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Place and Space in Albert of Saxony's Commentaries on the Physics

Published online by Cambridge University Press:  24 October 2008

Jürgen Sarnowsky
Affiliation:
Universität Hamburg, Historisches Seminar, Von-Melle-Park 6, IX, D-20146 Hamburg, Germany

Abstract

Albert of Saxony, master of Arts at Paris from 1351 until 1361/62, has left two commentaries on the Physics of Aristotle. Since he was well aware of the tradition, his writings may serve for an analysis of the transmision of ideas from the ancient and Arabic philosophers into the fourteenth century. In this paper, this is exemplified by the problems of place and space, especially by those of the definition of place and of the immobility of place, of natural place and of the location of the last and outermost sphere. As a result, four modes emerge how an author of the fourteenth century may have been influenced by tradition. Ancient Greek or Pre-Socratic philosophers were mainly known through Aristotle, and thus their opinions were mostly refuted; the same holds true for later ancient or Arabic authors known through the commentaries of Averroes; the influence of the authors of the thirteenth century was present though their texts may not have been directly consulted; and, finally, the contemporary authors were known, but nearly never quoted. Thus, though there was a line of tradition from Aristotle into the fourteenth century, there was also room for proper “medieval” solutions.

Albert de Saxe, maître ès arts à Paris de 1351 à 1361-1362, a laissé deux commentaires à la Physique d’Aristote. Dans la mesure où il avait une bonne connaissance de la tradition, ses écrits peuvent servir à analyser la transmission des idées à partir des Anciens et des philosophes arabes jusqu’au XIVe siècle. Dans cet article, on prend pour exemple le lieu et l’espace, et plus particulièrement celui de la définition du lieu et de son immobilité, celui du lieu naturel et celui de la localisation de la dernière sphère, la plus extrême. On trouve qu’il y a quatre sortes d’influence pour la tradition reçue par un auteur du XIVe siècle. Les anciens Grecs ou les philosophes présocratiques ont été surtout connus à travers Aristote, et ainsi leurs opinions étaient le plus souvent réfutées; la même chose est vraie pour les Anciens postérieurs et pour les auteurs arabes connus à travers les commentaires d’Averroès; I’influence des auteurs du XIIIe siècle était présente, bien que leurs textes n’aient pas toujours été directement consultés; et, finalement, les auteurs contemporains étaient connus, mais, la plupart du temps, sans être cités. C’est ainsi que, bien qu’il y ait eu une chaîne de tradition d’Aristote au XIVe siècle, il y a aussi la place pour des solutions “médiévale” originales.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1999

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References

1 See e.g. Lindberg, D., ‘The transmission of Greek and Arabic learning to the West’, in id. (ed.), Science in the Middle Ages (Chicago, 1978), pp. 5290;Google ScholarDod, B.G., ‘Aristoteles latinus’, in Kretzmann, N., Kenny, A., Pinborg, J. (ed.), The Cambridge History of Later Medieval Philosophy (Cambridge, 1982), pp. 4579;Google ScholarLeaman, O., Averroes and his Philosophy (Oxford, 1988), pp. 163–78.Google Scholar

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4 Cf. Sarnowsky, Theorie, pp. 38–40, 439–41, 450. Physics I survives partially or wholly in 19 manuscripts and about eight printed editions around 1500, Physics II (book 1–5) only in London, MS Wellcome Medical Historical Library, 15, fol. lra-99vb (Montpellier 1408). Thus, Physics II will be cited from this manuscript (in the part of the MS which is used below the foliation is missing). For Physics I, the 1516 Venice edition will be used (which is quite close to the early manuscripts):Google ScholarAcutissime Questiones super libros de Physica auscultatione ab Alberto de Saxonia edite, ed. Aloisanus, Jacobus Baptista (Venice, 1516), by the successors of Octavianus Scotus.Google Scholar

5 Terminus continentis immobilis primum locus est… (Aristotle, Physics, lib. 4, cap. 4, [Bekker] 212a20–21), cited here after the most widespread Latin translation (which was probably the basis for Albert's commentaries)Google Scholar in S. Thomae Aquinatis In octo libros Physicorum Aristotelis Expositio, ed. Maggiòlo, P. M. (Torino-Rome, 1954), here p. 224.Google Scholar — For the Aristotelian concept of place cf. Craemer-Ruegenberg, I., Die Naturphilosophie des Aristoteles (Freiburg-München, 1980), pp. 9499;Google ScholarJammer, M., Das Problem des Raumes (1969, transl. Wilpert, P.), 2nd ed. (Darmstadt, 1980), pp. 1522;Google ScholarGrant, E., ‘The Medieval doctrine of place: some fundamental problems and solutions’, in Maierù, A., Bagliani, A. Paravicini (ed.), Studi sul XIV secolo in memoria di Anneliese Maier (Rome, 1981), pp. 5779, here pp. 57–58;Google ScholarGosztonyi, A., Der Raum, Geschichte seiner Probleme in Philosophie und Wissenschaften, Orbis academicus, 1, 14 (Freiburg-München, 1976), vol. 1, pp. 90110.Google Scholar

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7 This will be the subject of the second part.Google Scholar

8 Locus est ultima superficies corporis continentis divisim immobilis immediata locatoGoogle Scholar (ibid., qu. 4, 2. art., fol. 46rb). — For Buridan see his Questiones in octo libros Physicorum, tertia lectura (Physics III), lib. 4, qu. 11, cited from the manuscript in the Biblioteca Apostolica Vaticana, Chigi E. VI. 199, here fol. 63rb–vb; and his Questiones super octo libros Physicorum Aristotelis (ultima lectura), ed. Dullaert, Johannes (Paris, 1509; repr. Frankfurt a. M., 1964) (Physics IV), lib. 4, qu. 4, fol. 70rb–va. For the different versions and manuscripts cf.Google ScholarMichael, B., Johannes Buridan, Studien zu seinem Leben, seinen Werken und zur Rezeption seiner Theorien im Europa des späten Mittelalters, 2 vols. (Phil. diss., Freie Universität Berlin, 1985), vol. II, pp. 560616;Google ScholarThijssen, J. M. M. H., Johannes Buridanus over het oneindige, Een onderzoek naar zijn theorie over het oneindige in het kader van zijn wetenschapsen natuurfilosofie, 2 vols. (Nijmegen, 1988), vol. I, pp. 5881.Google Scholar

9 There are some exceptions from this rule, e. g. concerning the problem of the ratio of forces and resistances in motion. But even here, the ‘false’ solution is not ascribed to Aristotle, but credited to the translator, cf. e. g. Albert, Physics I, lib. 7, qu. 8, Ad rationes, fol. 75vb (quoted in Sarnowsky, Theorie, pp. 74–5).Google Scholar

10 Albert, Physics I, lib. 4, qu. 1, 2. art., fol. 44va, cf. Aristotle, Physics, lib. 4, cap. 4, 211b5–212a8, p. 195;Google ScholarBuridan, Physics III, lib. 4, qu. 9, istis, fol. 61rb;Google Scholar and the remarks in Sarnowsky, Theorie, p. 174.Google Scholar

11 Aristotle, Physics, lib. 4, cap. 2, 209b12, p. 183, cf. Düring, I., Aristoteles. Darstellung und Interpretation seines Denkens (Heidelberg, 1966), p. 317.Google Scholar

12 Albert, Physics I, lib. 4, qu. 1, 2. art., 1. -3. concl., fol. 44va.Google Scholar

13 Cf. Grant, E., ‘Place and space in medieval physical thought’, in Machamer, P. K., Turnbull, R. G. (ed.), Motion and Time, Space and Matter, Interrelations in the History and Philosophy of Science (Ohio State University, 1976), pp. 137–67, here esp. pp. 139–43.Google Scholar

14 Tale spatium secundum omnes eius partes eiusdem esset rationis et sic in ipso sursum et deorsum non essent potentie naturales diverse et sic non esset ratio quare in tali spatio corpora plus moverentur ad unam partem quam ad aliam… (Albert, ibid.).

15 For the ‘history’ of this argument see Grant, E., ‘The principle of the impenetrability of bodies in the history of concepts of separate space from the Middle Ages to the seventeenth century’, Isis, 69 (1978): 551–71.CrossRefGoogle Scholar

16 Utrum locus sit ultima superficies corporis continentis distincta a corpore continenteGoogle Scholar(Albert, Physics II, lib. 4, qu. 1, fol. 64ra).Google Scholar

17 Locus non est ultima superficies corporis continentis distincta realiter a continente… Locus alicuius debet dici totum corpus continens capiendo totum categorematice. Hoc patet per Aristotelem 4° huius ubi ponit quod aer est in igne tamquam in loco et ignis est in celo tamquam in loco… (ibid., fol. 64va).

18 This opinion is introduced as follows: Allia (sic) opinio fuit quod locus erat spacium ymaginarium inter latera continentis. Et ista erat probabilior aliis opinionibus (Albert, Physics II, lib. 4, qu. 1, fol. 64rb).Google Scholar

19 Aristotle, Physics, lib. 4, cap. 4, 211b14–29, p. 195.Google Scholar

20 Sed facile esset evadere tales rationes tenendo quod locus sit tale spatium unde (sic!) diceretur quod tale spatium non esset nisi per ymaginationem, modo iste rationes arguunt ac (?) si tale spatium per se poneretur (Albert, ibid.). He adds: Et istud est probabile quia nihil videtur esse inmobile nisi tale spacium ymaginarium…

21 Vult autem immobilis locus esse; unde totus fluvius magis locus est, quia immobilis totus est… (Aristotle, Physics, lib. 4, cap. 4, 212a15–20, p. 195).Google Scholar

22 Utrum locus sit immobilis (Albert, Physics I, lib. 4, qu. 3, fol. 45va; Physics II, lib. 4, qu. 2, fol. 65ra).Google Scholar For Buridan's and Albert's solutions for the problem of the immobility of place cf. Zuanna, F. Dalla, Doctrina de spatio in Schola Nominalistica Parisiensi, Phil. Diss. (Rome, 1936), pp. 2324 and 44.Google Scholar

23 Cf. Averroes (Ibn Rushd), Commentaria magna in Aristotelis de Physico auditu libri octo (Physics), in Aristotelis Opera cum Averrois Commentariis, vol. 4 (editio Iuntina) (Venice, 1562; repr. Frankfurt a. M., 1962), here lib. 4, t(extus) c(ommenti) 41, fol. 140A, where he states:Google ScholarLocus est illud, ad quod movetur res, et quiescit in eo, et si aliquid movetur ad motam rem, tunc motus eius esset ociosus.Google Scholar

24 Breviter de dicta questione non est dubium si poneretur quod locus esset dimensio separata, tunc enim locus esset simpliciter immobilis, sed accipiendo locum pro ultima superficie etc. (eo modo quo aecipit Aristoteles locum in isto 4°, tune) questio habet dubitationemGoogle Scholar (Albert, Physics I, lib. 4, qu. 3, in opp., fol. 45va).Google Scholar

25 Locus non movetur essentialiter (Averroes, Physics, lib. 4, t. c. 41, fol. 140A [cf. n.22]).Google Scholar

26 Albert, Physics I, lib. 4, qu. 3, 2. art., 1. -2. concl., fol. 45va.Google Scholar

27 Quamvis iste conclusiones Commentatoris sint vere, tamen per eis non satisfit quibusdam difficultatibus circa istam materiam (ibid., fol. 45vb).

28 Giles of Rome, In octo libros physicorum Aristotelis (Venice, 1502; repr. Frankfurt a. M., 1962), lib. 4, lect. 7, fol. 80vb,Google Scholarcf. Duhem, P., Le système du monde, Histoire des doctrines cosmologiques de Platon à Copernic, 10 vols. (Paris, 19581984, various eds.), here vol. VII, pp. 181–3, 281;Google ScholarSarnowsky, Theorie, pp. 182–3. Neither Giles nor Thomas are mentioned by Albert.Google Scholar

29 Materialis locus dicitur ultima superficies corporis continentis, formalis autem locus dicitur distantia locati ad orbem vel ad res mundi quiescentes, ita quod hic terminus locus supponitur pro superficie et appellat distantiam ad orbem vel ad corpora quiescentia, ita quod secundum equivalentiam distantie idem est locus et secundum inequivalentiam alicuius, et idem non in numero sed secundum equivalentiam (Albert, Physics I, lib. 4, qu. 3, 3. art., fol. 45vb).Google Scholar

30 Here he adds that it is sufficient that the distance is the same according to equivalency: Res dicuntur quiescere ex eo quod continue manent in eodem loco, accipiendo locum pro eius formali, et non in eodem simpliciter sed in eodem secundum equivalentiam… Et ad istum sensum ego dico me esse in eodem loco in quo eram in principio lectionis, quia est equalis distantia inter me et orbem, modo qualis tune erat…. (ibid., 7. concl., fol. 46ra).

31 Albert, Physics II, lib. 4, qu. 2, opp., fol. 65ra; here the definition of place is quoted in the following form: Locus est ultimum corporis continentis immobilis (MS mobilis).Google Scholar

32 For the Aristotelian context see Aristotle, Categories, cap. 4, 1b25–2a4; for the problem of introducing the category of situs in an analysis of motion cf. e. g. Thomas Aquinas, Physics, lib. 4, lect. 7, n. 912–13, p. 202 (and below).Google Scholar

33 He concludes: Non sequitur .a. continue est in alio et alio loco, ergo continue .a. mobile movetur, sed oportet addere .a. continue est in alio et in alio loco vel situ et in alia et in alia distantia ad aliquod quiescens, ergo .a. mobile movetur…. (Albert, Physics II, lib. 4, qu. 2, et ex, fol. 65rb).Google Scholar

34 Ex istis etiam sequitur, quod esse in alio situ est continue esse in alia et in alia distantia ad aliquod quiescens, magis faciat cognoscere motum quam locum…. (ibid.).

35 Only the first conclusion can explicitly be found in Averroes, cf. n. 22.Google Scholar

36 Pono duas propositiones, prima est ista: Locus est sic inmobilis quod nunquam moveretur cum corpore locato ipsum dif(f)erens. Ista patet ex intencione Aristotelis in 4° huius ubi ponit et per hoc probat quod locus dif(f)ert a locato, sed recte locato locus debet esse. Secunda propositio est ista: quod locus est sic inmobilis, quod non movetur ad sua loca (MS locata) naturalia, quia frustra moveretur, cum corpora naturalia moveantur ad sua loca naturalia…. (Albert, Physics II, lib. 4, qu. 2, fol. 65va).Google Scholar

37 See e. g. Aristotle, Physics, lib. 4, cap. 4, 212a22–29, p. 195, also cap. 1, 208b10–24, p. 177;Google Scholarcf. Machamer, P., ‘Aristotle on natural place and natural motion’, Isis, 69 (1978): 377–87, here esp. p. 382;CrossRefGoogle ScholarWaterlow, S., Nature, Change and Agency in Aristotle's Physics (Oxford, 1982), pp. 103–5.CrossRefGoogle Scholar For some problems in this section see also Lang, Aristotle, pp. 63–84.Google Scholar

38 <Et propter hoc omnia in caelo sunt: caelum enim ipsum totum fortassis est. Est autem locus, non caelum, sed caeli quiddam ultimum, et tangens mobile corpus terminus quiescens.> Et propter hoc terra in aqua est, haec vero in aere, hie autem in aethere, aether vero in caelo, caelum autem non amplius in alio est…. (Aristotle, Physics, lib. 4, cap. 5, 212b18–21, p. 201,Google Scholar the translation is that of Hope, R., Aristotle's Physics [Lincoln-London, 1961], p. 67).Google Scholar

39 Cf. Sarnowsky, Theorie, p. 189.Google Scholar

40 Utrum terra sit in aqua sive in superficie concava ipsius aque tanquam in locosibi naturali et proprio, and Utrum concavum orbis lune sit locus naturalis ipsius ignis (Albert, Physics I, lib. 4, qu. 5 and 6, fol. 46va and 47ra).Google Scholar

41 Elementa sunt posita et situata secundum exigentiam suarum levitatum et gravitatum, quia ignis que est simpliciter levis est sursum, et aqua et aer que sunt gravia et levia sunt sursum et deorsum secundum quid: Aqua que est gravior aere est magis deorsum et aer que est levior est magis sursum…. (ibid., qu. 5, in opp., fol. 46va).

42 Accipiendo terram pro totali aggregato ex terra et aliis existentibus in terra, tunc superficies aeris concava ex una parte ubi terra est discooperta aquis et superficies concava aquis ex alia parte simul sumpte sunt locus proprius ipsius terre…. (ibid.,4. concl., fol. 46va–b), cf. Buridan, Physics III, lib. 4, qu. 12, 1.-4. concl., fol. 64ra–b; for the following see 5. concl.Google Scholar

43 For this theory (and Albert's solution) see e. g. Duhem, Système, vol. IX, pp. 215–19;Google Scholar id., Études sur Léonard de Vinci, 3 vols. (Paris, 19061913; repr. Paris, 1955), here vol. I, pp. 10–16;Google ScholarGrant, E., Physical Science in the Middle Ages (New York etc., 1971, 2nd ed. 1977), p. 70;Google ScholarBottin, F., La Scienza degli Occamisti. La scienza tardomedievale dalle origini dal paradigma nominalista alle rivoluzione scientifica, Studi di filosofia e di storia della filosofia, 4 (Rimini, 1982), pp. 271–3,Google ScholarSimek, K., Erde und Kosmos im Mittelalter. Das Weltbild vor Kolumbus (Munich, 1992), p. 129.Google Scholar

44 For the medieval concept of the center of gravity cf. Clagett, M., The Science Mechanics in the Middle Ages, Publications in Medieval Science, 4 (Madison, Wisc., 1959), pp. 590–3.Google Scholar

45 This explanation is — at least in some respect — contrary to that of Aristotle, cf. Machamer, Natural Place, pp. 378 and 386.Google Scholar

46 See Albert, Physics I, lib. 4, qu. 5, 6. concl., fol. 46vb, and the discussion which follows.Google Scholar

47 8° dico, quod aliqua pars terre est discooperta aquis. Patet hoc, quia terra non est universaliter gravis, et igitur medium magnitudinis terre est multum super medium gravitatis eiusdem, et medium gravitatis terre est multo ad unam superficiem convexam terre quam ad aliam. Et ideo quia aqua, ex quo est eque gravis tendens ad medium mundi quantum potest, fluit ad illam superficiem convexam terre que est propinquior centro gravitatis terre, et sic alia pars scil. alia superficies convexa terre, scil. que a centro gravitatis est remotior, derelinquitur discooperta aquis. Et causa finalis huius discoopertionis est salus et habitatio animalium (ibid., fol. 47ra).

48 The resistance of the surrounding water and air has to be taken into account for the equilibrium so that the weight difference must reach a certain degree, otherwise the earth will remain outside its natural place, ibid., 3° dico, fol. 46vb, where he gives an example.

49 Albert of Saxony, Questiones subtilissime in libros de celo et mundo, ed. Surianus, Hieronymus (Venice, 1492, Bonetus Locatellus for Octavianus Scotus), here qu. 2,25, 1. art., 2,26, 2. art., and 2,28, 2. art.,Google Scholar cf. Sarnowsky, Theorie, pp. 192–3. — For Buridan see Buridan, John, Quaestiones super libros quattuor de Caelo et Mundo, ed. Moody, E. A. (Cambridge, Mass., 1942), lib. 2, qu. 22, sed bene, pp. 231–2;Google Scholarcf. Grant, Science, p. 70.Google Scholar

50 Albert, Physics I, lib. 4, qu. 6, 1. art., fol. 47rb-va.Google Scholar

51 Albert refers probably to Aristotle, Metheorologica, lib. 1, cap. 7, 344a4–345a6.Google Scholar

52 Aristotle, De Generatione, lib. 2, cap. 3, 330a30–b3.Google Scholar

53 Albert, Physics I, lib. 4, qu. 6, 1. art., 3°, fol. 47va. Here Albert contradicts himself, because contrary to his earlier explanation (in qu. 5) here he argues that fire is better preserved in its own sphere propter multitudinem ignis.Google Scholar

54 5° arguitur auctoritate multorum philosophorum, que concordant in hoc et conveniebant in hoc, quod sub orbe lune esset orbis ignis, et deinde aer et deinde aqua et deinde terra (ibid.).

55 Ibid., Ad rat., 7, fol. 47vb–48ra; for a consequence of this theory cf. Sarnowsky, Theorie, p. 195, n. 285.Google Scholar

56 Utrum ignis sit in concavo orbis lune tanquam in suo loco naturali, and Utrum omne corpus naturale habeat sibi locum naturalem (Albert, Physics II, lib. 4, qu. 3 and 5, fol. 65va and 67va).Google Scholar

57 Hoc facit natura propter salutem animalium respirancium (ibid., qu. 3, in opp., fol. 65vb). Concerning one of the following dubia Albert refers (fol. 66ra) to a dictum of Porphyry, Isagoge, that locus est principium generationis. But water is not necessarily generated in earth (so that it is wrong to say that water is the natural place of earth).

58 Aristoteles vidit quod major pars ipsius terre locatur ab aqua quam ab aere, et a pluri debet fieri denominacio. Vel potest dici, quod ipsi aque magis convenit locus terre (esse) quam aeri, quia terra et aqua habent qualitates sinbolas [sic]… (ibid., ad aliam, fol. 66ra–b).

59 Ibid., et secundum and sed hic, fol. 66rb.

60 Corpora naturalia non sunt gravia nec levia in suis locis naturalibus, and: Omne corpus naturale posset habere locum naturalem possibilem sibi correspondentem…. (Albert, Physics II, lib. 4, qu. 5, iuxta istam and nunc dico, fol. 67vb and 68rb). As a proof (for the second conclusion) Albert refers to an Aristotelian dictum according which the generans not only grants the form but also the place of the body. This reference (to book 8) seems to be only an interpretation, butGoogle Scholarcf. e. g. Aristotle, Physics, lib. 8, cap. 4, 255b13–256a5, p. 464; and also Thomas Aquinas, Physics, lib. 7, lect. 3, n. 1812, p. 395: Generans movetur gravia et levia inquantum dat eis formam per quam moventur ad locum.Google Scholar

61 Possibly Albert refers to the following passage: Impossibile est enim in corporibus compositis aliqua componi aequaliter. Et nos post declarabimus: Et, si esset aliquod compositum aequaliter, contingeret, quod aliquod corpus non moveretur omnino, sed staret in quocunque loco, poneretur, scil. staret aut superius, aut inferius, aut in medio duorum contrariorum, et moveretur in ceteris, quod non invenitur, Averroes, Commentaria (magna) in libros de Coelo, in Aristotelis Opera…., vol. 5 (Venice, 1562; repr. Frankfurt a. M., 1962), fol. 1A-271M, here lib. 1, t. c. 7, fol. 6G–H.Google Scholar

62 Possibile est aliquod corpus sit compositum equaliter ex gravitate et levitate, modo tali corpori non poterit assignari locus, ut videtur Commentator innuere 2° (sic) celi, quia vel semper quiesceret vel semper moveretur…. (Albert, Physics II, lib. 4, qu. 5, contra conclusionem, fol. 68rb).Google Scholar

63 Aristotle, Physics, lib. 4, cap. 5, 212b9–17, p. 201.Google Scholar

64 Thomas, Physics, lib. 4, lect. 7, n. 907–927, pp. 202–4.Google Scholar These opinions were first quoted by Averroes, Physics, lib. 4, t. c. 43 and 45, fol. 141F (Themistius) and M (Avempace), 143A (Alexander) and 144E (Avicenna), for Averroes's own opinion cf. ibid., t. c. 43, fol. 142G.

65 Buridan, Physics III, lib. 4, qu. 13, fol. 64vb–66ra, cf. in general Dalla Zuanna, Doctrina, pp. 24–5 (according to Physics IV). — For the discussions on the place of the world and the last sphere cf. Grant, E., ‘Cosmology’, in Lindberg (ed.), Science, pp. 265–302, here pp. 272–5; id., Doctrine, pp. 72–9;Google Scholar Sarnowsky, Theorie, pp. 196–9. For the condemnations of 1277 cf. e. g. Grant, Science, pp. 27–35; id., ‘The condemnations of 1277, God's absolute power and physical thought in the late Middle Ages’, Viator, 10 (1979): 211–44; Sarnowsky, Theorie, p. 76; id., ‘God's absolute power, thought experiments and the concept of nature in the ‘New Physics’ of XIVth century Paris’, in Caroti, S., Souffrin, P. (ed.), La nouvelle physique du X1Ve siècle (Firenze, 1997), pp. 179201 (with further literature). Duns Scotus also discussed the Aristotelian doctrine of place in relation to the condemnations of 1277,Google Scholarcf. Lang, Aristotle, pp. 175–81.Google Scholar

66 Utrum omne ens sit in loco (Albert, Physics I, lib. 4, qu. 7, fol. 48ra).Google Scholar

67 Here Albert again refers to the Aristotelian dictum cited above n. 37. For the distinctions which follow cf. Sarnowsky, Theorie, pp. 199–200.Google Scholar

68 Totalis mundus non est in loco nec est alicubi (Albert, ibid., 2. art., 1. concl., fol. 48rb).

69 In the case of Themistius and Thomas the refutation is not quite clear, because first Albert rejects in general that the world is in place because of its parts, but then he points out that anything can be said of something per accidens in virtue of its parts which fits its parts per se – and this is Thomas's solution for the place of the last sphere; ibid., ad 3am, unde sciendum, fol. 48rb.

70 Ultima spera non est in loco. Probatur, qui(a) non est in continente aliquod circumdante ipsum…. 2° sicut primum movens est non motum, ita primum locans debet esse non locatum (ibid., 2. concl., fol. 48rb–va).

71 …Terra diceretur locus ultime spere, quia in habitudine ad ipsam cognoscimus celum moveri. Sed iste modus loquendi est improprius, unde sic Commentator dicit terram esse locum ultime spere (ibid., ex his, fol. 48va). — Albert ends his discussion by forming two conclusions on God and the angels: They are in place only in respect to the center of their activity or in respect to places where they operate (ibid., 6. -7. concl., fol. 48vb), cf. the distinction between esse in loco diffinitive and circumscriptive (ibid., 1. art., fol. 48ra-b).

72 De ista questione sunt diverse opiniones (Albert, Physics II, lib. 4, qu. 4, opp., fol. 66vb).Google Scholar

73 Commentatori autem non placet ista opinio, qui est expresse contra Aristotelem, qui ponit, quod celum movetur localiter, nec rationes valent. Probo. Prima: quia vel movetur secundum totum vel secundum partes (etc.), dicit Commentator quod non movetur secundum substantiam sed bene secundum formam, videtur dicere Commentator, quod movetur secundum se totum motu circulari et non recto (ibid., Commentatori, fol. 66vb, cf. Averroes, Physics, lib. 4, t. c. 45, fol. 144F–H).Google Scholar

74 Commentator recitat opinionem aliam Temistii quod ultima spera secundum se totam non est in loco sed secundum partes (partes twice), quia tota ultima spera non movetur secundum se sed secundum suas partes. Illud tamen est inconveniens, ut dicit Commentator, cum totum non sit alia res a suis partibus (Albert, ibid., fol. 67ra, cf. Averroes, ibid., t. c. 43, fol. 141G-I.) – Thus the basis for the rejection of Themistius's point of view seems to be a ‘nominalistic’ decision on the relation of the whole and its parts.

75 (Propter quod Commentator ponit quattuor conclusiones. Prima est ista, quod celum vel ultima spera non est in loco per se, quia non habet extra se alquid continens. Secunda est, quod celum est aliquomodo in loco sive (MS adds in) ultima spera, quia movetur localiter ergo est alicomodo in loco. Tertia est, quod) celum vel ultima spera est in loco per accidens (quia est alicomodo in loco et non per se, ergo per accidens. Quarta conclusio est quod) ultima spera est in loco per centrum sive per terram, quia ultima spera habet fixionem et stabilitatem cum centro, (ergo est in loco per centrum, quia corpus naturale habet a suo loco naturali (etc.)) (Albert, ibid., consequentia, fol. 67ra, cf. Averroes, ibid., fol. 142B-I).

76 Propter quod inter omnes opiniones opinio Alexandri et Avicene videtur esse melior, licet non bene (Albert, ibid., item etiam, fol. 67rb).

77 Ibid., 2° sic, fol. 67rb; for the earlier version cf. above n. 69. Albert ends his discussion of the place of the last sphere with some dubia and decisions. E.g. he states: Unde si quaeratur, ubi est ultima spera, convenienter potest responderi, quod nullicubi est, i. e. in nullo loco…. Thus he explicitly rejects his former conclusion.Google Scholar

78 Cf. note 63.Google Scholar

79 In his older commentary he only once cites a contemporary, William Heytesbury, cf. Sarnowsky, Theorie, p. 57. For the relationship between the philosophers of the ‘Parisian school’Google Scholarcf. Sylla, E. D., ‘Aristotelian commentaries and scientific change: The Parisian nominalists on the cause of the natural motion of inanimate bodies’, Vivarium, 31 (1993): 3783, here esp. pp. 78–9.CrossRefGoogle Scholar

80 Cf. n. 48. It is less probable that Albert depends on Oresme, because in Oresme's latin Questiones super De Celo, ed. Kren, C. (PhD diss., Madison, Wisc., 1965), lib. 2, qu. 13, pp. 667–71, there is only a negative allusion to the theory ofGoogle Scholar‘small movements’, while his Livre du Ciel et du Monde, ed. Menut, A. D., Denomy, A. J., transl. Menut, A. D., Publications in medieval science (Madison, Wisc., etc., 1968), here liv. 2, cap. 31, p. 569, has the general outline of the theory, but has been written after Albert's commentaries (1377).Google Scholar

81 Thus Lang, Aristotle, pp. 171–2, is right in pointing out that especially the questiones on the Physics do ‘not leave Aristotle's arguments or his conception of physics as a science untouched’. Though the Aristotelian ‘basis’ remains, new problems and new solutions enter the discussion which sometimes even lead to a change in principles, Sarnowsky, cf., Theorie, pp. 405–30.Google Scholar

82 Cf. n. 4 and the text. — The Roman number in brackets denotes the part of this paper in which the questions are treated; the sic or non following the question points to the first negative answer (et arguitur quod sic / non ….).

83 Cf. n. 4 and the text.

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