¹ Professors Marilyn McCord Adams, Norman Kretzmann, Lang, Helen, and Allen Wood, W. were kind enough to read this paper. I am most grateful for their useful and constructive comments. The errors which remain are my own.Google Scholar

² 215a24–215b20.Google Scholar

³ See Wood, R., ‘Walter Burley's Physics Commentaries,’ Franciscan Studies 44 (1984).Google Scholar

⁴ de Burley, Gualterus, Expositio super totum I t. c. 4–5, tr. 1; IV t. c. 42, tr. 1, c. 5; VI t. c. 24, tr. 1, c. 4 (Venice 1501; fols. 8^vb, 98^vb, 183^ra).Google Scholar

⁵ Duns Scotus, Ioannes, Ordinatio II, dist. 2, pars 2, q. 5, nn. 430–38 (ed. Vaticana 7 [Vatican 1973] 346–50). See Grant, Edward, Much Ado About Nothing (Cambridge 1981) 32f. Father Gál, G. has suggested that Burley may be arguing against Franciscus Rubeus de Marchia, who read the Sentences in 1320–23. A Sententia et compilatio super libros Physicorum by Marchia is preserved in MSS Vat. Ottob. lat. 1816, fols. 30–49^r, and Munich Clm 5874. See Lohr, Charles, ‘Medieval Latin Aristotle Commentaries, Authors A–F,’ Traditio 23 (1967) 411–12.Google Scholar

⁶ Burley, Gualterus, Quaestiones super libros Physicorum 39 (Lib. IV, quaest. 6: Utrum vacuum possit esse): MS Basel, Bibl. Univ. F.V.12, fol. 166^va–vb:Google Scholar

Quod autem in ista significatione non possit vacuum esse probo, quia si aliquod spatium esset separatum a corpore, et tamen hoc esset natum repleri corpore, sequitur quod duo corpora possunt esse simul et similiter duae dimensiones. Quia tale spatium separatum aut esset in aliqua substantia sicut in subiecto vel non. Si sic, tunc illa substantia esset substantia dimensionata, quia huiusmodi spatium esset dimensionatum. Et si sit substantia dimensionata, ergo est corpus. Si tunc illud spatium possit repleri aliquo corpore, sequitur quod duo corpora essent nata esse simul. Similiter sequitur quod plures dimensiones profundae distinctae possunt esse simul, et sic dimensiones penetrarent se.Google Scholar

Si tale spatium vacuum non sit aliqua substantia, nec in substantia sicut in subiecto, ergo ibi essent dimensiones separatae ab omni substantia, et per consequens quantitas esset sine subiecto, quod est contra naturam. Google Scholar

Similiter sequitur quod illae dimensiones possunt esse simul cum dimensionibus corporis intrinsecis. Hoc est falsum, quia per Philosophum, I huius, sola dimensio facit distare. Licet ergo illa dimensio esset separata ab omni subiecto, adhuc sic distaret ab aliis dimensionibus quod ei repugnaret simul esse cum aliis dimensionibus.Google Scholar

Si dicas quod talis dimensio separata potest esse simul cum aliis dimensionibus: Contra: si illa dimensio vacui permittat secum dimensiones corporis, et (?) multo fortiori permitteret secum aliam dimensionem vacuam [fol. 166^vb], et per consequens una pars vacui permitteret secum aliam partem eiusdem vacui, et sic esset possibile quod unum totum [or ro-um] maximum vacuum esset in puncto indivisibili. Quia quaelibet pars vacui permitteret secum aliam partem eiusdem vacui. Sequitur ergo quod dimensiones vacui non permittant secum alias dimensiones, et per consequens vacuum non est, intelligendo per vacuum spatium non repletum corpore, aptum tamen repleri.Google Scholar

⁷ Note that this is quantity separated from substance and sensible quality, not separated from substance and sensible quantity, as Grant maintains on the basis of a mistake in the printed edition he quotes: 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) 64. See appendix § 2.22–30, 78f., 102–5.Google Scholar

⁸ Grant's major discussion of Burley on motion in a vacuum is found in his 1978 Isis article 567f. In 1979, in an isolated paragraph of another study, Grant indicated that Burley argued for the possibility of motion in a vacuum on the hypothesis that quantity can exist separately: ‘The Condemnation of 1277, God's Absolute Power and Physical Thought in the Late Middle Ages,’ Viator 10 (1979) 233f. But the Isis article reappeared in 1981 without addition or revision: Much Ado About Nothing (above, n. 5) 33.Google Scholar

⁹ See appendix § 1.15–22; Scotus, Ordinatio II, dist. 2, pars 2, q. 5, nn. 421, 428–35 (ed. Vaticana 7.341, 344–48).Google Scholar

¹⁰ Ibid. Google Scholar

¹¹ See appendix § 2.14–17.Google Scholar

¹² Aristotle, Physica VI c. 8 (216a26–bl2).Google Scholar

¹³ See appendix § 2.18–34, 61–69, 80–86; § 3.8–11.Google Scholar

¹⁴ Grant, , ‘Impenetrability’ (above, n. 7) 569.Google Scholar

¹⁵ We might be tempted to speak of instantaneous motion, but many medievals considered this a contradiction in terms and reserved the term ‘mutation’ or ‘transmutation’ for this purpose. ‘Mutation’ described cases where a new form was introduced; this terminology is designed to avoid suggesting that gradual alteration, however rapid, could accomplish this substantial change. ‘Local mutation,’ or ‘mutation of place,’ sounds odd, but it is found in Latin translations of Aristotle, and it is used in preference to ‘instantaneous motion’ by authors as diverse as Giles of Rome and Peter John Olivi (Egidii Romani Commentaria in octo libros Phisicorum Aristotelis V lect. 3; III lect. 1 [Venice 1502; repr. Frankfurt 1968], fols. 119^ra–rb; 50^va--51^rb; Petrus Ioannis Olivi, Quodlibet I quaest. 1: An Deus possit in uno instanti transferre aliquam rem de uno loco ad alterum per spatium intermedium [Venice 1505; no pagination]). Cf. Ockham, , Expositio physicorum III c. 2 § 7 (ed. Richter, V., Guillelmi de Ockham Opera Philosophica [OPh] 4 [St. Bonaventure, , N.Y. 1985] 438f.).Google Scholar

¹⁶ See appendix § 2.35–40, 53–60.Google Scholar

¹⁷ See appendix § 2.41–52.Google Scholar

¹⁸ See appendix § 2.70–79.Google Scholar

¹⁹ See appendix § 2.80–93. The capacity of separated quantity to resist, or rather yield to a natural body entering it, arises from its being incompatible with that natural body, so that such separated quantity could not coexist with a body. It does not ‘arise from the distantia terminorum, that is from the impossibility that in an extended space a body can be in two distinct places simultaneously’ (Grant, ‘Impenetrability’ 567).Google Scholar

²⁰ See appendix § 3.3–15.Google Scholar

²¹ See appendix § 3.16–23. Here Burley has slipped, and spoken of ‘motus … subito et in instanti,’ where strictly speaking he should have said ‘mutatio … subito et in instanti.’Google Scholar

²² See appendix § 3.24–28.Google Scholar

²³ See appendix § 3.29–36.Google Scholar

²⁴ See appendix § 3.37–48; Grant, ‘Impenetrability’ 568 n.68.Google Scholar

²⁵ See appendix § 3.49–64.Google Scholar

²⁶ See appendix § 2.47–52, 70–79.Google Scholar

²⁷ See appendix § 5.5–25; Ockham, , Expositio physicorum IV c. 14 § 5 (edd. Wood, R., G. Gál, Green, R., Giermek, J.; OPh 5 [St. Bonaventure 1985] 155f.). This distinction is certainly not Burley's. His three kinds of resistance are borrowed from Averroës and stated in the fifth part of the large digression devoted to Averroës, ‘On the true causes of succession in motion’: Et dicit Commentator quod ista resistentia quam ponit inter motorem et rem motam contingit tripliciter: vel ex parte moti tantum sicut est in motu corporum caelestium, quoniam in motibus illorum non est aliqua resistentia nisi mobilis ad motorem. Alio modo contingit ista resistentia ex parte medii tantum sicut in motibus corporum simplicium levium et gravium, quoniam in illis res mota non dividitur in motorem et rem motam in actu. Tertio modo contingit ista resistentia ex utroque, scilicet ex re mota et ex mediis, sicut est dispositio in animalibus quae moventur in aqua (Expositio s. totum IV t. c. 71, tr. 2, c. 3, fol. 116^ra).Google Scholar

²⁸ See appendix § 6.3–11.Google Scholar

²⁹ See appendix § 6.12–20.Google Scholar

³⁰ Grant, , ‘Impenetrability’ 567.Google Scholar

³¹ Expositio Physicorum IV c. 12 § 3 (OPh 5.124).Google Scholar

³² Grant, , ‘Impenetrability’ 568.Google Scholar

³³ Expositio Physicorum IV c. 11 § 1; § 3 (OPh 5.122, 124).Google Scholar

³⁴ Expositio Physicorum IV c. 12 § 1; 14 § 7 (OPh 5.132, 162).Google Scholar

³⁵ Quodlibet I q. 8 (ed. Wey, J. C., Guillelmi de Ockham, Opera Theologica [OTh] 9 [St. Bonaventure 1980] 45–48). Buridan's similar remarks are quoted by Grant, , ‘The Condemnation of 1277’ (above, n. 8) 233.Google Scholar

³⁶ Magnus, Albertus, Physicorum libri VIII, ed. Borgnet, A. (Opera omnia III; Paris 1890) 279–94.Google Scholar

³⁷ Medievals considered it possible for a movable object to be transmuted from one limit of a vacuum to another instantaneously, without being in any intermediate position, but denied that any distance could actually be traversed instantaneously, without time.Google Scholar

³⁸ Magnus, Albertus, Physicorum libri VIII (above, n. 36) 285, 293.Google Scholar

³⁹ Aquinas, Thomas, In Physicorum Aristotelis IV lect. 10.Google Scholar

⁴⁰ Weisheipl, James, ‘Motion in a Void: Aquinas and Averroes,’ in A. Maurer (ed.), St. Thomas Aquinas, 1274–1974, Commemorative Studies (Toronto 1974) 1.467–88.Google Scholar

⁴¹ Magnus, Albertus, Physicorum libri VIII (above, n. 36) 290.Google Scholar

⁴² Expositio s. totum IV t. c. 71, tr. 2, c. 4, fol. 115^vb.Google Scholar

⁴³ Expositio Physicorum IV c. 14 § 5 (OPh 5.156, 158).Google Scholar

⁴⁴ Quodlibet I q. 8 (OTh 9.45–48); Brevis Summa IV c. 4 (ed. Brown, S.; OPh 6 [St. Bonaventure 1984] 70).Google Scholar

⁴⁵ Expositio Physicorum IV c. 14 § 4 (OPh 5.150f.). Ockham's exposition of t. c. 71 was written as a reply to Giles of Rome. Ockham attributed to Giles the view that a vacuum is a separated quantity. And he agrees with Burley that if quantity is assumed to be capable of independent existence, a vacuum consisting of a quantity of space lacking any substance or quality would require time for its traversal. But unlike Burley, Ockham held that such separated quantity would be completely inactive; it could coexist with, or be compatible with, the presence of a moving object. See Ockham, , Expositio Physicorum IV c. 14 § 4 (OPh 5.148). Cf. Moody, E., ‘Ockham and Aegidius of Rome,’ Studies in Medieval Philosophy, Science and Logic (Los Angeles 1975) 170–76.Google Scholar

⁴⁶ Expositio Physicorum IV c. 14 § 5 (OPh 5.155).Google Scholar

⁴⁷ Expositio Physicorum IV c. 14 § 5 (OPh 5.155f.).Google Scholar

⁴⁸ See appendix § 2.31–43. Note that Burley consistently maintained that sola quantitas facit distare; see his Quaestiones 39 (above, n. 6) fol. 166^va.Google Scholar

⁴⁹ Ockham, , Quaest. in IV Sent. 6 (edd. Wood, R., G. Gál, Green, R.; OTh 7 [St. Bonaventure 1984] 71). For a discussion of Ockham's views on the physics of the Eucharist, see Stump, E., Theology and Physics in De sacramento altaris,’ in N. Kretzmann (ed.), Infinity and Continuity in Ancient and Medieval Thought (Ithaca 1982) 213–16.Google Scholar