb] immo omnis linea et superficies sunt corpus, et omnis magnitudo est numerus. DUBIT ATUR SECUNDO Sed tune statim dubitatur quomodo et quare in talibus erit genus totum ad speciem magis quam econverso, et quomodo erit species pars subiectiva generis.

1 ter dicuntur] ETK om. V 3 alterum aliae ... utilia] ETK om. V 4 aliis] singulis add. E multis add. Vhuiusmodi add. K 5 rerum a rebus] EcTV rerum E a rebus K 5-6 rationum a rationibus] £CTV rationum E a rationibus K 6 eisdem] ETK diversis V 7 digressionem] disgressionem T disgregationem E distinctionem VK 8-9 secundum praedicationem] EVK om. T 9 sumptis] EVKpositis Tl/ inuno omnis] TKideo omnis Vomnis enim E 10-I I omne ... magnitudo] EVKetc. TI I tamen] TVK om. E II semper] ETK om. V II et in terrninis] ETK et V 13-I4 talibus terrninis] TK terrninis substantialibus EV I5-l6 est brutum] cum nee brutum est homo add. T quia nee homo est brutum add. V I6 nee ... equus] EVA om. T I6-17 est albedo ... rubedo] TVK est nigredo vel albedo E 18 non] ETK om. V 19 et. .. sunt] T est superficies et corpus EK est superficies V20 numerus] ETK corpus est numerus(') V 22 quare] ETK qualiter V II erit] TV omnis E om. K

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Respondeo quod licet non sit superioritas et subiectio quoad hoc quod est pro pluribus aut paucioribus supponere, tamen est superioritas et non-convertibilitas quantum ad intelligi sub tali vel tali ratione. Verbi gratia, hoc nomen 'quantitas', pro quibuscumque supponat, connotat divisibilitatem et mensurabilitatem. Dico "divisibilitatem" quia dicitur quinto Metaphysicae describendo 'quantum', "quod est divisibile in ea quae insunt etc.". Et dico "mensurabilitatem" quia dicitur ibidem "multitudo ergo quantum ad aliquid dicitur si fuerit numerabilis, magnitudo est mensurabilis". Ratio ergo generalis quantitatis est ratio plurium mensurabilium, ratio vero quantitatis continuae est ratio plurium mensurabilium quantum ipsa sunt 10 secundum extensionem, et ratio quantitatis discretae est ratio plurium mensurabilium quantum ipsa sunt secundum multitudinem. Est ergo sic superioritas et inconvertibilitas quia quaecumque intelliguntur esse plura commensurabilia quantum ipsa sunt secundum extensionem, illa intelliguntur esse plura mensurabilia, et non econverso; similiter quaecumque 1s intelliguntur esse plura mensurabilia quantum ipsa sunt secundum multitudinem, ipsa intelliguntur esse plura mensurabilia, et non econverso. Similiter est de magnitudine et de speciebus eius: magnitudo dicitur, ut est mensurabilis, quanta est extensive; et linea, ut est mensurabilis, quanta est extensive et est quanta secundum unam [E98va] diametrum, nihil considerando de ductione eius in alias diametros, 20 et superficies secundum ductionem unius diametri in aliam, nihil considerando de tertia diametro, et corpus secundum ductionem tertiae diametri in se. Et tune apparet manifeste superioritas et inconvertibilitas generis ad unamquamque illarum specierum. Nam omne [V98va] quod intelligo esse mensurabile quantum ipsum est extensive secundum unam diametrum et sine

5 Metaph. V 13, 1020a7-8. 6 Cfr. Metaph. V 15, 1020b26 sqq .. I et subiectio] Tsubiective E in subiecto VK II pro] ETK praedicari de V 3 intelligi] ETintellectum V intelligere K verbi gratia] EVK unde T 4 mensurabilitatem] TVK commensurabilitatem sic semper E II 4-5 dico divisibilitatem] EVK om. T 7 ad] E om. TVK II numerabilis] ETK materialis V 7-8 est mensurabilis] E si mensurabilis fuerit TV om. K 8 plurium] ETK om. VII mensurabilium] TVK commensurabilium sic semper E 9 plurium] ETK multorum V910quantum. .. extensionem] ETK om. V 11 multitudinem] et continuae quantum ipsasunt secundumextensionemadd.

v 12 inconvertibilitas] convertibilitas E 13 quantum] EVK om. T II secundum extensionem] Tom. EVK 14-16 similiter... econ verso] ETV om. K 15 quantum] TK quod E quot VII secundum multitudinem] TK om. EV 17 eius] si add. ETV II ut est] TVK om. E II mensurabilis] TVK commensurabilis ut est E II quanta est] Tom. EVK 18 et est] ET om. VK 19 nihil] TV non E om. K 20 superficies] EVK superficiem T II nihil] TK non E vel V2l ductionem] TVK deductionem E II diametri] EVK diametrorum T 22 manifeste] et quod add. E II inconvertibilitas) Tconvertibilitas EVK II ad JTVK est secundum E 23 intelligo] E intelligitur sic saepius TVK 24 ipsum] K om. ETV

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ductione in aliam, intellego esse mensurabile quantum ipsum est extensive, et non econverso; et simili modo de ratione superficiei et corporis. Hoc igitur Aristoteles intendebat quinto Metaphysicae dicens "magnitudines vero quae quidem ad unum continua, longitudo", idest linea, "quae vero ad duo, latitudo", idest superficies, "quae autem ad tria, profunditas", idest corpus; "horum autem pluralitas quidem finita, numerus". Et haec debent demonstrari secundo libro Physicorum. Nunc ergo ego revertor ad dicendum aliquas differentias inter di versos modos divisionum praeenumeratos. In hoc ergo differunt divisio generis in species et speciei in individua quoniam non potest dari sufficiens divisio speciei in individua propter infinitatem individuorum. Ideo descendentem a generalissimo ad specialissima per divisionem iubet Plato quiescere in specialissimis, ut C K differentes V 5 mentiuntur ]EcTVK intendunt E 7 quam per alias j ETV comparias( !) K

8 sed] tamen add. E quando add. K II ponentis] EK dicens Tom. V II quiditativa] dicentis add. V 9 substantiarum] TV om. EK IO transsumptum] TVK transpositum E I I septimo] coni. secundo ETVKG I2 alterum sunt] EcTVK om. E II elargita] EVelarga T illataK 14 qmcumque sint illi] EVK om. Tl! nisi] VK om. ETl/manifeste] enim add. E II termini] ETVtenninos KG II et terminus definitus] E haec definita Tet tenninos definiti KG om. V II significent] ETK om. V 15 differcnter] indifferenter] EcTV differt K II omnes] TVK om. E I6 vel per formas] T vel formales £C vel per formas vel formales V per formales K I 7 formal EcTVK om. E II solemus] ETVpossumus K I9 sic ultimate] EVK universaliter T II quia] K dicimus quod E cum 7V 20 nos] enim add. E 21 immo sic] ETVideo sicut K II mathematicis] ETKmechanicis VII multis] ETV om. K 22 vel eorum] ETV om. K23 termini] EVK illa T II differenter] TV indifferenter Ee dictas K om. E II aristoteles] enim add. T 24 per causas] EVK om. T

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8.9 [DE DEMONSTRATIONIBUS 'QlJIA'] [K174rb] (1) Determinantes autem de demonstrationibus 'quia' dicimus Aristotelem duos posuissemodos earum. Quorum unus est si sitdemonstratio causati per causam, sed non per primam et immediatam, idest non per praemissas ''secundum quodipsum'' et indemonstrabiles. Secundus modus est si sit demonstratio, non tamen causati per causam, sive sint praemissae ''secundum quod ipsum'' et indemonstrabiles sive non. Et posset secundum dicta prius addi tertius modus, scilicet si sit demonstratio causati percausam, idest per praemissas ''secundum quod ipsum'' et indemonstrabiles, et non sit scitum quoniam illius est causa. 8.9.1 [DE DIVERSIS MODIS DEMONSTRATIONIS 'QUIA'] (1) Sicut in praecedenti capitulo determinatum est de demonstratione 'propter quid', sic in isto septimo capitulo determinandum est de demonstratione 'quia'. (2)Etquia videturdicereAristotelesquoddemonstratio 'quia' et demonstratio 'propter quid' fiunt in eisdem terminis per modum circulationis, (3) videndumest de circulatione in demonstrationibus quomodo sit possibilis vel impossibilis. Habet autem hoc capitulum nonum quinque partes principales. Prima distinguit di versos mo dos demonstrationis 'qui a est'. Secunda ostendit [Vl26va] quomodo ad eandem scientiam vel ad diversas pertinet de eodem scire 'quia est' et 'propter quid

3 dicimus] V dicemus EK dicamus T 4 earum] Varn. ETK If quorum unus] E quorum primus TV unus eorum K II sit] £TV est K S primam] causam add. E II idest] ETKideo V 7 tamen] Vnon ET om. K II causam] ETVnon causam K 8 et indemonstrabiles] VK om. ET 9 addi] EVKponi T ff scilicet] ETV om. K 10 idest per] TVK om. E 10-11 et non ... causa] ETV om. K 11 sit scitum] EVK sicut T IS sic] enim add. T ff septimo] T no no VK om. E 15-16 de .. . quia] EVK om. T 17 fiunt] TV sint EK 18 circulationis] ETV circumlocutionis K ff de ... demonstrationibus] ETV om. K ff quomodo] hoc add. K 19 possibilis vel impossilis] ETV possibile vel impossibile K 20 nonum] septimum ET om. VK If principales] ETV om. K 21 demonstrationis] EK demonstrationum TV 22 et] £Kaut TV

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est'. Tertia ostendit quomodo consideranda est circulatio inter demonstrationem 'quiaest' et 'propterquidest'. Quartaostenditquomodositconsiderandainterplures demonstrationes 'propter quid'. Et quinta similiter ostendit quomodo sit possibilis inter plures demonstrationes 'quia est'. Secunda incipit ibi: "Aliquando autem"; tertia ibi: "Ex eisdem"; quarta ibi: "Et quia"; quinta ibi: "Adhuc autem". Prima pars habet tres clausulas secundum tres modos demonstrationum 'qui a'. Et prim us in primaclausula positus satis patetperexpositionem quae sibi subiungitur, et per determinata prius. Si tamen iste modus haberet conclusionem per modum propriae demonstrationis causalis, ibi demonstrareturquodammodo [El lSra] 'propter quid', quia concluderetur et sciretur ita esse et propter hoc ita esse. Tamen talis demonstratio non vocatur 'propter quid' secundum strictissimam acceptionem demonstrationis 'propter quid', ut prius dictum fuit. Ideo numeratur inter demonstrationes 'quia est'. Et iste modus dividi potest in tres. Unus est, si sit ex immediatis, idest ex indemonstrabilibus, sed deficiat primeitas et convertibilitas. Ali us est, si econ verso. Tertius est, si utroque modo. Ve! forte potest dici quod numquam sit demonstratio 'quia', si recedimus ademonstratione 'propterquid' propterdefectum immediationis, idest indemonstrabilitatis, sed alia ad demonstrationem 'propter quid' requisita salventur. Quoniam, si praemissa sit demonstrabilis, tune vel est praedemonstrata, et tune non obstat quin sit demonstratio 'propter quid', sicut dictum fuit prius, scilicet in quarta parte praecedentis capituli; vel ipsa non est praedemonstrata, et tune ipsa non est sci ta; ideo non facit scicntiam [Kl 75ra] conclusionis et, per consequens, sic nulla per earn fit demonstratio, si ve 'qui a' si ve 'propter quid'. Et hoc ego teneo. Secundus etiam modus est satis manifestus in secunda clausula. In qua etiam innuitur eius divisio, qui a possibile est quod ille modus sit ex praemissis ''secundum

1 consideranda] coni. concedenda ETVK 2 sit consideranda] Tsit concedenda EK scit concedenda VII inter] EVK in T 4 demonstrationes] V considerationes E7K 7 satis patet] est satis manifestus quia in prima clausula ponitur E II quae] ETV qui a K II sibi] £ibidem TK ibi V 9 propriae demonstrationis] TV propositionis VK II ibi , .. quodammodo] EVK secundum quod T JO quid] et add. E II concluderetur] VK etiam conclusio demonstraretur Tom. E II et propter. .. esse] TVK om. E 11 non] ETV om. K 12 demonstrationis] EVK quam nominamus T 14 tres] modes add. T II si sit] EVK sicut T II idest ex] ETV et K 15 sed] ET licet V et si fiat cum defectu vel K II primeitas] per se add. K II et] TVKidest E 16 utroque modo] Tutrumque deficiat EVK II forte] EVK om. T 17 recedimus] EK recedeat T recederet V 18 idest] £CV vel E et TK II sed alia] EVK si aliter T II requisita] EV om. TK 20 obstat] TK abest E obest VII quin] ETV quoniam K 23-24 et.. teneo] ETV om. K 25 qua] ponitur et add. E

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quod ipsum", idest convertibilibus, et possibile est quod ex non-convertibilibus. Sed etiam potest poni illius modi alia divisio, quia possibile est quod demonstratio sit a posteriori ex parte rerum significatarum, scilicet ab effectu ad causam, ut si per non scintillare demonstramus planetam esse prope. [T92va] Et possibile est quod non differant termini vel propositiones in ostendendo causam vel causatum, sicut dictum fuit prius esse in demonstrationibus mathematicis, ubi etiam dictum fuit quomodo et quare illae demonstrationes mathematicae soleant dici 'propter quid'. Deinde tertius modus [Vl26va] in tertiaclausula positus fuit satis manifestatus in toto capitulo praecedenti.

8.9.2 [QUOMODO AD EANDEM SCIENTIAM VEL AD DIVERSAS PERTINET DE EODEM SCIRE PROPTER QUID ET QUIA] ( 1) Aliquando au tern de eodem aliqua eadem sci en ti a demonstrat 'qui a est' vel 'propter quid est', scilicet si consideret differentiam et primaevitatem causarum ad causata ex parte rerum significatarum et quod non supponat principia suarum demonstration um ex alia scientia. (2) Aliquando autem de eodem pertinet ad unam scientiam scire 'quia' et ad aliam 'propterquid'. Et hoc contingit, cum una scientia in hoc est quodarnmodo alteri subaltemata. Tune enim saepe contingit quod subaltemata scit quia est et subaltemans demonstrat propter quid ita est.

20

Haec secunda pars ostendit quomodo ad eandem scientiam vel ad diversas spectat de eodem considerare qui a est et propter quid est. Et Aristoteles satis parum de hoc loquitur in primo Posteriorum. Dicit enim "Sed quia differt et propter quid scire,

23 Anal. Post. I 13, 78a22-23. 1 ex non] TV non ex EK duobus add. V 3 significatarum] vel praemissarum add. E II si] EVK om. T 4 non] ETV om. K II demonstramus] TVK demonstras E II planetam] sive planetas add. TV II propel ETproprie VK 5 differant] EVK demonstrant T II ostendendo] Tostendendo vel significando E significando VK 6 prius] itaadd. T llubi] TVK om. E 7 quarc] VK qualiter ET II demonstrationes] ETV divisiones K II mathematicae] EcTVK manifestae E 8 manifestatus] EK manifestus TV9 toto] EVK tertio T 13 aliquaeadem] coni eadem EVK aliqua Tl! scientia] scit vel add. T fit vel add. VII demonstrat] vel scit add. E fit add. K 14 differentiam] EVK scientiam T 15 supponat] EVK indigeat T 16 suarum] EVK illarum T II demonstrationum] vel supponat et tune non erit add. T 16-17 de eodem] ETK om. V 17 unam] EK eandem TV l 9 enim] EVK etiam T II scit] coni. sit ETV om. K 21 diversas] TVK diversam E 22 prius est] et ad aliam quia est et add. K 23 primo] TVK libro E II sed] EVK si T II differt] EVK om. T II quid] est add. TVK

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primum quidem in eadem scientia etc." Deinde post dicit "Alio vero modo differt ipsum 'propterquid' ab ipso 'quia' quodestperaliam scientiam utrumque speculari. Huiusmodi sunt autem quaecumque sic se habcnt quod alterum sub altero est etc.". Et addit "Fere autem univocae sunt harum quaedam scientiarum etc.". Sed tamen dicit postea quod multae scientiarum sunt - scilicet ad quarum unam spectat de eodem scire 'quia' et ad aliam 'propter quid' -quae non sibi invicem habent se sic, scilicet quod sint fere univocae sicut medicina ad geometriam, quia enim vulnera circulaiia tardius sananturmedici estscire 'quiaest', 'propterquid' autemgeometrae. Et haec verba Aristotelis non sunt omnino manifesta. Haec igitur pars habet duas c!ausulas. Prima est de scire qui a est et propter quid est in eadem scientia, et secunda in di versis. Quantum ad primum notandum est quod in [K175rb] scientiis naturalibus saepe effectus sunt nobis manifesti ad sensum quantum ad 'qui a est', et tamen non scimus sed multum dubitamus propter quid sunt, ignorantes causas earum. Verbi gratia, ad sensum videmus lunam eclipsari in oppositione eius ad solem, et nescimus propter quid ipsa eclipsatur. Considerantes igitur quod non po test in medietate lunae versa ad sol em deficere lumen nisi propter opacum medium [V127ra] interpositum, et quod non potest naturaliter intervenire opacum intermedium aliud quam terra, scimus hanc maiorem propositionem quod omnis defectus luminis a luna in eius medietate versa ad solem est propter terrae interpositionem; et subiungentes minorem, scilicet quod omnis eclipsis lunae est defectus etc., concludimus et scimus conclusionem propter quid, scilicet quod omnis eclipsis lunae est propter interpositionem etc. Igitur de eclipsi lunae scimus in sci en ti a naturali quiaestet etiam propterquidest, quia propterterrae interpositionem. Sed tamen hoc differenter scimus. Scimus enim quod eclipsis est tamquam principium indemonstrabile habens ortum suae evidentiae ex sensu, sed scimus

I Anal. Post. I 13, 78b34-37. 4 Anal. Post. 113, 78b39-79al. 5 Anal. Post. I 13, 79al3-17. l primum] propter add. E II quidem] T quid est EVK fl etc.] ET et etiam sic saepius K om. V 3 alterum] EVKunum T 4 addit] ETK adhuc VII fere] EV sunt T vere K fl quaedam] EVK quidem Tl/ sect tamen] ETV om. K 5-6 de eadem] EVK ad eandem T 7 fere] TVvere EK If sicut] TVK om. E 8 medici] EKmedicinac TV II scire quia est] ETKpropter scire V 9 et haec ... manifesta] EVK om. T 13 quantumadquia] EcTVK om. Ell ct] ETKsedquia V 14causas carum] EcTVK om. E //in] ETV om. K 16 in ... lunae] TV immediate luna EK II ad] £CTVK om. E If lumen] TVlumine K om. E 17 apacum ... interpasitum] TV abstaculum umbrosum intennedium EK 17-18 et quad ... intennedium] ETV om. K 17 ct quad] ETKin quadam V 18 aliud] coni. aliquod ET quad in V II propasitianem] TV om. VK 19 omnis] E1V tamen iste K If a luna] EVlunae TK 20 subiungentes] TV subiunget E subintelligentes K 21 etc.] ETV et etiam sic saepius K If cancludimus] EVK quare dicimus T 24 tamen] ETV om K If differenter] TV dubitanter EK

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quod est propter interpositionem teITae per demonstrationem 'propter quid' cuius praemissas non oportet resolvere in aliam scientiam. Sed etiam possibile est utrumque, scilicet quia est, et propter quid est scire de eodem in eadem scientia per demonstrationem. Ut quod Aristoteles in octavo Physicorum pro bare putavitl65 per 5 aetemitatem temporis quod primus motus est aetemus, et iterum quod ille primus motus est aetemus propter immutabilitatem Primi Motoris et aetemitatem primi mobilis. 2. Quantum ad secundam clausulam similiter manifestum est quod naturalis ex sensu scit iridem esse arcum seu portion em circuli, et ex perspectiva [EllSrb) scitur 10 propter quid ita est. Demonstrationes enim in tertio Meteorum ad hoc ostendendum sunt de perspectiva primo demonstrabiles. Similiter scimus demonstrative per astrologiam, ut apparet in tractatu De sphaera, quod terra est sphaerica, et sci mus per natural em sci en ti am etiam demonstrative propter quid ipsa est [T92vb) sphae1ica, scilicet quia propter omnes partes similiter graves tendere naturaliter ad medium 15 mundi, si fuerint extra, et naturaliter quiescere cum inibi fuerint. Sic enim probare intendit Aristoteles in secundo Caeli de aqua in mari quod sponte se habeat sub aere. Et sic exemplificat A1istoteles: medici ex experientia est scire 'quia' vulnera circularia tardius sanantur, geometrae vero est scire 'propter quid' hoc sit. Hoc enim 20

est quia ad sanationem vulneris opmtet latera coniungi et uniri, latera autem vulnerum circularium tardius reuniuntur propter hoc quod magis undique distant. Et hoc habet scire geometer secundum quod figurarum circularium latera maxime distant undique.

4 Physica VIII 1, 25la8-252a5. 10 Meteorologica III 2, 37lb26-372b!O. 12 Johannes de Sacro Bosco, De sphaera pp. 16 Cfr. De caelo II 4, 287a30-b 14. 17 Anal. Post. I 13, 79al5-17.

81-83.

1 propter interpositionem] ETVinterpositio K 2 praemissas] ETVpraemissae K II resolvere in] ETV om. K II etiam possibile] ETVimpossibile K 3 scientia] et add TVK 4 ut] ETV vel K II quod] TVK quia E 5-6 et iterum ... aetemus] ETV om. K 6 aetemus] P:TVK om. E II motoris] ETK mutatoris V 9 scit] idem add. T II arcum] EVK om. T et passiones add. T seu portionem add. VK II circuli] EVK eius Tet passiones eius add. V II scitur] ETV scientia K IO ita] ETV om. K 11 primo demonstrabiles] TV om. EK II demonstrative] coni. demonstrare K om. ETV 12 ut apparet] EVK om. T II et] quod add. E 13 scientiarn] ETV inclinationem K II etiarn demonstrative] Vet demonstrationes E etiam demonstrare K om. T 14 omnes ... graves] EK omnia simul gravia T omnes partes simpliciter gra\'es VII naturaliter] TVK necesse E 15 sic] ETK sicut V 16 caeli] et add. E et sic etiam add. VK II in mari] TVK et mari scilicet E II sub] EVK et de T 17 medici ex experiential Tmedicinae scientiae E ex apparentia medici V medici experientia K 18 geometrae] EVK geometrice T II vero] ETV non K II est] hoc add. K II sit] E est TK scit V 19 sanationem] coni. sanitatem E7VK II vulneris) EKvulnerum TV II prius lateral ETVlatere K II et uniri] TV om. EK 20 reuniuntur] EK sanantur T ruminantur(!) VII hoc] ETV om. K 21 secundum] ETK scilicet V II maxime] ETV om. K

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DlJBITATUR Sed [Vl27rb] circa hoc est dubitatio de hoc quod in illa secunda clausula addebatur, sci!icet quod hoc con tin git cum una scientia quodammodo alteri subaltematur. Hoc enim sumptum est ab Aristotele dicente "Huiusmodi autem sunt quaecumque sic se habent quod alterum sub altero est". Quomodo autem geometria et medicina de eodem considerant, una 'propter quid' et alia' qui a', cum neutra alteri subaltemetur? Similiter [Kl75va] est de perspectiva et naturali scientia. Hoc autem solvitur distinguendo de subaltematione. Potest enim dici una subaltematio simpliciter univoca et alia fere univoca et tertia remotior et minus proprie dicta. Univoca enim est prout species ponitur sub genere; et sic scientia de magnitudine secundum communem rationem magnitudinis se haberet ad scientias de lineis, de superficiebus et de omnibus corporibus secundum speciales rationes eorum; et hae scientiae iam dicuntur partes unius scientiae totalis quae dicitur geometria. Et sic etiam scientia de quantitate secundum eius communem rationcm subalternat sibi arithmetricam et geometriam, quae sunt de numero et magnitudine secundum rationes eorum speciales. Et istae tres scientiae iam dicuntur partes uni us scientiae totalis quae dicitur mathematica. Secunda subalternatio dicitur fere univoca, prout pars in modo per determinationem accidentalem ponitur sub toto in modo, ut magnitudo immobilis sub magnitudine. Quamvis enim omnis magnitudo sit mobilis, tamen posset aliquis imaginari magnitudinem immobilem, scilicet quodesset aliquamagnitudo immobilis, et omnino possum abstrahcre seu absolvere rationem magnitudinis a ratione mobilitatis. Sic etiam est magnitudo visualis sub magnitudine et numerus sonorus sub numero. Ideo sic geometria subalternat sibi astrologiam et perspectivam, et arithmetica music am. Et sic ultra perspectiva communis subaltemat sibi perspecti vam de iride vel de halo, et astrologia communis astrologiam mobilem.

4 Anal. Post. I 13, 78b36-37. 2 illa] EK om. TV //addebatur] EcTV habebatur EK3 hoc] ETV om. Kil cum] EcTVK om. El/una] communis add. V II alteri] ENCK alterius V 4 dicente] EVK dicens T II huiusrnodi] ETV cuiusmodi K 5 alterum] EVK unurn T II autem] EK ergo TV 6 cum] EcTV quia E et tarnen K II subaltemetur] VK subaltemaretur E subordinetur T 7 est] TK etiam EV 8 hoc ... solvitur EK om. TV II distingucndo] £CTVK om. Ell enirn dici] EVKresponderi quad T 9 sirnpliciter] dicituradd. Tllfere]ETVvcreK 11 scientias]TVKscientiarnE 12ornnibus]TVom. EK 13iam]ETVom. K//unius] EVKunivocae T II scientiae] EcTVK om. E 14 et sic] Vista ETK II rationern] EVK om. T 15 nurnero] ETKnurneris Vl6eorurn] TearumEVK II et istae] EC Vet essent illae TK om. E //iarn dicuntur] Vom. ETK 17 scientiae] V oni. ETK 19 ponitur] EVK positam est T II immobilis] £CV mobilis TK 20 aliquis] ETVK alius V21 irnaginari] TVK opinari E II rnagnitudinern ... scilicet] TV om. EK II esset] TVK estE 23 visualis] EVK sualis(!) T II sonorus] ETK senarius V24 sic] TVK om. E II prius et] Vom. ETK II alterum et] TV om. EK25 arithmetical Tarithmeticam EVK geornet(!) et add. K //ultra] TVetiarn vel in prirnomodo E in primo modo K II cornmunis] EVK om. T 26 astrologia] EVK astronornia T II communis] EVK habet T II rnobilem] £C naturalem rnobilern TV naturalem K om. E

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In hac autem subalternatione non reputo inconveniens quod eadem scientia diversis scientiis subaltemetur. Homo albus enim et est homo et est album; ideo scientia de homine albo subalternatur et scientiae de albo secundum se et scientiae de homine secundum se, et supponeret utrumque in suis processibus et 5 demonstrationibus. Sic ergo astrologia considerans de magnitudine mobili subalternatur [Vl27va] geometriae ratione magnitudinis, et naturali philosophiae ratione mobilitatis. Et ita de perspectiva de magnitudine visuali considerante. Et sic etiam musica considerans de numero sonoro vel de sono numerato subaltematur et arithmeticae ratione numeri et physicae ratione soni. lo Et ob hoc etiam multi dubitaverunt utrum dictae scientiae magis debeant dici mathematicae quam naturales, vel utrum magis naturales quam mathematicae. Et veritas mihi videtur quod nee debent dici simpliciter mathematicae nee simpliciter naturales, sed mediae per participationem extrinsecarum, quia in eis inveniuntur variae conclusiones, scilicet aliquae quarum principia habent suam evidentiam ex 1s principiis vel conclusionibus mathematicis, et aliae quarum principia habent suam evidentiam ex principiis vel conclusionibus naturalibus. Quantum ergo ad illas conclusiones dicuntur magis mathematicae, et quantum ad istas magis naturales. Secundum ergo quod in eis inveniuntur plures conclusiones per principia huius vel istius, dicuntur magis tales vel magis tales. 20

Tertia subaltematio potest assignari, [T93ra] quae non est secundum prima subiecta scientiarum totalium, sed secundum aliquas conclusiones partiales earum. Ideo [K17Svb] nullam illarum scientiarum totalium dicimus alteri subaltematam, sicut medicina non secundum se totam nee secundum eius magnam partem subaltematur geometriae, sed bene secundum aliquas eius conclusiones mixtas ex

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terminis medicinalibus et terminis mathematicalibus, sicut est ista conclusio quod

1 in ... quod] £CTVK om. E 2 album] EVK albus T 3 de homine] EfTVK om. E 5 astrologia] EVK astronomia T 6 geometriae] EVK magnitudini geometricae T II naturali] TV om. EK 7 mobilitatis] E motus TV mobilis K 8 sonoro] TV sonorum K om. E II vel ... numerato] EVvel de numerate sonorum K om. T 2 10 ob] ETV om. K 13 mediae] EcTVKmathematicae E II extrinsecarum] coni. coll. infra p. 191 extremorum EV exteriorum TK II quia] £7Vet K 14 suam] EVK unam T 15 principia] ETK conclusiones VII suam] TV om. EK 16 principiis vel] ETV om. K 17 conclusiones] mathematicas add. Em II magis] £CTVK om. E II istas] naturales add. Em dicuntur add. Tl/ magis] EcTVK om. E 18 per principia] T vel principia E et principiorum V huiusmodi principiorum K 20 quae] V quad ETK 21 secundum] ETV per K II partiales] TV particulares EK 22 ideo] secundum add. ETV II null am] TV naturam E neutram K II totalium] ETV notabilium K II dicimus] TVK dicitur E II subaltematam] VK subaltemata E subordinata(!) T 23 sicut] EVK quia T 24 conclusiones] EcTVK om. E II rnixtas] K commixtas E compositas TV 25 et ... mathematicalibus] EcTVK om. E 191

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vulnera circularia tardius sanantur quam oblonga. Et idea non esset inconveniens dicere quad tales conclusiones debent esse de una scientia media, non simpliciter de mathematica nee simpliciter de medicina. Sunt enim multae conclusiones et demonstrationes mediae inter mathematicam et medicinam [EllSva] et etiam inter mathematicam et naturalem aut moralem, sicut ponuntur aliquae conclusiones de iustitia commutativa et distributiva in quinto Ethicorum. Sed non facti sunt libri seorsum de illis mediis, propter paucitatem conclusionum aut non-principalitatem earnm. Sed adhuc mihi videtur quad non sit simpliciter verum quod geometriae sit scire 'propter quid' quad vulnera circularia tardius sanantur, quia ipsa nihil omnino considerat de is tis terminis 'vulnus' et 'sanari'; et etiam omnis scientia subalternans non sibi facit conclusiones contractas ad scientiam subalternatam, quia nihil habet considerare de terminis contrahentibus. Nee etiam neque medicus scit istam conclusionem 'propter quid', circumscripta geometria, neque alia scientia subalternata, circumscripta subaltemante, sciret aliquam conclusionem 'propter quid' cuius conclusionis aliqua praemissarum haberet evidentiam [V127vb] ex suis principiis vel ex conclusionibus scientiae subalternantis. Non enim sciret istam praemissam. Necesse est ergo in hoc casu scientem 'propter quid' conclusionem habere scientiam subaltemantem secundum quam sumat et sciat talem praemissam; et itcrum sci en ti am subalternatam secundum quam sumat et sciat ill a quae pertinent ad contractiones additas pertinentibus ad scientiam subalternatam.

1 quamoblonga] TVK om. E//ideo] TV om. EK 2dicere] TV om. EK!! debentesse] EdicerenturTessent VK 3 sunt] ETK sicut V !! multae] E mediae TVK 4 mediae] E om. TVK II alterum et] P:TVK aut E 5 naturalem aut moralem] E moralem aut naturalem TV naturalem K 6 iustitia] TVK iniustitia E II commutativa] ETK communitative(!) V !! quinto] TV secundo EK 7 seorsum] ETK om. V !! principalitatem] VK principia E paucitatem T IO quod] Tom. EVK !! sanantur] EVK curantur T II quia] K cum ET et V !! omnino) V om. ETK I I vulnus et sanari] EVK vulnus curatur T !! etiam omnis] ETK om. V !! scientia] sibi add. E 12 sibi facit] coni. sic ETK facit V !! conclusiones) vel propositiones communes add. TV vel propositiones add. K !! contractas] EV contractans K om. T !! ad ... subaltematam] £Tad scientiam naturalem K om. V !! quia nihil] EV quia vel K om. T 13 nee etiam] E sed etiam neque TVK !! scit] EVK sit T 14 conclusionem] EVK demonstrationem T 15 subaltemata] EVK subaltema T sibi add. E II aliquam] TVK om. E 16 cuius] ETVhuius K II aliqua praemissarum] V aliqua praemissa EVpraemissa T !! suis] ETV om. K 17 ex] TV ex suis E om. K !! non enim] EVK nisi T 18 praemissam] propter quid add. K 1820 necesse .. subaltematam] ETV om. K 18 scientem] V scire ETscientiae add. Ee If conclusionem] EV quam T 19 secundum ... praemissam] E virtute cuius sciatur talis praemissa TV 20 iterum] EV istarum T !! pertinent] EVK pertinet T 21 contractiones] EVK conclusiones T If pertinentibus] TVK partibus E

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Sed tu quaeres "quis ergo scit 'propter quid' quod vulnera circularia tardius sanantur?" Et ego dico quod medius artifex habens extrinsecas scientias. Seit enim per geometriam quod figurae circularis latera undique distant maxime, et scit per medicinam quod ad vulneris sanationem requiritur latera convenire, et media scientia hoc supponens complet residuum, hoc applicando ad ista. Sed protanto dicimus geometriam scire 'propter quid' quod vulnera etc., et omnino scientiam subalternantem scire 'propter quid' de conclusione subalternata, quia praemissa causalis in demonstratione illius conclusionis habet evidentiam suam in virtute principii vel conclusionis scientiae subalternantis. Haec igitur dicta sint de subalternatione scientiarum. 8.9.3 [DE CIRCULATIONE INTER 'PROPTER QUID' ET "QUIA'] (1) Ex eisdem terminis per modum circulationis fiunt duae demonstrationes, una 'quia', procedens a causato ad causam, alia 'propter quid', procedens econverso de causa ad causatum. Et exemplificat Aristoteles quod per planetas [Kl 76ra] non scintillare demonstramus quod sunt prope; et est demonstratio 'quia'. Et econ verso, pereasdemesse prope demons tram us eas non scintillare; et est demonstratio 'propter quid'. (2) Et hoc fit quia omnis demonstratio de bet procedere ex notioribus, et effectus sunt notiores causis quodamrnodo, quia nobis, et causae notiores effectibus quodamrnodo, quia simpliciter sive secundum naturam. Ista tertia pars agitde circulatione demonstration um inter 'quia' et 'propter quid'. Et talis circulatio fit saepe in naturalibus, ut quod ex aeternitate motus credidit

15 Anal. Post. 113, 78a30-32. 1 tuquaeres] EfTVK om. E II quod] Tom. EVK 2 sanantur] oblongis add. T II medius] et add. E fl extrinsecas] coni. ex'cas E extremas TVK 3 circul aris] ETV circulares K II distant maxime] ETV habent maxi me distantiam K 4 vulneris] £Kvulnerum TV!! sanationem] EVKsanitatem T //media] TVmedicinaK om. E 5 residuum] £TV medium K fl ista] TVK istam E II protanto) VK om. ET hoc add. K 6 geometriam] EVK geometriae T If quod vulnera etc.] T vulnera etc. EV om. K 7 subalternantem] TVK subaltematam E II scire ... quid] ETV om. K II subalternata] K subalternante ETV 7-8 quia ... suam] ETV scire K 8 causalis] EKtalis TV 9 principii] K primi principii ET sui principii sive primi V /Ivel] ETV et K passionisadd. necnon de!. V 10 subaltematione] ETVsubalternationibusK // scientiarum] clarissime add. V ad 14: nota bene add. vm 13 duae] suppl. om. ETVK 17 quia et] £CTVK om. E If econverso] EVK om. T II easdem] £7Veas K planetas add. ET II esse] EcTVK om.Enon add. E 18 omnis] EVK om. T 19 sunt] EcVKnon Tom. E 20 prius quodammodo ... quia] ETV om. K II causae] sunt add. E esse add. T 23 circulatio] EVK demonstratio T II quod] ETV om. K II credidit] TVK credit E

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Aristoteles demonstrare aetemitatem et immobilitatem Primi Motoris a posteriori et 'qui a est', et postea a priori ex aeternitateet immobilitate P1imi Motoris demonstrare

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aeternitatem motus 'propter quid'. Notandum est tamen quod ibi non est vera circulatio, qui a illa non est possibilis in demonstrationibus [V128ra] nisi idem sit respectu eiusdem magis et minus notum, quod est impossibile, nisi sic ut dicetur in quarta parte huius capituli. Verbi gratia arguamus 'quia est' sic: 'Si motus est aetemus, motor est aeternus et [T93rb] immobilis; sed motus est aeternus; ergo motor est aetemus et immobilis'. Deinde

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econ verso sic: 'Si motor est aetemus et immobilis, motus est aeternus; sed motor est aeternus et immobilis; ergo motus est aeternus'. Si ergo primum argumentum est demonstratio, necesse est illam 'motus est aeternus' esse notiorem ilia 'motor est aetemus et immobilis'. Et si secundum argumentum est demonstratio, necesse est econverso quod ilia sit notior 'motor est aeternus et immobilis' quam ista 'motus est aeternus'.

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Sed processus iste conversus esse debet non ad eandem conclusionem demonstrandam. Conclusivum igi tur primum argumentum ad demonstrandum quod Primus Motor est aetemus et immobilis. Sed secundus processus, concludens

mo tum esse aeternum, est petitio principii et non demonstratio, qui a habet minorem minus notam conclusione. Et iste processus, si esset demonstratio, tamen non esset 20 ad concludendum 'propter quid', cum non sit ibi aliqua praemissa causalis neque conclusio. Debet igitur sic converti processus: 'Si est motus aeternus, motus est aeternus propter aetemitatem et immobilitatem Primi Motoris; sed Primus Motor est aetemus et immobilis, prout probatum est in primo processu; igitur etc.'. Quamvis igitur ilia

2 a priori] £CTV ex priori E a posteriori K II aetemitate] EcTVK exirnitate E II imrnobilitate] EcTVK immutabilitate E II motoris] credidit add. K II demonstrare] EcTVK detenninare E 3 motus] TVK om. E II quid] est add. K 4 ilia] ETV ita K 5 nisi idem sit] E1V illud fit idem K II magis] notum add. K 6 nisi sic ut] coni. nisi sicut VK et satis ET II quarta] ETVsecundaK8 quiaest] ETV om. K II alterum aetemus] etimmobilis add. E 7-8 et immobilis] ETV om. K9 si] ETK om. V II et immobilis] ETV om. K lOmotusest aetemus] EVK om. T 12etimmobilis] EcTVK om. E 14 aetemus] et irnmobilis add. E 15 esse debet non] TV esse debet E non esse debet K 16 demonstrandam] V om. ETK II eonclusivum] coni. concludendi ET concludendum Ecv conceditur K II ad] TVK om. E II demonstrandum] est add. E 17 secundus] £CTVK om. E 18 aetemum] ETVprimum K 19 conclusione]ETK om. V lliste processus] EVK om. Tlltamen] EVK tune T 20 cum.. ibi] EVK quin sit T 23 primus motor] VK motor E om. T II aetemus] motor add. T et immobilis add. EVK 24 immobilis] quamvis add. V

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'motus est aetemus' sit notior illa 'motor est aetemus et immobilis', tamen ista 'motor est aetemus et immobilis' est notior ista 'motus est aetemus et immobilis propter aetemitatem et immobilitatem Primi Motoris'. Et sic utrobique est process us ex notioribus, immo etiam ex nobis notioribus. Quid enim prodesset ad faciendum no bis scientiam conclusionis, [Kl 76rb] si praemissae essent notiores vel simpliciter vel Deo secundum naturam et non nobis? Constat enim quod semper esset petitio principii [E115vb] et numquam concederemus conclusionem nobis dubiam propter praemissas adhuc nobis magis dubias, quantumcumque essent aliis notiores. DUBITATUR Sed tune est fortis dubitatio de secunda clausula huius partis. Quae videtur assignare causam quare fit conversio in demonstrationibus de effectu ad causam et de causa ad effectum, die ens hoc esse qui a effectus est notior no bis et causa notior naturaliter sive simpliciter. Dico ergo quod haec verba sunt satis obscura et fecerunt dubitare et multos errare. Sed videtur mihi quod debeant exponi concorditer praedictis. Ubi enim fit no bis simul scientia de aliquo [V128rb] 'quia est' et 'propter quid est', nisi prius sit nobis notum 'qui a est'? ldeo quicquid est alia re notius quantum ad 'quia est', hoc dicimus no bis notius et prius. Quiaergo in naturalibus utin pluribuseffectus sunt notiores causis quantum ad 'quia est', ideo dicuntur nobis notiores et priores, sed non priores simpliciter, immo causae sunt priores in essendo et secundum naturam. Sed tune iterum dubitatur quare causae dicantur simpliciter no ti ores et priores. Et ego dico quod per hoc non debemus intelligere nisi quod ipsae sint nobis priores et magis scitae quam effectus quantum ad istorum effectuum perfectam notitiam,

1 notior] quamadd EV II et immobilis] ETV om. K2 notior] quamadd. K 4priusnotioribus .. ex] TVK om. Ell etiam] ETV om. Kif quid] ETVquodK llprodesset] ETVprocessus K 5 scientiam] TVK om. E 5-6 simplicitervel] EVK om. T 6 deo] ETV om. K vel add. \! II naturam] demonstrabiles add. T a consequentia vel deo add. K II non] ETV om. K II constat] EVK constant T 7 concederemus] ETV consideramus K II nobis] ETV om. K 8 aliis] ETVilli K 12 dicens] TV dicitur E dicimus K II et ... notior] TV et causae notiores E causa notior K II naturaliter] coni.

naturae ETVK 13 verbal K orrmia ETV 14 concorditer] his add. V 15 enim] Knon ETenim non VII fit... scientia] TVscitur simul V simul non scitur K II simul] EVKsimili T llnisi] TVibi VK 16 nobis] E1V om. K 16-17 idea .. quia est] EVK om. T 16 ideo quicquid] ET\/ ratio propter quid K II alia re] coni. alteri T\!K alteris Ee alterius E 17 ergo] T\!K si Ee om. E II ut] TV aut E om. K 18 sunt] nobis add. K II quia] ita add. K 19 sed non priores] EK sed non Tom. V et notiores add. K II immo] TV primae E om. K II causae] quae add. \!K 21 dicantur] EcT\!K sint E II et priores] ETV om. K22 non] Ec1K om. EV II debemus] T\!K demus E II nisi] ETV prius K II nobis] EcTVK om. E

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quae est 'propter quid'. Scire enim de effectu solum 'quia est' est eius imperfecta notitia stans cum multa admiratione et dubitatione propter quid ita est. Sed scire 'propter quid ita est' est perfecta eius notitia, auferens huiusmodi admirationem et dubitationem, uthabeturin prooemio Metaphysicae. Causaergo sic dicitursimpliciter notior, quia etiam est notior nobis quantum ad 'propter quid' quam effectus est. 8.9.4 [DE CIRCULATIONE INTER PLURES DEMONSTRATIOr-..1ES PROPTER QUID] (1) Et quia etiam causae sunt sibi invicem causae, prout declarat Aristoteles secundo Physicorum et quinto Metaphysicae, ideo per modum circulationis fiunt demonstrationes 'propter quid' de una causa ad aliam causam, et econverso. (2) Verbi gratia, per causam finalem scimus quod ambulandum est post cenam propter conservationem sanitatis, et per causam efficientem scimus quod sanitas conservatur per ambulationem post ccnam Ista quarta pars est de circulatione demonstrationum [T93va] 'propter quid' adinvicem. Et manifestum est etiam quod isto modo circulatio non est proprie dicta circulatio. Conclusio enim dcmonstrata per aliquam praemissam non fit econverso praemissa ad demonstrandum priorem praemissam; esset enim ille processus unus modus petitionis principii, procedens de minus noto ad magis notum. Sedsunt in illis processibus diversae conclusiones, quarum neutra in aliquo istorum processuum fit praemissa. Verbi gratia, fiat sic argumentum 'propter quid' per causam finalem: 'per quod cibus descendit ad fundum stornachi, hoc est faciendum propter sanitatem

4Metaph. I 1, 98la29sqq. IO Physica II 3, 195a8-11; Metaph. V 2, 1013b9-I 1.

1 primum est] facta add. K 2-3 scire ... ita est] EcTVK om. E 4 ergo] TVK cum E 5 etiam] V om. ETK II quantum ad] TV quam E om. K II quam] K om. ETV II est] ETV om. K 9 etiam] TVK om. E II alterum causae] ETV om. K II declarat] ETV deterrninat K IO ideo] EVK om. T 11-12 de una ... econverso] ETK om. V 12 verbi gratia] VK om. Ff II causam] enim add. Ee II finalem] ETV~ formal em K 14 per ambulationem] Tex ambulatione EVK 16 isto ... circulatio] E isto modo circulationis Tin isto modo circulationis VKG 17 conclusio .. demonstrata] ETVom. K//aliquam] VKaliamET 17-!Snon ... praemissa]ETVom. K!Spraernissa] TVKom. Ellpriorem] Kprimam ETV 18-19 ille ... petitionis] coni. ille processus petitio Ee processus petitio E unus processus petitio TV unus modus petitionis K 19 procedens] Tprocedendo E procedentis V om. K 20 m ... processuum] EVK item T 21 praernissa . gratia] EfTVK prima vera E II praernissa] ad probandam reliquam add. T 22 est faciendurn] ETV fit K

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conservandam; sed ambulando [Kl 76va] post cenam hoc fit; ergo ambulandum est post cenam propter sanitatem conservandam'. Econverso autem arguitur 'propter quid' per causam efficientem sic: 'a quo cibus in stomacho descendit conservatur sanitas; ab ambulatione descendit etc.; ergo ab ambulatione conservatur sanitas. Ita etiam declarat Aristoteles secundo Posteriorum quod in his quae fiunt modo circulationis ex invicem, oportet demonstrationes fieri modo circulari, ut quad ex vapore fit nu bes, ex nu be pluvia et ex pluvia fit tena [V128va] depluta et humectata, ex qua iternm fit vapor, nubes etc. Capiamus ergo exemplum in generatione frumentorum, cum fiunt tria circulariter ab invicem, videlicet granum, spica et herba. Erunt ergo tres propositiones immediatae et non demonstratae, et aliae tres erunt mediatae et demonstrabiles; et non erit eadem demonstrata et demonstrabilis. Verbi gratia, immediatae sunt quad granum fit ex spica et spic a ex herba et herba ex grano. Mediatae autem et demonstrabiles sunt aliae tres. Una quod granum fit ex herba quia: 'spica fit ex herba; et granum ex spica; ergo granum ex herba'. Secunda

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quad spica ex grano quia: 'herba ex grano; et spica ex herba; igitur spica ex grano'. Tertia quod herba ex spica quia: 'granum ex spica; et herba ex grano; igitur herba ex spica. Manifestum est quad nullum est ibi quasi inconveniens nee quod in aliquo istorum processuum fit petitio principii, sed quaelibet fit ex notioribus; nee quod oporteat idem eodem modo esse magis notum et minus notum.

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8.9.5 [DE CIRCULATIONE INTER PLURES DEMONSTRATIONES QUIA] (1) Adhuc inter diversas conclusiones ex invicem consequentes contingit quodammodo circulatio demonstrationum quando ita est quad utraque conclusio fit, vel fieri potest, praemissa ad alteram demonstrandam; sic enim videtur Aristoteles procedere in primo capitulo sexti Physicornm. (2) Ex eo

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5 Anal. Post. II 12, 95b38-96a7. 25 Physica VJ I, 23la2lsqq. conservandam] EVK servandam T II ambulando] ETV per ambulare K II fit] EVK sit T 2 conservandam] coni. servandam T observandam VK om. E 4 ab ... etc.] TVK om. E 5 etiam] TVK om. E II aristoteles] £.l"TVK om. E II fiunt] ex add. V 6 ex invicem]TVK ad invicem E II fieri .. circulari] ETV esse aliquando ex K 7 ethumectata] TV et humida E om. K 8 ergo] EVK similiter T II generatione] EK genere TV9 cum fiunt]E cum fiant TV quad sunt K II circulariter] ETV circularia K II ab invicem] Tad invicem EVK //videlicet] EVut T vel K lOpropositiones] adinvicemadd. V 10-11 et non ... demonstrabilis] EVK om. T 12 granum fit] TVK grana sunt E 15 quia ... alterum herbal ETV om. K 15 quia ... alterum grano] ETK om. V 16 quia] TVK et E 17 est ibi quasi]TV est E contingit ibi K II in] EcTVK om. E 18 processuum] EVK om. T II fit] K est TV om. E 23 quodarnmodo] TVK om. E fl quando ita est] ETquia est ita VK24 conclusio] EVK om. T II fit vel] ETV om. K II demonstrandam] TVK demonstranda E 25 sexti] TVK sexto E

197

Johannes Buridanus, Summulae

enim quod nullum est continuum compositum ex indivisibilibus, concludit quod null um estdivisibile in indivisibilia, sed in semperdivisibilia; et iterum per hoc quod nullum est divisibile in indivisibilia, concludit quod nullum est compositum ex indivisibilibus.

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Ista quinta pars ponit unum modum circulationis demonstrationum, quern puto quodarnmodo concessibilem. Ponamus enim quod duae conclusiones, scilicet a et b manifeste sese consequantur; et quod sint ambae demonstrabiles, et possibile est quod multae demonstrationes sunt qui bus istae conclusiones demonstrari [E116ra] possunt; et quod aliquae earum evidentius inferant a quam b, et aliae econverso. Pono igitur quod Socrates invenerit demonstrationem manifeste inferentem a, nihil considerans de b. Constat quod per illam sciat a. Sed tune ultra per a scitam demonstrabit b, arguens sic: 'si a est, best; sed a est, prout demonstratum est; ergo best'. Et ita per scire a esse ille sci et b esse. Econ verso au tern, si Plato inveniat aliam demonstrationem evidenter concludentem b, per quam sciet b, nihil considerans de a, et postea per b sci tam demonstrabit a, tune erit utraque demonstratio faciens scire ex per se notis et notioribus conclusione. Et non est inconveniens idem [T93vb;V128vb] respectu eiusdem esse magis notum et minus notum [Kl76vb] diversis hominibus, ut quod a esse Socrati est magis notum quam b esse, quia sic demonstrata est sibi; et econverso Platoni, pari ratione. Sed tu quaereres, ponendo casum quodP!ato consideret ambos istos process us, utrum ergo sibi a esse sci tum sit per b esse, et b esse per a esse. Et ego credo quod non. Et tamen demonstratum est sibi a esse per b esse, et econ verso b essc per a esse. Hoc dictum fuit supra primam partem septimi capituli huius tractatus, scilicet quod non omnis demonstratio facit scire suam conclusionem, sed sufficit ad hoc quod sit demonstratio quod faceret scire suam conclusionem, si non esset praescita iam per

1 null um] EcTVK om. Ell est continuum] TV continuum est EK l-4concludit... indivisibilibus] ETV om. K 2 in semper] ETK semper in VII et] TVK sed E 6 concessibilem] EK esse possibilem T esse concessibilem VII ponamus] E pono TVK II enim] EVK om. T II quod duae] V quod ET duas K 6-7 scilicet a et b] TVKistae aristotelis E quae add. K 7 demonstrabiles] ET dubiae VK 12 demonstrabit] ETK dubitabit VII best] quia ponuntur manifeste consequi add. E cum illae ponantur manifeste scqui add. TV 13 scire a esse] Ka esse ET a VII ille] V om. ETK II sciet] ETV scirem K II si] E om. TVK fl aliam] EValiquam TK 14 sciet) EcTV c et K om. E 14-15 considerans de a] E7V consideranda K 15 tune] coni. et ETVK I I utraque) ETVquaelibet K 16 per se] EcTVK praemissis E II et non est] ETVfitenim K 17 magis notum] ETVnotius K II minus notum] ETV ignotius K 18 esse socrati] £CTVK solum E 19 sibi] ETV socrati K 20 tu) ETK tune VII plato] TVK socrates E habcat et add. K 21 ergo) EVK om. T II et b esse per a esse) EVK om. T II alterum a esse) TVK a E 23 fuit] EcTVK om. E 24-25 sed ... conclusionem] EcTVK om. E 25 iam] TV om. EK

198

De Demonstrationibus

aliam demonstrationem. Prosunt enim tales demonstrationes plures, sive circulares sive non, ad eandem conclusionem, non quia posterius advenientes faciant scire conclusionem, sed quia faciunt scire evidentius. Sicut enim luminosum, iustum et prudens recipiunt magis et minus sine admixtione contrarii, sic etiam firmum et 5 evidens. Unde, quamvis omnia prima principia et indemonstrabilia, in nobis suo debito modo habita, sint firma et evidentia, tamen est bene unum, quod ponit Aristoteles quarto Metaphysicae, omnibus aliis, sive pluribus, firmius et evidentius, firmissimum et evidentissimum. Adhuc propterquosdam obviantes ego declaro quomodo duae conclusiones ad 10 invicem consequentes habent diversas rationes et demonstrationes, per quarum unam una evidentius demonstratur, et per aliam alia. Consequitur enim quod omnis magnitudo est in infinitum sive in semper divisibilia divisibilis, et quod nulla magnitudo est composita ex indivisibilibus. Et tamen primam istarum manifestius et directius quam secundam demonstrat ilia ratio Aristotelis, sexto Physicorum, ubi 1s dicit quod super eandem vel aequalem magnitudinem potest moveri unum mobile velocius et alterum tardius; tardius autem in eodem tempore transit minorem magnitudinem, et velocius eandem magnitudinem in minore tempore. Ideo mobile tardius arguit semper divisionem magnitudinis et velocius divisionem temporis; vide rationem, si vis. 20

[V129ra] Sed iterum Aristoteles demonstrat illam conclusionem manifestius in principio illius sexti per hoc quod non possunt ista indivisibilia se habere ad invicem continue nee contigue nee consequenter se habentia, et per multas etiam alias rationes. Et tandem de circulatione demonstrationum ego concludo quod

7 Metaph. IV 3, 1005bl2-20. 15 Physica VI 2, 232a23sqq. 20 Physica VI I, 231a21-bl8. I demonstrationem] ETV conclusionem K 1-8 prosunt ... evidentissimum] ETV om. K I enim] coni. ergo E autem TV 2 scire] firrnius et add. V 6 debito] IV deterrninato E 8 evidentissimum] ut dicitur ibidem add. V 9 quomodo] EVK quodammodo T II duae] ETV istae K IO rationes et] E om. TVK 10-11 per. .. una] VK una per unam E una T 11 aliam] ETV alteram conclusionem K II alia] quae sequitur add. VII consequitur enim] £CVC consequitur EV consequuntur enim T enim sequitur se K 12 in semper] TVK semper E 13 magnitudo] ETV materia K //primam]EVprima TK 14secundam]EVKsecunda Ti/ilia] ETVom. Kllaristotelis]EVK om. T 14-15ubi