« The Four Elements in the Work of William of Conches », dans Guillaume de Conches: Philosophie et...

Irene Caiazzo

THE FOUR ELEMENTS IN THE WORKOF WILLIAM OF CONCHES

The theory of the four elements occupies a central place inWilliam of Conches’ philosophy of nature, where, far from beingstatic, it developed over the years*. However, while historians areunanimous in acknowledging the importance of this theory, its con-tent and evolution have never been fully studied. They limitedthemselves to reconstructing the theory by putting together quota-tions extrapolated from the most diverse contexts, while assuming itto have remained unchanged. Furthermore, they focused their atten-tion either on the Philosophia or on the Dragmaticon philosophiae.Due to these selective and somewhat arbitrary approaches, historiansfailed to understand William of Conches’ thought, and several oftheir reconstructions simply prove to be incorrect.

Previous studies of William of Conches’ theory of the elementshave emphasized, above all, the key role played by Arabic medicine.Also, since the word elementatum was first used in twelfth-centurywritings, and since the distinction between elementum and elementa-tum constitutes one of the more prominent features of William’stheory – as first expounded in the Philosophia and subsequently innear-identical form in the Glosae super Platonem –, considerableattention has been paid to this new terminology. However, the pre-vailing selective approaches have led to a number of misunderstan-dings, which need to be dispelled from the outset. Generally speak-ing, elementum refers to the element in its pure state, while elementa-tum refers to the element as apprehended by sense perception, i.e.seen and perceived in an impure state, mixed with other elements.Still, merely the occurrences of the distinction elementum/elementa-

3

* Translated by Michael Chase (CNRS, Paris). I am grateful to Barbara Obrist(CNRS, Paris) and Édouard Jeauneau (CNRS, Paris) for their valuable remarks.

«Micrologus’ Library» 42 SISMEL Edizioni del Galluzzo, 2011

tum in the Philosophia have been studied in any detail, while thosein William of Conches’ other works remain to be investigated. Thisis mainly due to the fact that the Glosae super Boetium were notpublished in a full critical edition until 1999, while the only printedversion of the Dragmaticon philosophiae prior to 1997 was a sixteenth-century Basel edition. The Philosophia was included twice in thePatrologia latina, the author being given once as Honorius Augusto-dunensis and once as the Venerable Bede 1.

The elementum/elementatum theory is to be found in William ofConches’ very first work, the Glosae super Boetium. Yet, at this earlystage he rejects the theory, stating that he is unable to see its perti-nence. He does not mention it at all in his Glosae super Macrobium,then refers to it in the Philosophia and the Glosae super Platonem, andfinally abandons it in the great dialogue of his maturity, the Drag-maticon philosophiae. William of Conches’ use of elementum/elementa-tum thus changes considerably over time and should be examinedboth in the range of philosophical contexts in which it occurs andin the context of the development of his thought. In accordancewith this aim, the present study will retrace the development ofWilliam of Conches’ theory of the four elements step by step, fol-lowing the chronological order of his works. This method involvesdating the works in question as precisely as possible, a task that hasbeen greatly facilitated by Édouard Jeauneau’s groundbreakingresearch, which remains as valid as ever. He studied both the doctri-nal aspect of William of Conches’ works and cross-referencesbetween the texts, as their author repeatedly refers to his otherwritings, declaring them either available or forthcoming. Accordingto Jeauneau, the works were written in the following order: Glosaesuper Boetium, Glosae super Macrobium, Philosophia, Glosae superPriscianum, Glosae super Platonem, Dragmaticon philosophiae, and thesecond version of the Glosae super Priscianum 2.

4

IRENE CAIAZZO

1. In volumes 172 and 90 respectively.2. Guillelmus de Conchis, Glosae super Platonem, ed. É. Jeauneau, Paris 1965,

Introduction, 14-16; Id., Gloses de Guillaume de Conches sur Macrobe. Note sur lesmanuscrits, in «Archives d’histoire doctrinale et littéraire du Moyen Âge», 27(1960), 25-26: «Lorsqu’il commente Macrobe, notre auteur n’évoque ses glosessur le Timée que comme un ouvrage qui n’a pas encore vu le jour et qu’il sepromet d’entreprendre si Dieu lui prête vie: “Hoc totum, Deo annuente<vitam>, in Platone exponemus”. Ceci, joint à l’observation faite précédem-ment au sujet de l’absence de citations de Constantin l’Africain et de Johanni-tius, nous invite à placer les gloses sur Macrobe avant les gloses sur le Timée etavant la Philosophia. Par ailleurs, on sait que, dans ses gloses sur Boèce, Guillaume

Richard Lemay studied the issue of chronology as well. He hasbeen influential in arguing that the presence of the distinction ele-mentum/elementatum represents a key factor in dating William ofConches’ works, maintaining that it reflects the use of John ofSeville’s Latin translation (1133) of Abu Ma‘sar’s Introductorium maius,which, Lemay claims, includes the earliest clearly dated occurrenceof elementatum 3. However, the very same term had been used pre-viously in Salernitan medical texts, which William of Conches drewon for several of his medical theories.

Lemay’s hypothesis is further to be rejected on the grounds thatit obliges one to date William of Conches’ first work, the Glosaesuper Boetium, to after 1133, as it refers to the elementum/elementatumtheory. This late date is however not acceptable, for William’s Drag-maticon philosophiae addresses his protector Geoffrey Plantagenet asCount of Anjou and Duke of Normandy and, as it happens, Geof-frey bore the title of Duke of Normandy from 1144 to 1149, beforepassing it on to his son Henry. Moreover, William wrote the Drag-

5

THE FOUR ELEMENTS IN THE WORK OF WILLIAM OF CONCHES

renvoie aux gloses qu’il se promet de faire sur Macrobe: “Quare autem ibi fin-gantur, super Macrobium dicemus”. Si ces indications doivent être prises à lalettre, l’ordre de composition des différentes gloses est le suivant: 1° Gloses surBoèce, 2° Gloses sur Macrobe, 3° Gloses sur le Timée. Mais rien ne s’oppose àce qu’au cours de sa longue carrière Guillaume de Conches ait lu plusieurs foisle Timée et qu’à l’occasion de nouvelles lectures il ait remanié le texte de sesgloses. Dans ce cas, il nous est bien difficile de savoir si Guillaume de Conchesrenvoie au texte primitif ou au texte remanié. Et, par conséquent, la chronolo-gie que nous tentons d’établir entre les différents écrits du philosophe deConches ne semble pas devoir dépasser les limites de la probabilité». This chro-nology, further studied in the new edition of Guillelmus de Conchis, Glosaesuper Platonem, ed. É. Jeauneau, Turnhout 2006 (CCM, 203), XXXVIII-XL, remainsvalid, although it is now clear that William drew on the work of Constantinethe African in the Glosses on Macrobius: cf.T. Ricklin, Vue et vision chez Guillaumede Conches et Guillaume de Saint-Thierry, Le récit d’une controverse, in La visione elo sguardo nel Medio Evo, Florence 1997 (Micrologus, 5), 19-41; Id., Der Traum derPhilosophie im 12. Jahrhundert. Traumtheorien zwischen Constantinus Africanus undAristoteles, Leiden-Boston-Cologne 1998 (Mittellateinische Studien und Texte,24); I. Caiazzo, Lectures médiévales de Macrobe. Les Glosae Colonienses superMacrobium, Paris 2002 (Études de philosophie médiévale, 83); Ead., Mainscélèbres dans les marges de Macrobe, in Scientia in margine. Études sur les margina-lia dans les manuscrits scientifiques du Moyen Âge à la Renaissance, edd. D. Jacquart,C. Burnett, Geneva 2005 (EPHE, Hautes Études Médiévales et Modernes, 88),171-89. D. Jacquart, Les emprunts de Guillaume de Conches aux théories médicales,published in the present volume, demonstrates that William of Conches drew onmedical works translated from the Arabic in his Glosae super Boetium.

3. R. Lemay, Abu Ma ‘shar and Latin Aristotelianism in the Twelfth Century. TheRecovery of Aristotle’s Natural Philosophy Through Arabic Astrology, Beirut 1962, 178sqq. Cf. Abu Ma‘sar Al-Balh

¯ı (Albumasar), Liber introductorii maioris ad scientiam

judiciorum astrorum, ed. R. Lemay, Naples 1995-96.

maticon not only for the Duke, but also for his sons, and Henry wasin Normandy between 1147 and 1149 4. These facts lead to theinevitable conclusion that the Dragmaticon philosophiae was writtenwithin this latter time span. Elsewhere in the same work Williamnotes that he has been teaching for over twenty years (per vigintiannos et eo amplius alios docui) 5, while also criticizing some of thearguments set forth in his Philosophia, written when he was youngand immature (in iuventute nostra imperfectum, utpote imperfecti, compo-suimus) 6. These remarks indicate that the beginnings of William ofConches’ career are to be dated to ca. 1120-1125, when, as a youngman, he wrote the Glosae super Boetium and the Glosae super Macro-bium. He then must have composed the Philosophia in around 1125-1130, that is, before John of Seville translated Abu Ma‘sar’s Introduc-torium maius into Latin.

Having clarified the issue of the chronology of William ofConches’ works, we now turn to his theory of the elements and itsevolution, as first set forth in the Glosae super Boetium and culmi-nating in the Dragmaticon. For each component of this theory, wewill attempt to sketch, by way of brief doxographical excurses, theirhistory and also their immediate historical and doctrinal contexts.

1. William of Conches’ first approach to the question of the elements:The Glosae super Boetium

1.1. Are the elements formed by a mixture of the four elements?a) Elementatum in the early twelfth century

1.2. The qualities of and links between the elementsa) Calcidius, Macrobius, Nemesius of Emessa and Boethiusb) Boethius and his medieval commentators

6

IRENE CAIAZZO

4. Cf. Guillelmus de Conchis, Dragmaticon philosophiae, ed. I. Ronca,Turnhout1997 (CCM, 152), Introduction, XIX. Cf. ibid., I, 1, 5, 5: «In te tamen et in filiistuis aliquid spei consistit, quos non, ut alii, ludo alearum, sed studio litterarumtenera aetate imbuisti, cuius odorem diu servabunt, iuxta illud Horatii: “Quosemel est imbuta recens servabit odorem testa diu”. Spe igitur ista excitati etincitati, tibi et filiis tuis aliquid quod ad scientiam pertineat scribere propo-suimus». For a brief overview of William of Conches’ life and career, see T. Gre-gory, Anima mundi. La filosofia di Guglielmo di Conches e la Scuola di Chartres,Florence 1955, 1-4, 7. See also C. Burnett, The Introduction of Arabic Learning intoEngland, London 1997 (The Panizzi Lectures, 1996), lecture 2: «The Education ofHenry II».

5. Guillelmus de Conchis, Dragmaticon philosophiae,VI, 1, 1, ed. Ronca, 179.6. Ibid., I, 1, 8, 7.

1.1. Are the elements formed by a mixture of the four elements?

William of Conches’ gloss on the famous metrum 9 in Boethius’Consolation of Philosophy, Book III, states that God created matter –i.e. the four elements 7 – ex nichilo. He categorically rejects the pos-sibility that this creation could have taken place in several stages,with the elements being created in a state of chaos before beingarranged in order. Following a long digression on chaos 8, William ofConches lists the various opinions on the four elements, which hedescribes as topics of scholarly debate (dubitatio est inter scolares). Hebegins by rejecting the widely held theory that the visible elements– earth, water, air, and fire – are not elements but elementata, or ele-mentary components:

Dicunt enim fere omnes non esse elementa quae videntur a nobis, scilicetterra, aqua, aer, ignis, sed elementata [elementa ed.], id est ab elementiscomposita, asserentes hoc auctoritate Platonis qui quaerit quare magis istudterra dicatur quam aqua, cum dissolvatur in aquam. Postea dicit illud quodita dissolvitur non debere dici terra, sed terreum; et sic de aliis. Hoc etiamaliis rationibus volunt probare quod ex omnibus elementis sunt composita.Neque enim aqua calefieret vel terra, neque ex lapide ignis excuteretur, nisiin eis esset ignis. Et huiusmodi philosophi, immo philosofolli 9, concedunt se

7


7. In some of William of Conches’ works, matter coincides with the four ele-ments, while in others it precedes or contains the four elements. Cf. I. Caiazzo,La materia nei commenti al Timeo del secolo XII, in «Quaestio. Rivista di storia dellametafisica», 7 (2007), 245-64.

8. Cf. M.-D. Chenu, Nature ou histoire? Une controverse exégétique sur la créationau XIIème siècle, «Archives d’histoire doctrinale et littéraire du Moyen Âge», 28(1953), 25-30; É. Jeauneau, Du désordre à l’ordre (Timée 30a), in Platons Timaios alsGrundtext der Kosmologie in Spätantike, Mittelalter und Renaissance. Plato’s Timaeusand the Foundations of Cosmology in Late Antiquity, the Middle Ages and Renaissance,edd. T. Leinkauf, C. Steel, Louvain 2005 (Ancient and Medieval Philosophy, I,vol. 34), 253-63; H. Merle, Sic dissolutum est Chaos. Monographie sur le mythe etla notion de Chaos, héritage de l’Antiquité au Moyen Âge, in L’art des confins.Mélanges offerts à Maurice de Gandillac, edd. A. Cazenave, J. F. Lyotard, Paris 1985,365-86; S.Viarre, Cosmologie antique et commentaire de la création du monde. Le chaoset les quatre éléments chez quelques auteurs du Haut Moyen Âge, in La cultura anticanell’Occidente latino dal VII all’XI secolo, Atti della XXII Settimana di studio (Spo-leto, 18-24 aprile 1974), Spoleto 1975, 541-73; G. Garfagnini, Cosmologie medievali,Turin 1978. For the question of primordial chaos, which cannot be adequatelystudied within the scope of the present study, see A. Fidora, Le débat sur la créa-tion: Guillaume de Conches, maître de Dominique Gundisalvi?, and D. Poirel, Entrephysique et théologie: une querelle entre Guillaume de Conches et Hugues de Saint-Victor à propos du chaos originel, in the present volume.

9. Cf. Bernardus Traiectensis, Commentum in Theodolum, III, 45, ed. R. B. C.Huygens, Spoleto 1977, 77: «De diis enim inter philosophos, immo philosophol-los litigium fuit».

habere ignem et cetera elementa in capillis et in barba. Sed inter eos quidicunt ista non esse elementa, dubitatio est quid sint elementa 10.

According to William of Conches, partisans of the elementatatheory draw on Plato’s Timaeus, which first questioned why this ele-ment is called earth rather than water, since earth dissolves in water,before arguing that what dissolves should not be called terra, butrather terreum 11. Furthermore, these partisans base their argument onsensory experience to prove that bodies consist of all the elements.Water can be heated and fire can be obtained by striking stonestogether because they contain fire. These philosophers – or philoso-folli – are then obliged to maintain that even their beards and haircontain all four elements, including fire.

It is not clear precisely which contemporaries William of Concheshad in mind when referring to the philosofolli. Many ancient andmedieval authors and works held that the four elements are com-bined in sensible bodies, including Ambrose 12, Calcidius, Macrobius,Isidore of Seville 13, the Venerable Bede, Johannes Scottus Eriugena,Remigius of Auxerre, Abbo of Fleury, ‘Alı ibn al-‘Abbas al-Magusı(in Constantine the African’s translation of the Pantegni) 14, Nemesius

8

IRENE CAIAZZO

10. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. L. Nauta, Turn-hout 1999 (CCM, 158), 162. Both readings, elementa and elementata, occur in themanuscripts. Elementata is found in ms. Leipzig, Universitätsbibliothek, lat. 1253[s. XIIIin], ms. Heiligenkreuz, Bibliothek des Zisterzienserstifts, 130 [s. XIIex], ms.Erlangen, Universitätsbibliothek, 436 [s. XIII/XIV], ms. Leiden, Bibl. publica Lug-duno-Batava, 191A, [s. XIII], and ms. Prague, Státní Knihovna, IV.F.14 (720) [s.XIIIex]. L. Nauta tentatively adopted the term elementa in his edition: cf. hisIntroduction, LV-LXI, and Id., The glosa as Instrument for the Development of Nat-ural Philosophy: William of Conches’s Commentary on Boethius, in Boethius in theMiddle Ages. Latin and Vernacular Traditions of the Consolatio Philosophiae, edd.J. F. M. Hoenen, L. Nauta, Leiden-New York-Cologne 1997, 31-37. Cf. the criti-cal remarks by T. Kobusch, Der Timaios in Chartres, in Platons Timaios alsGrundtext der Kosmologie, 235-51.

11. Plato, Timaeus 49d, in Timaeus a Calcidio translatus commentarioque instruc-tus, ed. J. H. Waszink, Leiden-London 19752 (Plato latinus, 4), 47.

12. Ambrosius Mediolanensis, Hexaemeron, I, 6, 20, PL 14, [133-288], 143C:«Elementa autem quatuor, aer, ignis, aqua et terra, quae in omnibus sibi mistasunt. Siquidem et in terra ignem reperies, qui ex lapidibus et ferro frequenterexcutitur».

13. Isidorus Hispalensis, Etymologiarum sive originum libri XX, XIII, 3, 3, ed. W.M. Lindsay, Oxford 1911; repr. Oxford 1962: «Quapropter omnia elementaomnibus inesse, sed unumquodque eorum ex eo quod amplius habet accepissevocabulum».

14. Constantinus Africanus, Pantegni,Theorica, I, 4, ed. C. Burnett,Verba Ypo-cratis preponderanda omnium generum metallis. Hippocrates on the Nature of Manin Salerno and Montecassino, with an Edition of the Chapter on the Elements in the

of Emessa (in Alfano of Salerno’s late-eleventh-century transla-tion) 15, Petrus Alfonsi 16, Adelard of Bath, the author of the Glosaesuper Platonem (attributed to Bernard of Chartres by P. E. Dutton) 17,and the anonymous author of the so-called «Digby» commentary onthe Isagoge Iohannitii 18. At any event, in the gloss of ConsolatioPhilosophiae, II, m. 8, William of Conches seems to agree with thetheory according to which bodies are composed of all four ele-ments 19. This gloss clearly shows William’s ambivalent relation withmedical sources in his first work.

9


Pantegni, in La scuola medica salernitana. Gli autori e i testi, edd. D. Jacquart, A.Paravicini Bagliani, Florence 2007 (Edizione nazionale «La scuola medica saler-nitana», 1), [59-92], 77-78: «De elementis. Philosophi diffiniunt simplam et mini-mam compositi corporis particulam esse elementum. Simplam autem dicimusrem quae, cum eadem sit in essentia, similis est in partibus, ut ignis, aer, aqua,terra esse videntur. Sunt tamen quaedam visu simpla, intellectu composita, utlapides, metalla et similia. Philosophi ergo, videntes elementa intellectu simpla etomnia corpora constructioni et destructioni subiecta ex eis esse composita,vocaverunt ea prima elementa; posteriora secunda et tertia. Unde quaedamvocantur universalia, quaedam particularia, quaedam vero media». Ibid., 80: «Cumenim omnia corpora sub lunari circulo posita videantur sibi esse commixta etdissimilia – etsi enim quaedam appareant incommixta et similia, intellectu tamencomprobantur commixta et dissimilia – elementa et sensu et re ipsa constat essesimpla et similia. Unde digne vocantur elementa».

15. Nemesius Emesenus, Premnon physicon a N. Alfano archiepiscopo Salerni inlatinum translatus, 5, ed. C. Burkhard, Leipzig 1917 (Bibliotheca scriptorum grae-corum et romanorum Teubneriana), 62: «Sed nullum horum sensibilium elemen-torum simplex et non infectum est alio elemento».

16. Petrus Alfonsi, Dialogi contra Iudaeos, 10, PL 157, [535-672], 640; Diálogocontra los Judíos, 10, ed. K.-P. Mieth, Huesca 1996 (Larumbe, 9), 151: «Scias, quiaanimalia omnia de quatuor sunt elementis composita. Que etiam inter se variasunt pro ipsorum varietate elementorum in eorum compositione secundumqualitates et quantitates suas impariter adiunctorum, inde etenim diversarumprovenit dissimilitudo specierum». Cf. I. Resnick, Humoralism and Adam’s Body:Twelfth-Century Debates and Petrus Alfonsi’s Dialogus contra Judaeos, in «Viator»,36 (2005), 181-95.

17. In the Glosae attributed to Bernard of Chartres, the term elementaria desi-gnates the pure elements, which become elements in actu in the physical world.Cf. Bernardus Carnotensis, Glosae super Platonem, 8 (Tim. 49b-c); 8 (Tim. 49e); 8(Tim. 51b), ed. P. E. Dutton, Toronto 1991 (Studies and Texts, 107), 223, l. 131-42;223-24, l. 152-54; 227-28, l. 246-56. The attribution to Bernard of Chartres isdoubtful: cf. Caiazzo, Lectures médiévales de Macrobe, 132-41; Ead., Sur la distinctionsénéchienne idea/idos au XII e siècle, in Image et Représentation dans la philosophieancienne. Numéro double dédié au professeur Jean Jolivet, ed. A. Vasiliu, in «Chôra.Revue d’études anciennes et médiévales. Philosophie, théologie, sciences», 3-4(2005-2006), 91-116.

18. Cf. Commentary on Isagoge Iohannitii, ms. Oxford, Bodleian Library, Digby108, f. 7r: «Quatuor elementorum, quibus omne corpus a lunari circulo estconstitutum, duo sunt levia, duo gravia».

19. Guillelmus de Conchis, Glosae super Boetium, II, m. 8, ed. Nauta, 125. Cf.Nauta’s remarks in the apparatus criticus, 162.

a) Elementatum in the early twelfth century

Since the origins of the term elementatum have yet to be tho-roughly explored, we now turn to a brief discussion of the debatesurrounding the term in recent historiography.

As we have seen, Richard Lemay assumed that the first occur-rence of the word elementatum in the Latin West was in the Arabo-Latin translation of Abu Ma‘sar’s Introductorium maius, which led himto date William of Conches’ Philosophia erroneously to after 1133 20.This chronological argument against Lemay’s assumption can be fur-ther reinforced by reference to vocabulary. John of Seville makes useof elementatum, elementata, elementans, elementavit and other forms,while William of Conches limits himself to distinguishing betweenelementatum/elementata. John of Seville translates t.aba’i‘ as elementa ornaturae, with both terms designating the four elements: fire, air,water, and earth. In some cases, he uses both terms, translatingt.aba’i‘ as elementa sive naturae. The term elementatum corresponds tomat.bu‘ and elementata to the plural mat.bu‘at, while t.abı’iyya is trans-lated as elementatorum or elementatis 21. The terms in question arederived from the word «nature», t.abı’a, from which is further derivedmat.bu‘ (as a past participle, hence the Latin suffix –atum, e.g. natura-tum). Mat.bu‘ is used in Arabic in the sense of «formed by nature» insuch-and-such a way. There was no self-evident reason for John ofSeville to translate mat.bu‘ as elementatum unless the existing Latinterm seemed to the translator to correspond to the «natured» 22.

Theodor Silverstein, whose research sparked the debate over theterm elementatum, eventually concluded after much hesitation thatWilliam of Conches must have coined the word himself 23. However,

10

IRENE CAIAZZO

20. Lemay, Abu Ma’shar and Latin Aristotelianism, 178 sqq.21. Albumasar, Liber introductorii maioris ad scientiam judiciorum astrorum, I, 4, in

vol. 5, t. II, Deuxième partie: Traduction de Jean de Séville révisée par Gérard de Cre-mone, ed. Lemay, 27: «Elementata autem sunt que conficiuntur ex his quatuornaturis de universis individuis»; ibid., 26: «Et nominantur quatuor nature: ignis,aer, aqua, terra».

22. Warmest thanks to my colleague Marc Geoffroy (CNRS, Paris) for hisprecious help in this paragraph.

23. T. Silverstein, Elementatum: Its Appearance Among the Twelfth-Century Cos-mogonists, in «Mediaeval Studies», 16 (1954), 156-62; Id., Guillaume de Conches andthe Elements: Homiomeria and Organica, in «Mediaeval Studies», 26 (1964), 363-67; Id., Salerno and the Development of Theory, Conferenza tenuta nella seduta del27 ottobre 1977, Accademia nazionale dei Lincei, anno 375, quaderno n. 240,Rome 1978, 10: «[…] Guillaume distinguishes between the elements and theordered hierarchy of parts that make up the body – the humors, the similar orhomogeneous parts and the organs made of those parts – all of them given in

Silverstein bases his analysis solely on the Philosophia, and althoughaware of the existence of the Glosae super Boetium, he overlooks thefact that this work dismisses the theory according to which the ele-mentata are composed of elements – a theory associated with philoso-folli. Peter Dronke rejects the argument that William of Conchesdepended on the Latin translation of Abu Ma‘sar’s Introductoriummaius on chronological grounds, while maintaining that Williamcoined the word elementatum 24.

Dorothy Elford has put forward a third possibility for the originof the word elementatum 25. William of Conches may have comeacross the term in the so-called «Digby» commentary on the IsagogeIohannitii (a Latin adaptation of H. unain ibn Ish. aq’s Questions on me-dicine), dating from the beginning of the twelfth century 26. Thisappears to be the most convincing explanation, and as such deservesfurther exploration. William of Conches is known to have drawnfrequently upon «Iohannitius», quoting him on the subject of ele-ments and their combinations in bodies several times in thePhilosophia 27. He is likely to have had access to a commentary onthe Isagoge Iohannitii, at least one copy of which was probably avai-lable at Chartres in the twelfth-century 28. The early-twelfth-century

11


an ascending order from simplest to most composite. Our interest in that part ofGuillaume’s book lies in two directions; the first has to do with his special defi-nition of the elements as simple parts in quality and minimal parts in quantity,and as not perceptible to the human senses but deducible by an exercise of theintellect; these he calls elementa.Those which we perceive by the senses in natureare not true elements, since they are not simple and/or minimal parts: they areto be called, not elementa, but elementata. […] I think that as a noun and in itsparticular meaning Guillaume de Conches invented the word». Cf. also R.McKeon, Medicine and Philosophy in the Eleventh and Twelfth Centuries: the Problemof Elements, in «The Thomist», 24 (1961), 211-56.

24. P. Dronke, New Approaches to the School of Chartres, in «Anuario de estu-dios medievales», 6 (1969), [117-140], 128-31: Peter Dronke gives a completesurvey of the debate on the origin of the word elementatum.

25. D. Elford, William of Conches, in A History of Twelfth-Century Western Phi-losophy, ed. P. Dronke, Cambridge 1988, [308-27], 312.

26. Cf. D. Jacquart, À l’aube de la renaissance médicale des XIe-XIIe siècles: L’Is-agoge Johannitii et son traducteur, in «Bibliothèque de l’Ecole des chartes», 144(1986), 209-40; G. Maurach, Johannicius, Isagoge ad Techne Galieni, in «SudhoffsArchiv», 62/2 (1978), 148-74.

27. Guillelmus de Conchis, Philosophia, I, 23; IV, 31, ed. G. Maurach, Pretoria1980, 28; 104.

28. C. Burnett, The Contents and Affiliation of the Scientific Manuscripts Writtenat, or Brought to, Chartres in the Time of John of Salisbury, in The World of John ofSalisbury, ed. M. Wilks, Oxford 1984, 127-60. On the commentaries on the Isa-goge Iohannitii, cf. P. O. Kristeller, Bartholomaeus, Musandinus and Maurus of Salernoand Other Early Commentators of the Articella, with a Tentative List of Texts and

Chartres commentary on the Isagoge Iohannitii (as transmitted in theBury St. Edmunds manuscript) includes the definition elementata, idest ex elementis composita 29, as does the Digby commentary on theIsagoge Iohannitii, which is slightly later 30.

12

IRENE CAIAZZO

Manuscripts, in «Italia medioevale e umanistica», 19 (1976), 57-87; Italian transl.,in P. O. Kristeller, Studi sulla scuola medica salernitana, Naples 1986, 97-151; M. D.Jordan, Medicine as Science in the Early Commentaries on «Johannitius», in «Tradi-tio», 43 (1987), 121-45; Id., The Construction of a Philosophical Medicine. Exegesisand Argument in Salernitan Teaching on the Soul, in «Osiris», 6 (1990), 42-61; F.Wallis, The Articella Commentaries of Bartholomaeus of Salerno, in La scuola medicasalernitana, 125-64; I. Caiazzo, Un inedito commento sulla Isagoge Iohannitii conser-vato a Parigi, in La scuola medica salernitana, 93-123.

29. Commentary on Isagoge Iohannitii, ms. Chartres, Bibliothèque municipale,171, f.1rb: «Elementum sic describitur: elementum est simpla et minima compo-siti corporis particula. Simpla autem ita intelligo, id est indivisibilis, que et sensuet intellectu simpla consistit. Sunt enim quedam sensu simpla, intellectu verocomposita, ut lapides, metalla et elementorum individua, ut hec terra, hic igniset cetera. Que si elementa dicuntur, inproprie tamen. Elementa [elementata ms.Bury St. Edmunds; transcr. by F. Wallis, McGill University, Montreal], namquedicuntur, id est ab elementis composita. Elementum sic describitur, sed sic divi-ditur: elementum aliud ignis, † [since the Chartres manuscript was destroyedduring the Second World War, the rest of the quotation is taken from F. Wallis’transcription of the ms. Bury St. Edmunds] aliud aer et cetera. Hic videndum estquot qualitates unumquotque elementum habeat et quomodo habeat illas, sive ase, sive ab altero, et utrum habeat substantialiter sive accidentaliter. Ignis habetduas qualitates, caliditatem et siccitatem alteram, scilicet caliditatem ex natura suisibique substantialem, alteram vero mutuatur ab assidue volutione circuli lune –teste Constantino, in Pa<n>tegni, que tamen sibi est substantialis. Aer vero habetcaliditatem et humiditatem, caliditatem ab igne, humiditatem ex natura sui, etutraque, sibi substantialem. Aqua vero frigiditatem habet et humiditatem, frigidi-tatem ex natura sui, humiditatem ab aere, et utraque substantialem. Terra est fri-gida et sicca, sicca ex natura sui, frigida ab aqua, et hoc substantialiter. Sciendumest quod due qualitates sunt active: videlicet calor et frigiditas, et due passivevidelicet siccitas et humiditas. Calor agit in siccitatem faciendo eam et frigiditasin humiditatem constringendo eam. Modo videndum est quomodo corpora tamanimata quam inanimata constituantur ab ipsis elementis».

30. Commentary on Isagoge Iohannitii, ms. Oxford, Bodleian Library, Digby 108,f. 5v. Transcription from ms. London, British Library, Addition 18210, f. 107vb:«Elementum est simpla et minima corporis compositi particula. Minima quan-tum ad quantitatem aliarum corporis partium dicitur, simpla quantum ad seipsam. Simplam enim rem dicimus secundum Costantinum, quae, cum sit una eteadem in essentia, similis est in partibus, non quod simplicia elementa parteshabeant, sed sunt similia in partibus, id est simplicia, quia unumquodque ele-mentum alii idem corpus componenti in simplicitate simile est. Vel dicatur hocde elementatis; ex hoc tamen quidam habere volunt quod non sint elementa nisihaec quae diximus elementata, et haec dicunt simplicia quantum ad alia magiscomposita, sicut consimilia membra dicuntur simplicia, haec autem sunt in par-tibus similia. Simplam autem rem intelligo quae intellectu solo simpla consistit.Quaedam enim sensu sunt simplicia, ratione composita, ut lapides qui sensualitersunt simplices, ratione considerati, compositi ex elementis concipiuntur, ut istaelementa – hic ignis, hic aer et sic de aliis – quae secundum precedentia non

Generally speaking, the Digby commentary has numerous med-ical theories in common with the works of William of Conches.Brian Lawn and Mark Jordan briefly mention these convergentinterpretations, which are, however, deserving of fuller study. Williamof Conches clearly borrowed several theories from the Digby com-mentary, including those relating to the complexion of brain cellulae,vision and digestion, and gynaecology 31. Moreover, the Digby com-mentary is the source for his typology of the four temperaments 32.For example, as early as the Glosae super Boetium,William of Conchesuses the word cellula to refer to the various parts of the brain wherethe cognitive faculties of imagination, reason, and memory arelocated. The use of this word proves that he was already drawing onmedical treatises when writing the Glosae super Boetium, as demon-strated by Danielle Jacquart in the present volume. Furthermore, itindicates that he had the Digby commentary open before him, sinceit was the first twelfth-century work to use the word cellula to di-stinguish between parts of the brain and to attribute a complexion tothem (William of Conches’ earliest mention of the complexion ofthe cellulae is in the Philosophia) 33. Mark Jordan convincingly arguesthat the Digby commentary was doubtless the work of the unidenti-fied Salernitan author who wrote the Seconda dimostrazione anatomica,published in Salvatore de Renzi’s Collectio Salernitana 34.

13


debent dici elementa, sed elementata, id est ex elementis composita». The wordelementatum, rather than elementum, is also found in some of the earliest manus-cripts of Adelard of Bath’s Natural Questions, such as the ms. Paris, Bibliothèquenationale de France, lat. 6628, dating from 1140-1150. On Natural Questions, cf. C.Burnett, William of Conches and Adelard of Bath, published in the present volume.

31. Elford, William of Conches, 325-26, points out parallels between William ofConches’ thinking on gynaecology and the Digby commentary. Cf. also TheProse Salernitan Questions, Edited from a Bodleian Manuscript (Auct. F. 3. 10). AnAnonymous Collection Dealing with Science and Medicine Written by an Englishman c.1200, with an Appendix of Ten Related Collections, ed. B. Lawn, London 1979 (Auc-tores Britannici medii aevi, 5), Introduction, XX; 2-16.

32. Cf. R. Klibansky, E. Panofsky, F. Saxl, Saturno e la Melanconia, transl. Turin2002, 98.

33. On the correspondence between the vocabulary used by William ofConches and the Digby commentary, cf. Jordan, Medicine as Science, 136; Id., TheConstruction of a Philosophical Medicine, 52. Excerpts on the cellulae from theDigby commentary are published in I. Caiazzo, Imagination et intellect chez lesmaîtres salernitains, in Intellect et imagination dans la philosophie médiévale, Actes duXIe Congrès international de philosophie médiévale de la SIEPM (Porto, 26-28août 2002), edd. M. C. Pacheco, J.-F. Meirinhos, Turnhout 2006, [1009-25], 1017.

34. Seconda dimostrazione anatomica, in Collectio Salernitana ossia documentiinediti, e trattati di medicina appartenenti alla scuola medica salernitana, II, ed. S. deRenzi, Naples 1853 (remprinted with a preface by A. Garzya, Naples 2001), 391-

The argument that both the definition elementata, id est ex ele-mentis composita and the word elementatum have a Salernitan origin isfurther strengthened by the Apex phisice, a treatise on natural phi-losophy, in all probability addressed to Robert of Selby († 1151). Itsauthor criticizes the distinction elementum/elementatum, which heattributes to the Salernitans 35. The comparison between William ofConches’ early works and Salernitan medical literature clearly showsthe latter’s influence. However, the nature of the contacts betweenSalerno and Francia remains far from clear.

We now return to the discussion of elements in the Glosae superBoetium. William observes that those who maintain that man isunable to behold the true elements disagree as to their nature,dividing them into three groups:

1) Some say that the properties of elements are themselves ele-ments, and that therefore everything is constituted by the four pro-perties of the elements 36. This thesis is found in the Pantegni 37 andis criticized in Nemesius of Emessa’s De natura hominis (translated by

14

IRENE CAIAZZO

401. On this text and the various Salernitan anatomies, see R. Martorelli Vico,Gli scritti anatomici della Collectio Salernitana, in La Collectio Salernitana di Sal-vatore De Renzi, Convegno internazionale Università degli Studi di Salerno (18-19 giugno 2007), edd. D. Jacquart, A. Paravicini Bagliani, Florence 2008, 79-88.

35. This testimony is mentioned by Silverstein, Elementatum: Its AppearanceAmong the Twelfth-Century Cosmogonists, 162. Cf. the edition of the Apex phisiceanonymi by H. Lemke and G. Maurach in «Abhandlungen der braunschweigi-schen wissenschaftlichen Gesellschaft», 45 (1994), 171-263; 49 (1999), 7-80; cf. 45(1994), 232: «Sed nobis Salernitani prave opponunt dicentes: “elementa non suntsimpla, ut superius exposuistis.Videmus enim intra terram aquam, ignem, aerem,et e converso in aqua aerem, ignem. Et hec terra, que videtur, aqua, aer, ignis, quevos dicitis elementa, non sunt elementa sed elementata”». On the Apex phisice, seeJ. Cadden, Two Definitions of Elementum in a 13th-Century Philosophical Text, inScience et Philosophie: Antiquité – Moyen Âge – Renaissance, Actes du XIIe Congrèsinternational d’Histoire des Sciences (Paris 1968), Paris 1971, t. III A, 33-36.

36. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. Nauta, 162: «Etdicunt alii proprietates elementorum esse elementa, et ita constare omnia exquatuor elementis, id est ex quatuor proprietatibus elementorum».

37. Constantinus Africanus, Pantegni, Theorica I, 4, ed. Burnett, 85-86: «Palamest ergo elementa esse quattuor quae sensu apparent simpla intellectu vero com-posita. Nunquam enim subsistit terra sine aquae, ignis aeris, parte aliqua, nequecetera similiter. Quodcumque tamen horum sua propria qualitate est contentum,illud proprie est elementum. Quod, etsi non sensui patet, tamen intellectui.Unde philosophi dixere in mundo quattuor esse elementa, id est calidum, frigi-dum, siccum, humidum. Neque in his solas qualitates intelligunt, set subiectaearum. Calidum enim actualiter perfectum ignem esse dicunt, frigidum actualeet perfectum, aquam, humidum actualiter perfectum aerem, siccum actualiter etperfecte dicunt terram esse».

Alfano of Salerno) 38. William was to return to this subject in hisGlosae super Platonem 39.

2) Others dream imagining that the true elements are the speciesof which these elements are individua 40. This theory may be com-pared to the Pantegni and to a passage from the Digby commentaryon the Isagoge Iohannitii 41.

3) Others maintain that the true elements are those of which theelements we see are composed: pure earth (not combined with theproperties of the other elements), pure water, pure fire, and pure air.These pure elements exist only potentially (natura) and never in act,because they are always mixed in a body. If one were to mix winewith water, it would be impossible to distinguish the wine from thewater.Yet the wine is one thing, and the water another. Likewise, thefour elements can never be distinguished in separate states, althougheach element is different from the others 42.The two kinds of mixture(true mixture and the juxtaposition of simple particles) are evoked inNemesius’ De natura hominis, but Alfano’s Latin translation does notuse the same terms as William of Conches, nor does it mention theexample of wine and water 43. On the other hand, this example is to

15


38. Nemesius Emesenus, Premnon physicon, 5, ed. Burkhard, 62: «Sed nequequalitates per se possunt esse elementa».

39. Guillelmus de Conchis, Glosae super Platonem, 158 (Tim. 27D), ed.Jeauneau, 285: «NEC NATURAM MODO ILLAM VETEREM QUAE FUIT ANTE CON-CRETIONEM. Vera et vetus natura elementi est illa substantialis qualitas quamhabet ex se. Cum enim unumquodque duas qualitates habeat, unam habet ex se,alteram ab alio ut ait Constantinus; ut terra ex se est sicca, ex aqua est frigida,aqua frigida ex se, ex aere humida, aer est humidus ex se, ex igne calidus, ignisest calidus ex se, ex terra siccus».

40. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. Nauta, 162-63:«Alii somniant species, quorum elementa ista sunt individua, elementa esse».

41. Commentary on Isagoge Iohannitii, ms. Oxford, Bodleian Library, Digby 108,f. 5v: «Sed ut stricte accipiantur, dicimus elementa universalia illa simplicia, etparticularia considerata in corporum constitutione, id est individuata in cor-poribus constitutis».

42. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. Nauta, 163:«Alii dicunt elementa esse ea ex quibus constant ista elementa, scilicet puramterram sine proprietatibus aliorum, et puram aquam et aera et ignem. Sed cumquaeritur ab eis ubi est pura terra et purus ignis et cetera, dicunt nusquam essepura actu sed natura, quia in omnibus corporibus mixta sunt, veluti si omnevinum et omnis aqua mixta essent, non inveniretur vinum per se neque aqua perse; et tamen aliud esset vinum, aliud aqua. Sic quamvis non inveniantur separataquatuor elementa, tamen unum est diversum ab alio, sed ita non potest actuinveniri».

43. Nemesius Emesenus, Premnon physicon, 5, ed. Burkhard, 66.

be found in the Pantegni 44, and is quite likely that William of Conchesredefined the information he adopted from this medical work.

None of the reviewed theories appeals to William of Conches,and he rejects them all. Following a very detailed plan that showsthe complexity of his reasoning, he moves on to the next stage andreveals his own opinion: the elements are what we see in a separatestate in the sensible world, namely earth, water, air, and fire. Earth isinhabited by men and reptiles, water by fish, air by birds, and fire bycelestial animals – the stars 45.

William then counters the arguments of his adversaries, who hebelieves misinterpret Plato. Some arguments criticized by William ofConches stem from Calcidius’ Commentary on the Timaeus, where arebeing discussed ignis purus and igneum, and where it is stated thatignis purus is the species of sensible fire 46. One wonders whetherWilliam’s attacks are directed against Calcidius or else against Cal-cidius’ followers. However, William of Conches explains that Platodid not state that one element dissolves into another, but rather thatpart of an element, which he calls terreum, igneum, etc., dissolves intoanother. Terreum dissolves in water, and what remains after such dis-solution is the element earth 47. Earth and water heat up not becausethey have fire in them naturaliter, since their nature is cold, butbecause earth and water receive the heat of fire from elsewhere, acci-dentaliter 48. Similarly, fire is not contained in stone, but when a body

16

IRENE CAIAZZO

44. Constantinus Africanus, Pantegni, Theorica, I, 4, ed. Burnett, 88: «Harumcommixtionibus et naturae suae in hac quam non habebant commutationibusefficitur quicquid struitur. Neque tamen ita quomodo a nobis diversa commis-centur corpora. Si enim vinum et aquam misceamus, commixta sensualiter unumesse videntur. Set unumquodque in sui natura subsistit et intellectu neque inaliud esse mutatur, sicut in sanguine panis comestus traducitur, semen mandatumterrae naturam accipit herbe».

45. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. Nauta, 163:«Sed nec istud nec illud michi placet. Immo placet michi elementa esse quaevidentur a nobis separata, scilicet terra et aqua et cetera. Et unum de elementisinhabitant homines et reptilia, scilicet terram; sed aliud aquatilia, scilicet aquam;aliud volatilia, scilicet aera; aliud caelestia videlicet ignem».

46. Cf., for example, Calcidius, Commentarius in Timaeum, 272, ed.Waszink, 276.47. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. Nauta, 163-64:

«Quod vero Plato quaerit quare magis dicatur terra quam aqua, et postea affir-mat terreum non terram, et sic de aliis, intelligendum est Platonem hoc dixissenon de elementis, immo de partibus eorum quae in alia dissolvuntur. Numquamenim totum elementum in aliud resolvitur. Dicatur igitur secundum Platonem:quod dissolvitur in aquam, terra non est sed terreum, id est pars terrae; quodvero remanet, terra est et elementum; et similiter de ceteris elementis».

48. Ibid., III, m. 9, 164: «Quod vero dicunt terram et aquam numquam cale-fieri nec ex lapide ignem excuti nisi in eis esset ignis, aperte falsum est. Calor

strikes a stone, the air moves quickly and heats up. It is then illumi-nated and transformed into fire. Sound is produced by the collisionbetween iron and air rather than coming forth from the air (a refe-rence to Macrobius, Commentarii in Somnium Scipionis, II, 1) 49.

William of Conches concludes that the matter of the world – andindeed the world itself and all it contains – is made up of these ele-ments, not the fictitious elements dreamed up by fools. As Platostates, God wanted to make the world indissoluble and ageless, thusleaving nothing outside the world. The world is perfect, composedof perfect and integral elements. If anything existed outside theworld, it would represent a threat to its equilibrium, since externalelements could be added to the elements contained within theworld or attract the elements that constitute the world, underminingits stability 50.

1.2. The qualities of and links between the elements

William of Conches is indebted to previous traditions for his theo-ries of the qualities and links between the elements. It is thereforeuseful to outline the theories of such authors as Calcidius, Macro-

17


enim alius est naturalis, alius accidentalis, et ita quaedam calent naturaliter, quae-dam accidentaliter. Sed quae naturaliter calent, in se habent quo calent; quaevero ex se non calent sed ex accidente, extra se habent quo calent. Terra vero etaqua naturaliter sunt frigida; est enim terra naturaliter frigida et sicca, aqua fri-gida et humida. Cum ergo calent, ex accidente calent, et extra se habent quocalent. Falsum est ergo in eis esse ignem quo calent». Cf. Commentary on IsagogeIohannitii, ms. Oxford, Bodleian Library, Digby 108, f. 7r: «Accidentaliter ut aquacalida quae calorem illum a se non habet sed ab igne».

49. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. Nauta, 164:«Quod autem dicunt ex lapide ignem non posse excuti nisi in eo esset, falsumest. Cum enim lapis percutitur ex violenta duorum corporum collisione move-tur aer, aer motus calefit, calefactus resplendet, et fit ignis. Non ergo exit ignisde lapide, sed fit ex violenta lapidis et alterius corporis collisione, quemadmo-dum sonus non exit ex aere, sed fit ex collisione ferri et aeris».

50. Ibid., III, m. 9, 165: «Materia ergo mundi sunt ista quatuor elementa, nonillorum stultorum ficticia. Ex istis fit mundus et omnia quae in eo sunt. Sed, utait Plato, volens deus facere mundum citra senium et dissolutionem, id est talemqui nec senescere posset nec aliquo casu dissolvi excepta creatoris sui voluntate,nichil de elementis extra mundum dimisit, sed eum perfectum ex perfectis etintegris elementis composuit. Videbat enim quod si aliquid de elementis extramundum esset, importune accedendo vel recedendo ei nocere posset, quodvideri in homine potest. Importune enim accedendo terra suffocat, aqua sub-mergit, aufert aer anhelitum, ignis comburit. Similiter importune recedendoeidem noceret. Importune enim recedendo ignis reddit hominem frigidum, aersine vitali anhelitu, aqua sine humore, terra sine pondere. Quod ut abessetmundo, nichil de elementis dimisit extra mundum».

bius, Boethius, Nemesius of Emessa, as well as those of the majormedieval commentators on Boethius’ Consolation of Philosophy. All ofthese constitute the conceptual frame for William of Conches’ Glosae.

Boethius evokes the links between the four elements, consistingof numbers, in the Consolation of Philosophy meter 9, Book III: Tunumeris elementa ligas, ut frigida flammis arida conveniant liquidis. This isa reference to the Timaeus, in which Plato set forth his theory ofthe elements. Plato argued that each element is a regular polyhe-dron: fire is a pyramid, air an octahedron, water an icosahedron, andearth a cube.The elements also possess qualities arising directly fromtheir geometrical form. For instance, fire, in the form of a pyramid,is mobile, sharp, penetrating, and light. Earth, in the form of a cube,is immobile (Tim. 55e-57a). The faces of the three polyhedra Platochose for fire, water, and air can be broken down into scalene trian-gles; the face of the cube, chosen for earth, breaks down into isosce-les triangles. Plato also added a fifth polyhedron, the dodecahedron,which the demiurge used in creating the ultimate arrangement ofthe All (nothing further is mentioned about this fifth element, a factwhich has caused much difficulty for exegetes of the Timaeus) 51.Earth can be broken down into isosceles triangles by the penetratingaction of fire, but it cannot be transformed into another element. Itstriangles can merely be taken apart and put back together again. Inshort, decomposed earth can only produce earth.

The section of the Timaeus (55a-57d) in which Plato attributespolyhedra to the elements was not translated by Calcidius. Never-theless, it was not entirely unknown in the medieval Latin world,since the theory of the elements in the Timaeus gave rise to differ-ing interpretations among authors of Late Antiquity, including Cal-cidius, Macrobius, Nemesius of Emessa, and Boethius.

a) Calcidius, Macrobius, Nemesius of Emessa and Boethius

Calcidius’ Commentary on the Timaeus interprets Plato’s theory ofthe elements in qualitative terms to explain the reciprocal transfor-

18

IRENE CAIAZZO

51. L. Brisson, Le Même et l’Autre dans la structure ontologique du Timée dePlaton. Un commentaire systématique du Timée de Platon, Sankt Augustin 19942,358-93; Id., La théorie de la «matière» dans le Timée de Platon et sa critique par Ari-stote dans la Physique, in L’alchimie et ses racines philosophiques. La tradition grecqueet la tradition arabe, ed. C.Viano, Paris 2005, 15-35; Id., How and Why do the Build-ing Blocks of the Universe Change Constantly in Plato’s Timaeus (52a-61c)?, in PlatoPhysicus. Cosmologia e antropologia nel Timeo, edd. C. Natali, S. Maso, Amsterdam2003, 189-205.

mations among the elements. He tackles the question of the ele-ments and of solid, three-dimensional bodies in general in his com-ments on Timaeus 31, in which Plato deals with the generation ofthe sensible world. Plato first mentions fire and earth, located at theopposite extremities of the world, before explaining that two furtherintermediary elements must be introduced to link these twoextremes and create continuity in the body of the world, accordingto the principle of continuous proportion, «which the Greeks callsyneches analogia» 52. This explanation follows the rules of geome-trical proportions: to link together two solids (fire and earth), twomeans are required 53. Calcidius explains these passages with the helpof figurae. However, at the end of this long passage, he concludesthat the solids chosen by Plato for earth and the other three ele-ments are incommensurable, since they do not have equal angles.The faces of these polyhedra are made up of either isosceles or sca-lene triangles, which prevents the complete and reciprocal transfor-mation of one element into another. Furthermore, Plato expresslystates that earth is immobile, and is not transformed at all. Calcidiusis obliged to argue that Plato foresaw this difficulty and stated thatthere are similarities not merely in formis et figuris sed etiam in poten-tiis et qualitatibus 54. The introduction of three qualities for each ele-ment ensures the ratio continui competentis, the analogia between theparts of the world. Plato mentions these secondary qualities in pas-sing, but they are a key point of Calcidius’ argument, enabling himto link the four elements, particularly fire and earth, which have noquality in common at all. Each element thus has three qualities: fire issubtle, mobile, and sharp (subtilis, mobilis, acutus); air is subtle, mobile,and blunt (subtilis, mobilis, obtunsus); water is blunt, corpulent, andmobile (obtunsa, corpulenta, mobilis); earth is blunt, corpulent, andimmobile (obtunsa, corpulenta, immobilis) 55. These six qualities enablethe elements to transform and form links, which must take place in

19


52. Calcidius, Commentarius in Timaeum, 18, ed. Waszink, 68.53. Ibid., 13-20, 65-71.54. Ibid., 21, 71-72: «Dixit enim [scilicet Plato], si meminimus, similitudinem

non solum in formis et figuris sed etiam in potentiis et qualitatibus quaeri opor-tere, cum ita dixit: “Cum in tribus sive numeris seu molibus seu potentiis per-inde erit medietas imo, quem ad modum summitas medio [Tim. 31c-32a]”.Quare si inter ignem et terram nulla est in specie et velut in vultu similitudo,quaerenda erit in naturis ac qualitatibus ipsorum elementorum iuxta quas faciuntaliquid aut patiuntur et in his proprietatibus ex quibus utriusque elementi vis etgermanitas apprime designatur».

55. Ibid., 22, 72-73.

either ascending or descending order: one cannot go from fire toearth, and vice versa, without passing through water and air. Thesequalities, established by Calcidius, were widely adopted in theMiddle Ages.

Macrobius’ Commentarii in Somnium Scipionis introduces a briefexposition on the four elements when illustrating the power of thenumber seven. He first evokes Timaeus 31-32 (giving a rather freetranslation), affirming that the artisan god introduced air and waterbetween fire and earth in order to link these elements indissolubly.He does not rely explicitly on a mathematical explanation to illus-trate the links between the elements, and the allusions to solidbodies are simply analogies 56. However, he draws on the four Aris-totelian qualities – hot, wet, cold, and dry – to explain how thelinks between the elements are established, namely through circula-rity: fire is not completely opposed to earth, because they have dry-ness in common; water and air are linked by means of wetness, andso on. This creates a continuous cycle of reciprocal transformationsbetween the elements. Macrobius states that each element reachesout to its two neighbors by means of their shared qualities 57. Subse-quently, the image of the elements embracing each other was trans-posed into the pictorial level in medieval manuscripts 58.

In his De institutione arithmetica (II, 46) Boethius affirms that hewill provide a useful explanation for the very difficult cosmogony ofthe Timaeus (32a-b). To be linked to one another, all plane figuresrequire a single mean term, whereas cubes require two. Introducing6 is enough to connect 4 and 9 (the first two plane figures resultingfrom the squares of the first even number and the first oddnumber), while 12 and 18 must both be introduced to link 8 and 27(the first two solids resulting from the cubes of the first evennumber and the first odd number) 59. This chapter of the De arith-metica, which provides a clear key to the Timaeus, seems to be the

20

IRENE CAIAZZO

56. Macrobius, Commentarii in Somnium Scipionis, I, 6, 22-24, ed. et transl. M.Armisen-Marchetti, Paris 2001, 29-30.

57. Ibid., I, 6, 25-33, 30-32.58. For the ancient sources of the physics of the elements, cf. B. Obrist, La

cosmologie médiévale. Textes et images. I. Les fondements antiques, Florence 2004(Micrologus’ Library, 11), 227-310, and particularly the rich iconographicalappendix, which includes several figurae representing the links between the ele-ments.

59. Boethius, De institutione arithmetica, II, 46, ed. et transl. J.-Y. Guillaumin,Paris 1995, 153-55.

main source for the medieval commentators of the Consolation ofPhilosophy in their glosses on the verses from meter 9, Book III: Tunumeris elementa ligas.

Nemesius of Emessa’s De natura hominis explains the connectionsbetween the four elements by retaining two Aristotelian qualities foreach element. He sets forth the Platonic theory of the polyhedraand assigns three qualities to each element, but in a form that dif-fers from that of Calcidius 60. His treatise was not available in Latinbefore the late eleventh century.

These ancient sources present two alternative models for explain-ing the links between the elements discussed by Plato in theTimaeus. On the one hand is a mathematical explanation whichconsiders the four elements to be solid bodies with three dimen-sions, and which, in the case of Calcidius, concludes with the theoryof the six qualities (three for each element). On the other is a phy-sical explanation based on the four Aristotelian qualities, which takesno account of the three dimensions of the elements. Medievalauthors drew on these two models.

b) Boethius and his medieval commentators

Boethius expresses himself poetically in his discussion of the fourelements in the Consolation of Philosophy, which led medieval com-mentators to interpret the discussion in a wide variety of ways.Before tackling these interpretations, it should be noted that follow-ing the aforementioned authors of Late Antiquity, Isidore of Sevillejuxtaposes the four Aristotelian qualities (cited after Ambrose’sHexaemeron) and the six Platonic qualities, with no theoreticalexplanation 61. During the High Middle Ages, authors simply enu-merated the Aristotelian and Platonic qualities, introducing a fewvariations on Calcidius, and occasionally praising the links thatensure continuity between the elements and the different parts ofthe world. They did not seem to question the theoretical feasibilityof the reciprocal transformations of the elements, although it wasCalcidius’ questions over this doctrinal point from the Timaeus thatled him to attribute three qualities to each element in his Commen-tary on Timaeus.

21


60. Nemesius Emesenus, Premnon physicon, 5, ed. Burkhard, 68-69.61. Isidorus Hispalensis, De natura rerum, XI, 1-3, ed. J. Fontaine, Bordeaux

1960; repr. Paris 2002, 213-17.

In the commentary on the Consolation of Philosophy attributed toRemigius of Auxerre, only the Aristotelian theory of the four qua-lities is used to illustrate the links between the elements 62. Theselinks are called sinzugiae, a term spelt in a variety of ways in Latin(syzugia, sinzugia, synzugia, zinzugia), and found in Aristotle’s Decaelo, De generatione et corruptione, and Meteorologica to indicate thelinks between the elements. The commentator specifies that sinzu-giae are mediatae or inmediatae, depending on whether two elementscan be directly linked to one another or require the mediation of athird element. The term synzugia (in the sense intended by thecommentator) is found in Johannes Scottus’ Latin translation ofGregory of Nyssa’s De imagine, where only the Aristotelian theoryof the four qualities is mentioned when it comes to the four ele-ments 63. It is therefore no surprise to encounter the term sinzugia inthe commentary on the Consolation of Philosophy attributed toRemigius of Auxerre. However, no reference is made to Calcidius’explanation based on the six qualities, which suggests that theauthor was unfamiliar with the Latin translation of the Timaeus andthe Commentary by Calcidius 64.

22

IRENE CAIAZZO

62. The attribution to Remigius of Auxerre has often been questioned. Cf. F.Troncarelli, Per una ricerca sui commenti altomedievali al De Consolatione diBoezio, in Miscellanea in Memoria di Giorgio Cencetti, Turin 1973, [363-80], 377-78;Id., Tradizioni perdute. La Consolatio Philosophiae nell’ alto medioevo, Padua 1981,144-49. Cf. also J. Wittig, The «Remigian» Glosses on Boethius’s ConsolatioPhilosophiae in Context, in Sources of Wisdom: Old English and Early MedievalLatin Studies in Honour of Thomas D. Hill, edd. C. D. Wright, F. M. Biggs, T. N.Hall, Toronto 2007, 168-200, and M. Godden, The Latin Commentary Tradition andthe Old English Boethius: the Present State of the Question, Paper given at the first an-nual symposium of «The Alfredian Boethius Project», University of Oxford, July2003, retrieved from http://www.english.ox.ac.uk/boethius/Symposium2003.html;cf. also Id., Alfred, Asser, and Boethius, in Latin Learning and English Lore: Studiesin Anglo-Saxon Literature for Michael Lapidge, I, edd. K. O’Brien O’Keeffe, A.Orchard, Toronto 2005, 326-48.

63. M. Cappuyns, Le De imagine de Grégoire de Nysse traduit par Jean ScotÉrigène, in «Recherches de théologie ancienne et médiévale», 32 (1965), [205-62],257, l. 28. In Dyonisius Exiguus’ translation, entitled De opificio hominis, the termconiugatio is used instead of synzugia, cf. PL 67, 401B. Macrobius uses the wordsyzygia, in Greek, in Saturnalia, VII,7, 19, to indicate the seven «couples» ofnerves that originate in the cavities of the brain. He does not, however, use itfor the links between the four elements.

64. Various extracts from the commentary on the Consolation of Philosophyattributed to Remigius of Auxerre have been published and a complete editionis planned in the series Corpus Christianorum, continuatio Mediaevalis. For thecommentary on Book III, m. 9, cf. E. T. Silk, Saeculi Noni Auctoris in BoetiiConsolationem Philosophiae Commentarius, Rome 1935, Appendix, 334-35: «TUNUMERIS ELEMENTA LIGAS id est coniungis. NUMERIS id est quatuor monadibus.

The eleventh-century author Adalbold of Utrecht illustrated theverse Tu numeris elementa ligas with a mathematical explanationbased on the theory of means: since two means (12 and 18) areneeded to link the two solid numbers 8 and 27, air and water mustsimilarly be introduced to link fire and earth. His exposition isclearly based on the De institutione arithmetica. He also speaks of azinzugia (which he glosses with the word copulatio) between the ele-ments. The «copulative» action exerted by air and water is supposedto hold the world together, preventing fire from flying away andearth from sinking. Adalbold of Utrecht does not mention either thesix «Platonic» qualities mentioned by Calcidius’ Commentary on theTimaeus (a work of which he was clearly unaware) or the four Aris-totelian qualities 65.

In concluding this section, we note a commentary on the Conso-lation of Philosophy, probably written in the very early twelfth cen-tury, that needs to be viewed alongside the teaching of a certainmagister Menegaldus 66. The author, as yet unidentified, presents a verycomplete exposition on the links between the elements. He proba-bly draws on the commentary attributed to Remigius of Auxerre incommenting on the zinzugiae (which he glosses with coniunctiones)mediatae and immediatae produced among the elements by means of

23


Nam quatuor sunt elementa quorum sex sunt coniunctiones quas Graeci sinzu-gias vocant. Quorum quatuor sunt inmediatae et duae mediatae. Inmediatae suntistae. Aer calidus et humidus est. Huius caliditas coniungitur caliditati ignis quiest calidus et siccus. Ignis est calidus et siccus. Huius caliditas aeris caliditaticoniungitur siccitas autem terrae copulatur quae est frigida et sicca. Terra frigidaest et sicca. Huius siccitas ignis siccitati coniungitur. Frigiditas vero aquae frigi-ditati nectitur. Aqua frigida est et humida. Eius frigiditas terrae frigiditati humi-ditas autem aeris humiditati sociatur. Mediatae sinzugiae hae sunt, id est quaecontrariae sunt nec possunt coniungi sine aliqua medietate. Ignis et aqua contra-ria sunt, quia ignis calidus est et siccus, aqua frigida et humida. Nam ut frigidi-tas aquae ignis conveniat caliditati terrae frigiditas est media. Ut autem aquaehumiditas siccitati ignis aptetur aeris humiditas media intervenit. UT FRIGIDAFLAMMIS: terra frigida coniungitur igni ex ea parte qua siccus est. ARIDA CONVE-NIANT LIQUIDIS: terra arida coniungitur aquae ex ea parte qua est frigida».

65. Adalboldus Traiectensis, Commentarius in Boetii Consolationem Philosophiae,ed. R. B. C. Huygens, Serta Mediaevalia. Textus varii saeculorum X-XIII, Turnhout2000 (CCM, 171), [121-40], 133: «UT FRIGORA FLAMMIS / ARIDA CONVENIANTLIQUIDIS, NE PURIOR IGNIS/ EVOLET AUT MERSAS DEDUCANT PONDERA TERRAS.Frigora flammis per aeris zinzugiam, id est copulationem, arida liquidis peraquarum copulationem conveniunt: liquida enim est aqua, sed liquidior est aer.Qualitates ignis evolationem, qualitates terrae quaerunt dimersionem, sed sicduobus mediis adinvicem ligantur, ut nec ista dimergi nec ille possit evolare».

66. Cf. I. Caiazzo, Magister Menegaldus, l’anonyme d’Erfurt et la ConsolatioPhilosophiae, in «Revue d’histoire des textes», N.S., 6 (2011), forthcoming.

the four Aristotelian qualities: hot, cold, dry, and wet 67. Surprisingly,he is also aware of the six qualities mentioned in Calcidius’ Com-mentary on the Timaeus. After adducing the explanation of the arith-metical and geometrical means (either basing himself directly onBoethius’ De arithmetica or taking up Adalbold of Utrecht’s com-mentary), the anonymous commentator of the school of magisterMenegaldus provides a very careful exposition, explaining that sinceearth and fire have no qualities in common, two intermediate ele-ments must be introduced: air, which has two qualities identical tofire and one different from it, and water, which has two qualitiesidentical to earth and one different from it. He adds that the con-junction is made in the likeness of solid numbers 68. The authorclearly understands that Calcidius established a relation between thesolids, the four elements, and the qualities. He then explains theconjunction arising between the elements in the likeness of planenumbers. In this case, a single intermediary suffices; fire, which is hotand dry, is linked to water, which is cold and wet, by means of air,which is both hot and wet 69. The commentator relies on the fourAristotelian qualities to explain this second type of conjunction. Hethus makes use of both the mathematical explanation, which he usesas an analogy, and the physical explanation, evoking the Calcidianqualities at one point and the Aristotelian qualities at another.

Following our excursus on the qualities of and links between theelements, which helps put into perspective William of Conches’contribution to the debate on these issues, we now turn to his

24

IRENE CAIAZZO

67. Excerpts from this commentary, also known as the Anonymus Erfurtensis,have been published by N. Häring, Four Commentaries on the De ConsolationePhilosophiae in MS. Heiligenkreuz 130, in «Mediaeval Studies», 31 (1969), 287-316. For the zinzugiae mediatae and immediatae, cf. ibid., 309-10.

68. Ibid., 308: «Sciendum quoque est quomodo dicit deum ligare ELEMENTApredicta, scilicet terram et ignem, NUMERIS. Quod ad similitudinem dictum est.Sicut enim duo cubici [numeri add. ed. Häring] et solidi numeri dimensioneinter se distantes uno medio firmo et eadem proportione non possunt copu-lari sed indigent duobus mediis ex se confectis ad suam copulationem sic deuselementa media ex qualitatibus supradictorum que prorsus inter se differuntfecit ad ipsorum firmam copulationem».

69. Ibid., 309: «Potest quoque alia similitudine dici ELEMENTA ligata esseNUMERIS, scilicet ad modum planorum numerorum. Plani numeri dicuntur quitantum habent duas dimensiones, scilicet longitudinem et latitudinem, ut bisbini et ter terni. Hic vero uno medio possunt coniungi sic: […]. Nam si demusigni siccum et calidum et aque humidum et frigidum poterunt hec duo copu-lari per aerem qui ab igne calidum recipit et ab aqua humidum. Et per terramsimiliter que ab aqua frigidum et ab igne recipit siccum firma copulatione».

Glosae super Boetium. William of Conches draws on earlier commen-taries on the Consolation of Philosophy in explaining the verse Tunumeris elementa ligas. He starts by stating that the elements are con-nected in the manner of numbers, ad modum numerorum. Havingencountered the term sinzugia in one of the earlier commentaries(doubtless that attributed to Remigius of Auxerre or the unknownauthor from the school of magister Menegaldus), he proposes an ori-ginal new interpretation, coining the terms sinzugia plana and sinzu-gia cubica. The sinzugia plana is a conjunction that requires a singlemean term, as is the case for surface numbers. It connects two ele-ments such as earth (cold and dry) and air (hot and wet), requiringa single intermediary element – water (cold and wet) 70. The sinzu-gia cubica concerns cubic numbers and requires two mean terms.Thesinzugia cubica is used to connect fire and earth, although William ofConches does not tell us how. He illustrates the sinzugia cubica withmathematical examples identical to those in Boethius’ De institutionearithmetica, Adalbold of Utrecht’s commentary, and the commentaryfrom the school of magister Menegaldus. Following this mathematicalexcursus, he returns to Boethius’ verse and changes subjects. Heprovides no explanation of how the two intermediaries are posi-tioned between fire and earth. This somewhat awkward expositionproves that he has not yet mastered the links between the elementsin writing his glosses on the Consolation of Philosophy. He combinesthe typical vocabulary of the Peripatetic tradition, sinzugia, withmathematical explanations of a Platonic kind. This indicates that hewas doubtless unfamiliar with Calcidius’ Commentary on the Timaeusat this stage of his career. Nor, moreover, does he cite the six qua-lities Calcidius attributed to the four elements, although as we haveseen, these qualities feature in the commentary from the school ofmagister Menegaldus. Interestingly, even though William of Conchesdoes not mention the six qualities, the scribes of the Leipzig manu-script containing his Glosae super Boetium added a diagram repre-senting the links. The same folio also includes a circular diagram

25


70. Guillelmus de Conchis, Glosae super Boetium, III, m. 9, ed. Nauta, 168:«Similiter inter terram et aera invenitur aqua, quae aequali proportione habet sead utrumque. In quanto enim est levior aqua terra in tanto est gravior aere, etaccipit unam proprietatem ab utroque. Cum enim sit terra frigida et sicca, aercalidus et humidus, aqua frigida est et humida, et accipit frigiditatem a terra, abaere vero humorem. Similiter diligens lector inter ignem et aquam inveniet, etsic de aliis. Sic sapienti satis dictum est de plana sinzugia numerorum et ele-mentorum».

representing the links between the four elements by means of theAristotelian qualities, containing the words «Superficialis colligatioque fit per unum medium» 71. This diagram is often found in manu-scripts of Boethius’ Consolation of Philosophy; indeed it is reproducedtwice in the Leipzig manuscript, at the beginning of the Consolationand at the end of William of Conches’ Glosae super Boetium. This isa significant example of a phenomenon noted by Barbara Obrist:there is often no relation between figurae and texts they are sup-posed to explain in manuscripts – or at least, the relationship is nolonger apparent to the reader.

2. Glosae super Macrobium: Bodies are made up of a mixture of thefour elements

The first change in William of Conches’ theory of the elementsoccurs in the Glosae super Macrobium – a work that remains unpu-blished to date 72 – when he accepts the idea that all bodies are madeup of the four elements. As is his custom, he begins with a refuta-tion of the theory he does not favour. He argues that some authorshave misunderstood the Macrobian lemma (Commentarii in SomniumScipionis, I,6,35: IIII elementorum), since they argue that some bodiesare formed from a single element, others from two elements, othersfrom three, and others still from four. William of Conches dismissesthem: Quod nichil est. Every body is made up of the four elements,although not all four are dominant. It must be acknowledged that astone, for instance, is made up of the four elements, as is wood andthe air that surrounds us. William of Conches notes that this senten-tia is neglected because of the vulgar objections raised by somepeople. The objection is the one he had earlier raised himself in theGlosae super Boetium to criticize those who maintain that the fourelements are to be found in all bodies: that is true, then there is firein my beard, and water in my hand:

26

IRENE CAIAZZO

71. Plate 6 of the edition by L. Nauta, taken from ms. Leipzig, Universitäts-bibliothek, lat. 1253, f. 83v.

72. H. E. Rodnite Lemay is currently editing the text. Cf. H. E. Rodnite, TheDoctrine of the Trinity in Guillaume de Conches’s Glosses on Macrobius: Texts andStudies, New York 1972 (PhD diss.), and her article, The Science of the Stars inWilliam of Conches’ Glosae super Macrobium, published in the present volume.

IIIIOR ELEMENTORUM. Hoc autem quidam sic exponunt: quod omniacorpora constant <ex> quattuor elementis, id est multitudo omnium, nonquod unumquodque videlicet ex quattuor constet, sed quia nullum ex alioconstet, nec est aliquid quod non constet vel ex omnibus quattuor vel extribus vel ex duobus vel ex uno. Quemadmodum si dicerem tota Frantiapossidetur ab istis duobus eo quod est pars, scilicet illius ab uno, pars esset abaltero possessa, non quod quelibet et pars illius ab utroque sit possessa, scili-cet ab isto tota vel ab illo, et isti concedunt quod est quoddam corpus visi-bile quod constat ex solo igne, quoddam ex solo aere, et sic de aliis; quodnichil est. Non est enim corpus quod non constet ex quattuor elementis, etsinon omnia in eo dominantur; concedimus etiam quod in hoc lapide suntomnia elementa, et ignis et aer et cetera. Similiter in hoc ligno et in hocaere et ita de singulis quidem rationibus phisicis in loco suo facile potestprobari. Hec tamen sententia postposita est a multis propter huiusmodi vul-gares obiectiones quod tunc [est] in barba mea est ignis. Hoc enim secun-dum vulgare habet dicere quod in barba habeam ignem et in manu aquam 73.

William of Conches concedes that there are four elements in thestone, perhaps because he now accepts fully the arguments presentedin the Digby commentary on the Isagoge Iohannitii 74. The remark onfire in the beard is again cited and explained in the Glosae super Pla-tonem 75. This new stage in the development of the theory of thefour elements is confirmed by other passages, such as the gloss onthe Commentarii I, 6, 40 76 and the Commentarii II, 12, where Macro-bius affirms that the world is in a sense immortal, like the soul, sinceits parts change but are not completely dissolved. Once the humanbody is deprived of its soul, the elements that make it up return totheir source: the elements. William of Conches follows Macrobiusclosely, and even adds his own touch, stating:

27


73. Versio longior, ms. Munich, Bayerische Staatsbibliothek, clm 14557, f. 126r.The text seems corrupt in the versio brevior, cf. ms. Bamberg, Staatsbibliothek,Class. 40 (HJ.IV.21), f. 11ra.

74. Cf. the passage on the stone cited supra, n. 30.75. Guillelmus de Conchis, Glosae super Platonem, 127, ed. Jeauneau, 231: «Et

nota quod non dicit ex qualitatibus elementorum humanum corpus constare utquidam gartiones confingunt, garrientes quod si ex igne constaret homo, habe-ret ignem in barba et sic exureretur, ignorantes qualiter elementa transeant inhumores, humores spissati in homiomira, homiomira in organica».

76. Versio longior, ms. Munich, Bayerische Staatsbibliothek, clm 14557, f. 127r:«EX IIIIOR (Comm. I,6,40). Ostenso quod IIIIor sunt elementa et tria eorumintersticia, subiungit quod omne corpus ex illis constat IIIIor elementis et tribuseorum coniunctionibus et ita in compositione apparet dignitas ternarii et qua-ternarii».

Omnia que in mundo sunt et habent aliquam originem reverti ad ori-ginem suam. Unde cum omne corpus constet ex IIIIor elementis in ipsadissolvitur, quia quod in eo est spissum et terrenum transit in terram, quodin eo aliquantulum est tenue transit in superiora elementa, et sic nichil inmundo adnichilatur, sed omnia concedimus mutari, quia natura est mutabi-lium. Unde Ovidius: omnia mutantur, nichil interit 77.

3. Philosophia: elements and elementata

The Philosophia marks a new stage compared to developments inthe Glosae super Boetium and the Glosae super Macrobium. It should benoted that Paul Dutton identified two versions of the Philosophia,the first written around 1125-1130 and the second around 1141, sub-sequent to William of Saint-Thierry’s letter to Saint Bernard onWilliam of Conches’ errors 78. However, given that there are no si-gnificant differences in the theory of the elements in the versio priorand the versio altera, the following analysis will draw on the versioprior of the Philosophia, critically edited by Gregor Maurach in 1980.

After discussing the «things that are and cannot be seen», Williamof Conches moves on to the «things that are and can be seen».There are two potential manners of approach to these visible things:that of the philosophers, which is necessary, not probable, and thatof the physici, which is probable, not necessary 79. Among the latter,

28

IRENE CAIAZZO

77. Versio longior, ms.Vatican City, Biblioteca Apostolica Vaticana, Urbinate lat.1140, f. 148r; ms. Copenhagen, Det Kongelige Bibliotek, Gl. Kgl. S. 1910 4°, f.123v. Cf. Ovidius, Metamorphoses, XV, 165.

78. For the date of the versio altera, cf. P. Dutton, The Mystery of the MissingHeresy Trial of William of Conches, Toronto 2006 (The Etienne Gilson Series, 28),25-27; Id., The Little Matter of a Title: Philosophia Magistri Willelmi de Conchis,published in the present volume. On the Philosophia, see the articles cited supraat nn. 23 and 24, and G. Rialdi, Il De philosophia mundi XII sec. L’autore, lastoria, il contenuto medico, Genua 1965; H. Schipperges, Die Schulen von Chartresunter dem Einfluss des Arabismus, in «Sudhoffs Archiv», 40/3 (1956), [193-210], 202-05; Id., Die Assimilation der arabischen Medizin durch das lateinische Mittelalter, in«Sudhoffs Archiv. Beiheft», 3 (1964), 113-18; W. Stürner, Natur und Gesellschaft imDenken des Hoch-und Spätmittelalters, Stuttgart 1975, 36-42; Gregory, Animamundi, 201-09; D. Elford, Developments in the Natural Philosophy of William ofConches: A Study of his Dragmaticon and a Consideration of its Relationship to thePhilosophia, Cambridge 1983 (PhD diss.); A. Speer, Die entdeckte Natur. Unter-suchungen zu Begründungsversuchen einer scientia naturalis im 12. Jahrhundert,Leiden-New York-Cologne 1995 (Studien und Texte zur Geistesgeschichte desMittelalters, 45).

79. Guillelmus de Conchis, Philosophia, I, 7, 19; I, 7, 24, ed. G. Maurach, Pre-toria 1980, 26; 29. Cf. A. Fidora, A. Niederberger, Philosophie und Physik zwischen

some moderns have dealt with these questions in a manner that ismore probable (probabilius) than others. This twofold approach tophysical questions is introduced for the first time in the Philosophia;it is doubtless connected to the disputatio epoptica and the disputationaturalis discussed in Calcidius’ Commentary on the Timaeus 80. All vi-sible things are bodies; all bodies are made up of elements.Thereforethe discussion of visible things begins with the elements. This sub-ject may be approached in the manner of Constantine, who was aphysicus, or in the manner of the philosophers, for whom the ele-ments are parts of the world. William of Conches then gives thefamous definition which he attributes to Constantine the African:

Elementum ergo, ut ait Constantinus in Pantegni, est simpla et minimapars alicuius corporis - simpla ad qualitatem, minima ad quantitatem; cuiusexpositio talis est: elementum est pars simpla, i.e. cuius non sunt contrariaequalitates. Sed quia hoc totum videntur habere ossa et similia, ut removeatilla, addit «minima», i.e. quae ita est pars alicuius, quod nihil est pars eius-dem. Unde litterae per simile dicuntur elementa, quia ita sunt partes syl-labae, quod nihil est pars illarum 81.

Elements are simple. They do not contain contrary qualities; forinstance, they are hot and wet (air) or hot and dry (fire). However,since this definition can also apply to bones or to otherhomoeomeric parts of the body, it is necessary to add that elementsare also minimal; in other words, they are parts of something but donot have parts themselves. The definition is somewhat different inConstantine’s Pantegni 82. Constantine writes that the simple does notadmit of plurality, «eadem in essentia, ut ignis, terra», whereasWilliam of Conches argues that the simple does not admit of con-trariety. For Constantine, the element fire is heat in act, and the fourelements are the four qualities in act, while for William of Conches,each element possesses two qualities. It is possible that William ofConches drew from several different sources for his definition of theelementum, such as Alfano of Salerno’s translation of Nemesius of

29


notwendigem und hypothetischem Wissen. Zur wissenstheoretischen Bestimmung derPhysik in der Philosophia des Wilhelm von Conches, in «Early Science and Medi-cine», 6 (2001), 22-34. The two approaches to the question of the elements havealso been discussed by Nauta, The glosa as Instrument for the Development of Natu-ral Philosophy, 32-33.

80. Calcidius, Commentarius in Timaeum, 272, ed. Waszink, 277.81. Philosophia, I, 7, 19, ed. Maurach, 26.82. Cf. supra, n. 14.

Emessa’s De natura hominis, which defines the elements as the sim-plest of all bodies 83. By far the most likely hypothesis, however, isthat he put together extracts from different parts of the Digby com-mentary on the Isagoge Iohannitii. This follows Constantine, explain-ing that elements are simple «cum sit una et eadem in essentia, si-milis est in partibus». However, it defines the relations that existbetween the elementa and the elementata by comparing the former tohomoeomeric parts of the body, which are held to be simple, asopposed to the body itself, which consists of several homoeomericparts 84. William of Conches may have misunderstood this compari-son from the Digby commentary, turning the elementa into minimalhomoeomeric parts, viz. minimal pieces with the same essence, i.e.without contrary qualities.

Other indications reveal that William of Conches borrowed fromAlfano of Salerno’s translation of Nemesius of Emessa’s De naturahominis, using the terms «homoeomeres» and «organics» a few linesafter his definition of the elements 85. These terms do not appear inthe works of Constantine the African, who uses similia membra andofficialia membra. William of Conches uses these constantinian termsto gloss the terms from the De natura hominis 86. This demonstratesthat William of Conches draws on various sources, at the risk of let-ting a few incoherencies slip through.

The second part of the definition postulates that the element is aminima pars. Constantine the African did not say much about thisaspect, whereas William of Conches considers this second characte-

30

IRENE CAIAZZO

83. Nemesius Emesenus, De natura hominis, 5, ed. Burkhard, 62: «Elementummundanum est pars minima confectionis corporum. Sunt autem elementa quat-tuor: terra, aqua, aer, ignis, coordinata secundum dicendum ordinem ab inferio-ribus ad superiora corpora. Ipsaque sunt prima et simplicia corpora quantum adalia».

84. Commentary on Isagoge Iohannitii, ms. Oxford, Bodleian Library, Digby 108,f. 5v: «Ex hoc tamen quidam habere volunt quod non sint elementa nisi haecquae diximus elementata, et haec dicunt simplicia quantum ad alia magis com-posita, sicut consimilia membra dicuntur simplicia, haec autem sunt in partibussimilia»; cf. supra, n. 30 for the entire passage.

85. Guillelmus de Conchis, Philosophia, I, 7, 20, ed. Maurach, 27: «Voluitautem iste Constantinus ex IIII elementis constare humores, ex humoribuspartes tam omiomiras, i.e. consimiles ut est caro ossa, quam organicas, i.e. offi-ciales ut manus pedes et similia, ex utrisque vero partibus humanum corpusconstare».

86. Nemesius Emesenus, De natura hominis, 4, ed. Burkhard, 59: «[…] ut sitipsa quattuor elementorum commixtio quattuor humores, humorum vero sinthomiomera id est similes partes habentia, quae sunt membra corporis; ibid.,60: «[…] vocantur autem et haec organica id est officialia».

ristic just as important as simplicity. In addition to the Digby com-mentary, he may have used Priscian’s Institutiones grammaticae, whichargues in the chapter on the littera that the littera is the pars minimaof the vox composita 87. William of Conches commented on the Insti-tutiones grammaticae; the first version of his glosses, written after thefirst version of the Philosophia, explains that the word minimum canbe understood either as compared to something of the same kind,or in an «absolute» way 88. This hypothesis is confirmed by the factthat immediately after giving his definition of the element, Williamof Conches cites Priscian on the comparison between the letters ofthe alphabet and the elements, with the letters, which themselveslack parts, being the parts of the syllable.

William of Conches then states that according to Constantine,the four humors are formed from the four elements. Thehomoeomeric parts and the organic parts (or members) are bothformed from the four humors, and in turn constitute the body.According to William of Conches, therefore, the visible elements –earth, water, air, and fire – are not elements as such, since they areneither simple nor minimal. Rather, the elements are the tiny parti-cles that form the four visible elements. These elements may beunderstood through reason by means of a process of division. Forinstance, the human body can be divided into homoeomeres andorganic parts, but only through reason can the homoeomeres andorganic parts then be divided into the four humors and the fourhumors into the four elements. Citing Boethius’ Commentary on theIsagoge Porphyrii, William of Conches explains that the force of theintellect is to separate what is joined and to join what is separate 89.

31


87. Priscianus Caesariensis, Institutiones grammaticae, I, 3, ed. M. Hertz, inGrammatici Latini II, ed. H. Keil, Leipzig 1855 (= GL II), 6: «Litera est parsminima vocis compositae, hoc est quae constat compositione literarum, minimaautem, quantum ad totam comprehensionem vocis literatae – ad hanc enimetiam productae vocales brevissimae partes inveniuntur – vel quod omnium estbrevissimum eorum, quae dividi possunt, id quod dividi non potest».

88. Guillelmus de Conchis, Glosae super Priscianum, ms. Florence, BibliotecaMedicea Laurenziana, San Marco 310, f. 4rb: «Littera est pars minima vocis com-positae. Minimum duobus modis dicitur: et in respectu aliorum, scilicet eiusdemgeneris, et absolute. In respectu ut cum hunc montem vel illum minimum essedicimus quam nullus adeo parvus potest inveniri; absolute ut athomus diciturminima, id est indivisibilis».

89. Guillelmus de Conchis, Philosophia, I, 7, 21-22, ed. Maurach, 27: «Quaeelementa numquam videntur, sed ratione divisionis intelliguntur. Dividitur enim,ut figuraliter dicatur, humanum corpus in organica, scil. in manus etc., organicavero in omiomira, i.e. consimilia, videl. in particulas carnis et ossis etc., omiomira

The «small» elements are located only in bodies. When separatefrom bodies, they cannot be perceived by the senses. It is thereforeboth correct and appropriate to call the elements we see elementataand the particles we understand by intellect elementa 90. William ofConches then repeats almost word for word what he wrote in hisGlosae super Boetium with reference to Timaeus 49d, where Plato di-stinguishes between terra and terreum: that which is dissolved intothe other elements is not terra but terreum, a part of terra; that whichremains after dissolving retains the properties of terra, and mayrightly be called elementum. William promises (deo annuente) toreturn to this question in further detail, which he does in the Glosaesuper Platonem 91.

32

IRENE CAIAZZO

autem in humores, melancoliam etc., humores in elementa, i.e. in simplas et min-imas particulas. Cuius divisionis pars actu, pars sola ratione et cogitatione fieripotest, corpus enim humanum in membra, membra in omiomira actus dividerepotest, sed omiomira in humores, humores in elementa solus intellectus dividit,quia – ut ait Boethius in commentario super Porphyrium: “vis est intellectusconiuncta disiungere, disiuncta coniungere”. Sed quaerat aliquis: “Ubi sunt ele-menta?”. Nos vero dicimus: “In compositione humani corporis et aliorum sicutlittera est in compositione syllabae, etsi non per se”». Sed sunt quidam qui ut rus-tici nesciunt aliquid esse nisi sensu possint illud comprehendere, quia animalishomo non percipit quae spiritus sunt, cum sapienti plus sint inquirenda insensi-bilia quam sensibilia. Cum ergo illae simplae et minimae particulae elementasunt, quae est frigida et sicca, terra est; quae frigida et humida, aqua est; quaecalida et humida, aer est; quae calida et sicca, ignis est». Cf. Boethius, In IsagogenPorphyrii Commenta, editio secunda, I, 11, ed. S. Brandt, Vienna-Leipzig 1906(Corpus scriptorum ecclesiasticorum latinorum, 48), 165. In fact, William seemsto quote from Peter Abelard’s logical writings, possibly the Logica «Ingredientibus».

90. Guillelmus de Conchis, Philosophia, I, 7, 22-23, ed. Maurach, 28: «Cumigitur haec IIII quae videntur ex illis composita sunt, illud in quo dominanturparticulae frigidae et siccae, nomine illius elementi dicitur terra; in quo frigidaeet humidae, aqua; in quo calidae et siccae, ignis. Si ergo illis digna velimusimponere nomina, particulas praedictas dicamus “elementa”, ista IIII quae viden-tur “elementata”. Sunt quidam, qui neque Constantini scripta neque alteriusphysici umquam legerunt, ex superbia ab aliquo discere dedignantes, ex arro-gantia quae nesciunt confingentes, ne nihil dicere videantur, dicunt elementaesse proprietates istorum quae videntur, calorem scil., siccitatem, frigiditatem ethumorem. Sed istis Physicam velut in partem praedae detrahentibus reclamateadem ore Platonis vocantis elementa materias, cum nullae qualitates materiaalicuius esse possint. Est etenim materia quod accepta forma transit in aliud.Reclamat item ore Ioannicii qui in Isagogis suis ait aliud esse elementa, aliudcommistiones eorum, quae sunt calidae et siccae, et sic de aliis».

91. Ibid., I, 7, 26, 29-30: «Quod iterum dicunt Platonem quaesisse, quaremagis dicatur terra quam aqua, cum sic dissolvatur, sic intelligimus illum nonloqui de elemento ibi, sed de parte elementi quae dissolvitur, numquam enimtotum elementum dissolvitur. Dicit ergo id, quod dissolvitur, non terram, sedterreum i.e. partem terrae; sed quod remanet retinens proprietates terrae dicitterram et elementum. Sed de hoc deo annuente vitam satis dicemus. Sunt ergo

William of Conches’ thinking on the elements has thus shiftedconsiderably since the Glosae super Boetium. Not only does he acceptthe elementatum theory and the doctrine of the physici, but he alsolambasts the ignoramuses who have not read the works of Constan-tine or Iohannitius and the other physici.

This exhortation to read the works of the doctors should becompared to Petrus Alfonsi’s Letter to the Peripatetics, written shortlyafter 1116, in which the masters of Ile-de-France are urged to setaside the arts of the trivium and rather to study medicine (physica)and above all astronomy – although Macrobius’ teaching on thissubject is to be forbidden 92. Petrus Alfonsi shows that he is familiarwith the translations of Constantine, who is mentioned by name, aswell as with technical medical terms such as «complexion» and«degree» 93.

William of Conches no doubt followed Petrus Alfonsi. However,despite his openness toward natural philosophy and the works of thephysicians in the Philosophia, he still finds room to include thetheory of the four elements as propounded in the Glosae superBoetium. Consequently, he writes that those who argue that the vi-sible elements are the true elements rely on the testimony of Juve-nal, who wrote that gluttons seek pleasure in all the elements 94.William of Conches explains that this theory does not contradictConstantine, who, as a physicus, focused on the simple and minimalparticles that are the first principles of bodies. Philosophers, on theother hand, are concerned with the creation of the world, not withindividual bodies. They therefore argue that the four visible ele-ments are the elementa mundi, since the world is made up of them.They further argue that these elements were created first, and all

33


elementa corporum praedictae particulae, ut ait Constantinus, sed elementamundi, quae videntur. De quibus huiusmodi tractatus habendus videtur, quareunumquodque factum sit, quare IIII nec pauciora». The versio altera also refers toa future work.

92. Petrus Alfonsi, Epistola ad Peripateticos, ed. J. Tolan, Petrus Alfonsi and HisMedieval Readers, Gainesville 1993, 164-72.

93. Ibid., 166: «Ad phisicam vero ad numerandum elementa, complexiones,species et gradus ipsarum, pondera medicinarum. […] sicut Constantinus inlibro suo quem de lingua sarracena transtulit in Latinam testatur». For the wordcomplexio, cf. D. Jacquart, De crasis à complexio: note sur le vocabulaire du tempéra-ment en latin médiéval, in Mémoires,V,Textes médicaux latins antiques, ed. G. Sabbah,Saint-Etienne 1984, 71-76, repr. in D. Jacquart, La science médicale occidentale entredeux renaissances (XIIes.-XVes.), Aldershot 1997.

94. Iuvenalis, Saturae, XI, 14.

things were created from them. William of Conches considers thatthe philosophers’ theory of the four elements is just as true as thatof the physici, and above all: Nulla ergo inter hos contrarietas 95.

4. Glosae super Platonem: Plato and Constantine the African

4.1. The qualities of the elements and the connections betweenthem

4.2. The elements and hyle

William of Conches further develops his theory of the four ele-ments in the Glosae super Platonem. Although some passages repeatthe theory of the physici set forth in the Philosophia word for word,he adds new explanations for the connections and qualities of theelements and expands on the relations between the four elementsand the primordial matter, mentioned in passing in his earlier works.

Taking up Calcidius’ tripartite division between opus dei, opus natu-rae and opus artificis imitantis naturam 96, William of Conches writesthat the opus creatoris (not dei as in Calcidius) is the «prima creatiosine preiacente materia, ut est creatio elementorum, et spirituum,vel ea que videmus fieri contra consuetum cursum naturae, ut partusvirginis, et cetera» 97. He also returns to the problem of the primor-dial chaos, explaining the confusion of the four elements mentionedby some authors. Before God’s intervention, each element possessedits substantial quality, but not its accidental quality, hence the confu-sion of the elements 98.

34

IRENE CAIAZZO

95. Guillelmus de Conchis, Philosophia, I, 7, 24, ed. Maurach, 28-29: «Sunt aliiqui dicunt ista quae videntur esse elementa comprobantes hoc auctoritate Iuve-nalis, qui de gulosis loquens ait: “Gustus per omnia elementa quaerunt”, in terrascil. venationes, in aqua pisces, in aere volucres. Et quia ista sententia vera estnec aucoritati Constantini contraria, qualiter cum illa stare possit, exponamus:Constantinus igitur ut physicus de naturis corporum tractans simplices illorumet minimas particulas elementa quasi prima principia vocavit; philosophi vero decreatione mundi agentes, non de naturis singulorum corporum, ista IIII quaevidentur elementa mundi dixerunt quia ex istis constat, et ista prima creata suntet deinde ex eis ut elementis cetera omnia vel creata sunt vel creantur vel crea-buntur, ut in sequentibus ostendetur. Nulla ergo inter hos contrarietas».

96. Calcidius, Commentarius in Timaeum, 23, ed. Waszink, 73.97. Guillelmus de Conchis, Glosae super Platonem, 37, ed. Jeauneau, 69.98. Ibid., 51, 89: «Nostra vero sententia est elementa in prima creatione fuisse

ubi nunc sunt et easdem quas nunc habent substantiales qualitates optinentia, sednon accidentales». On the question of chaos, cf. supra, n. 8.

William of Conches explains that Plato deals with the four ele-ments that are the «material cause» of the world in Timaeus 31b. Heincludes a long excursus beginning with Constantine the African’sdefinition of the element, reproducing the pages from thePhilosophia word for word 99. The only difference is that he omits theattack against those who have not read the works of the doctors.However, he then repeats that there are two ways to discuss the ele-ments: that of the physici, who concentrate on the particles (i.e. onthe elements of the body) and that of the philosophi, who debate thevisible elements (i.e. the elements of the world) 100.

4.1. The qualities of the elements and the connections betweenthem

Plato states in Timaeus 31b that after creating the extreme ele-ments, fire and earth, God introduced two intermediary elements inorder to connect them. The creation of the four elements and theirconiunctio occurred simultaneously rather than sequentially, since«tanta enim fuit artificis potentia et sapientia quod illa simul crearepotuit» 101. William of Conches then continues with a further excur-sus on commixtio and coniunctio, which he had already included inthe Philosophia. The former is a complete mixture between the qua-lities, while the latter is a mixture in which the two componentsmaintain their properties. This implies an intermediary to balancethe active contrary qualities 102. One intermediary is sufficient insome cases: water suffices between earth and air, for instance,whereas fire and earth require two intermediaries. Plato states thatthese links can be realized vel numeris vel molibus vel potentiis, alemma that William of Conches glosses rapidly, explaining the kindof contrariety in question and how it can be surmounted. In thecase of a contrariety between numbers, such as 4 and 9, for instance,it is enough to insert an intermediary number, such as 6. William ofConches states that he will discuss contrariety between geometricalfigures at the proper time. Likewise, contrariety between powers

35


99. Ibid., 58-59, 101-05. On the Glosae super Platonem, cf. T. Ricklin, Wilhelmvon Conches: Glosae super Platonem, in Hauptwerke der Philosophie. Mittelalter, ed.K. Flasch, Stuttgart 1998, 151-74.

100. Guillelmus de Conchis, Glosae super Platonem, 59, ed. Jeauneau, 105.101. Ibid., 60, 106.102. Ibid., 61, 106-7.

(i.e. qualities) requires the inclusion of an intermediary sharing onequality with each element 103. A few lines further on, he adds thatthe coniunctio of two elements with two contrary qualities takesplace through one intermediary, such as water between earth andair. This conjunction is called sinzugia plana because of its similarityto a two-dimensional plane surface. The coniunctio of two elementswith three contrary qualities is called sinzugia solida by analogy withthree-dimensional solids. This coniunctio solida, requiring two inter-mediaries, is necessary between fire and earth, which have threecontrary qualities: earth is obtusa (sic), corpulenta, immobilis, while fireis acutus, subtilis, mobilis. This is the sole occurrence of Calcidius’ sixqualities in the Glosae super Platonem.William of Conches underlinesthe fact that the comparison with plane surfaces and solids is purelyan analogy and is not intended to imply that the elements have twoor three dimensions in space 104. This is important, since it reveals anunderlying reflection on the corporeality of the elements that willbecome fully apparent in the Dragmaticon philosophiae.

4.2. The elements and hyle

William of Conches tries to define materia prima (or hyle) in asection entitled Tractatus de primordiali materia by the editor of theGlosae super Platonem 105. He dismisses the possibility that materiaprima is the four elements at the outset, since the four elements havea form and qualities, whereas materia prima has neither 106. Rather,materia prima is the matter of the elements 107, which, in turn, are the

36

IRENE CAIAZZO

103. Ibid., 62, 108-9.104. Ibid., 63, 111: «Similiter, in contrariis quorum contrarietas in duabus

qualitatibus est, unum sufficit medium, ut aqua inter terram et aera. Sed sicontrarietas est in tribus, duo media sunt necessaria, ut supra docuimus. Etnotandum quod coniunctio contrariorum in duabus qualitatibus plana dicitursinzugia propter similitudinem cum plano, id est superficie quae duas habetdimensiones, sive illa sint solida corpora sive non. Coniunctio vero contrariorumin tribus qualitatibus solida dicitur sinzugia quia solida tres habent dimensiones,ut coniunctio terrae et ignis dicitur solida, terrae et aeris plana, etsi illa nichilo-minus sint solida. Ergo inter terram et ignem duo media fuerunt necessaria:eorum enim contrarietas in tribus est qualitatibus. Est enim terra obtusa, corpu-lenta, immobilis; ignis acutus, subtilis, mobilis».

105. Cf. Caiazzo, La materia nei commenti al Timeo.106. Guillelmus de Conchis, Glosae super Platonem, 154, ed. Jeauneau, 278.107. Ibid., 154, 278-79: «Est ergo nostra sententia quod materia elementorum

est prima materia. Quod materia sit, nulla dubitatio est. Quod prima est, proba-tur quia nichil est eius materia. Si enim esset aliquid illius materia, esset eiusdem

matter of the world, which God created simultaneously («fuit enimDeus tantae potentiae quod simul elementa et eorum materia crearepotuit») 108. This materia prima or hyle can be understood intellectu-ally by abstracting all the qualities and the forms it contains;Williamof Conches quotes Calcidius to explain that «primordialis materiaintelligitur non intelligendo» 109.

Hyle can also be understood directly through the reciprocal trans-formations of the four elements. Reason indicates the existence of amatter common to the four elements and capable of receiving theirqualities 110. Hyle can thus be understood by a study of the elements.This is why the way the transformations take place must be studiedclosely. Water is transformed into earth by coldness and dryness,which thicken it and make it solid 111. This process of reciprocaltransformation is established for each element. This opens the que-stion of why something is called an element despite having no stableproperties, which means it cannot be referred to by a noun or pro-noun. The noun «element» signifies the stable (certa) quality that iswith (circa) substance, just as the noun «earth» signifies the qualities«cold» and «dryness». Yet these qualities are not stable in the visibleelements, because they are present to a greater or lesser degree 112.

37


et forma, quia quidquid habet formam, habet et materiam: esset ergo materiaelementorum quiddam constans ex materia et forma, et sic esset corpus. Sed siesset corpus, esset elementum vel factum ex elementis. Sed neque elementumneque factum ex elementis est materia elementorum. Est ergo materia elemen-torum talis materia cuius nichil est materia: est ergo prima materia».

108. Ibid., 155, 280-81.109. Ibid., 155, 279.110. Ibid., 158, 285-86: «Has perpessiones potius considerat, quia per istas, ut

ait Calcidus, aperte intelligitur hyle. Cum enim terra in aquam mutatur vel aquain terram, variantur qualitates. Sed omnis variatio qualitatum fit circa aliquammateriam quae potest illas suscipere. Ergo in hac mutatione terrae et aquaeoportet aliquam materiam esse quae qualitates terrae et aquae possit recipere.Sed hoc non potest esse terra: est enim una qualitas aquae, scilicet humiditas,quae non potest inesse terrae. Similiter non potest esse aqua nec aliud elemen-tum. Ergo perpendit ratio in mutabilitate elementorum esse quandam materiamcommunem istis quae huius et illius qualitates in se possit recipere. Et hoc esthyle». Cf. ibid., 161, 292.

111. Ibid., 112, 294.112. Ibid., 163, 296: «Prius ergo ostendamus quare nullum istorum nomine

elementi debeat designari nec pronomine demonstrari. Quodlibet ergo nomenelementi circa substantiam certam qualitatem determinat, ut hoc nomen “terra”frigiditatem et siccitatem: illius ergo debet esse nomen cui insunt istae quali-tates. Sed huic visibili elemento non insunt constanter, et modo insunt modonon insunt in uno, immo aliae. Similiter de aliis intelligatur. Iterum pronominedemonstrari non debet. Pronomen enim debet demonstrare substantiam inaliqua propria qualitate. Sed nulla est istorum propria nec certa».

Plato stated in Timaeus 49d that ignis should in fact be called igneum,and terra should be called terreum, and so on. William of Conches’earliest works promised an explanation of this passage, which hascaused difficulties for all exegetes of the Timaeus, ancient andmodern alike. Calcidius explained it by arguing that when firechanges into air, its qualities are transformed; hence fire should notbe referred to by pronouns that denote substance, such as hoc orillud, but rather pronouns that denote quality, such as tale or illiusmodi. Mere habit is behind the use of substantial pronouns to desi-gnate the four elements, which «semper enim et sine intermissioneullius temporis fluunt». Because fire is unstable and subject to muta-tion, it must not be considered as fire, but rather as «the fiery»,writes Calcidius, citing Plato’s own words: «“Itaque”, inquit, “ignisiste qui velut exudans in aereas auras dissolvitur, cum instabilismutabilisque sit nec habeat perpetuam proprietatem, non est igniscensendus, sed igneum quiddam, […]”» 113.

William of Conches does not accept Calcidius’ distinctionbetween pronouns of substance and pronouns of quality. Rather, heexplains that the noun ignis names the qualities that are found with(circa) substance – dryness and heat – whereas igneum refers to thatwhich has something of ignis 114. What changes is not the ignis(which in fact loses its qualities when transformed) but the igneum,which still retains something of the ignis 115. William of Conchesargues that the igneum, i.e. the visible element we perceive throughthe senses, has something of fire within it; its ontological status istherefore more firmly grounded than the igneum as presented byPlato and interpreted by Calcidius 116. In short, the sensible world isnot merely a pale image of the intelligible world. This point is cru-

38

IRENE CAIAZZO

113. Calcidius, Commentarius in Timaeum, 325-326, ed. Waszink, 320-21.114. On nouns and adjectives, cf. J. Brumberg-Chaumont, Grammaire et

logique du nom d’après les Gloses sur Priscien de Guillaume de Conches, publishedin the present volume.

115. Guillelmus de Conchis, Glosae super Platonem, 163, ed. Jeauneau, 296-97:«Sed quaeritur: Si propter sui mutabilitatem non potest vocari ignis, quare potestvocari igneum? Cui dicimus quod ignis, hoc nomen, circa substantiam nominathas qualitates, siccitatem et calorem; igneum vero quod in se aliquid de ignehabeat. Hoc ergo mutabile non est ignis, quomodocumque mutetur – amittitenim aliquando has qualitates – sed semper est igneum, quia semper habet ali-quid de igne».

116. As J. Brumberg-Chaumont explains in her article, William of Conchesgroups adjectives together with nouns of substances in the category of nounsthat «signify substance with quality».

cial for understanding William of Conches’ theory of the elementsand indeed his entire approach to the sensible world and Platonicphilosophy. He continues with a further excursus which sets forthwhy these elements cannot be called such and explaining what mustbe referred to as elements. He begins by outlining the opinions heconsiders erroneous before propounding his own «sentence». Hereturns to certain opinions previously rejected in the Glosae superBoetium, refuting them with new, clearer arguments, reflecting thedevelopment of his theory of the elements. Authors who argue thatthe elements are species of which the visible elements are indivi-duals or that the elements are the qualities of those that can be seenare wrong. Indeed, the philosophers accept that the elements are thematter of all bodies, but no incorporeal can be the matter of bodies.He then turns to the opinion associating the theory of the elemen-tum/elementatum with the passage of Timaeus 49d, where the subjectof discussion is ignis/igneum, a comparison made in the Glosae superBoetium. This opinion holds that only a small part of the visible ele-ment ever dissolves, while most of it remains. The part that dissolvesis the elementatum; the elementum is what remains. In other words,the part of the ignis that dissolves is the igneum, and the ignis is whatis left behind 117. This is how William of Conches interprets the pas-sage from the Timaeus in the Philosophia, promising to return to thesubject for a more in-depth analysis. He does not openly reject thisinterpretation in the Glosae super Platonem, but mentions it alongsidethe interpretations he considers erroneous.

In fact, he gives his own interpretation of Timaeus 49d a few linespreviously, framing the question in somewhat different terms inorder to reconcile the passage with the doctors’ theory of the ele-ments and to prepare the way for what follows. Ignis does notchange; igneum, which changes and can be seen, always containssomething of ignis. This interpretation is compatible with his theorythat the visible element, or igneum, is made up of simple, minimal,and immutable particles (immutabiles, a characteristic not mentionedin the earlier Philosophia). The particle fire has two substantial qua-lities, hot and dry, just as other particles have other substantial qual-

39


117. Guillelmus de Conchis, Glosae super Platonem, 164, ed. Jeauneau, 298:«Alii dicunt istud visibile nunquam dissolvi, sed minorem partem dissolvi, maio-rem remanere. Quod ergo de unoquoque dissolvitur, non est elementum sedelementatum; sed quod remanet semper, est elementum. Quod ergo dissolviturde igne est igneum; quod remanet, ignis est. Et sic de aliis intelligatur».

ities, air (hot and wet), water (cold and wet), and earth (cold anddry). These particles are never found separately, although they canbe conceived of individually. The four visible elements take on the(improper) name of the dominant particles they contain.Visible fireis so called, for instance, because it contains a majority of hot anddry particles. The elements are in fact these particles, which are cor-poreal substances found in the visible elements 118.

The definition of the elements as particles is still in use in theGlosae super Platonem. It should be noted, however, that William ofConches uses the term elementatum less frequently than in thePhilosophia, often preferring to speak of «the element that is seen» orthe element of the world. He also begins his exploration of the cor-poreal nature of the particle-element, later continued in the Drag-maticon philosophiae.

40

IRENE CAIAZZO

118. Ibid., 164, 298-99: «Nos vero dicimus haec quatuor magna corpora con-stare ex quibusdam minimis et simplis particulis et immutabilibus quarumquaedam habent has solas substantiales qualitates, calorem et siccitatem, et istaeproprie dicuntur ignis; quaedam habent has solas, calorem et humiditatem, quaeproprie dicuntur aer; quaedam has solas, frigiditatem et humiditatem, quae pro-prie dicuntur aqua; quaedam frigiditatem et siccitatem, quae proprie dicunturterra. Nec tamen praedictae particulae unquam separatae inveniuntur, etsi sepa-rate intelligantur. Cum vero ex illis constant ista quatuor corpora, unumquodquenomine particularum in se dominantium, quamvis improprie, vocatur. Sunt ergopraedictae particulae elementa. Unde Constantinus: Elementum est simpla etminima alicuius corporis particula. Si quaerent an illae particulae sint substantiae,dicimus: Etiam, et corporeae. Si dicunt: Ergo sunt in aliquo, concedimus verumesse. Et ubi? Ubicumque sunt elementa».William repeats his opinion a few pagesfurther on, when glossing Timaeus 51b: cf. ibid., 170, 309-10: «Dixerat superiushoc quod videtur non proprie dici ignis sed igneum. Sed id quod semper est etcuius proprietas manet, id proprie dicitur ignis. Sed istud potest intelligi per se,non tamen existere per se: omnia enim vera elementa mixta sunt. Sed “vis estintellectus coniuncta disiungere”: ea enim separatim intelligimus quae separatanon sunt. Et similiter de aliis elementis est intelligendum. Sunt ergo vera ele-menta quaedam quae per se non existunt, per se tamen intelliguntur. Et quamvisper se non sint, tamen sunt mixta in singulis corporibus. Sed sunt quidam bes-tiales homines qui nichil putant esse nisi tangere illud possint, et ideo creduntvera elementa non esse, neque ideas, neque alia intelligibilia. Propter tales ergoquaerit utrum aliqua intelligibilia sint, ut probet illa esse».

5. Dragmaticon philosophiae5.1. Beyond the doctors

a) Infinita minimab) Are the elements visible?c) Are the elements bodies?d) Translatio

5.2 Toward the center and away from the center

William of Conches wrote the Dragmaticon philosophiae in around1147-1149, when he was at the court of the Plantagenets. It takesthe form of a dialogue between a philosopher (William himself) andGeoffrey the Handsome, Count of Anjou and Duke of Normandy.Several researchers have demonstrated that the Dragmaticonphilosophiae is not simply a reworking of the Philosophia followingWilliam of Saint-Thierry’s attack, but an original work in its ownright, which not only re-interprets subjects previously dealt with inthe Philosophia but also broaches new ones 119.

The Dragmaticon philosophiae marks a new stage in William’sthinking on the four elements. It has six main characteristics:

1) the disappearance of elementatum2) a new definition of the element, close to Hermann of

Carinthia’s De essentiis3) a reflection on size and infinity, drawing on Boethius’ De insti-

tutione arithmetica and De institutione musica4) a reference to atoms and the Epicureans 5) the acceptance of the existence of primordial chaos 6) the movement of the elements toward their natural places.

Not all the sources used in the Dragmaticon philosophiae have beenidentified. Barbara Obrist has recently shown the role played byMasha’allah’s Liber de orbe in astronomy and geography 120. It shouldalso be borne in mind that when William of Conches draws onsources already used in earlier works, in many cases he interpretsthem differently or focuses on new passages.This constant hermeneu-

41


119. Cf. Elford, Developments in the Natural Philosophy of William of Conches,and I. Ronca, Ragione e Fede in Guglielmo di Conches: per una edizione critica delDragmaticon, in Studi di filologia classica in onore di Giusto Monaco, IV, Palermo1991, 1535-59.

120. B. Obrist, William of Conches, Masha’allah and Twelfth-century Cosmology,in «Archives d’histoire doctrinale et littéraire du Moyen Âge», 76 (2009), 29-87.

tic labor makes attempting to reconstruct the development of Williamof Conches’ thought a real challenge for the historian.

5.1. Beyond the doctors

In the first book of Dragmaticon philosophiae, the Duke asks thephilosopher about the four elements, since many authors have writ-ten about them without coming to the truth. The philosopherpoints out that he can only present probable, not necessary, reasonson this question; the Duke is free to read other authors’ works onthe subject and to prefer their viewpoints. The Duke answers thathe will be satisfied with probability where a necessary argumentproves impossible. The philosopher therefore provides a definition ofthe element not found in William of Conches’ earlier works:

Elementum est quod in constitutione corporis inuenitur primum, in reso-lutione postremum. Primum est in constitutione quod constituit, sed nonconstituitur; postremum in resolutione quod diuidit, sed non diuiditur 121.

As scholars have pointed out, this new definition must be com-pared with Hermann of Carinthia’s De essentiis, written in 1143:«quae vero in compositione prima, eadem in resolutione ultima» 122.William of Conches may have had access to this work. The Drag-maticon’s approach to the question of the elements differs from thatof William’s earlier works. William’s argument is clearly structuredand focuses on three questions touched upon in passing in hisGlosae super Platonem:

1) Are the elements indivisible? 2) Are the elements sensible? 3) Are the elements corporeal?

42

IRENE CAIAZZO

121. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 2, ed. Ronca, 22.122. Hermannus de Carinthia, De essentiis, I, 60vB-D, ed. et transl. C. Bur-

nett, Leiden-Cologne 1982 (Studien und Texte zur Geistesgeschichte des Mitte-lalters, 15), 92: «Hec itaque semina easque notas si quis rerum materias et formasesse concipiat, eum recte arbitrari opinor. Sunt itaque rerum materie primaomnis compositionis semina. Que vero in compositione prima, eadem in resolu-tione ultima. Ita ergo hec, in rebus compositis, et prima sunt et ultima. Omnisautem compositi resolutio in commixtiones, commixtionum demum in genera-lia IIII principia, que, quoniam simplicia sunt, ulterius resolvi non possunt. Suntergo in resolutione ultima, quapropter et in compositione prima». Cf. ibid.,Introduction, 22-25, and the commentary, 252-60; cf. Elford, Developments in theNatural Philosophy of William of Conches, 8, and Ead., William of Conches, 306.

These questions were at the heart of the debate among twelfth-century philosophers of nature. As Charles Burnett rightly pointsout, Hermann of Carinthia’s De essentiis raises very similar que-stions: Are the elements corporeal or incorporeal? What is to beunderstood by minima pars?

a) Infinita minima

The various sources available in the twelfth century were contra-dictory on occasion. William of Conches was keen to find a com-promise; however, this meant that his own theories often containednumerous inconsistencies. The new definition of the element intro-duced in the Dragmaticon philosophiae espouses the indivisibility ofthe element, which is found, or discovered, at the end of the processof decomposition of a sensible body. To explain this decomposition,the philosopher relies on arguments taken from mathematical textssuch as Boethius’ De arithmetica and De musica. Rational reasoningsuggests that since each body can be divided into two maximalparts, then it can also be resolved into infinite minimal parts (infinitaminima). Each body has limits in the form of a beginning and anend, and in each body there are parts that compose and are, in turn,not compound. These parts are first in the composition of a bodyand last in its decomposition 123. The Duke replies that the philoso-pher contradicts himself with this explanation, which preaches botha division in infinita minima and ultimate parts beyond which onecannot go in the decomposition of bodies. Furthermore, in theDuke’s opinion, the philosopher also contradicts Boethius, whoaffirms that «magnitudo decrescit in infinitum» 124. The Duke’s reply,based on a direct, albeit abbreviated, quotation from the De institu-tione musica 125, offers the philosopher the opportunity for an excur-

43


123. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 2, ed. Ronca, 22-23:«(P): Ratio vero exigit ut, quemadmodum omne corpus in duo maxima potestdividi, sic in infinita minima possit resolvi. Omne namque corpus terminumhabet et finem. Sunt igitur in unoquoque corpore quaedam quae ita componuntipsum, quod ex partibus non componuntur. Haec sunt ad constitutionem prima,ad resolutionem postrema».

124. Ibid., I, 6, 3, 23: «(D): In uno et eodem tibi et Boetio contradicis: dicisenim omne corpus posse resolvi in infinita minima, deinde subiungis quaedamesse in corporibus postrema ad resolutionem, Boetius iterum dicit: Magnitudodecrescit in infinitum».

125. Boethius, De institutione musica, II, 3 ed. et transl. C. Meyer, Turnhout2004, 100: «Omnis vero quantitas secundum Pythagoram vel continua vel discretaest. Sed quae continua est, magnitudo appelatur, quae discreta est, multitudo.

sus on the various meanings of the term «infinite», explaining whathe means by describing these minimal parts in such terms. He doesnot contradict Boethius, who explains elsewhere in the same chap-ter of the De institutione musica that for the sake of clarity in apply-ing his theory he considers infinite quantities as finite, seeking «ter-minatedness» in infinite things 126. This rejection of infinity is typicalof the Neoplatonists of Late Antiquity, who were sources forBoethius’ treatises on the quadrivium. The De arithmetica repeats theidea that philosophy shuns indeterminacy and infinity:

All multitude, starting out from a single term, grows to infinite increasesof progress; magnitude, for its part, beginning with a finite quantity, has nolimit in its division, admitting the most infinite divisions of its body. Phi-losophy spontaneously repudiates this infinite nature and indeterminatepotentiality, for nothing that is infinite can be embraced by science orgrasped by the mind.Yet from this, reason itself derives for itself objects onwhich it may exercise its skill in seeking the truth. From the infinite plu-rality of multitude, it chooses a term of finite quantity, and rejecting theendless division of magnitude, it demands for itself limited spaces as itsobjects of knowledge 127.

According to the philosopher, infinity can be said in number, inmeasure, or in species. He is particularly interested in numericalinfinity, which may also be understood in various ways. There arethings changing constantly in number, such as Plato’s «infinite indi-viduals» which change constantly in number as a result of the ge-

44

IRENE CAIAZZO

Quorum haec est diversa et contraria paene proprietas. Multitudo enim a finitainchoans quantitate crescens in infinita progeditur, ut nullus crescendi finisoccurat; estque ad minimun terminata, interminabilis ad maius, eiusque princi-pium unitas est, qua minus nihil est. Crescit vero per numeros atque in infinitaprotenditur nec ullus numerus, quominus crescat, terminum facit. Sed magni-tudo finitam rursus suae mensurae recipit quantitatem, sed in infinita decrescit».

126. Ibid., II, 3, 100: «Cum igitur haec ita sint infinita, tamen quasi de rebusfinitis philosophia pertractat, inque rebus infinitis repperit aliquid terminatum,de quo iure posset acumen propriae speculationis adhibere».

127. Boethius, De institutione arithmetica, I, 1, 6, ed. Guillaumin, 8: «Illudquoque addendum arbitror, quod cuncta vis multitudinis ab uno progressa ter-mino ad infinita progressionis augmenta concrescit; magnitudo vero a finitainchoans quantitate modum in divisione non recipit; infinitissimas enim sui cor-poris suscipit sectiones. Hanc igitur naturae infinitatem indeterminatamquepotentiam philosophia sponte repudiat. Nihil enim quod infinitum est vel scien-tia potest colligi vel mente comprehendi, sed hinc sumpsit sibi ipsa ratio, inquibus possit indagatricem veritatis exercere sollertiam. Delegit enim de infini-tae multitudinis pluralitate finitae terminum quantitatis et, interminabilis magni-tudinis sectione reiecta, definita sibi ad cognitionem spatia depoposcit».

neration and corruption of bodies. Then there are things said to benumerically infinite because man cannot know their exact numberwith any certainty. Boethius has the second case in mind in statingthat magnitude is infinitely divisible and that bodies are resolvedinto infinite minimal parts (infinita minima). Human reason thereforehas no access to the exact number of tiny parts into which bodiesare resolved 128.

The philosopher suggests understanding Boethius’ phrase «magni-tude decreases infinitely» by what he refers to as a further philo-sophical formulation from another chapter of the De institutionemusica, which discusses discrete and continuous quantities 129. Discretequantity (multitudo) increases to infinity, while continuous quantity(magnitudo) decreases to infinity. The larger the division of continu-ous quantities, the smaller the number that designates them and viceversa. A quarter is smaller than a third; a third is smaller than a half.In saying «magnitude decreases to infinity», the names used to desig-nate its parts are infinite, not the number of parts 130. This explana-

45


128. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 3-4, ed. Ronca, 23:«(P): Infinitum diverso modo dicitur numero, mensura, specie. Nec etiam unomodo dicuntur aliqua numero infinita. Dicuntur enim numero infinita quaenumquam in eodem numero permanent, sicque dicit Plato individua infinita:cum enim generationi et corruptioni subiacent, modo sunt plura modo pau-ciora. Alia dicuntur numero infinita, non quia non sint in numero, sed quiaeorum numerus vix aut numquam potest homini esse certus. Omnia igitur suntin numero, sed quaedam modo in uno modo in alio, quaedam semper in eodem,sed excedente hominis cognitionem, quae dicuntur numero infinita. Cum igiturdiximus quod corpus potest resolvi in infinita minima, et quando Boetius dixitmagnitudo decrescit in infinitum, hoc ultimo modo infinitum est positum».

129. Boethius, De institutione musica, I, 6, ed. Meyer, 42: «Nam cum sit aliaquidem discreta quantitas, alia vero continua, ea quae discreta est in minimoquidem finita est, sed in infinitum per maiora procedit. Namque in ea minimaunitas eademque finita est, in infinitum vero modus pluralitatis augetur, utnumerus, qui, cum a finita incipiat unitate, crescendi non habet finem. Rursusquae est continua, tota quidem finita est, sed per infinita minuitur. Linea enim,quae continua est, in infinita semper partitione dividitur, cum sit eius summa velpedalis vel quaecumque alia definita mensura. Quocirca numerus semper in infi-nita crescit, continua vero quantitas in infinita minuitur».

130. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 5, ed. Ronca,24: «(P): Est alia philosophica sententia quae ait quod, quemadmodum multitudocrescit in infinitum (non tamen omnis vel aliqua, omnis enim habet certum ter-minum), sic magnitudo decrescit in infinitum (non tamen omnis vel aliqua, sedquia non invenitur nomen tam parvae partis quin, si natura minorem illa face-ret, nomen illius esset). (D): Quod dicis, dic apertius. (P): Omnis pars, quanto amaiore numero denominatur, tanto minor est, et quanto a minore, maior. Undedecrescente numero partium crescit quantitas, et crescente decrescit: maior enimest media pars quam tercia, et tercia quam quarta. Magnitudo igitur decrescit ininfinitum non quantum ad numerum partium, sed quantum ad nomina earum».

tion is also based on a passage from the De musica in which Boethiusexplains the characteristics of ratios: multiplicity increases to infinityand behaves like a number, i.e. a discrete quantity. In contrast, super-partiality (superparticularitas), which diminishes to infinity, behaveslike a continuous quantity: it diminishes the smallest, since it alwayscontains the smallest plus its half, third, or quarter 131.

These minima, joined together, constitute a large body and arecalled elements. As the philosopher explains, this theory echoes thedefinition of the element given by Constantine the African in thePantegni: «elementum est simpla et minima corporis particula». Par-ticles that are hot and dry are called fire, those that are cold and dryare called earth, the cold and wet ones are water, and the hot andwet ones air 132. Constantine’s authority is less clearly affirmed thanin William’s earlier works; it is evoked merely to corroborate histheory of elements. William of Conches may also have felt the needto consolidate the «constantinian» theory with mathematical argu-ments because of Hermann of Carinthia’s open critique of doctorsand his clear preference for astrologists 133. Times have changed sincethe Philosophia: the doctors are no longer popular. The theory of theelementatum is no longer evoked in the Dragmaticon philosophiae.Instead, William provides a new, systematized version of his theoryof the elements.

The Duke asks the philosopher how to reconcile the fact that theparticles are infinite and that the various bodies are made up of dif-ferent particles with the fact that there are only four elements, andthat all bodies are said to be made up of these four elements. The

46

IRENE CAIAZZO

131. Boethius, De institutione musica, I, 6, ed. Meyer, 42: «Multiplicitas igitur,quoniam finem crescendi non habet, numeri maxime servat naturam. Superpar-ticularitas autem, quoniam in infinitum minorem minuit, proprietatem servatcontinuae quantitatis. Minuit autem minorem, cum semper eum continet et eiusvel dimidiam partem vel tertiam vel quartam vel quintam. Nam semper pars amaiore numero denominata ipsa decrescit. Nam cum tertia a tribus denominatasit, quarta vero a quattuor, cum quattuor tres superent, quarta potius quam tertiaminutior invenitur».

132. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 6, ed. Ronca, 24-25: «(P): Sunt igitur in unoquoque corpore minima, quae simul iuncta unummagnum constituunt; haec a nobis dicuntur elementa. Huic sententiae concor-dat Constantinus, ubi ait: Elementum est simpla et minima corporis particula.Harum particularum quaedam sunt calidae et siccae, quae proprie ignis dicun-tur; quaedam frigidae et siccae, hae sunt terra; quaedam frigidae et humidae, ethae proprie dicuntur aqua; quaedam calidae et humidae, sed hae proprie aervocantur».

133. Hermannus de Carinthia, De essentiis, I, 60vF-61rB, ed. Burnett, 92-93.

philosopher answers by means of a comparison with grammar: thefour elements are indeed the four kinds in which the particles aredistributed 134. The Duke further accuses the philosopher of agreeingwith the Epicureans, who argued that the world is composed ofatoms. The philosopher concedes that the Epicureans were right tothink that the world is made up of atoms. However, they werewrong to consider them to be without a beginning, scatteredthroughout the void before they were clustered together to formthe four elements, since nothing except God exists without a begin-ning and without a place. On the contrary, particles were created byGod at the same time as the bodies they constitute. God can createthe parts and the whole composed of those parts at the same time(simul). This argument is already present in William of Conches’ ear-lier works 135.

The references to the Epicureans are too brief for their exactsource to be identified. The hypothesis that William had access toLucretius’ De rerum natura is controversial and it should be borne inmind that information on the atomists was available in several Latinauthors of Antiquity, including Servius, Persius, Cicero, Lactantius,the pseudo-Clementine Recognitiones, and Calcidius 136, as well as

47


134. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 7, ed. Ronca, 25-26: «(D): Cum particulae istae sint infinitae, diversaque corpora ex diversisconstant particulis, quomodo stare poterit quod dictum est elementa esse qua-tuor et omnia ex eisdem constare elementis? (P): Quemadmodum omnis dictioest pars orationis, octo tamen sunt partes orationis, sic dicimus unamquamqueparticulam esse elementum, quatuor tamen esse elementa, quia in quatuor gene-ribus comprehenduntur. Et quomodo dicimus has duas orationes “Socrates legit”et “Plato disputat” ex eisdem partibus orationis constare, non tamen ex eisdemvel particulis vel dictionibus, sic dicimus corpora ex eisdem elementis constare,non tamen ex eisdem particulis. Ex his quatuor generibus particularum diversisconiunctionibus creavit Deus corpora ratione quam dicturi sumus».

135. Ibid., I, 6, 8-9, 26: «(D): Ut michi videtur, in sententiam Epicureorumfurtim relaberis, qui dixerunt mundum constare ex athomis. (P): Nulla tam falsaest secta quae non habeat aliquid veri admixtum, sed tamen illud admixtionecuiusdam falsi obfuscat. In hoc vero quod dixerunt Epicurei, mundum constareex athomis, vere dixerunt. Sed quod dixerunt illas athomos sine principio fuisseet divisas per magnum inane volitasse, deinde in quatuor magna corpora coactasfuisse, fabula est: non enim sine principio et loco aliquid praeter Deum potestesse. Dicimus igitur has particulas Deum simul creasse non divisas, sed in uniusconstitutione (de quo statim dicturi sumus), quemadmodum duas medietatesterrae non divisas vel ante terram, sed in terra et cum terra creavit. Qui enimdixit et facta sunt, partes et totum simul creare potuit».

136. For an exhaustive table of the ancient sources, cf. B. Pabst, Atomtheoriendes lateinischen Mittelalters, Darmstadt 1994, 21-56. On William of Conches’ rela-tion to classical atomism, see H. Flatten, Die Philosophie des Wilhelm von Conches,

Isidore of Seville and the commentary on the Consolation of Philoso-phy attributed to Remigius of Auxerre.

b) Are the elements visible?

The Duke asks a second question: are the particles of the ele-ments visible or invisible? If visible, they must have dimensions; ifinvisible, they cannot be perceived by the senses. As Lucretius says,«nothing sensible can be born from the insensible», while Macrobiusaffirms that a quality doubled can never lead to its contrary 137. Thisline from Lucretius is quoted by Priscian, among others, yet Williamof Conches does not comment on it in his glosses on the Institu-tiones grammaticae, simply observing that sensibile et sensile idemsunt 138. Likewise, when he illustrates the boethian lemma Nam nichilex nichilo, vera sententia est in his Glosae super Boetium, he does notmention atoms, the void, or the Epicureans 139.

The philosopher defines the insensible as that which can never beperceived by the senses, whether alone or combined with somethingelse of the same kind. The soul, for example, can never be perceivedby the senses, whether it is alone or with other souls. This is not thecase for particles. It is impossible to sense a single particle, but it canbe perceived when joined to others. In fact, bodies are simply con-glomerates of particles linked together. Since a particle is joined toanother particle, its doubled quality increases, but there can be noquestion of a contrary quality, as Macrobius explains 140.

48

IRENE CAIAZZO

Koblenz 1929, 113-27, Gregory, Anima mundi, 207-12, and Elford, Developments inthe Natural Philosophy of William of Conches, 26-41.

137. Macrobius, Commentarii in Somnium Scipionis, II, 15, 30, ed. et transl. M.Armisen-Marchetti, Paris 2003, 74: «Omnis enim qualitas geminata crescit;numquam ex duplicatis similibus contrarietas emergit».

138. Priscianus Caesariensis, Institutiones grammaticae, IV, 27, GL II, 132, com-mented in Glosae super Priscianum (second version), ms. Paris, Bibliothèquenationale de France, lat. 15130, f. 44va. The same gloss is to be found in the firstversion of the Glosae super Priscianum, cf. ms. Florence, Biblioteca Medicea Lau-renziana, San Marco 310, f. 40va.

139. Guillelmus de Conchis, Glosae super Boetium, V, pr. 1, ed. Nauta, 290-91.140. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 10-11, ed. Ronca,

26-27: «(D): Has particulas, quas esse elementa constituis, esse visibiles an invisi-biles dicis? Sed si sunt visibiles, non carent omni dimensione; si sunt invisibiles,cum nullo sensu percipiantur, quomodo stabit hoc quod ait Lucretius: Ex insen-sibili ne credas sensile nasci, et Macrobius: Omnis qualitas geminata crescit, numquamsuum contrarium operatur? Unde insensibile insensibili adiunctum numquam perfi-ciet sensibile, cum sit suum contrarium. (P): Insensibile est quod neque solumneque aliis sui generis adiunctum sensu corporeo percipi potest, sicuti est anima,quia neque unam animam neque animarum moltitudinem sensus percipit. Sed si

c) Are the elements bodies?

Having established that the elements are indivisible and sensible,the Duke wants to know whether elements are bodies. If the parti-cles are sensible, then they are bodies. If they are bodies, then theyhave three dimensions, since Boethius states that no body can existwithout three dimensions 141. The philosopher accuses the Dukeasking all these questions because he is not familiar with the imposi-tio and the translatio (a displacement of meaning) of nouns. Men usethe noun «body» to refer to that which is made up of the four ele-ments and is visible. William of Conches indicates that this naming –the result of an act of will – is illustrated in Boethius’ commentaryon Aristotle’s Categories 142. When philosophers subsequently exa-mined the first principles of the bodies made up of the four elements,they transposed or transferred the noun «body» to the principles:

(D): Si sensibiles sunt istae particulae, corpora sunt. Sed si sunt corpora,tres habent dimensiones, id est longum et latum et spissum, quia, ut aitBoetius, nullum corpus sine his dimensionibus inveniri potest. (P): Molesta istacongeries interrogationum ex hoc profluit quod impositiones et transla-tiones nominum nescis. Qui hoc nomen ‘corpus’ imposuit, constituto exquatuor elementis, quod oculis occurrebat, illud imposuit. Unde ait Boetius:Rebus existentibus et in naturae constitutione manentibus humanus animus vocabulaimposuit, constitutionem naturae vocans constitutionem ex quator elementis.Deinde prima principia rerum considerantes, philosophi nomina ad prin-cipia 143 transtulerunt, vocantes prima principia corporum corpora, sed addifferentiam compositorum simplicia. Quemadmodum ergo est simplexpraesens, est compositum, sic est simplex corpus, est compositum 144.

Hermann of Carinthia used the word principia to indicate thatwhich is at the foundation of bodies 145, while William of Conches’Philosophia states that the elements are quasi prima principia 146.

49


una particula per se sentiri non possit, adiuncta tamen aliis sentitur. Quid autemaliud est corpus quam particulae simul iunctae? Cum igitur particula particulaecomponitur, qualitas geminata crescit, non operatur contrarium».

141. Boethius, De institutione arithmetica, II, 4, 7, ed. Guillaumin, 91; the pas-sage is cited infra, n. 154.

142. Boethius, In Categorias Aristotelis, 1, PL 64, [159-294],159A.143. Italo Ronca emends the text here to particulas instead of principia, against

the entire manuscript tradition. The change is unnecessary.144. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 12-13, ed. Ronca,

27-28.145. Hermannus de Carinthia, De essentiis, I, 60vB-D, ed. Burnett, 92, cited

supra, n. 122.146. Guillelmus de Conchis, Philosophia, I, 7, 24, ed. Maurach, 29.

d) Translatio

William of Conches introduces the notion of translatio to discussthe distinction between simple and complex bodies. A few historicaland historiographical reference points are required to elucidate thispassage from the Dragmaticon philosophiae. The notion of translatiocomes from the arts of the trivium: ordinary language is not alwaysable to express the content of thought or of natural reality, hencethe recourse to improper discourse to signify something other thanthe primary or proper sense of nouns in ordinary language as insti-tuted by mankind 147. The lack of proper terms may be one reasonfor the use of improper or transferred terms. There are several typesof transfer, all based on an identifiable relationship between theimposed and the transferred term, obeying rules analyzed at lengthin twelfth-century grammatical and logical texts, including those byAbelard 148.William of Conches’ discourse is too succinct to allow usto understand at once on what relation the transfer carried out bythe philosophers is based when they shift from principles to bodies.Is it a relationship of resemblance, or of cause and effect? Boethiusis one of the main sources for impositio and translatio, particularly hiscommentaries on Aristotle’s Categoriae and De interpretatione. Thenotion is primarily used in a theological context in the twelfth cen-tury, with translatio being used to speak of God and the divine.Abelard is the first to accord importance to this notion, first in hisLogica «Ingredientibus», and later in the three different versions of hisTheologia. William of Conches may have found the notion of trans-latio in Abelard and applied it to the new field of natural philoso-phy. However, Abelard’s discussion has no real echo in the passagefrom the Dragmaticon philosophiae that proposes a relation between

50

IRENE CAIAZZO

147. I. Rosier-Catach, Prata rident, in Langages et philosophie. Hommage à JeanJolivet, edd. A. Elamrani-Jamal, A. de Libera, A. Galonnier, Paris 1997, [155-76],155: «Trope ou figure de sens pour les grammairiens et les rhéteurs, variation designification constituant un mode de l’équivocité pour les dialecticiens, déplace-ment sémantique intervenant dans tout discours sur Dieu pour les théologiens,la notion de transfert sémantique (translatio, transumptio) est au carrefour des artsdu langage et de la théologie».

148. Cf. I. Rosier, Évolution des notions d’equivocatio et univocatio au XIIe

siècle, in Ead., L’ambigüité, cinq études historiques, Lille 1988; Ead., Prata rident, 155-76; Ead., La notion de translatio, le principe de compositionalité, et l’analyse de laprédication accidentelle chez Abélard, in Langage, sciences, philosophie au XIIe siècle, ed.J. Biard, Paris 1999, 125-64. For an overall view of translatio in the twelfth cen-tury, see L. Valente, Logique et théologie. Les écoles parisiennes entre 1150 et 1220,Paris 2008, esp. ch. 1, «Impropriété et translatio dans le discours théologique».

the meaning of imposed words and the meaning of transferredwords, based on a proportion or analogy between the four terms.William of Conches simply states that just as there is the simplepresent and the compound present, there is also a simple body anda compound body.

Although William of Conches does not use the term «propor-tion», Boethius did so in classifying the various types of equivocalsin his Commentary on the Categories. Among the things that areequivocal because of a voluntary act of mankind were those that areequivocal according to proportion. The point is the principle of theline, just as the unit is the principle of number. In Boethius, thisproportion means that both the point and the unit can be equivo-cally called a principle 149.

Before turning to William of Conches’ use of proportion, a briefexcursus on the simple present and the compound present – thetwo terms of the proportion that correspond to simple and com-pound bodies – may be useful. As I. Ronca, editor of the Dragmati-con philosophiae, has pointed out, this distinction is based on gram-mar. The lemma-by-lemma commentaries on Priscian’s Institutionesgrammaticae shed light on the passage from the Dragmaticon. Priscianstudies verb tenses at Inst. VIII, 39. After discussing the perfect andpluperfect past tenses, he comments briefly on the instant, notingthat some call it «imperfect»: «Instans autem est individuum, quodvix stare potest. Unde merito a quibusdam instans ‘imperfectum’nominatur. Nisi enim sit imperfectum, in eo adhuc esse actus intel-legi non potest» 150. The twelfth-century commentators on the Insti-tutiones grammaticae discuss this instant in terms of the present tense,distinguishing it from the present that includes duration in time,such as «I am reading». The unidentified author of the Glosulae superPriscianum (in the version of the Metz and Cologne manuscripts)does not dwell on this distinction between two presents, nor doeshe use the term «simple present». He defines the instant as the pointthat unites the past and the future, but which itself has no parts. In

51


149. Boethius, In Categorias Aristotelis, 1, PL 64, [159-294], 166B: «[…]; aliasecundum proportionem, ut principium, namque principium est in numerounitas, in lineis punctus. Et haec aequivocatio secundum proportionem esse dici-tur». Gilbert of Poitiers’ commentary on Boethius’ De Trinitate explains that thelanguage used in natural science may be transferred to other sciences; this trans-latio is based on proportions. Cf. The Commentaries on Boethius by Gilbert of Poi-tiers, ed. N. M. Häring, Toronto 1966, 115.

150. Priscianus Caesariensis, Institutiones grammaticae,VIII, 39, GL II, 406, l. 6.

contrast, the present to which the verb refers is «compositum»because it is made up of parts: that which is in the past, that whichis now, and that which is in the future 151. In other words, it is apresent that has duration in time.

The first version of William of Conches’ Glosae super Priscianum,written after the Philosophia (i.e. after 1125-1130), contains an exten-sive lacuna in Book 8, just where a discussion of the simple presentand the compound present would be expected. The second versionof the Glosae super Priscianum, a late work written after the Drag-maticon, illustrates the difference between the two presents; unfortu-nately, the Paris manuscript is somewhat unclear at that point 152.

52

IRENE CAIAZZO

151. Glosulae in Priscianum maiorem, transcription by E. Lorenzetti, revised byK. M. Fredborg, in progress: «INSTANS AUTEM. Praeteritum tempus ita diuiditur,sed INSTANS, idest praesens, EST INDIUIDUUM; hic nota eum agere de praesenti,quod est quasi punctus copulans praeteritum et futurum, non de eo presenti dequo quaeritur in uerbo cuius temporis. Illud enim partes habet quod praeteriit,quod est et quod futurum est, hoc uero partibus caret. Sed quia compositumpraesens gratia huius partis, scilicet suae, praesens dicitur, ideo de hoc instantiagit et etiam ut ostendat in significatione huius indiuidui temporis nos nonposse uti diuiduis, et diuiduis uocibus sicut in praeterito utimur». Warmestthanks to Margareta Fredborg for the transcription of this passage from the Glo-sulae, whose typography I have maintained.

152. Cf. supra, concerning Jeauneau’s chronology. Ms. Paris, Bibliothèquenationale de France, lat. 15130, f. 60va-b: «INSTANS AUTEM ETC. Ostenso in quoet quare diuidatur preteritum, reuertitur ad presens ut appareat ex natura illiusquare diuidatur. Et secundum quosdam hoc est de simplici presenti ad cuiusintellectum dicamus quod aliud presens est simplex, aliud compositum. Simplexautem presens est de quo nichil est preteritum, nichil futurum, sed in uno sim-plici presenti nichil potest agi. Statim enim transit. Unde tale presens, inquam,<non> consignificatur a uerbo nisi substantiuo et uocatiuo, de quibus in locosuo dicemus. Presens uero compositum est cuius pars preteriit, pars futura est etpars existit. Sed tamen (tum ms.) illud compositum dicitur presens propter sim-plicem particulam sui que existit. In tali presenti potest aliquid agi, unde talepresens a uerbo consignificatur. Secundum quosdam igitur de sinplici presentihic agit, sic exponentes literam: PRETERITUM DIUIDITUR IN PRESENTI, sed ins-tans id est simplex presens est, inquam, caret partibus id est quod uix potest starequia statim transit et <in> aliud uoce cedit. Unde etc. Tam simplex est quianichil in eo (ex se lectio dubia ms.) perfectum ponit. Nominatur etiam a quibus-dam instans per hoc uero ut instans est imperfectum + quia hoc+ etc., Hec sen-tencia non placet. Cum enim hic agitur de tempore quod a uerbo consignifica-tur de illo instanti sic agitur in quo potest actio esse, in quo potest aliquid agi,quod est compositum. Littera secundum hanc sententiam sic legitur, continuaturet exponitur. Preteritum tempus in grammatica diuiditur in diuersas species etdiuersis nominibus designatur. Autem id est “sed” instans id est presens in eademgrammatica indiuiduum id est quia in ea non diuuiditur in diuersas species necdiuersis nominibus nominatur. Vocatur ergo instans indiuiduum non quia nonposset diuidi per species ut in presentem horam, diem, mensem, etc. et perpartes ut in presentem preteritam et presentem futuram, sed quia non diuiditurin grammatica, ut diuersis uocibus designentur quia instans uix potest stare quia

However, William of Conches expresses himself in terms so similarto Petrus Helias’ Summa super Priscianum, written in the 1140s, thatthe lacunae in the Glosae super Priscianum can be filled in 153. Fol-lowing the Glosulae, the idea of the two presents has developed con-siderably; the discussion now seems to unfold around the notion of«consignificatio», which derives from Aristotle’s De interpretatione.William of Conches gives the following general definition of time:«the verb signifies the passion and action, and co-signifies time». Hebegins by discussing the opinion that the divisible instant men-tioned by Priscian is the simple present, which has no past or future,but that one cannot act in such a present, because it passes immedi-ately.This is why some thinkers argue that the simple present can beco-signified by a substantial or a vocative verb. The compound pre-sent has one part in the past, one part in the future, and one partthat is current; the compound present is called «present» because ofthe current simple particle. This particle allows action to unfold, andmay be co-signified by the verb. The simple present, on the otherhand, does not allow the unfolding of any action and must thereforebe called «imperfect instant». William of Conches rejects this opi-nion and argues that Priscian’s «indivisible instant» is in fact the com-pound present – a time in which action can unfold, and which canbe co-signified by a verb. William of Conches explains that in thecontext of grammar, the expression «indivisible instant» necessarilyrefers to a present co-signified by a verb, i.e. the compound present.This present can be divided into smaller parts such as months, days,and hours; however, this division does not pertain to grammar.These observations are useful in understanding the discussion in theDragmaticon. The first opinion (which, according to William, evokesa division that does not pertain to grammar) sheds useful light onthe comparison in the Dragmaticon. The simple present is an indivi-sible instant that scarcely exists, yet it is part of the compound pre-

53


minima pars eius est presens, maior preterita uel futura. Unde quia uix stat etaliquid de <e>o sit futurum, nominatur a quibusdam instans imperfectum quiaomni presenti aliqua pars futura est. Nisi enim.Vere instans quod consignificatura uerbo si perfectum est iam transit, si transitum est non est in eo actus. Ut ergoactus sit in presenti opportet de eo aliquid esse futurum et aliquid preteritum.Si enim de eo nichil est futurum iam totum transiit, similiter si nichil de eotransiit, tantum est futurum nec adhuc est actus in eo». Warmest thanks to Mar-gareta Fredborg for the transcription of this passage from William of Conches’Glosae super Priscianum, whose typography I have maintained.

153. Cf. Petrus Helias, Summa super Priscianum, De tempore, ed. L. Reilly,Toronto 1993 (Studies and Texts, 113), 489-91.

sent, which exists and has continuous duration in time because it ismade up of simple parts.

After presenting his analogy – the simple present is to the com-pound present as a simple body is to a compound body – Williamof Conches explains that in the extract from the De arithmeticaquoted by the Duke, Boethius asserts that bodies have three dimen-sions because he is referring to the meaning of the first impositionof the noun «body» rather than to the meaning due to the philo-sophical displacement (translatio) of the noun «body»:

(P): Cum igitur dicit Boetius: Corpus sine his tribus dimensionibus non potestinveniri, iuxta primam nominis impositionem, non iuxta philosophicamtranslationem hoc dixit. Sunt igitur iuxta philosophicam translationem prae-dictae particulae corpora, non tamen tres habent dimensiones 154.

In the philosophical translatio, the particles are bodies by virtue ofbeing the principles of bodies, despite not having three dimensions.The nature of this dimensionless body raises questions. William ofConches may again have taken his inspiration from Boethius, whoin the paragraph of the De arithmetica that follows the discussion ofthe characteristics of solid bodies explains how the indivisible pointhas no dimensions despite being the principle of all dimensions. TheGreeks called such points «atoms» because no parts are to be foundin them 155.

54

IRENE CAIAZZO

154. Guillelmus de Conchis, Dragmaticon philosophiae, I, 6, 13, ed. Ronca, 28.Cf. Boethius, De arithmetica, II, 4, 7, ed. Guillaumin, 91: «Necesse est autem utquicquid fuerit solidum corpus, hoc habeat longitudinem latitudinemque et alti-tudinem, et quicquid haec tria in se continet, illud suo nomine solidum uoce-tur. Haec enim tria circa omne corpus inseparabili coniunctione uersantur et innatura corporum costituta sunt».

155. Ibid., II, 4, 8-11, 91-92: «Quare quicquid uno interuallo caret, illudcorpus solidum non est. Nam quod duo sola interualla retinet, illud superficiesappellatur. Omnis enim superficies sola longitudine et latitudine continetur. Ethic eadem illa conuersio remanet. Omne enim quod superficies est longitudi-nem et latitudinem retinet, et quod haec retinet, illud est superficies. Haecautem superficies uno tantum interuallo solidi corporis dimensione superatur,quae uno rursus interuallo lineam uincit, quae longitudinis naturam retinenslatitudinis expers est; quae linea, quod unius est interualli sortita naturam, asuperficie uno interuallo, a soliditate duobus spatiis uincitur. Punctum igitur aliorursus interuallo a linea uincitur, ipsa scilicet quae reliqua est longitudine. Quaresi punctum uno quidem interuallo a linea supergreditur, idem a superficie uin-citur duobus, tribus uero interualli dimensionibus a soliditate relinquitur, constatpunctum ipsum sine ulla corporis magnitudine uel interualli dimensione, cum etlongitudinis et latitudinis et profunditatis expers sit, omnium interuallorum esseprincipium et natura insecabile, quod Graeci atomon uocant, id est ita diminu-

The Dragmaticon introduces significant developments in the theoryof the elements: William completes and harmonizes the teachingsdrawn from medical writings with an in-depth reading of Boethius’De arithmetica. This text was widely influential from the 1140s on,possibly due to the teaching of Thierry of Chartres 156. Furthermore,grammar (focused on the interpretation of Priscian’s Institutionesgrammaticae in the first half of the twelfth century) provides the toolsfor a radically new explanation of the relationship between the bodyas an element and the body composed of elements. William ofConches no longer uses the word elementatum, perhaps because ofHermann of Carinthia’s criticisms or because he no longer foundthe theory fully convincing. However, the word elementatumremained in use at the end of the twelfth century, by the Salernitandoctors Maurus and Urso, for example. Indeed, it survived into themodern age, being taken up by Pierre Gassendi, among others.

5.2 Toward the center and away from the center

The Dragmaticon philosophiae introduces other significant develop-ments in the theory of the elements. It accepts the existence of pri-mordial chaos, which William of Conches had hitherto rejected. Itfurther accepts that the particles are created by God himself, linkingelementary physics to a general theory of the cosmos. There will beno discussion of primordial chaos in the following pages, since twoarticles in the present volume are devoted to this question. Rather,we now focus on William’s renewed interest in the four elementsand their movements within the cosmos, which may have beensparked by the criticisms expressed by Hermann of Carinthia in theDe essentiis against the medici who focused solely on the four ele-

55


tum atque paruissimum ut eius pars inueniri non possit. Est igitur punctumprimi interualli principium, non tamen interuallum, et lineae caput, sed nondumlinea, sicut linea quoque superficiei principium est, sed ipsa superficies non est,et secundi interualli caput est, secundum tamen interuallum ipsa non retinet.Idem quoque et in superficiei rationem cadit, quae et ipsa solidi corporis et tri-plicis interualli naturale sortitur initium, ipsa uero nec trina interualli dimen-sione distenditur nec ulla crassitudine solidatur».

156. Cf. I. Caiazzo, Il rinvenimento del commento di Teodorico di Chartres al Dearithmetica di Boezio, in Adorare caelestia, gubernare terrena, International Confe-rence in Honour of Paolo Lucentini (Naples, 6-7 november 2007), edd. P. Arfé,I. Caiazzo, A. Sannino, Turnhout 2011, forthcoming.

ments and their transformations in the sublunary world, neglectingwhat happens above the moon 157.

The opus creatoris consists in the creation ex nichilo of souls andthe four elements and in the realization of miracles 158. It should benoted that God himself creates the particles, i.e. the elements, withtheir qualities, and assembles them with a view to locating them inthe various parts of the cosmos – fire at the very top, earth at thebottom, and air and water in between. Thus located, the elementsmove away from the center or toward the center of the cosmos. Inthe Philosophia William of Conches had previously discussed twoapproaches to this question: the physici focus on the particles as ele-ments of bodies, while the philosophi, bearing in mind the creationof the world, are interested in the elementa mundi, or the elements aswe see them, i.e. the elementata. But now, in the Dragmaticon, he ini-tiates a new phase in his theory of the elements, distinguishing lessclearly than in his previous works between the approaches of thephysici and the philosophi. The two approaches become the two sidesof the same coin, their unity being guaranteed by divine interven-tion: God creates the elements and fashions the elementata (to usethe vocabulary of the Philosophia).

William of Conches’ earlier works described the place of the ele-ments in the universe in terms of layers of earth, water, air, and fire,using the metaphor of the egg inherited from the ancient tradi-tion 159. However, he did not explain the movement of the elementswithin the universe. In the Dragmaticon philosophiae, William returnsto the metaphor of the egg:

Mundum istum ad similitudinem ovi constitutum esse philosophi confir-mant. Ut igitur in medio ovi est meditullium – ex cuius omni parte estalbumen, circa albumen tela, circa quam testa, extra quam nichil est de ovo– sic in medio mundi est terra, circa eam ex omni parte fluit aqua, circaaquam aer, circa quem ignis, extra quem nichil est 160.

56

IRENE CAIAZZO

157. Hermannus de Carinthia, De essentiis, 61rB, ed. Burnett, 92. Hermannprefers the explanation of the astrologi to that of the medici. Cf. ibid., Introduc-tion, 24.

158. Guillelmus de Conchis, Dragmaticon philosophiae, I, 7, 2, ed. Ronca, 30:«Opus creatoris est elementorum et animarum ex nichilo creatio, mortuorumresuscitatio, partus virginis et similia».

159. On the cosmic egg, cf. P. Dronke, Fabula. Explorations into the Uses ofMyth in Medieval Platonism, Leiden-Cologne 1974 (Mittellateinische Studien undTexte, 9), 79-99.

160. Guillelmus de Conchis, Dragmaticon philosophiae, II, 2, 8, ed. Ronca, 39.

This passage is of special significance as it marks the transitionfrom elementary to celestial physics, from the theory of particles tothe theory of the elements of the world. Taking up explanationsfrom his former works, William of Conches here explains the reasonfor God’s having created two intermediary elements between fireand earth. He develops his own theory of their mutual links byintroducing the distinction between solid and plane sinzugie. Thesesyntagms have been coined by William of Conches as early as by thetime of the Glosae super Boetium. But now, in the Dragmaticonphilosophiae, he adds two explanatory figures (descriptio) to his text,for the sake of clarification.

Another innovation of the Dragmaticon philosophiae concerns themotion of the elementary bodies. When addressing the question ofthe difference between natural and accidental motion, William ofConches discusses for the first time the direction of the motion ofthe elements (i.e. the elements of the world): they head «toward thecenter» or «away from the center». The two lower elements (waterand earth) move toward the center, while the higher ones (air andfire) move away from the center. The existence of these naturalmovements is proved by accidental motion: when an external causethat pushes water and earth upwards ceases its action, the two ele-

57


Fig. 1: Sinzugia plana and sinzugia solida. William of Conches, Dragmati-con philosophiae, II, 5, 1. Ms. Montpellier, Bibliothèque interuniversitaire,section médecine, H 145, f. 9r (XIIth century).

ments fall back downwards in accordance with their natural motion,the speed of their fall depending on their weight. Earth is heavierthan water, so it falls more quickly and is situated lower down. Like-wise, if fire or air are accidentally lowered toward the center, theyimmediately move away from the center as soon as the accidentalcause ceases. Fire is lighter than air, so it rises more quickly andregains its place at the very top of the universe, far from the center.Nevertheless, neither fire nor earth move according to their naturalmotion 161. Fire, whose nature dictates it must move away from thecenter, does not move away from it, because God has placed it atthe summit of the cosmos. It is blocked from above, and since thereis no place above it toward which it might move, it cannot exerciseits natural motion, which pushes it to move away from the center.Nor does it descend toward the center, as to do so would be con-trary to its nature. Fire remains in the same place although itmoves 162. Similarly, earth, whose natural motion pushes it towardthe center, does not move either, as it is already at the center of theuniverse. Nor does it move upward in order to lower itself towardthe center, for this motion would be contrary to its nature 163. TheDuke challenges the philosopher to explain how earth can movewhile remaining in the same place. The answer is amusing: think ofa philosopher who has drunk too much at a meal and has theimpression that the earth is moving, although of course it is not

58

IRENE CAIAZZO

161. Ibid., II, 6, 5, 50: «Duo igitur inferiora elementa ad centrum moventur,duo superiora a centro. Hoc autem ex partibus eorum probari potest. Nullaenim est pars terrae vel aquae quae, si aliqua causa sublevetur, cessante causa nondescendat; et quantum terra gravior est aqua, tanto in hoc motu est velocior.Similiter, si pars ignis vel aeris aliquo accidente descendat, eo cessante statim acentro movetur et ascendit; sed ignis, quanto est aere levior, tanto est in hocmotu velocior. Quamvis tamen his duobus motibus naturaliter moventur, neutrotamen illorum actu moventur».

162. The philosopher returns to the motion of fire within itself in Book III,explaining that it is also called ‘ether’ because of this circular motion. The fifthelement will not be discussed in the present study.

163. Ibid., II, 6, 6, 50-51: «Ignis igitur, qui naturaliter a centro est mobilis, acentro tamen non movetur. Cum enim nullus locus supra ipsum est, ascenderenon potest. Nulla vero specie translationis movetur: descendere non potest, quiahoc est ad centrum moveri, quod est contra eius naturam, maxime cum omnislocus inferior spissioribus corporibus sit plenus; alia specie translationis nonpotest, quia nullus locus extra ipsum est; sua vero levitas ipsum stare prohibet. Inquo ergo potest et habet, in eodem loco consistens movetur. Terra vero, cumnaturaliter ad centrum movetur, quia ipsa centrum est, hoc motu non moveturnec transfertur. Cum enim est infima, ad nullum locum transire potest, quinascendat; sed hoc est a centro moveri, quod est contra eius naturam».

moving at all 164. The Duke protests, demanding the opinion of anauthority. The philosopher then gives Ambrose’s opinion that earthremains immobile. The earth remains suspended in the midst of theair surrounding it on all sides, without falling or moving, becausefire, which also surrounds it on all sides, exerts an attractive forceupon it. The earth tries to resist this attraction exerted on all sides bymeans of the force that naturally pushes it toward the center of theuniverse.These two contrary forces cancel each other out, so that theearth is held in the air by fire and remains in the center of the uni-verse 165. The two intermediary elements do not move according totheir natural motions because they have no place to move to; how-ever, they do contribute to maintaining balance in the cosmos byexerting their repulsive and attractive forces. They also move whileremaining in the same place, thereby causing the meteorological phe-nomena discussed in Books V and VI.Thanks to these movements, themachina mundi exists, possesses equilibrium, and preserves itself 166.

The idea that the earth is suspended in the middle of the cosmoswas widely held by ancient and medieval authors, including Mar-tianus Capella 167, Macrobius 168, Isidore of Seville 169, and Adelard of

59


164. Ibid., II, 6, 7, 51.165. Ibid., II, 6, 9, 52: «Alia est ratio, quare non movetur: cum ignis undique

terram circumdet et aequaliter ab ea distet, vi attractiva, quam habet, superioreparte sui nititur eam attrahere, sed opposita pars repugnat. Similiter fit ante etretro, dextrorsum et sinistrorsum, quemadmodum de sepultura Macomi audivi-mus, quae, cum sit ferrea, magnete undique sustinetur. Unde, si etiam in aereterra esset, vi attractiva ignis sustineri posset». I. Ronca suggests Embrico ofMainz’s Vita Mahumeti, written c. 1133-1148, as a source (ed. G. Cambier, Brus-sels 1961, 92) in his apparatus criticus. However, there are no textual correspon-dences between the two works.

166. Guillelmus de Conchis, Dragmaticon philosophiae, II, 6, 11-12, ed. Ronca,53-54: «Si quae dicta sunt de motu extremorum ventis non tradidisti, de motuistorum diu non dubitabis. Cum enim omnis locus praeter terram superior estaqua, et est contra naturam eius ascendere, infimusque locus solidiore elementoest occupatus, nulla specie translationis moveri potest. Similiter cum solus ignissupra aera sit – unde ascendere non potest, descendere vero contra eius est natu-ram – transferri non potest. Duo igitur media in eodem loco moventur. Demotu vero aeris, quo aura vento turbine fulgure fulmine scintillationibus move-tur, cum de sublimibus loquemur, disseremus. De aestuationibus maris et acci-dentalibus commotionibus aquarum, cum de infimis erit sermo, dicemus. Manetigitur mundi machina inconvulsa, quia non habent quo transferantur ea quae aquibusdam dicuntur elementa».

167. Martianus Capella, De nuptiis Mercurii et Philologiae, VI, 599-600, edd. A.Dick, J. Préaux, Stuttgart 1978 (Bibliotheca scriptorum Graecorum et Romano-rum Teubneriana), 296-97.

168. Macrobius, Commentarii in Somnium Scipionis, I, 22, 1-8, ed. Armisen-Marchetti, 131-32.

169. Isidorus Hispalensis, De natura rerum, XII, 4, ed. Fontaine, 219-21.

Bath 170. Pliny and Macrobius stand out as authors who discuss thesubject in great detail, specifying that the earth maintains itself inthe center by means of contrary forces 171. However, direct kinshipbetween these texts and William of Conches’ work can only bedemonstrated in rare instances. Furthermore, the «vis attractiva» offire is a medical concept, which, borrowed from the Pantegni, is nowbeing applied to cosmology. This is a groundbreaking innovation,not found in any of the older sources.

Similarly, it is not easy to identify the precise sources used byWilliam of Conches to develop his theory of the motions of ele-ments. Macrobius’ discussion of the soul and its ability to move itselfin the Commentarii in Somnium Scipionis includes a brief couplet onthe movement of the heavy elements downward (deorsum) and ofthe light elements upward (sursum), but does not refer to the centerof the universe 172. William of Conches’ glosses on Macrobius’ Com-mentarii do not go into detail on the passage in question; his remarksare confined to the main subject of the chapter – the motions ofthe soul. Macrobius cannot be William of Conches’ sole source, asWilliam’s exposition is much more complex and seems to draw onconcepts from the Peripatetic tradition. However, the De caelo,whose main subject was the theory of the natural places of the ele-ments and their movements toward the top or bottom of the uni-verse, i.e. from the middle of the universe toward the periphery orfrom the periphery toward the middle, depending on their weight,was not translated by Gerard of Cremona until about 1175, too latefor William of Conches to have read it. Nor can he have consultedthe Liber celi et mundi 173, Gundissalinus and Iohannes Hispanus’

60

IRENE CAIAZZO

170. Adelardus Bathoniensis, Questiones naturales, 48-49, edd. C. Burnett, I.Ronca, P. Mantas España, B. van den Abeele, Cambridge 1998; repr. 2006, 178-82.

171. Plinius Secundus, Historia naturalis, II, 4, 5, ed. et transl. J. Beaujeu, Paris1950, 11.

172. Macrobius, Commentarii in Somnium Scipionis, II, 14, 12-13, ed. Armisen-Marchetti, 61: «Natura vero moventur vel gravia cum per se deorsum, vel leviacum sursum feruntur; sed et haec dicendum est ab alio moveri, licet a quohabeatur incertum. Ratio enim, ait [scilicet Aristoteles], deprehendit esse nescioquid quod haec moveat. Nam si sponte moverentur, sponte etiam starent, sednec unam viam semper agerent, immo per diversa moverentur si spontaneo fer-rentur agitatu. Cum vero hoc facere non possint, sed levibus semper ascensus, etdescensus gravibus deputatus sit, apparet eorum motum ad certam et constitu-tam naturae necessitatem referri». Here Macrobius translates passages from Aris-totle, Phys.VIII, 4.

173. Gerard of Cremona’s translation has been edited by I. Opelt, beneaththe text of P. Hossfeld’s edition of Albert the Great’s commentary on the Decaelo, in Alberti Magni Opera omnia V.1, Aschendorff 1971.

Arabic-Latin translation (c. 1150-1175) of H. unain ibn Ish. aq’s para-phrase of the first two books of Aristotle’s De caelo 174. In any case,William’s terminology does not match that of the Latin translations,which always follow Aristotle in using «middle» (ad medium / demedio) rather than «center» (ad centrum / de centro)175.

In fact, several ancient works contain references to physics in theAristotelian tradition. Cicero’s De natura deorum 176 and Priscian ofLydia’s Solutiones ad Chosroem 177, both known in the twelfth century,refer to the movements of the elements toward the middle (medium)and away from the middle of the universe. Ambrose’s Hexaemerongives a very brief explanation of the natural and accidental motionsof the elements, particularly of fire 178. It should be noted, however,that William of Conches refers to the center (mobile ad centrum) forthe direction of the elements, whereas all the other works listed usemedium. Book VIII (De astronomia) of Martianus Capella’s De nuptiisMercurii et Philologiae explains that the earth is in the middle, i.e. atthe center of the universe, but says nothing about the direction ofthe elements 179. Macrobius does not discuss the direction of the ele-ments when explaining that the earth is at the center of the uni-verse 180. Pliny refers to the fact that the world obeys a centripetalforce, whereas the earth possesses a centrifugal force, in the chapterin which he provides proof of the earth’s roundness 181.

61


174. Pseudo-Avicenna, Liber celi et mundi, ed. O. Gutman, Leiden-Boston,2003 (Aristoteles Semitico-Latinus, 14).

175. Cf. I. Caiazzo, Urso of Salerno on Prime Matter between Plato and Aristotle,in Animé/Inanimé. Des théories de la matière à la pratique médicale (XIIe-XVe siècle),edd. D. Jacquart – N. Weill-Parot, forthcoming.

176. Cicero, De natura deorum, II, 33, edd. O. Plasbeg, W. Ax, Leipzig 1933, 82.On the presence of the De natura deorum in the 12th century, cf.T. Silverstein, Ade-lard, Aristotle and the De natura deorum, in «Classical Philology», 47/2 (1952), 82-86.

177. Priscianus Lydus, Solutiones ad Chosroem,VII, ed. I. Bywater, Berlin 1886,78-79.

178. Ambrosius Mediolanensis, Hexaemeron, I, 6, 23, PL 14, 146A-B: «Nam quilevibus accommodus est, fit incommodus gravioribus elementis. Itaque quandoad superiora motus caeli est necessarius, terrenis gravatur; quando ad inferioradecursus expetitur, igneus vigor ille violenter attrahitur. Etenim contra naturaesuae usum deorsum cogitur. Omne autem quod in contrarium cogitur, non na-turae serviens, sed necessitati, cito solvitur, et in ea scinditur ex quibus videturesse compositum, in suam quamque regionem singulis recurrentibus».

179. Martianus Capella, De nuptiis Philologiae et Mercurii, VIII, 814, ed. Dick,Préaux, 430-31: «Mundus igitur ex quattuor elementis isdemque totis in sphaeraemodum globatus terram in medio imoque defixam. […] quarum circa medium,quod dixere centron, aquae primum aerisque sequens».

180. Cf. supra, n. 168.181. Plinius Secundus, Historia naturalis, II, 160, ed. Beaujeu, 70: «[…] mundus

in centrum vergit, at terra exit a centro».

The references to the center in the Dragmaticon philosophiae seemto draw on astronomical terminology and geometrical constructionsof figurae. This is the case, for instance, in the De nuptiis Mercurii etPhilologiae, where the brief exposition on the four elements serves asan introduction to astronomy, just as Macrobius’ Commentarii inSomnium Scipionis uses a diagram to demonstrate why rain falls tothe earth. In Masha’allah’s Liber de orbe, the word centrum is used forthe center of the figure representing the motion of the elements,although in the text the elements move ad medium or de medio 182.Petrus Alfonsi’s Dialogi contra Iudaeos includes a figura placing theearth at the center of the universe, but there is no indication of themotions of the elements 183. Likewise, Hermann of Carinthia’s Deessentiis uses geometrical constructions to explain the motions of theplanets with reference to the center, but not in relation to the direc-tion to the motions of the elements. William of Conches may havetaken inspiration for his theory from a figure alongside one of thesetexts while studying ancient and contemporary sources. It is alsopossible, although less likely, that William of Conches consulted theLiber Mamonis 184, a cosmology by a Latin author dating from around1140 that is indebted to what has been called the al-hay’a tradition,which consists of non-technical treatises on the «configuration» ofthe world. The Liber Mamonis has a clearly identified Arabic model,the De forma mundi by Ibn al-Haytam (the Latin Alhazen), whichwas translated into Latin by an unknown author, most likely in thetwelfth century 185. The elements in De forma mundi are divided into

62

IRENE CAIAZZO

182. Cf. Obrist, William of Conches, Masha’allah and Twelfth-century Cosmology.183. Petrus Alfonsi, Dialogi contra Iudaeos, 13, PL 157, 548; the figura is repro-

duced in Tolan, Petrus Alfonsi, 54.184. C. Burnett, Antioch as a Link between Arabic and Latin Culture in the

Twelfth and Thirteenth Centuries, in Occident et Proche–Orient: Contacts scientifiquesau temps des Croisades, edd. A. Tihon, I. Draelants, B. van den Abeele, Louvain-la-Neuve 2000, 1-78; Id., The Transmission of Arabic Astronomy via Antioch and Pisa inthe Second Quarter of the Twelfth Century, in The Enterprise of Science in Islam: NewPerspectives, edd. J. P. Hogendijk, A. I. Sabra, Cambridge (Mass.), 2003, 23-51.

185. J. M. Millás Vallicrosa, Las traducciones orientales en los manuscritos de laBiblioteca Catedral de Toledo, Madrid 1942, 285-312. Cf. Ibn al-Haytam (Alhazen),On the Configuration of the World, transl. Y. Tzvi Langermann, New York-London1990, Introduction, 1: «Ibn al-Haytam’s On the Configuration of the World is a non-technical exposé of basic astronomical teachings; it was written in particular forthose whose main interests were in the areas of philosophy and natural scienceand who, accordingly, had a particular interest in relating the mathematicaldevices employed by professional astronomers to the heavenly bodies mentionedin the philosophical literature. I refute previous assertions that On the Configura-tion represents a mere reworking of Ptolemy’s Planetary Hypotheses or that Ibn al-

three species – heavy, light and medium – which move respectivelytoward, away from, and around the center. The medium or circularspecies is ether 186.

The direction of the elements also features in the treatise LiberMarii de elementis, which seems to be based on Arabic sources avail-able in Spain in the first quarter of the twelfth century, although theprecise date of composition is still a subject of debate among spe-cialists. It argues that heaviness makes earth and water move towardthe center, and adds the interesting detail that physici call this«movement toward the middle» 187. Marius elsewhere asserts that

63


Haytam proposed in this work to resolve any of the outstanding problems ofmedieval cosmology». Cf. ibid., 25 sqq., the chapter entitled: «Predecessors andthe hay’ah tradition».

186. Liber Mamonis, unpublished edition by R. Lemay, New York 1990, 7 (ms.Cambrai, Bibliothèque municipale, 930, f. 2v-3r): «Ea autem quibus impleturmundus corpora discordia sunt specie, que dividuntur in IIIa: leve, grave etmedium. Grave est id quod ab omni parte mundi in centrum eiusdem suo pon-dere refertur. Leve illud esse dicimus quod a centri puncto vel ei proximis locissua levitate in exteriora <scilicet> in partem circularem defluit. Circularisautem pars que et medium intelligitur, illa est que nec in centrum nec a centrofugit, sed circa ipsum continuo motu quietis inscia volvitur. Locus igitur gravispartis medius est locus mundi, medie vero circularis et exterior, horum mediumlevis pars vendicat».

187. Marius, On the Elements. A Critical Edition and Translation by Richard C.Dales, Berkeley–Los Angeles–London 1976, 47: «(M): Quae etiam ponderositas etterram et aquam moveri facit ad centrum; quem motum vocant phisici “motumad medium”». Scholars disagree on the dating and paternity of the Liber Marii deelementis. Cf. R. M. Thomson, Liber Marii de elementis: The Work of a HithertoUnknown Salernitan Master?, in «Viator», 3 (1972), 179-89; R. C. Dales, Marius Onthe Elements and the Twelfth-Century Science of Matter, in «Viator», 3 (1972), 191-218. J. Reuter-Beaumont’s unpublished doctoral dissertation, which I have beenunable to consult, follows a suggestion by R. Hunt in maintaining that PetrusAlfonsi is the author of the Liber de elementis, and that he used Arabic sourcesavailable in Spain in the first half of the twelfth century; cf. Tolan, Petrus Alfonsi,205-8. M.-T. d’Alverny accepts this attribution in her article, Pseudo-Aristotle, Deelementis, in Pseudo-Aristotle in the Middle Ages: the Theologia and Other Texts,edd. J. Kraye, W. F. Ryan, C. B. Schmitt, London 1986, 63-83. J. Tolan is likewiserather favorable to the attribution to Petrus Alfonsi, cf. his Petrus Alfonsi, 207-08.C. Burnett, in contrast, rejects this attribution: cf. The Works of Petrus Alfonsi:Questions of Authenticity, in «Medium Aevum», 66/1 (1997), 56-61. He accepts D.Gottschall’s hypothesis that the Marius of the De elementis is Marius Salernita-nus, teacher of Godefroid of Viterbo (c. 1125-1192/1200), mentioned in Viterbo’sPantheon (Marius Salernitanus und Gottfried von Viterbo, in «Sudhoffs Archiv», 75[1991], 111-13). C. Burnett identifies a link between Petrus Alfonsi, Marius and«Alcantarus» (i.e. Masha’allah’s Liber de orbe). The references to movementstoward the center or away from the center in Petrus Alfonsi’s Dialogi are toovague to be William of Conches’ source. Cf. Diálogo contra los Judíos, I, ed.Mieth, 38: «Rursus omnis motio in corpore fit, sive sit recta motio, veluti cumquis unum deserens locum occupat alium, seu sit motio in gyrum, cum aliquid

physici call the upward movement of air (which can be seen invapor) and fire (which can be seen in flames) «motus de medio» 188.There is no way of knowing which «phisici» Marius had in mind,because the term «phisicus» could equally refer to a doctor or a na-tural philosopher in the twelfth century. What is important is thatMarius often mentions the directions of the elements and distin-guishes those who use the term «center» from those who use«middle» 189. Other indications suggest that the Liber Marii de elemen-tis is linked to the Dragmaticon. Marius does not accept the elementa-tum theory and does not use the term in his treatise. He uses theexample of milk, in which the four elements are combined and thenseparated by man 190.This example is found in the Dragmaticon, whenWilliam discusses the initial chaos. God creates the elements, whichare initially combined, then separated. This is compared to milk:«Similiter in lacte mixtim creat quatuor substantias, quas posteahomo, adiuvante natura, artificio separat» 191. There are doubtlessother parallels.

A certain number of sources dealing with the motion of the ele-ments were available in the Latin West as William of Conches waswriting his Dragmaticon in the late 1140s. These included works fromAntiquity or late Antiquity and treatises translated from the Arabicor based on Arabic sources. It is hard to say which texts Williamactually consulted, since he reworked and reordered his sources.However, the movements toward and away from the center (centrum)

64

IRENE CAIAZZO

scilicet in eodem existens loco ut firmamentum in orbem versatur, sive sit motiopartium alicuius rei ad invicem facta vel ab extremis ad medium vel a medio adextrema, veluti fit in partibus aeris, seu sit motio rei in eodem quidem loco exis-tentis, sed se per quedam quasi incrementa hac illacque spatiantis, quemadmodumin ramis arborum paulatim ad omnes partes crescentibus fit».

188. Marius, De elementis, ed. Dales, 55: «(M): Videmus namque flammamsemper atque festinanter sursum conscendere, vaporem vero, non nisi paulatimalicuius caloris vigore cogente. De motu autem isto, dicunt phisici, quia est“motus de medio”».

189. Marius also uses different formulations: cf. ibid., 71-73: «Omnis corporismotus vel de loco ad locum, et hic dicitur directus motus; vel est circularis; velest de centro foras; vel est de foris ad centrum».

190. Ibid., 129-31: «(M): Vellem modo compositum lactis illud divideres etelementa unumquodque ab alio separares, ita enim lucidius atque potentiusargumentum haberes. […] (M): Si itaque aliquis lac moveret, nunquid non statimpinguedo, hoc est butirum, superemineret? (D): Utique faceret. (M): Quod siemissa pinguedine quod remanet in vas commiserit, ac sicut de aqua rosata fit deeo fecerit, scias quia dulcis inde atque potabilis aqua exibit. Si vero etiam fecemque in vasis fundo remanserit comburet, cinis quidem atque ita terra fiet».

191. Guillelmus de Conchis, Dragmaticon philosophiae, I, 7, 4, ed. Ronca, 31.

seem characteristic of Arabic scientific treatises. The term «center» isnot used in Aristotelian physics; rather, it is typical of Post-Ptole-maic Arabic cosmology 192. However, it cannot be stated with anydegree of certainty which texts were behind William of Conches’choices of terminology. What is clear is that his choices had animpact on Latin scientific production in the latter half of the twelfthand the early thirteenth century. Ralph of Longchamp, Daniel ofMorley, Maurus and Urso of Salerno all refer to the centrum ratherthan the medium, despite having access to Aristotelian translationsthat contained the word medium.

6. Conclusions

The theory of the four elements is central to the work ofWilliam of Conches. He developed his innovative thinking by har-monizing sources from Antiquity and late Antiquity with dataderived from translations of Arabic scientific writings and contem-porary Latin texts, which were in turn based either on Arabic trea-tises or on translations. William of Conches adjusted and recom-bined his ideas and theories throughout his career. Accordingly, histheory of the elements underwent considerable changes between theGlosae super Boetium and the Dragmaticon philosophiae. His principalaim in developing the theory was to explain the relationshipbetween the elements, the constitutive principles of bodies, andbodies themselves – the relation between the indivisible and thedivisible – as a means of founding a scientia naturalis on a solid epi-stemological basis. The Glosae super Boetium reject the theory of theelementata found in commentaries on the Isagoge Iohannitii. Williamlater accepts this theory in the Philosophia and the Glosae super Pla-tonem, yet is silent on the matter in the Dragmaticon philosophiae. Thisreflects the impact of his new readings and new perspectives. It isironic that William owed his fame to the theory of the elementata,which proved highly influential, given that he eventually abandonedthe idea. The elementum/elementatum pairing is found widely in

65


192. William does not seem to have consulted twelfth-century translations ofAristotle, contrary to P. Dronke’s argument in William of Conches and the «NewAristotle», in «Studi medievali», 43/1 (2002), 157-63. Cf. L. Nauta’s response,William of Conches and the «New Aristotle»: A Reply to Peter Dronke, in «Studimedievali», 45/1 (2004), 445-57.

twelfth-century Latin works on natural philosophy and medicine.Yet full agreement on the nature and composition of elementata wasnever achieved over the course of the century; it is also the case thatthe expression res elementata was frequently used, giving the adjec-tive elementatus rather than the noun elementatum. Nevertheless, themanifold interpretations and nuances of the elementum/elementatumdebate were to remain influential well beyond the twelfth century;its impact can be traced as far as the seventeenth century. Finally, byfusing peripatetic and platonic philosophical traditions, William ofConches introduced the syntagms of sinzugia plana and sinzugiasolida in order to develop his own theory of the links between thefour elements. However, while being present in all of his works,these syntagms do not appear to have had much of an impact. Still,they represent a distinctive feature of the physics of the philosopherfrom Conches and might well help identify texts that haveremained, so far, unknown.

ABSTRACT

The theory of the four elements occupies a central place in William ofConches’ philosophy of nature. He developed his innovative thinking byharmonizing sources from Antiquity and late Antiquity with data derivedfrom translations of Arabic scientific writings and contemporary Latin texts,which were in turn based either on Arabic treatises or on translations.William of Conches adjusted and recombined his ideas and theoriesthroughout his career. Accordingly, his theory of the elements underwentconsiderable changes between the Glosae super Boetium and the Dragmaticonphilosophiae. His principal aim in developing the theory was to explain therelationship between the elements, the constitutive principles of bodies, andbodies themselves – the relation between the indivisible and the divisible –as a means of founding a scientia naturalis on a solid epistemological basis.

Irene CaiazzoCNRS, Paris

[email protected]

66

IRENE CAIAZZO

« The Four Elements in the Work of William of Conches », dans Guillaume de Conches: Philosophie et...

Documents

Transcript of « The Four Elements in the Work of William of Conches », dans Guillaume de Conches: Philosophie et...