¹ The original argument occurs in Aristotle, Physics IV, chapter 8, 215a 24 − 215b 20.Google Scholar

² For a history of scholastic discussions centering about Text 71 — discussions which appear to provide a direct link to Galileo's Pisan dynamics — see A. Moody's, E. scholarly article, ‘Avempace and Galileo,’ Journal of the History of Ideas 12 (1951) 163–193, 375-422. See also Maier, A., An der Grenze von Scholastik und Naturwissenschaft (Rome 1952) 143-219.Google Scholar

³ The medieval commentators, that is, were not cognizant that the Alexandrian Neo-Platonist, Joannes Philoponus, had previously stated and developed the implications of the position known to them simply as ‘Avempace's theory.’ For more on Philoponus’ commentary on Aristotle's Physics, see Duhem, P., Le Système du monde I (Paris 1954) 350–371,Google Scholar

⁴ Aristotelis Opera omnia cum Averrois commentariis (Venice 1560) IV 131^v,Google Scholar

⁵ Although others are presented, this is the argument which is central to Averroes’ rejection of Avempace's explanation. See ibid. 131^v-133^r. As Moody, E. A. shows in op. cit., Avempace's insistence on the fact that the successive, temporal character of motion is a function of the mobile's passage through a divisible continuum — the physical characteristics of that continuum not-withstanding — is of great interest from the viewpoint of early modern mechanics. For it constitutes a sound definition of motion in its kinematic aspect. Nevertheless, Avempace's implicit faith that the ‘everything that is moved’ principle expressed an inviolable law of nature, led him to construe his fundamentally sound kinematic analysis of what motion is, as simultaneously a definition of motive force. Averroes, on the other hand, insisting on the dynamic aspect of motion, arrived at a basically correct conception of motive power — i.e., the ability to overcome material resistance (to perform ‘work’), measured by the time required to do so. The same assurance, however, that the ‘everything that is moved’ dictum was sacrosanct, led Averroes to assume that his definition of force was, at one and the same time, a kinematic definition of what motion is. ‘Being, in motion,’ so far as Averroes was concerned, was always an instance of ‘being, moved by something,’ and motion, therefore, must always be a case of overcoming material resistance.Google Scholar

⁶ St. Thomas dismisses Averroes’ arguments in this way: ‘… haec omnino videntur esse frivola.’ See Thomae Aquinatis, S. In octo libros Physicorum Aristotelis expositio 4.1.12 (ed. Marietti, , Romae 1954) 258.Google Scholar

⁷ Other prominent thirteenth-century supporters of Avempace's position were Roger Bacon, Peter John Olivi, William of Ware and Duns Scotus. Besides Albert and Giles, Siger of Brabant and John of Jandun are known to have backed Averroes.Google Scholar

⁸ Clearly, in respect of Text 71, what is wanting is not a synthesis of both positions, but rather a careful separation between them: a separation that would mark the distinction, fundamental to our mechanics, between the state of being in motion and the state of being moved by something. As Moody, E. A. shows in op. cit., this separation was actually effected by William Ockham. (See also Shapiro, H., Motion , Time and Place According to William Ockham [St. Bonaventure, N. Y. 1957]). The fact, however, that Burley was ‘wrong’ while Ockham was ‘right’ from the point of view of subsequent developments in the history of science, in no way detracts from the instrinsic interest and philosophical value of Burley's handling of the problem under survey.Google Scholar

⁹ These passages occur in Lib. IV, 101^vb-103^rb of our primary source: Walter Burley, Super octo libros Physicorum (Venetiis 1491). In transcribing from this source, I have expanded all abbreviations, modernized punctuation, and added italics, but have not altered the spelling from its common medieval form.Google Scholar

¹⁰ Ibid. 103^rb. Although Burley's handling of the second and third dubia are of great interest, the problems of which they treat were judged to go beyond the scope of the present paper; hence, in the sequel we shall limit ourselves to examining Burley's treatment of Text 71 as it is set forth in response to the first dubium. Google Scholar

¹¹ Ibid. 103^rb-103^va.Google Scholar

¹² These occur ibid. 103^va.Google Scholar

¹³ As example, Burley's second proof per rationem, ibid., reads: ‘Item, omne mobile est continuo in loco sibi equali, ut patet 8° huius. Si igitur grave subito descenderet in vacuo, in eodem instanti esset sursum et deorsum et in toto medio. Ergo, si minimum grave, ut terra minima, moveretur in maximo vacuo, illa terra in uno instanti occuparet totum vacuum, et per consequens esset equalis toti vacuo, quod est impossibile, quia ponamus quod vacuum sit maius in centuplo quam ista terra minima.’Google Scholar

¹⁴ Burley, ibid. restates Aristotle's objection in this way: ‘In contrarium est Philosophus hic qui vult quod posito vacuo motus corporum simplicium gravium et levium fieret subito et in instanti et non in tempore. Item, ratio Philosophi ad hoc est talis: qualis est proportio medii ad medium in subtilitate, talis est proportio motus ad motum in velocitate. Sed medii pieni ad medium vacuum nulla est proportio in subtilitate; ergo, motus facti in vacuo ad motum factum in pleno, nulla est proportio; sed cuiuslibet motus facti in tempore ad motum factum in tempore est aliqua proportio, sed motus factus in pleno fit in tempore, ergo motus factus in vacuo fit in non tempore.’Google Scholar

¹⁵ Ibid. 104^ra.Google Scholar

¹⁶ Ibid. 103^va: ‘Ad questionem istam, dicendum est quod tres sunt significationes vacu(i) … Vacuum uno modo significat illud in quod nihil est. Secundo modo significat illud in quo non est corpus sensibile. Et istis duobus modis accipitur vacuum transumptive; quia verum vacuum non est illud in quo nihil est, quia sic punctum esset vacuum. Nec verum vacuum est illud in quo non est corpus sensibile, quia sic locus in quod est aer esset vacuum. Tertio modo accipitur vacuum pro spacio receptivo corporis naturalis privato tamen corpore naturali.’Google Scholar

¹⁷ Ibid. ‘… Et illud (i.e., third meaning of ‘vacuum’) potest intelligi dupliciter: uno modo quod in illo spacio nec sit corpus naturale nec quantitas separata. Primus intellectus claudit contradictionem, scilicet, quod sit aliquod receptivum corporis carens omni quantitate, quia ponere hoc est ponere quantum sine quantitate. Nihil enim recipere(t) quantum nisi quantum. Secundus intellectus est minus impossibilis, scilicet, quod sit aliqua quantitas longa, lata et profunda, separata ab omni quantitate (read: ‘qualitate’) sensibili …’ See also ibid. 103^vb, where Burley continues: ‘… Alio modo potest intelligi … illa quantitas (separata) … quod sola quantitas facit distare; ut si corpus cubum separatum ab omni substantia et ab omni quantitate (read: ‘qualitate’) sensibili poneretur in aqua, faceret tamen de aqua distare quantum est corpus cubum.’Google Scholar

¹⁸ That Burley is conscious of the profound theological ramifications of this position on ‘separated quantity’ is made explicit when he defends this conception ibid. 103^va, by pointing out that ‘secundum theologos illud est possibile apud Deum, sicut in Sacramento Altaris est quantitas sine omni substantia corporea in qua sit sicut in subiecto, ita Deus posset facere quantitatem esse sine omni qualitate, et talem quantitatem separatam receptivem Corporis …’ Although it is quite well known that William Ockham directed some of his most withering dialectical fire against those who espoused precisely this realist view of quantity (see in particular the ‘Venerable Inceptor's’ De Sacramento Altaris), Professor Moody has provided solid documentation proving that Ockham's primary and original target was Giles of Rome, not Walter Burley. See A. Moody, E., ‘Ockham and Aegidius of Rome,’ Franciscan Studies 9 (1949) 417–442. It should be noted that Burley, while he has here obviously adopted Giles’ notion of ‘separated quantity,’ yet employs it in a wholly original way; for Giles of Rome, whom we have already marked as a supporter of Averroes’ thesis (supra, at n. 7), backed his defense of Averroes on the more traditional, Aristotelian grounds.CrossRefGoogle Scholar

¹⁹ Ibid. 103^vb.Google Scholar

²⁰ Ibid.Google Scholar

²¹ Ibid. 104^ra: ‘Dicendum quod raritas et densitas seu spissitudo et subtilitas uno modo sunt qualitates consequentes calidum et frigidum … Si accipiantur raritas et densitas ut sunt qualitates tangibiles consequentes calidum et frigidum, et Commentator loquitur de istis septimo huius, Commento 150, sic dico quod in quantitate separata non sunt raritas et densitas, et quod quantitas bene potest separari a raritate et densitate que sunt qualitates tangibiles. Et idem dico de spissitudine et subtilitate. Et isto modo loquendo de istis non est verum universaliter quod qualis est proportio medii ad medium in raritate et densitate, quod talis est proportio motus ad motum in velocitate et tarditate.’Google Scholar

²² Ibid.: ‘Alio modo accipiuntur pro approximatione partium quantitatis ad invicem, vel pro elongatione partium ad invicem. Et sic vel sunt de genere quantitatis, vel relationes necessario fundate in quantitate … Si … accipiantur raritas et densitas ut sunt remotio vel propinquitas partium quantitatis inter se … dico loquendo de raritate et densitate secundo modo, scilicet, secundum quod sunt relationes necessario consequentes quantitate … sic verum quod qualis est proportio medii ad medium in subtilitate, talis est proportio motus ad motum in velocitate.’Google Scholar

²³ Burley devotes the balance of his reply ad primum dubium to removing objections which might be raised against his solution on sophistical grounds. See ibid. 104^ra-104^rb. His response to the second dubium commences on 104^rb.Google Scholar