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William of Ockham, the Subalternate Sciences, and Aristotle's Theory of metabasis

Published online by Cambridge University Press:  05 January 2009

Steven J. Livesey
Steven J. Livesey
Affiliation:
Department of the History of Science, University of Oklahoma, 601 Elm, Room 621, Norman, Oklahoma, 73069, USA.
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Extract

Historians of fourteenth-century science have long recognized the extraordinary work at both Oxford and Paris in which natural philosophy was becoming highly mathematical. The movement to subject natural philosophy to a mathematical analysis and to quantify such qualities as heat, color, and of course speed surely stands as one of the most significant aspects of late medieval science. Yet as Edith Sylla has observed, because qualities and quantities pertain to different categories in Aristotelian theory, one might expect Aristotelian theorists to avoid quantifying qualities. Even more serious still, the very task of quantifying physical qualities exposes a tension in the nature of science that was discussed first by Aristotle in his Posterior Analytics.

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Research Article
Information
The British Journal for the History of Science , Volume 18 , Issue 2 , July 1985 , pp. 127 - 145
Copyright
Copyright © British Society for the History of Science 1985

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References

1 The literature on the subject is immense, but in particular Wilson, Curtis [William Heytesbury: Medieval Logic and the Rise of Mathematical Physics (Madison, Wisc. 1960)]Google Scholar and Crosby, H. Lamar Jr., [Thomas of Bradwardine: His ‘Tractatus de proportionibus.’ Its Significance for the Development of Mathematical Physics (Madison, Wisc. 1955)]Google Scholar have both called attention to the physico-mathematical nature of this early fourteenth-century work. Concerning the use of mathematics in other sciences, see in particular Murdoch, John E., ‘Mathesis in philosophiam scholasticam introducta: the Rise and Development of the Application of Mathematics in Fourteenth-Century Philosophy and Theology,’ in Arts libéraux et philosophie au moyen âge, Actes du quatrième congrès international de philosophie médiévale (Montréal 1969) 215–254.Google Scholar More recently David Lindberg has also addressed the use of mathematics in natural philosophy; see ‘On the Applicability of Mathematics to Nature: Roger Bacon and his Predecessors,’ British Journal for the History of Science 15 (1982) 3–25.Google Scholar

2 Sylla, Edith, ‘Medieval Quantification of Qualities: The “Merton School”,’ Archive for History of Exact Sciences 8 (1981) 9–39 at p. 9.CrossRefGoogle Scholar

3 Posterior Analytics 1.7 75a38ff; 1.9; and 1.13; Metaphysics XIII.3 1077b31–1078a6.

4 See, in particular, Pedersen, O., ‘The Development of Natural Philosophy 1250–1350,’ Classica et mediaevalia 14 (1953) 86–155.Google Scholar

5 See the passages from the Posterior Analytics cited in note 3 as well as Physics II.2. Concerning the subalternate sciences, see McKirahan, Richard D., ‘Aristotle's Subordinate Sciences,’ British Journal for the History of Science 11 (1978) 197–220.CrossRefGoogle Scholar

6 Concerning Ockham's life and works, see Baudry, L., Guillaume d' Occam. L'Homme et les oeuvres (Paris 1950)Google Scholar; Moody, Ernest, ‘William of Ockham,’ The Encyclopedia of Philosophy (New York 1967) 8. 306–317Google Scholar, repr. in Studies in Medieval Philosophy, Science, and Logic (Berkeley 1975) 409–439Google Scholar; and more recently, Leff, Gordon, William of Ockham: The Metamorphosis of Scholastic Discourse (Manchester 1975).Google Scholar Concerning Ockham's influence on physical theory in the fourteenth century, see Weisheipl, James A., ‘Ockham and Some Mertonians,’ Mediaeval Studies 30 (1968) 163–213CrossRefGoogle Scholar; Weisheipl, , ‘The Place of John Dumbleton in the Merton School,’ Isis 50 (1959) 439–454CrossRefGoogle Scholar; and Moody, Ernest, ‘Ockham, Buridan, and Nicholas of Autrecourt,’ Franciscan Studies n.s. 7 (1947) 113–146, esp. 144–146, also reprCrossRefGoogle Scholar. in Studies, pp. 127–160.Google Scholar However, support for Ockham's ideas was not universal; as Katherine Tachau has shown recently, at Oxford there seems to have been no following for Ockham's denial of sensible species. See ‘The Problem of the Species in medio at Oxford in the Generation after Ockham,’ Mediaeval Studies 44 (1982) 394–443Google Scholar and ‘The Response to Ockham's and Aureol's Epistemology (1320–1340),’ English Logic in Italy in the Fourteenth and Fifteenth Centuries, ed. Maieru, Alfonso (Naples 1982) 185–217.Google Scholar

7 Scriptum in librum primum Sententiarum Ordinatio, Prologue, q. 1; ed. Gál, Gedeon and Brown, Stephen, Opera theologica 1 (St. Bonaventure, N.Y. 1967)Google Scholar‘Utrum sit possibile intellectum viatoris habere notitiam evidentem de veritatibus theologiae;’ at p. 7.Google Scholar Concerning this question and the remainder of the Prologue, see Guelluy, R., Philosophie et théologie chez Guillaume d'Ockham (Louvain 1947) esp. 79ff.Google Scholar

8 Ordinatio, Prol. q. 1Google Scholar; OTh 1.7.

9 See, for example, Categories VIII 8b25–34 and 9a3–9Google Scholar as well as Metaphysics V.18 1022b4–14.Google Scholar

10 Ordinatio, Prologue q. 8Google Scholar; OTh 1.217–220. Concerning Ockham's theory of habits, see Leff (note 6 above) 553–560. But regarding Ockham's following at Oxford on this issue, see the articles by Tachau (note 6 above).

11 Ordinatio, Prol. q. 1Google ScholarOTh 1.8–11;cf. Quodlibeta V, q. 1Google Scholar; ed. Wey, Joseph C.OTh 9 (St. Bonaventure 1980) 475–476.Google Scholar

12 Ordinatio, Prol. q. 1Google Scholar; OTh 1.7–8.

13 Ordinatio, Prol. q. 1Google Scholar; OTh 1.8: ‘Confirmatur: quia istae sunt passiones entis, igitur veritates in quibus probantur pertinent ad scientiam de ente et ad nullam aliam scientiam. Consequentia patet, quia eiusdem scientiae est considerare aliquod subiectum et passiones ipsius; igitur ad nullam scientiam pertinet consideratio de passionibus nisi ad quam perunet considerare subiectum.’ My italics.

14 Ordinatio, Prol. q. 1Google Scholar; OTA 1.12: ‘Ad secundum dico quod talis veritas potest pertinere ad utramque scientiam primo modo dictam. Si dicatur quod tune illae duae scientiae erunt una scientia, sicut scientia de anima et scientia de anima intellectiva sunt una scientia, dico quod non oportet quod illae scientiae faciant unam scientiam isto modo dictam, nisi illae scientiae essent praecise de subiecto illius veritatis et non considerarent nisi passiones debito modo ordinatas. Si autem illae scientiae considerant multa, sive subiecta sive passiones, non habentia ordinem determinatum requisitum ad unitatem scientiae, tales non oportet quod faciant unam scientiam, sicut est de metaphysica et de theologia, quia theologia considerat multa, tam subiecta quam passiones, quae non pertinent ad metaphysicam.’

15 According to Aristotle, quia demonstrations provide only knowledge of the fact; propter quid demonstrations, on the other hand, provide knowledge of the fact through its causes. See Posterior Analytics 1.13 and 27.Google Scholar

16 Ordinatio, Prol. q. 1Google Scholar; OTh 1.12–14.

17 Ordinatio, Prol. q. 1Google Scholar; OTh 1.8: ‘Praeterea, I Posteriorum, conclusione 8, ‘Non contingit demonstrantem descendere a genere in genus.’ Sed si eadem veritas pertineret ad distinctas scientias, contingeret per principia unius scientiae probare conclusionem alterius scientiae, et hoc esset descendere a genere in genus; igitur etc.’ The reference to ‘conclusio 8’ derives from Robert Grosseteste's commentary on the Posterior Analytics.

18 Ordinatio, Prol. q. 1Google Scholar; OTh 1.14: ‘Dico quod Philosophus loquitur de scientiis distinctis habentibus omnia subiecta distincta et omnes passiones distinctas, et de talibus verum est quod non contingit per principia unius scientiae demonstrare conclusionem alterius scientiae. Quando autem subiectum aliquod unius continetur sub aliquo subiecto alterius, tune bene contingit, sicut patet per ipsum, ibidem, quia scientias sic se habentes excipit ibidem ab illa conclusione. Sic est in proposito, quia Deus, qui est subiectum theologiae, continetur sub ente quod est subiectum partiale metaphysicae.’

19 See above, argument 1.

20 Ordinatio, Prol. q. 1Google Scholar; OTh 1.14–15: ‘Et si dicatur quod Philosophas non excipit nisi scientiam subalternantem et subalternatam, sicut patet ibidem, dicendum quod per hoc excipit scientiam subalternantem et subalternatam intendit excipere, quamvis non exprimat, quasdam alias aliter subordinatas. Unde sciendum est quod non est inconveniens theologiam quantum ad aliquam sui partem subalternari metaphysicae et e converso, ad modum quo medicina secundum aliquam sui partem subalternatur geometriae sicut docet Philosophus I Posteriorum.’

21 Posterior Analytics 1.13 79a13ff. Several authors have argued that this example of geometry and medicine itself violates Aristotle's prohibition of metabasis; see, for example, Barnes, Jonathan, Aristotle's Posterior Analytics (Oxford 1975) 153.Google Scholar

22 For much of what follows concerning this topic, I am indebted to Maurer, Armand, ‘Ockham's Conception of the Unity of Science,’ Mediaeval Studies 20 (1958) 98–112CrossRefGoogle Scholar and ‘The Unity of a Science: St. Thomas and the Nominalists,’ St. Thomas Aquinas: 1274–1974. Commemorative Studies (2 volumes, Toronto 1974), 2.269–291.Google Scholar

23 Sententia super Posteriora Analytica, I lect. 41; ed. Leonine, (Rome 1882) 1.306Google Scholar; Summa Theologiae 1.1.3 resp.

24 Henry, of Ghent, , Quodlibeta IX, q. 4Google Scholar; (Paris 1518) fol. 354r-356r. Cf. also Ockham, , Ordinatio, Prologue q. 8Google Scholar; OTh 1.211–212.

25 Ordinatio, Prol. q. 8Google Scholar; OTh 1.208.

26 Ordinatio, Prol. q. 8Google Scholar; OTh 1.212. See also Henry, of Ghent, , Summa quaestionum ordinariarum a. 27Google Scholar, q. 1; (Paris 1520) 1. fol. 161v.

27 Ordinatio, Prol. q. 8Google Scholar; OTh 1.218.

28 Expositio in I–III libros Physicorum Aristotelis, Prologue; ed. V. Richter and G. Leibold, Opera philosophica 4Google Scholar, part 1 (in press) p. 7: ‘… metaphysica non est una scientia numero, nee similiter philosophia naturalis, sed philosophia naturalis est collectio multorum habituum, sicut dictum est. Nee est aliter una, nisi sicut civilas dicitur una vel populus dicitur unus vel exercitus comprehendens homines et equos et cetera necessaria dicitur unus vel sicut regnum dicitur unum vel sicut universitas dicitur una vel sicut mundus dicitur unus.’ Trans. Boehner, , Philosophical Writings (London, 1957) 7.Google Scholar Ockham nods in passing to those authors who speak of a ‘first subject’ of a discipline, but qualifies this notion to such a degree that it loses its impact: ‘Tamen pro dictis aliquorum auctorum qui videntur assignare unum subiectum talium scientiarum, est sciendum quod non intendunt quod aliquid sit proprie subiectum primum totius, sed intendunt dicere quod inter omnia subiecta diversarum partium est aliquod unum primum aliqua primitate, et aliquando unum est primum una primitate et aliud est primum alia primitate. Sicut in metaphysica primum inter omnia subiecta primitate praedicationis est ens, sed primum primitate perfectionis est Deus. Similiter in philosophia naturali primum subiectum primitate praedicationis est substantia naturalis vel aliquid aliud, et primum primitate perfectionis est homo vel corpus cadeste vel aliquid tale. Et hoc intendunt auctores per talia verba, et nihil aliud.’ Exposilio, p. 10.Google Scholar Ockham summarizes his position at Ordinatio, Prol. q. 8Google Scholar; OTh 1.219–220: ‘Dico quod Philosophus accipit scientiam unam vel pro collectione multorum, ordinem determinatum habentium, vel pro multis conclusionibus scitis, habentibus ordinem determinatum. Posunt autem conclusiones habere multiplicem ordinem: vel penes praedicta tantum vel penes subiecta tantum vel penes utraque. Exemplum primi: si de eodem subiecto praedicentur multae passiones ordinatae secundum superius et inferius, sicut de figura possunt ostendi passiones magnitudinis et similiter passiones suae propriae et similiter passiones suorum inferiorum; sed tune est conclusio particularis. Exemplum secundi: si passiones communes demonstrentur de primis suis subiectis et de inferioribus, sicut si passiones animalis ostendantur non tantum de animali sed etiam de inferioribus. Exemplum tertii: si passiones animalis praedicentur de animali et passiones specierum contentarum praedicentur de illis speciebus. Et ita propter ordinem talem, vel etiam consimilem, potest dici scientia aliqua una, qualiter alia non potest quae caret ordine consimili. Et sic accipit Philosophus scientiam unam et alii philosophii et doctores.’ I would like to thank the editors and Franciscan Institute Publications for allowing me to refer to page proofs of the forthcoming edition of the Expositio in libros Physicorum.

29 Grosseteste, Robert, Commentarius in Postenorum Analyticorum libros, ed. Rossi, Pietro (Florence 1981) 259–260Google Scholar: ‘Aggregandi autem sunt qui sunt unificati in aliquo uno ex quo est scientia una, propter hoc oportet determinare ex quo habeat scientia unitatem. Propter hoc in principio huius capituli [i.e. in Posterior Analytics 1.28] ponit Aristoteles diffinitionem unius scientie dicens quod una est scientia que subicit genus unum, ut arithmetica numerum et geometria magnitudinem inmobilem, et quia nichil scitur nisi ex principiis propriis inmediatis, ad hoc quod scientia sit una oportet ut habeat propria principia nota unificata in unitate subiecti unius, ex quibus demonstratur. … Hec igitur tria aggregantur ut sit scientia una: unitas subiecti super quod erigitur demonstrado, principia inmediata unificata in subiecto ilio ex quibus fit demonstratio, et quod subiectum habeat aut species aut partes aut per se accidentia ex quibus complectatur conclusio demonstrativa.’ It is perhaps also worthy of mention that this idea of an aggregate science continued to be cited late in the sixteenth century, even by those whose philosophical orientation was not alligned with that of Ockham. See, for example, Valla, Paulus, Logica (2 volumes, Lyons 1622)Google Scholar 2.637ff. and Suarez, Francesco, Disputationes metaphysicae, XLIV, xi, 55Google Scholar; Opera omnia (28 volumes, Paris 1856–1878) 26.711.Google Scholar

30 Thus, Maurer may be overextending the role of Ockham's nominalism when he says [‘Ockham's Conception …’ (note 22 above) 108], ‘With his usual sureness of insight, he saw clearly the consequences of his nominalism for the unity of science. If the universe is composed of individual realities from which all community in nature is rigorously excluded, the science related to this universe cannot have a greater unity than that of a collection or ordered whole. If science is understood as a mental habit, a total science is an ordered collection of such habits; if understood as a written book, it is an ordered collection of propositions. In either case, science has only a unity of order; it is not something one in number.’ The question is not that Ockham does see science as a collection, but whether his nominalism might also allow him to formulate another system; it is, therefore, the distinction between the logical requirements of nominalism and the actual system which Ockham devises.

31 I owe this observation to Marilyn Adams. Although I have reservations about areas of his theory, this distinction seems analogous to Thomas Kuhn's remarks about boundaries of exemplars in ‘Second Thoughts on Paradigms,’ in The Structure of Scientific Theories, ed. Suppe, Frederick (Urbana, III. 1974) 459–482, esp. at 480.Google Scholar

32 Buridan, John, Quaestiones super octo libros Physicorum I, q. 2Google Scholar; (Paris 1516) fol. 3rb; Albert, of Saxony, , Quaestiones super libros PosteriorumGoogle Scholar (Venice 1497) fol. Cvb6–Dra1. Marsillius, of Inghen, , Quaestiones super librum PosteriorumGoogle Scholar, Venice, Marc. lat. VI. 146, fol. 215vb–216rb.

33 Summa Logicae III, ii, ch. 20Google Scholar; ed. Gál, Gedeon and Brown, Stephen, Opera philosophica 1 (St. Bonaventure, N.Y. 1974) 538.Google Scholar

34 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.539:‘… sciendum est quod non ideo dicuntur aliquae scientiae ‘subalternans’ et ‘subalternata’ quia eandem conclusionem una scientia scit quia vera est et alia eandem scit propter quid. … Et ideo sicut eadem conclusio potest esse scita in scientiis disparatis, ita eadem conclusio potest sciri in scientia subalternante et subalternata, licet hoc non sit quia una est subalternans et alia subalternata.’

35 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.539–540: ‘… dicitur una scientia subalternans et alia subalternata quia scientia subalternata cognoscit conclusionem, scientia subalternans scit principium universale illius conclusionis. Unde, universaliter, quando per aliquam scientiam evidenter cognoscitur aliqua conclusio et non principium et per aliam scientiam evidenter scitur principium et non conclusio, tune est una subalternans et alia subalternata. Sicut nauta multas conclusiones scit et nescit principia, e converso astrologus novit principia et nescit conclusiones, quia ad eum non pertinent.’

36 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.540.

37 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.540: ‘Oportet autem seire quod cum scientia subalternans et etiam scientia subalternata sit quaedam collectio multorum habituum, ordinem determinatum habentium, non est impossibile quin aliqua scientia secundum unam partem subalternetur uni scientiae et non secundum aliam partem, sicut perspectiva secundum aliquam sui partem subalternatur geometriae et non secundum omnem.’

38 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.540: ‘Similiter etiam possibile est quod una scientia secundum eandem partem diversis scientiis subalternetur, quando scilicet una scientia scit unum principium respectu unius conclusionis et alia scientia scit aliud principium respectu eiusdem conclusionis.’

39 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.541: ‘Sciendum est etiam quod una pars unius scientiae potest subalternari uni scientiae et altera alteri, sicut una pars scientiae naturalis potest subalternari geometriae et alia arithmeticae.’

40 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.541: ‘Verumtamen una talis scientia non dicitur subalternata respectu alterius propter unam conclusionem vel paucas, nisi tota scientia vel pro maiori parte sit sibi subalternata. Propter quod una et eadem scientia non est subalternans et subalternata respectu eiusdem, quamvis non sit impossibile quod una pars unius totalis scientiae sit subalternans sibi aliquam partern alterius scientiae totalis et alia pars eiusdem scientiae totalis sit subalternata alteri parti alterius scientiae.’

41 Samma Logicae III, ii, ch. 21Google Scholar; OPh 1.541: ‘Et est sciendum quod hoc nomen ‘scientia subalternans’ et similiter hoc nomen ‘scientia subalternata’ dupliciter accipi potest, scilicet large et stride. Large potest dici scientia subalternans vel secundum se vel secundum aliquam partem sui quandocumque aliqua scientia totalis cognoscit principium universale alicuius conciusionis vel proprium et alia scientia totalis cognoscit conclusionem, ita tamen quod istae scientiae non constituunt unam totalem scientiam. Per quod excluduntur scientiae de per se superiori et per se inferiori. Et sic locutus sum prius de scientia subalternante et scientia subalternata. Et sic vult Philosophus quod medicina quantum ad aliquam sui partem subalternatur geometriae, quia medicine cognoscit hanc conclusionem ‘vulnera circularia tardius sanantur’ et geometer cognoscit principium universale respectu istius conclusionis, scilicet quod ‘circulus est figura cuius latera secundum omnem dimensionem maxime distant’. Et isto modo non est inconveniens quod logica et metaphysica secundum aliquas partes subalternent sibi aliquas partes particularium scientiarum.’ Note, however, that in Posterior Analytics I.13Google Scholar, Aristotle says explicitly that medicine and geometry are not in this relationship, but that they nevertheless possess the property that one knows the fact, while the other knows the reason for the fact. Ockham, on the other hand, suggests that these two sciences are subalternate. Concerning this passage, see also Moody, , The Logic of William Ockham (London 1935) 255–257Google Scholar and Leff (note 6 above) 329–330.

42 Grosseteste, Robert, Commentarius in Posteriorum Analyticorum libros (note 29 above) 197.Google Scholar

43 Summa Logicae III, ii, ch. 21Google Scholar; OPh 1.542: ‘Scientia subalternans stricte accipitur quando principium scitur per unam scientiam et conclusio per aliam et simul cum hoc subiectum unius est per accidens inferius ad subiectum alterius vel aliquod subiectum unius importat partem significati per subiectum alterius. Et sic accipit Lincolniensis scientiam subalternantem et scientiam subalternatam, et sic forte logica nullam scientiam aliam sibi subalternat nee forte etiam metaphysica.’ Leff (note 6 above) discusses this passage at p. 330 and surmises that Ockham is referring to sciences which are per se more universal, but does not mention the corresponding alternative, that the subjects are related as genus and species. Nevertheless, Ockham's text (which Leff does not cite in its entirety) and the reference to Grosseteste would indicate that we must consider this possibility.

44 Pinborg, Jan, ‘The English Contribution to Logic before Ockham,’ Synthese 40 (1979) 19–42CrossRefGoogle Scholar; Murdoch, John, ‘The Analytic Character of Late Medieval Learning: Natural Philosophy without Nature,’ in Roberts, Lawrence, ed., Approaches to Nature in the Middle Ages (Binghamton, NY 1982) 171–213Google Scholar; and Murdoch, , ‘Propositional Analysis in Fourteenth-Century Natural Philosophy: A Case Study,’ Synthese 40 (1979) 117–146.CrossRefGoogle Scholar

45 Auriol, Peter, Scriptum super I Sententiarum, ed. Buytaert, Eligius (St. Bonaventure, NY 1952) Prologue, q. 4 (pp. 250–284)Google Scholar; concerning this material, see Spade, Paul Vincent, ‘The Unity of a Science According to Peter Auriol,’ Franciscan Studies 32 (1972) 203–217Google Scholar. According to Ockham's own admission [Ordinatio I, d. 27, q. 3Google Scholar; OTh 4.238], he saw Auriol's work, but only briefly. Among the sources upon which Auriol drew, Radulphus Brito, in his Quaestiones super Priscianum Minorem (ante 1317), speaks of the science of grammar as a habitus of many conclusions acquired through several demonstrations, although his brief discussion leaves unclear the relationship between his position and those of Ockham and Auriol; Quaestiones, ed. Enders, Heinz W. and Pinborg, Jan (Stuttgart-Bad Cannstatt 1980) 1.90.Google Scholar

46 Grosseteste, Robert (note 29 above) 195–196Google Scholar; Kilwardby, Robert, De ortu scientiarum, chapter 43, section 401Google Scholar; ed. Judy, Albert (London 1975) 139–140Google Scholar. Likewise, the thirteenth-century Liber Jordani de ponderibus notes that the science of statics is subalternated to both geometry and natural philosophy; Ernest Moody and Clagett, Marshall, The Medieval Science of Weights (Madison, Wise. 1960) 150–151.Google Scholar

47 Romanus, Acgidius, Expositio in libros Posteriorum. (Venice 1488) foi. Dva8Google Scholar: ‘… si geometria descendit in perspectivam non est descensus in idem subiectum simpliciter sed in idem quodammodo. Duobus ergo modis potest fieri descensus in idem genus vel in idem simpliciter ut in partem subiectivam vel in idem quodammodo ut in scientiam subalternatum. …’

48 Burley, Walter, Super libros Posteriorum Analyticorum Aristotelis (Venice 1514Google Scholar; repr. Frankfurt/Main 1966) fol. 42rb: ‘… Adhuc propter quid et quia differunt in diversis scientiis quarum una non subaiternatur alteri nee secundum partem nee secundum totum.’

49 See, for example, Giles of Rome, , Expositio (note 47 above) fol. Dj–v8Google Scholar; Burley, Walter, Super libros Posteriorum (note 48 above) fol. 41v–42rGoogle Scholar; Boethius of Dacia, , De aeternitate mundi, ed. Green-Petersen, Nicolaus Georgius (Copenhagen 1976) 353–354.Google Scholar

50 Boethius of Dacia (note 49 above) p. 351.431–432: ‘… unus artifex non possit causare vel scire ex suis principiis veritates scientiarum aliorum artificum …’; p. 351.335–336: ‘… nullus artifex potest aliquid causare, concedere vel negare nisi ex principiis suae scientiae;’ Modi significandi sive quaestiones super Priscianum Maiorem, ed. Pinborg, Jan and Roos, Heinrich (Copenhagen 1969) p. 20.47–49Google Scholar: ‘… artifex enim quilibet solum illa considerat, quae per se attribuuntur suo scibili quicumque fuerit iste modus attributionis…’ Concerning this, see Wilpert, Paul, ‘Boethius von Dacien—Die Autonomie des Philosophen,’ Miscellanea mediaevalia 3 (Berlin 1964) 135–152.Google Scholar

51 Peter Auriol (note 45 above) 279, sec. 87. Duns Scotus likewise presents an interesting contrast to Ockham's discussion of metabasis. In the context of discussing whether proofs of astronomy are subalternated to mathematics or physics, he presents the objection that Aristotle had prohibited the descent to more than one genus in proofs; but rather than expand the classes of subalternation, as we have seen Ockham do, Scotus denies that the propositions under consideration in fact belong to two different sciences. See Quaestiones in VIII libros Physicorum II, q. 6, n. 7Google Scholar; ed. Wadding, (Lyon 1639) 2.124–125Google Scholar. In addition, it is well known that Ockham's contemporary, Walter Chatton, opposed Ockham's position in his own commentary on the Sentences [Reportatio I, Prologue, q. 1, a. 3Google Scholar; ed. Reina, Maria Elena, ‘La prima questione del Prologo del ‘Commento alle Sentenze’ di Walter Catton,’ Rivista critica di storia della filosofia 25 (1970) 48–74, 290–314 at 296–302]Google Scholar, and that Ockham returned to Chatton's objections in his Quodlibeta V, q. 1Google Scholar; OTh 9.475–480. The closest approach to Ockham's revision of subalternation of which I am aware occurs in the version of Burley's commentary on the Posterior Analytics found in Lambeth Palace MS 70, fol. 158vb, again regarding the relationship between medicine and geometry: ‘… ita habent diverse scientie considerare una scientia dicit propter quid et alia quia, et hoc potest esse tripliciter: aut quia una scientia simpliciter subalternata alteri quomodo perspectiva subalternata geometrice, aut quia una scientia non subalternata alteri simpliciter sed quantum ad aliam partem eius, et sic scientia naturalis subalternata per perspectivam, aut quia una scientia universalia alia propositione de qua dicit quia de qua alia dicit propter quid, quomodo se habent scientia medicinalis et geometria (ut) dictum est.’

52 Such an assessment would be most interesting for scholars at Oxford in the second quarter of the fourteenth century. However, commentaries on the Posterior Analytics are somewhat less numerous at Oxford, and particularly among scholars at Merton, during this period. I have discussed several techniques of fourteenth-century Oxonian work that avoided Aristotle's prohibition of melabasis in ‘The Oxford Calculators, the Quantification of Qualities, and Aristotle's Prohibition of metabasis,’ forthcoming in Vivarium.

53 Buridan, , Quaesliones super octo libros Physicorum (Paris 1516) fol. 3rbGoogle Scholar: ‘… dicit Aristoteles ibidem quod illud genus subiectum non oportet semper esse unum secundum unionem sed sufficit quod sit unus secundum analogiam et attributionem. Ideo ipse concludit unam esse scientiam que speculatur ens inquantum ens et que huic insunt secundum se, scilicet quia ens est unum genus commune omnibus licet non univocum sed analogum et Aristoteles toti methaphysice assignat subiectum sibi proprium et adequatum.’

54 Ibid: ‘… nunquam multa quorum quodlibet est unum aliquod in actu dicuntur unum nisi propter aggregationem earum in eodem loco vel in eodem subiecto; quod patet quia multi lapides dicuntur unus cumulus et multi homines dicuntur unus populus propter unam continuationem vel colligationem eorum, et multa ligna vel stramina dicuntur unum onus vel propter ordinem vel ordinationem seu attributionem ad unum principium illorum ad quod omnia alia attribuuntur. Ut quod exercitus dicitur unus propter attributionem omnium ad unum principem vel aliquo alio modo, ita quod omnino necesse est assignare causam et rationem quare illa dicuntur unum sic inter se et non cum aliis sed in totali scientia naturali multe et diverse sunt conclusiones et cuiuslibet scientie partialis est unus habitus scientificus in actu distinctus ab habitu scientifico alterius scientie et tamen omnes illi habitus partiales dicuntur esse una scientia totalis distincta contra methaphysicam. Igitur necesse est assignare causam et rationem propter quid illa dicantur esse una scientia.’

55 See, for example, the remarks of Godfrey of Fontaine, , Quodlibet XIII, q. 1Google Scholar; Les Philosophes Belges: Textes et Etudes, ed. Hoffmans, J. (Louvain 1932) 5.175Google Scholar, and Brito, Radulphus, Quaestiones super Priscianum Minorem (note 45 above), 1.104.Google Scholar

56 Auriol, Peter, Scriptum super I Sententiarum (note 45 above) Prologue, q. 4 (at p. 267, no. 54)Google Scholar, where he discusses the aggregate habits of grammar, logic, and geometry, and draws the analogy of multi lapides in cumulo uno. Comparison of Buridan's text cited in note 53 and Ockham's in note 28 shows agreement in the examples of populus and exercitus.

57 Albert of Saxony, Quaestiones (note 32 above) fol. Drb: ‘Sed diceret aliquis ex quo sunt plures scilicet modi quibus convenit descendere de una scientia in aliam; quare Aristoteles pluries dicit non convenit demonstrantem descendere de genere in genus?’ In his response, Albert argues that Aristotle did not restrict the subalternating and subalternate sciences, and the examples which he gives are very close to the mechanism of subalternation of Ockham's wider interpretation.