Abstract
The history of medieval science has for some time now been of age; it is not merely a recognizable, but a recognized area of study. This is, to be sure, all to the good, especially in the eyes of its practitioners. What is more, with this increased recognition has come a corresponding specialization. This too is all to the good, for what better means are there for the discovery, investigation, and understanding of the primary sources of medieval science than an active cadre of historians whose training and interests are focused primarily on the Middle Ages?
Much of the research into the primary sources upon which the present paper is based was supported by a research grant from the National Science Foundation.
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Notes
See, for example, P. Glorieux, ‘Sentences (Commentaires sur les)’, Dictionnaire de théologie catholique, 14, col. 1875.
Book I, dist. 37, for example, whose concern is, to use St. Thomas’s words, quibus modis dicatur Deus esse in rebus, accommodates the examination of the possible infinite capacity of an entity like the soul (R. Killington, BN 14576, 150r-161r: Utrum omnis creatura sit sue nature cum çertis limitibus circumscripta), a detailed discussion of the possible composition of continua out of indivisibles (Gerard of Odo; see note 16 below), and an extensive examination of imaginary infinite void space (Jean de Ripa; see Traditio 23 (1967) 191 – 267 ).
P. Glorieux, 6Jean de Falisca: La formation d’un maître en théologie au XlVe siècle’, Archives d’hist. doct. et litt. du moyen âge, 33 (1966) 23–104. The MSS are (for theology) BN 16408, BN 16409, BN 16535 and (for science) BN 16621. On the last see, for example, P. Duhem, Le système du monde, vol. 7 (Paris, 1956) p. 607ff; L. Thorn- dike, ‘Some Medieval and Renaissance Manuscripts on Physics’, Proceedings of the American Philosophical Society 104 (1960) 189–191.
For details, see Franciscan Studies 26 (1966) 213–214.
On Rosetus and his Sent. in general see note 82 below. For MSS of Q.l, art. 1 as a separate tract see Archivum franciscanum historicum 46 (1953) 91, to which one can add Oxford, Can. misc. 177, 17r-182r; Sevilla, Colomb. 7-7-29, 147r-167r. That one of these copies (viz. Erfurt, Ampi. Q° 107,87r-10v) belonged to Peter of Candia is learned from its explicit: is te caternus... est ad usum fratris Petri de Candia ordinis Minor um provincie Romane.
Chartularium Univ. Paris., vol. 3, p. 144, cited by Glorieux op. cit. (above, note 10) col. 1876.
MS BN 16408, 123r: In omnibus hiis, potissime in primo articulo, victa (!) et vitare te pretende cavendo processum logicum ac mathematicum, solum philosophicum speculativum ac moralem et processum methaphisicum et theologicum prosequendo. D. Trapp (Augustinianum 4 (1964) 403) has cited this text from its clean copy in BN 16409, 185r; but he has omitted the first six words and missed te, while the last six words do not appear in BN 16409. For the possible intention behind this note, see the table of contents of MS 16408 as published in Glorieux, op. cit. (above, note 14) p. 26.
See the incisive analysis of Ockham’s treatment of this problem by Robert Guelluy, Philosophie et théologie chez Guillaume d’Ockham (Louvain/Paris, 1947). For other fourteenth century treatments, see Josef Kürzinger, Alfonsus Vargas Toletanus und seine theologische Einleitungslehre, Beit. z. Gesch. Phil. Mittelalters 22, Heft 5-6 (Münster, 1930).
Ernest Moody, Empiricism and Metaphysics in Medieval Philosophy’, Philosoph-ical Review 67 (1958) 161.
In Book II of his Sent. (MS. Valencia, Cated. 200), Gerard of Odo asks (dist. 13, QQ1-2): Utrum lumen vel lux multiplicet speciem suam in instanti vel in tempore; Utrum lux ista que fuit facta prima die multiplicaverit lumen suum sicut modo sol mul- tiplicat lumen suum (52r-53r). In dist. 15, Q. 1: Utrum yris sit unum de operibus 6 dierum (64r-65v). Finally, in Book I, dist. 23, Gerard asks no less than twelve questions directly relating to first and second intentions (MS Valencia, Cated. 139,88r-101v). For the introduction of gravia and levia, see the questiones of Franciscus Mayronis as reported in Franziskanische Studien 53 (1971) 207. For the investigation of astrology, see principium to Book II by Pierre Ceffons as cited by D. Trapp, ‘Peter Ceffons of Clair- vaux’, Recherches de théologie ancienne et médiévale 24 (1957) 105; Cf. p. 103, n. 2. The fascination with the ninth sphere is also that of Ceffons (in dist. 1 of Book II; Trapp, op. cit., p. 104).
See, for example, the recent book of Fritz Hoffmann, Die theologische Methode des Oxforder Dominikanerlehrers Robert Holcot, Beit Gesch. Phil. Theol. Mittelalters, Neue Folge, 5 (Münster, 1971 ).
Egidius flourished at Paris ca. 1370–1395; student of theology at the College of Harcourt, attached to Norman Nation ca. 1371, lectured on Sentences 1377–1378, licentiate in theology 1384, Master of House of Navarre in 1389; made cardinal by John XXIII in 1411, died 15 March 1413. His Comm. Sent. has not yet been discovered. Inasmuch as the text of his regule is brief and interesting, I give it here in toto (from MS Vat. lat. 3088, 26r-26v)
Lurtz (fl. ca. 1390) wrote a Tractatus de paralogismis consuetis fieri in materia Trinitatis (see L. Meier, ‘Contribution à l’histoire de la théologie à l’Université d’Erfurt’, Revue d’histoire ecclésiastique, 50 (1955) 455–470). He even cites Egidius and his régulé (op. cit., p. 460).
Bk. II, Q.2: Quia postulas amice dilectissime, o Bernarde, ut alica de logicalibus in huius secundi libri principio diligenter annectam, idcirco alica logicalia que dudum multa velocitate composui que tibi in scolis non protuli hic annecto, que tuo prospicaci reliquuntur examini, nec correctionis limam diligentis horrescunt. Et quoniam in hiis diebus nonnulli dubitari videretur de scire et opinari, quero utrum circa idem scire et opinari contingat (MS Troyes 62, 87r–96r). Bk. II, Q.3 : Quia petitur a me ut, si quidquam de insolubilibus novi, de ipsis aliquid hie pertractarem, idcirco in hac lectura secundi sententiarum quero utrum beatus augustinus vel etiam magister petrus lumbardus vel aliquis alius theologus fidelis per aliquod insolubile potuerunt ad in- conveniens deduci (MS cit., 96r–101r). Ceffons was also willing to put together on the spot disquisitions de proportionibus and drop them into his Comm. Sent.; See J. Murdoch, ‘Mathesis in philosophiam scholasticam introducta: The Rise and Development of the Application of Mathematics in Fourteenth Century Philosophy and Theology’, Arts libéraux et philosophie au moyen âge (Paris/Montréal, 1969) p. 233. Ceffons, in- cidentally, seems to have been quite familiar with Oxford philosophy, citing Roger Swineshead, Killington and others.
Hie est advertendum quod nulli (lege nonnulli?) logicam despiciunt totadie sumen- tes: “Linquo coax ranis, era corvis vanaque vanis, et cetera” ; et sumentes illud dictum senece: “Mus caseum rodit, et cetera.” Despiciuntque tam insolubilia que solvere nunquam noverint quam obligationes... Hie tamen bene aude astruere quod nunquam vidi peritum logicum qui logicam diffamerei, ignotos logicos logicam contempnere vidi... et propter ignorantiam logice multi in vanos prolabantur errores, sicut et olim nonnulli propter ignorantiam logice defeciunt pro ut scimus astrucxisse philosophum et eius commentatorem averoys (MS Troyes 62, 96r–96v). The quotation from Seneca (Epist. ad Lucilium, 48) points a satirical finger at the triviality of “solving” the likes of: “Mus syllaba est. Mus autem caseum rodit; syllaba ergo caseum rodit.” The other reference made by Ceffons is medieval: a couplet (the line not quoted by Ceffons is: “Ad logicam pergo, que mortis non timet ergo.”) ascribed to the twelfth century English scholar and poet Serio of Wilton. The story is that Serio composed the verses upon being converted from the vanities of a secular life to a monastic one. Cf. F .I.E. Raby, A History of Christian-Latin Poetry from the Beginnings to the Close of the Middle Ages, 2d. ed. (Oxford, 1953), pp. 340–41.
This is not, to be sure, to deny that reductionism (often from connotative to absolute terms) was not of extreme importance in natural philosophy (see, for example, the De succès s ivis compiled from Ockham’s writing [ed. P. Boehner (St. Bonaventure, 1944)] and the analysis of it by Herman Shapiro, Motion, Time and Place According to William Ockham [St. Bonaventure, 1957]). Furthermore, it is also not to claim that the analy-tical languages in question could not, and were not, applied by those who did not ad-here to Ockham’s “particularism.”
Cf. J. Murdoch, op. cit. (above, note 1), 62–63. At times, one even finds the decision of when, and when not, to ascribe some property to a subject directly based upon the measurement of the degree of that property in the subject; see Nicole Oresme’s question: Utrum quodlibet sit ita album sicut aliqua eius pars est alba, in his Quaestiones super geometriam Euclidis (ed. H. L. L. Busard; Leiden, 1961 ) pp. 41–45.
A convenient listing of such vocabulary can be found in the Summulus de motu incerti auctoris in M. Clagett, The Science of Mechanics in the Middle Ages (Madison, 1959 ) pp. 445-462. For the development of different meanings for some of the vocabulary, and for the whole intension and remission language in general, see the articles of Edith Sylla, ‘Medieval Quantifications of Qualities: The “Merton School’”, Archive for History of Exact Sciences 8 (1971) 9-39; and ‘Medieval Concepts of the Latitude of Forms: The Oxford Calculators’, Archives d’hist. doct. et litt. du moyen âge 30 (1973) 223–283. Note should also be made of the fact that terms for the subjects to which the languages were applied also formed part of the relevant vocabulary, but it is best seen save in the instances of the three “limit” languages to be described below - as separate from the vocabulary of the language applied. Thus, for the most part, such “subjectum” vocabulary will be ignored in what follows.
Thus, a subject that varies uniformly in heat from zero degrees at one extreme to 8 degrees at the other is “just as hot” as if it were uniformly hot in degree 4 throughout. A special case of this “mean degree” algorithm is, of course, the familiar Mean Speed Theorem of the Middle Ages. On the whole, see M. Clagett, op. cit. (above, note 44) ch. 5.
For the three examples given: (1) Thomas Bradwardine, Tractatus de continuo (MS Torun, R 4° 2, p. 166): Nullius forme suscipientis magis et minus remississimum gra dum esse; (2) Richard Swineshead, Liber calculationum (ed. Venice, 1520,2r): Intensio habet attendi penes distantiam a non gradu et remissio penes approprinquationem ad non gradum (there was considerable controversy concerning this algorithm and its al-ternatives: See M. Clagett, ‘Richard Swineshead and Late Medieval Physics’, Osiris 9 (1950) 131–161; and E. Sylla, “Medieval Concepts...” [above, note 44]); (3) Richard Swineshead, op. cit., 54v: Si subiectum uniformiter difforme terminatum ad summum alteretur uno gradu uniformi per totum, isto subiecto aliunde non moto nec facta muta- tione illius alterationis, per illud subiectum gradus summus uniformiter inducetur.
See L. Crosby, op. cit. (above, note 48) and M. Clagett, op. cit. (above, note 44) ch. 7. A similar algorithm was applied within medieval pharmacology: See M. McVaugh. Clagett, op. cit. (above, note 44) ch. 7. A similar algorithm was applied within medieval pharmacology: See M. McVaugh, ‘Arnald of Villanova and Bradwardine’s Law’, Isis 58 (1967) 56–64.
On all three languages: Curtis Wilson, William Heytesbury: Medieval Logic and the Rise of Mathematical Physics (Madison, 1956) ch. 2–3. Herman and Charlotte Shapiro have edited Walter Burley’s De primo et ultimo instanti [Archiv fiir Geschichte der Philosophie 47 (1965) pp. 157–173], but it contains a number of errors and should be consulted with care.
See, in particular, J. Murdoch, ‘Superposition, Congruence and Continuity in the Middle Ages’, Mélanges Koyré (Paris, 1964 ) 1, 416–441.
Treatment of ‘infinita’ as a logical term can be found in Peter of Spain, Summule logicales, ed. L. M. DeRijk (Assen, 1972) pp. 230–32 and in William of Sherwood, Syncategorernata, ed. J. R. O’Donnell, Mediaeval Studies, 3 (1941) 54-55. Relevant secondary literature on the “categorematic vs. syncategorematic” infinite is: P. Duhem, op. cit. (above, note 14) vol. 7, pp. 3–157; Anneliese Maier, Ausgehendes Mittelalter, vol. 1 (Rome, 1964), pp. 41–85, 460–62. A later, but still thoroughly medieval, source is Jean Mair, Le traité de l’infini, ed. & tr. H. Elie (Paris, 1938).
William & Martha Kneale, The Development of Logic (Oxford, 1962) pp. 246–274; Ernest Moody, Truth and Consequence in Mediaeval Logic (Amsterdam, 1953) ch. 1–3; Philotheus Boehner, Collected Articles on Ockham (St. Bonaventure, 1958) pp. 174–267; L. M. De Rijk, ‘The Development of Suppositio naturalis Mediaeval Logic’, Vivarium, 9 (1971) 71–107; 11 (1973) 43–79 and the other articles of De Rijk cited in the biblio-graphy to his recent edition of Peter of Spain (above, note 60).
The problem is not basically one of the possible origins of the languages themselves, but rather that of the origins of their wholesale application. Of course, a great deal of the substance (i.e., the vocabulary and algorithms) of these languages developed, even originated, during the course of this application, but it is also true that a good deal existed beforehand. One can point, for example, to an unravelling of the notion of latitudo before it was used to measure things, or to the availability of the notion of first and last instants in Aristotle before they were made to serve a similar role. On this “pre- application” stage of the development of some of the languages see: Anneliese Maier, Zwei Grundprobleme der scholastischen Naturphilosophie, 3 AufL (Rome, 1968); E. Sylla, ‘Medieval Quantifications...’ (above, note 44); C. Wilson, references in note 52 above; L. M. De Rijk, Logica modernorum, 2 vols, in 3 (Assen, 1962–1967).
See particularly Ockham’s Prologue to his Expositio on the Physics (in his Philosophical Writings [ed. & tr. P. Boehner; Edinburgh, 1957] pp. 2–16); cf. note 42 above. All of this also bears directly on the problem of the “object” of a proposition (the dictum sive significatum proposition!’s). For the latest literature on this: E. A. Moody, ‘A Quodlibetal Question of Robert Holcot, O. P., on the Problem of the Objects of Knowledge and Belief’, Speculum 39 (1964) 53-74; T. K. Scott, ‘John Buridan on the Objects of Demonstrative Science’, Speculum 40 (1965) 654-73; H. Schepers, ‘Holkot contra dicta Crathorn’, Philosophisches Jahrbuch 79 (1972) 106–136.
Guy Beaujouan, ‘Motives and Opportunities for Science in the Medieval Universities’, Scientific Change, ed. A. C. Crombie (London, 1963 ) pp. 220 - 21.
P. Vignaux, op. cit. (above, note 38) col. 763 and Nominalisme au XlVe siècle (Montréal, 1948) pp. 22–26; H. Oberman. Vignaux, op. cit. (above, note 38) col. 763 and Nominalisme au XlVe siècle (Montréal, 1948) pp. 22–26; H. Oberman, ‘Some Notes on the Theology of Nominalism’, H.rvard Theological Review 53 (1960) 60–61; David Knowles, The Religious Orders in England, vol. 2 (Cambridge, 1955 ) p. 76.
V. Doucet,4Le Studium franciscain de Norwich en 1337 d’après le MS Chigi B.V.66 de la Bibliothèque Vaticane’, Archivum franciscanum historicum 46 (1953) 88–93; 83
A. B. Emden, A Biographical Register of the University of Oxford to A.D. 1500, vol. 2 (Oxford, 1958) pp. 850–51. (See now, however, W. J. Courtenay, ‘Some Notes on Robert of Halifax, O.F.M.’, Franciscan Studies 33 (1973) 135–14284 This theme is so central to Ripa that one comes upon it throughout his works. The late André Combes published (at times with the assistance of P. Vignaux or F. Ruello) a good amount of Ripa: Determinationes (Paris, 1957), Conclusiones (1957), Lect. Sent. I, QQ Prol. (1961–1970), Degradu Supremo (1964). They are all relevant to the point at issue here. To this one should add Combes’s posthumous article ‘L’intensité des formes d’après Jean de Ripa’, Archives hist. doct. litt. du moyen âge 27 (1970) 17–147. Cf. J. Murdoch, op. cit. (above, note 31) pp. 241, 246.
A more curious kind of “fitting” of God is found in the Centiloquium theologicum attributed (wrongly) to Ockham (ed. P. Boehner, Franciscan Studies 23 (1942) 262–63) where God’s eternal existence outside time and His creation of time are put together with the temporal language of de incipit et desinit.86 Richard Killington, Comm. Sent., Q.l: Utrum Deus sit super omnia diligendus… [Conclusiones]: (1) Quod quecumque dilectio Dei super omnia quam habet quis, est maior dilectio quam sit dilectio eiusdem meritoria respectualicuiuscreature… (2) Quod quecumque dilectio Dei super omnia in alico infinite excedit dilectionem creature in eodem… (3) Quod non est possible amplius diligere Deum super omnia propter bene- ficium factum sibi vel proximo… (4) Secundum nullam proportionem que est vel esse posset inter finitum et finitum eiusdem rationis vel speciei est Deus amplius diligendus quam alias foret sine benefìciis (MSS VA 4353, lr–2r; Bruges 503, 80r–80v).
Roger Rosetus, Sent., Q. 5: Utrum caritas augeatur per opera meritoria... Secundus articulus erit quod tangitur in secundo argumento quod caritas potest esse infinite (proved in that argument by considering meritorious acts over the infinity of propor-tional parts in a day), ideo queritur utrum alica creatura posset esse infinita (MS Bruges 192, 42r–44r ).
Jean Mirecourt, Apologia prima, ed. F. Stegmiiller, Recherches de théologie ancienne et médiévale 5 (1933) 71–72.
Robert Holcot, Sent. I, Q. 3, arg. prin. 8 (ed. Lyon, 1518 reprt. Frankfurt, 1967 fol. b iiiiv): It is argued that, if the will has a libertas contradictionis with respect to frui and uti, then it can elicere duos actus oppositos successive et immediate; but this is not per-missible, the argument proceeds, because on the authority of Anselm omne quod aliquid vult libere, prius movet se ad volendum illud. In his reply to this Holcot simply says that we should dispense with this “authority”: Dico quod argumentum stat in pondere auctoritatis Anselmi; ideo videtur quod facile est homini volenti ilio onusto pondere seipsum deonerare, negare illam auctoritatem (ad sign, in mg. EE).
For some indication of this literature see Martin Grabmann, Die Sophismataliteratur des 12. und 13. Jahrhunderts, Beit. z. Gesch. d. Phil. u. Theol. Mittelalters 36, Heft 1 (Münster, 1940).
For an example of a sophisma from a work of natural philosophy consider the following from Richard Swineshead’s Liber Calculationum (ed. Venice, 1520; Fr): A nunc est solum finite intensum, et per rarefactionem finitam solum subito fiet infinite intensum. For its “resolution” see the reference in note 137. Cf. below, note 152.
To do so would make almost all indirect arguments ending with a bizarre absurdity something like sophismata, which is certainly not my intention.
There are other instances of arguments applying measure languages in natural philosophy that are sophismata in a more straightforward sense inasmuch as they transfer the substance of more genuine sophisms to the context of some more general problem under investigation. This occurs quite frequently in investigations of the composition of continua. For an example, see note 65 above. One can compare this kind of discussion of the “continuum problem” with the numerous sophisms dealing with the term ‘infinitum’ (found from the thirteenth century on) and especially with the likes of Immediate sunt partes continui (Albert of Saxony [ed. Paris, 1494], Sophisma 178).
See, for example, the work called A est unum calidum, apparently by one Johannes Bode: H. L. L. Busard, ‘Unendliche Reihen in A est unum calidum’, Archive for History of Exact Sciences 2 (1965) 387–397.
Frequent as the occurrence of such a point of view is within late medieval theology, it is hard to escape noticing it. But to interpret it as something like “the inferential logic expressed in consequentiae” (E. Synan, Mediaeval Studies 25 (1963) 261) misses what it is and what importance it held.
The terms are those of Damasus Trapp (Augustinianum 4 (1964) 404; 5 (1965) 269). One should also note Trapp’s unappreciative evaluation of the measurement tradition in his ‘Augustinian Theology of the 14th Century’, Augustiniana 6 (1956) 148–149.
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Murdoch, J.E. (1975). From Social into Intellectual Factors: An Aspect of the Unitary Character of Late Medieval Learning. In: Murdoch, J.E., Sylla, E.D. (eds) The Cultural Context of Medieval Learning. Boston Studies in the Philosophy of Science, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1781-7_9
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