Mathematics and Physics of First and Last Instants: Walter Burley and William of Ockham

in Vivarium
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In his De primo et ultimo instanti, Walter Burley paid careful attention to continuity, assuming that continua included and were limited by indivisibles such as instants, points, ubi (or places), degrees of quality, or mutata esse (indivisibles of motion). In his Tractatus primus, Burley applied the logic of first and last instants to reach novel conclusions about qualities and qualitative change. At the end of his Quaestiones in libros Physicorum Aristotelis, William of Ockham used long passages from Burley’s Tractatus primus, sometimes agreeing with Burley and sometimes disagreeing. How may this interaction between Burley and Ockham be understood within its historical context?

Mathematics and Physics of First and Last Instants: Walter Burley and William of Ockham

in Vivarium




See S. Knuuttila“Remarks on the Background of the Fourteenth Century Limit Decision Controversies,” in The Edition of Theological and Philosophical Texts from the Middle Ages. Acts of the Conference Arranged by the Department of Classical Languages University of Stockholm 29-31 August 1984ed. M. Asztalos (Stockholm 1986) 245-266 and A. de Libera “La problématique de l’instant du changement au xiiième siècle: contribution à l’histoire des sophismata physicalia” in Studies in Medieval Natural Philosophy ed. S. Caroti (Florence 1989) 43-93.


R. Plevano“Richard Rufus of Cornwall and Geoffrey of Aspall: Two Questions on the Instant of Change,” Medioevo 19 (1993) 167-232; idem “Two British Masters and the Instant of Change” in Aristotle in Britain During the Middle AgesProceedings of the International Conference at Cambridge 8-11 April 1994 Organized by the Société Internationale pour l’Ėtude de la Philosophie Médiévale ed. J. Marenbon (Turnhout 1996) 91-115; C. Trifogli “Thomas Wylton’s Question ‘An contingit dare ultimum rei permanentis in esse’” Medieval Philosophy and Theology 4 (1994) 91-141.


L.O. Nielsen“Thomas Bradwardine’s Treatise on ‘incipit’ et ‘desinit’. Edition and Introduction,” Cahiers de l’Institut du Moyen-Âge grec et latin 42 (1982) 1-83.


See E. Sylla“Infinite Indivisibles and Continuity in Fourteenth-Century Theories of Alteration,” in Infinity and Continuity in Ancient and Medieval Thoughted. N. Kretzmann (Ithaca ny 1982) 231-257 at 237-239 and Appendices B and C; Sylla Oxford Calculators 483-487.


For these theories see E. Sylla“Medieval Concepts of the Latitude of Forms: The Oxford Calculators,” Archives d’histoire doctrinale et littéraire du moyen âge 40 (1973) 223-283at 230-238 and of course the pertinent section of A. Maier Zwei Grundprobleme der scholastischen Naturphilosophie (3rd ed. Rome 1968).


See Sylla“Averroes and Fourteenth-Century Theories of Alteration” 148-154 169-172.


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