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The Logic of Where and While in the 13Th and 14Th Centuries
The Logic of Where and While in the 13th and 14th Centuries Sara L. Uckelman Department of Philosophy, Durham University Abstract Medieval analyses of molecular propositions include many non-truthfunctional con- nectives in addition to the standard modern binary connectives (conjunction, dis- junction, and conditional). Two types of non-truthfunctional molecular propositions considered by a number of 13th- and 14th-century authors are temporal and local propositions, which combine atomic propositions with ‘while’ and ‘where’. Despite modern interest in the historical roots of temporal and tense logic, medieval analy- ses of ‘while’ propositions are rarely discussed in modern literature, and analyses of ‘where’ propositions are almost completely overlooked. In this paper we introduce 13th- and 14th-century views on temporal and local propositions, and connect the medieval theories with modern temporal and spatial counterparts. Keywords: Jean Buridan, Lambert of Auxerre, local propositions, Roger Bacon, temporal propositions, Walter Burley, William of Ockham 1 Introduction Modern propositional logicians are familiar with three kinds of compound propositions: Conjunctions, disjunctions, and conditionals. Thirteenth-century logicians were more liberal, admitting variously five, six, seven, or more types of compound propositions. In the middle of the 13th century, Lambert of Auxerre 1 in his Logic identified six types of ‘hypothetical’ (i.e., compound, as opposed to atomic ‘categorical’, i.e., subject-predicate, propositions) propo- sitions: the three familiar ones, plus causal, local, and temporal propositions [17, 99]. Another mid-13th century treatise, Roger Bacon’s Art and Science of Logic¶ , lists these six and adds expletive propositions (those which use the connective ‘however’), and other ones not explicitly classified such as “Socrates 1 The identity of the author of this text is not known for certain. -
Jean Buridan Qui a Étudié Les Arts Libéraux S’Est Intéressé Aux Dis- Cussions Sur Le Modèle De L’Univers Et Sur La Théorie Du Mouvement D’Aristote
Jean Buridan qui a étudié les arts libéraux s’est intéressé aux dis- cussions sur le modèle de l’univers et sur la théorie du mouvement d’Aristote. Il a redécouvert et diffusé la théorie de l’impetus. Éla- borée à Alexandrie, cette théorie visait à combler une lacune de la théorie du mouvement d’Aristote. Jean Buridan 1295-1358 Jean Buridan Discussion du géocentrisme Si la terre reste toujours immobile au Jean Buridan est né à Béthune au Pas de centre du monde; ou non ... [et] si, en Calais, en 1295 et est mort vers 1358. supposant que la terre est en mouve- Il étudie à l’université de Paris où il est ment de rotation autour de son cen- un disciple de Guillaume d’Occam. Tra- tre et de ses propres pôles, tous les phé- ditionnellement, pour se préparer à une nomènes que nous observons peuvent carrière en philosophie, les aspirants étu- être sauvés? dient la théologie. Buridan choisit d’étu- dier les arts libéraux (voir encadré) plu- Peut-on, en considérant que la Terre est tôt que la théologie et il préserve son in- en rotation sur elle-même, expliquer dépendance en demeurant clerc séculier tous les phénomènes que nous obser- plutôt qu’en se joignant à un ordre reli- vons ? Buridan donne une série d’argu- gieux. ments en accord avec la rotation de la Buridan enseigne la philosophie à Pa- Terre et une autre série à l’encontre de ris et est élu recteur de Angleterre Calais Belgique cette hypothèse. Il écrit : Lille Allemagne l’Université en 1328 et en Béthune Il est vrai, sans aucun doute, que si la 1340. -
Philoponus on Topos
Philoponus on τόπος. Redefining Place in Late Antiquity D i s s e r t a t i o n zur Erlangung des akademischen Grades Doctor philosophiae (Dr. phil.) eingereicht an der Philosophischen Fakultät I der Humboldt-Universität zu Berlin und verteidigt am 25. October 2013 von Ioannis Papachristou Der Präsident der Humboldt-Universität zu Berlin Prof. Dr. Jan-Hendrik Olbertz Der Dekan der Philosophischen Fakultät I Prof. Michael Seadle, PhD Gutachter Erstgutachter: Prof. Dr. Christoph Helmig Zweitgutachter: Prof. Dr. Christian Wildberg The dissertation attempts to interpret afresh, on the one hand, the form, methodology and structure of Philoponus’ commentary on the Physics and, on the other hand, to study in depth his theory of place (topos). The book extends over five chapters and includes a preface, an epilogue and a bibliography. Philoponus attempts a double determination of place. He distinguishes between the place which is void, three-dimensional extension that is ontological different from bodies, and the concept of place that is filled by bodies. Philoponus wishes to redefine the relationship between place and body and he underlines the ontological difference that a bodiless extension should have from a bodily extension. The thesis also focuses on Philoponus’ critique of Aristotle’s definition of place and the Peripatetic tradition (Eudemus, Themistius) regarding the place of the heavens. The book concludes that, Philoponus’ strategy in the digressions of the commentary, but also in certain parts of his exegeses, can be seen in three stages: first, he repudiates the cogency of Aristotle’s and Themistius’ critique to the concept of local extension; second, he attacks the Aristotelian definition of place by showing its weaknesses and inconsistencies with the nature of things; and third, he establishes his own theory of place. -
375 A. Mark Smith A. Mark Smith's Lucidly Written Account of The
book reviews Early Science and Medicine 21 (2016) 375-377 375 A. Mark Smith From Sight to Light: The Passage from Ancient to Modern Optics (Chicago: University of Chicago Press, 2015), pp. 480, $45.00 (cloth), ISBN 978 02 261 7476 1. A. Mark Smith’s lucidly written account of the history of optics, from the an- cient world to the late seventeenth century, is comprehensive in scope and presents a radical break from the traditional narrative of the role medieval per- spectiva played in Johannes Kepler’s visual theory. Smith argues in a convinc- ing manner that while Kepler was clearly aware of perspectival sources, several elements of his thinking, and particularly his decision to accept the inverted retinal image as the principal means of sight, indicates a revolutionary turn away from the medieval tradition. This “Keplerian turn” had both analytic and epistemological elements, which Smith details at great length in his penulti- mate chapter. Smith characterizes his work as a “revamping” of David Lind- berg’s equally grand historical narrative Theories of Vision from Al-Kindi to Kepler, first published in 1976 (p. 4). In many ways this is an accurate assess- ment, barring Smith’s significant argumentative departure from the idea that Kepler relied on a firm grounding in perspectiva. Smith shifts his focus away from solely technical descriptions of optical theories, which can be found in Lindberg, and provides a much more inclusive history that treats the im- portance of psychological and theological texts in the development of perspec- tiva. Smith begins his narrative by exploring the earliest roots of perspectiva in the ancient sources, particularly Plato, Aristotle, Galen, Euclid, and Ptolemy. -
E D I T O R I a L
E D I T O R I A L “RETRO-PROGRESSING” As one browses through the history section of a library, one of the volumes that is likely to catch one’s attention is The Discoverers by Daniel Boorstin.1 It is an impressive, 700-page volume. Published in 1983, it chronicles in a semi-popular style selected aspects of man’s discoveries. Two chapters entitled “The Prison of Christian Dogma” and “A Flat Earth Returns” deal with the outlandish con- cept of an earth that is flat instead of spherical. Boorstin has impressive academic credentials from Harvard and Yale, and has held prestigious positions such as the Librarian of Congress, Director of the National Museum of History and Tech- nology, and Senior Historian of the Smithsonian Institution. In The Discoverers he reflects the popular view that the ancient Greeks, including Aristotle and Plato, believed Earth to be a sphere; however, after the rise of Christianity a period of “scholarly amnesia” set in which lasted from around 300 to 1300 A.D. During this time, according to Boorstin, “Christian faith and dogma replaced the useful [spherical] image of the world that had been so slowly, so painfully, and so scrupulously drawn by ancient geographers.” The “spherical” view was replaced by the concept of a flat earth, which Boorstin characterizes as “pious caricatures.”2 Boorstin bolsters his case by mentioning a couple of minor writers — Lactantius and Cosmas — who believed in a flat earth and lived during this “dark age.” He also implicates the powerful authority of St. Augustine of Hippo (354-430), who “heartily agreed” that antipodes “could not exist.”3 Antipodes represented lands on the opposite side of a spherical earth where trees and men, if present, would be upside down, with their feet above their heads; hence, the “antipodes” (opposite-feet) designation. -
Buridan-Editions.Pdf
Buridan Logical and Metaphysical Works: A Bibliography https://www.historyoflogic.com/biblio/buridan-editions.htm History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: [email protected] Buridan: Editions, Translations and Studies on the Manuscript Tradition INTRODUCTION I give an updated list of the published and unpublished logical and metaphysical works of Buridan, and a bibliography of the editions and translations appeared after 2000. A complete list of Buridan's works and manuscripts can be found in the ' Introduction' by Benoît Patar to his edition of "La Physique de Bruges de Buridan et le Traité du Ciel d'Albert de Saxe. Étude critique, textuelle et doctrinale" Vol. I, Longueil, Les Presses Philosophiques, 2001 (2 volumes), pp. 33* - 75*. SUMMARY LIST OF BURIDAN'S LATIN WORKS ON LOGIC AND METAPHYSICS Logical Works: N. B. The treatises known as Artes Veterem and commented by Buridan were the Isagoge by Porphyry and the Categoriae (Predicamenta) and the Peri Hermeneias by Aristotle. 1. Expositio Super Artes Veterem 2. Quaestiones Super Artes Veterem 3. Expositio in duos libros Analyticorum priorum Aristotelis 4. Quaestiones in duos libros Analyticorum priorum Aristotelis 5. Expositio in duos libros Analyticorum posteriorum Aristotelis 6. Quaestiones in duos libros Analyticorum posteriorum Aristotelis 7. Quaestiones in octo libros Topicorum Aristotelis 8. Quaestiones in librum 'de sophisticis Elenchis' Aristotelis Summulae de dialectica, commentary of the Summulae logicales by Peter of Spain, composed by the following treatises: 1. De propositionibus 2. De praedicabilibus 3. In praedicamenta 4. De suppositionibus 5. De syllogismis 6. De locis dialecticis 1 di 10 22/09/2016 17:30 Buridan Logical and Metaphysical Works: A Bibliography https://www.historyoflogic.com/biblio/buridan-editions.htm 7. -
Sauterdivineansamplepages (Pdf)
The Decline of Space: Euclid between the Ancient and Medieval Worlds Michael J. Sauter División de Historia Centro de Investigación y Docencia Económicas, A.C. Carretera México-Toluca 3655 Colonia Lomas de Santa Fe 01210 México, Distrito Federal Tel: (+52) 55-5727-9800 x2150 Table of Contents List of Illustrations ............................................................................................................. iv Acknowledgments .............................................................................................................. v Preface ............................................................................................................................... vi Introduction: The divine and the decline of space .............................................................. 1 Chapter 1: Divinus absconditus .......................................................................................... 2 Chapter 2: The problem of continuity ............................................................................... 19 Chapter 3: The space of hierarchy .................................................................................... 21 Chapter 4: Euclid in Purgatory ......................................................................................... 40 Chapter 5: The ladder of reason ........................................................................................ 63 Chapter 6: The harvest of homogeneity ............................................................................ 98 Conclusion: The -
Aquinas and Buridan on the Possibility of Scientific Knowledge
Zita Veronika Tóth Aquinas and Buridan on the Possibility of Scientific Knowledge 1. Th is paper examines a specifi c but basic problem of Aristotelian natural philosophy which arises if we consider the following three propositions, stated as necessary requirements towards knowledge in the proper sense (quoted now from Aristotle): I. Th e soul never thinks without an image.1 II. Th e object of knowledge is of necessity and of the universal.2 III. We understand something when we know its causes.3 In the following, I deal only with the fi rst two, that is, with the possible reconciliation of the empiricist and the universalistic claim. After outlining the solution of Th omas Aquinas and some criticism of it in the 14th century, I shall call attention to John Buridan, who – despite his apparent Nominalism –, in certain respects, turns out to be surprisingly Th omistic. 2. Aquinas accepts these two claims, and regards them as preconditions of all scien- tifi c knowledge. First, as he writes in his “De veritate”, “there is nothing in the intel- lect, which was not prior in the senses”4 (this empiricist slogan, at least since Duns Scotus, has been often – and incorrectly – attributed to Aristotle). Apart from this and similar statements, as e.g. “the human intellect is at fi rst like a clean tablet on which nothing is written”,5 his empiricism can be observed at several points: he ar- gues against innate knowledge throughout an article in the Summa,6 the concept of 1 On the Soul 431a18. All Aristotle translations are from Barnes, Jonathan, ed., Th e Complete Works of Aristotle, the Revised Oxford Translation, 2 vols (Princeton: Princeton University Press, 1995) 2 Posterior Analytics 71b15, Nicomachean Ethics 1139b23 3 Cf. -
Intermediary Structural Analysis Force
Intermediary Structural Analysis Force Victor E. Saouma [email protected] University of Colorado, Boulder Fall 2017 Victor E. Saouma; CVEN 4525/5525; Univ. of Colorado Introduction 1/12 Table of ContentsI 1 What is Force Aristotelian Medieval Newtonian Victor E. Saouma; CVEN 4525/5525; Univ. of Colorado Introduction 2/12 What is Force What is Force? Force is in general defined as the cause of acceleration. Since acceleration is observable, its cause must be something real. Thus, force is real. However, some physicists and philosophers of science have, pointed out that force does not exist in reality. Broadly speaking, we can distinguish two movements: Aristotelian (pre 17th century) Newtonian (17th century onward) may possibly add one “Einstenian”. Excellent reference Concept of Force by M. Jammer. Victor E. Saouma; CVEN 4525/5525; Univ. of Colorado Introduction 3/12 What is Force Aristotelian AristotelianI Aristotle (384 BC-322 BC), pupil of Plato, tutor of Alexander the Great, writings cover physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theater, music, rhetoric, linguistics, politics and government and constitute the first comprehensive system of Western philosophy. Rather than assigning a “divine” explanation of nature, through observation he sought to discover the principles and causes of (and not merely to describe) and then developed systematic set of ideas by categorizing things: most famously believed that earth was made up of four main elements: earth, air, water, and fire. Likewise, he classified motion as either Natural associated with celestial motion (circular), or terrestial (rectilinear). Violent: Force responsible for motion had to be in constant physical contact with the moved body. -
Emotions in Medieval Thought
c Peter King, forthcoming in the Oxford Handbook on Emotion. EMOTIONS IN MEDIEVAL THOUGHT No single theory of the emotions dominates the whole of the Middle Ages. Instead, there are several competing accounts, and differences of opin- ion — sometimes quite dramatic — within each account. Yet there is consensus on the scope and nature of a theory of the emotions, as well as on its place in affective psychology generally. For most medieval thinkers, emotions are at once cognitively penetrable and somatic, which is to say that emotions are influenced by and vary with changes in thought and belief, and that they are also bound up, perhaps essentially, with their physiological manifesta- tions. This ‘mixed’ conception of emotions was broad enough to anchor me- dieval disagreements over details, yet rich enough to distinguish it from other parts of psychology and medicine. In particular, two kinds of phenomena, thought to be purely physiological, were not considered emotions even on this broad conception. First, what we now classify as drives or urges, for in- stance hunger and sexual arousal, were thought in the Middle Ages to be at best ‘pre-emotions’ (propassiones): mere biological motivations for action, not having any intrinsic cognitive object. Second, moods were likewise thought to be non-objectual somatic states, completely explicable as an imbalance of the bodily humours. Depression (melancholia), for example, is the pathological condition of having an excess of black bile. Medieval theories of emotions, therefore, concentrate on paradigm cases that fall under the broad concep- tion: delight, anger, distress, fear, and the like. The enterprise of constructing an adequate philosophical theory of the emotions in the Middle Ages had its counterpart in a large body of practical know-how. -
Avicenna's Theory of Minima Naturalia Jon Mcginnis University of Missouri-St
University of Missouri, St. Louis IRL @ UMSL Philosophy Faculty Works Philosophy 1-2015 A Small Discovery: Avicenna's Theory of Minima Naturalia Jon McGinnis University of Missouri-St. Louis, [email protected] Follow this and additional works at: http://irl.umsl.edu/philosophy-faculty Part of the Philosophy Commons Recommended Citation McGinnis, J. "A Small Discovery: Avicenna’s Theory of Minima Naturalia." Journal of the History of Philosophy, vol. 53 no. 1, 2015, pp. 1-24. Project MUSE, doi:10.1353/hph.2015.0002 http://irl.umsl.edu/philosophy-faculty/1 This Article is brought to you for free and open access by the Philosophy at IRL @ UMSL. It has been accepted for inclusion in Philosophy Faculty Works by an authorized administrator of IRL @ UMSL. For more information, please contact [email protected]. A Small Discovery: Avicenna’s Theory of Minima Naturalia Jon McGinnis Journal of the History of Philosophy, Volume 53, Number 1, January 2015, pp. 1-24 (Article) Published by Johns Hopkins University Press DOI: https://doi.org/10.1353/hph.2015.0002 For additional information about this article https://muse.jhu.edu/article/566924 Access provided by Missouri @ St Louis, Univ of (17 Feb 2017 19:06 GMT) A Small Discovery: Avicenna’s Theory of Minima Naturalia JON MCGINNIS* ABSTRACT There has been a long-held misconception among historians of philosophy and science that apart from brief comments in Aristotle and Averroes, the theory of minima naturalia had to await Latin Schoolmen for its full articulation. Recently scholars have shown that far from sporadic comments on minima naturalia, Averroes in fact had a fully developed and well-integrated theory of them. -
Jean Buridan's Theory of Individuation
c Peter King, in Individuation and Scholasticism (SUNY 1994), 397–430 BURIDAN’S THEORY OF INDIVIDUATION* 1. Introduction URIDAN holds that no principle or cause accounts for the individuality of the individual, or at least no principle or B cause other than the very individual itself, and thus there is no ‘metaphysical’ problem of individuation at all—individuality, unlike gen- erality, is primitive and needs no explanation. He supports this view in two ways. First, he argues that there are no nonindividual entities, whether existing in their own right or as metaphysical constituents either of things or in things, and hence that no real principle or cause of individuality (other than the individual itself) is required. Second, he offers a ‘semantic’ inter- pretation of what appear to be metaphysical difficulties about individuality by recasting the issues in the formal mode, as issues within semantics, such as how a referring expression can pick out a single individual. Yet although there is no ‘metaphysical’ problem of individuation, Buridan discusses two associated problems at some length: the identity of individuals over time and the discernibility of individuals. The discussion will proceed as follows. In §2, Buridan’s semantic frame- work, the idiom in which he couches his philosophical analyses, will be * References to Buridan are taken from a variety of his works (with abbreviations listed): Questions on Aristotle’s “Categories” (QC); Questions on Aristotle’s “Physics” (QSP); Questions on Aristotle’s “De caelo et mundo” (QCM); Questions on Aristotle’s “De anima” (QA); Questions on Aristotle’s “Metaphysics” (QM); Treatise on Supposi- tion (TS); Sophismata; Treatise on Consequences (TC).