The Logic of Where and While in the 13Th and 14Th Centuries
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Peter Thomas Geach, 1916–2013
PETER GEACH Peter Thomas Geach 1916–2013 PETER GEACH was born on 29 March 1916 at 41, Royal Avenue, Chelsea. He was the son of George Hender Geach, a Cambridge graduate working in the Indian Educational Service (IES), who later taught philosophy at Lahore. George Geach was married to Eleonore Sgnonina, the daughter of a Polish civil engineer who had emigrated to England. The marriage was not a happy one: after a brief period in India Eleonore returned to England to give birth and never returned to her husband. Peter Geach’s first few years were spent in the house of his Polish grandparents in Cardiff, but at the age of four his father had him made the ward of a former nanny of his own, an elderly nonconformist lady named Miss Tarr. When Peter’s mother tried to visit him, Miss Tarr warned him that a dangerous mad woman was coming, so that he cowered away from her when she tried to embrace him. As she departed she threw a brick through a window, and from that point there was no further contact between mother and son. When he was eight years old he became a boarder at Llandaff Cathedral School. Soon afterwards his father was invalided out of the IES and took charge of his education. To the surprise of his Llandaff housemaster, Peter won a scholarship to Clifton College, Bristol. Geach père had learnt moral sciences at Trinity College Cambridge from Bertrand Russell and G. E. Moore, and he inducted his son into the delights of philosophy from an early age. -
Projectile Motion Acc
PHY1033C/HIS3931/IDH 3931 : Discovering Physics: The Universe and Humanity’s Place in It Fall 2016 Prof. Peter Hirschfeld, Physics Announcements • HW 1 due today; HW 2 posted, due Sept. 13 • Lab 1 today 2nd hour • Reading: Gregory Chs. 2,3 Wertheim (coursepack), Lindberg (coursepack) • HW/office hours 10:40 M,T, 11:45 W email/call to make appt. if these are bad Last time Improvements to Aristotle/Eudoxus Appolonius of Perga (~20 -190 BCE) : proposed: 1) eccentric orbits (planet goes in circle at const. speed, but Earth was off center) 2) epicycles (planet moves on own circle [epicycle] around a point that travels in another circle [deferent] around E. His model explained • variation in brightness of planets • changes in angular speed Ptolemy (AD 100 – c. 170): Almagest summarized ancient ideas about solar system. He himself proposed “equant point”: eccentric point about which planet moved with constant angular speed. Not true uniform circular motion, but explained data better. Ptolemaic universe (Equant point suppressed) • Note: this picture puts planets at a distance relative to Earth corresponding to our modern knowledge, but Ptolemaic system did not predict order of planets (or care!) • Exception: inner planets had to have orbits that kept them between Earth and Sun • Why epicycles? Not asked. Clicker quickies Q1: Ptolemy’s model explained retrograde motion of the planets. This means that A. Some planets moved clockwise while others moved counterclockwise along their orbits B. Some planets moved outside the plane of the ecliptic C. Some planets were observed to stop in the sky, move apparently backwards along their path, forward again D. -
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. -
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. -
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. -
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). -
William of Sherwood, Singular Propositions and the Hexagon of Opposition
William of Sherwood, Singular Propositions and the Hexagon of Opposition Yurii Khomskii∗ Institute of Logic, Language and Computation [email protected] February 15, 2011 Abstract In Aristotelian logic, the predominant view has always been that there are only two kinds of quantities: universal and particular. For this reason, philosophers have struggled with singular propositions (e.g., \Socrates is running"). One modern approach to this problem, as first proposed in 1955 by Tadeusz Cze_zowski, is to extend the traditional Square of Opposition to a Hexagon of Opposition. We note that the medieval author William of Sherwood developed a similar theory of singular propositions, much earlier than Cze_zowski, and that it is not impossible that the Hexagon itself could have been present in Sherwood's writings. 1 Introduction In traditional Aristotelian logic, the predominant view has always been that there are only two kinds of quantities: universal and particular. In accordance, the four proposition types which figure in the classical theory of syllogisms are the universal affirmative (\Every man is running"), universal negative (\No man is running"), particular affirmative (\Some man is running") and particular negative (\Some man is not running"). We will abbreviate these by UA; UN; PA and PN, respectively. When two propositions share both the subject term and the predicate, they are related to one another in one of the following ways: con- tradictory, contrary, subcontrary or subalternate. This doctrine has frequently been represented by the Square of Opposition, as in Figure 1 below. ∗The author is supported by a Mosaic grant (no: 017.004.066) by the Netherlands Organ- isation for Scientific Research (NWO). -
Aristotle's Theory of the Assertoric Syllogism
Aristotle’s Theory of the Assertoric Syllogism Stephen Read June 19, 2017 Abstract Although the theory of the assertoric syllogism was Aristotle’s great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is a conditional proposition deduced from a set of axioms. There is even unclarity about what the basis of syllogistic validity consists in. Returning to Aristotle’s text, and reading it in the light of commentary from late antiquity and the middle ages, we find a coherent and precise theory which shows all these claims to be based on a misunderstanding and misreading. 1 What is a Syllogism? Aristotle’s theory of the assertoric, or categorical, syllogism dominated much of logical theory for the succeeding two millenia. But as logical theory de- veloped, its connection with Aristotle because more tenuous, and doctrines and intentions were attributed to him which are not true to what he actually wrote. Looking at the text of the Analytics, we find a much more coherent theory than some more recent accounts would suggest.1 Robin Smith (2017, §3.2) rightly observes that the prevailing view of the syllogism in modern logic is of three subject-predicate propositions, two premises and a conclusion, whether or not the conclusion follows from the premises. -
What the Middle Ages Knew IV
Late Medieval Philosophy Piero Scaruffi Copyright 2018 http://www.scaruffi.com/know 1 What the Middle Ages knew • Before the Scholastics – The Bible is infallible, therefore there is no need for scientific investigation or for the laws of logic – Conflict between science and religion due to the Christian dogma that the Bible is the truth – 1.Dangerous to claim otherwise – 2.Pointless to search for additional truths – Tertullian (3rd c AD): curiosity no longer necessary because we know the meaning of the world and what is going to happen next ("Liber de Praescriptione Haereticorum") 2 What the Middle Ages knew • Before the Scholastics – Decline of scientific knowledge • Lactantius (4th c AD) ridicules the notion that the Earth could be a sphere ("Divinae Institutiones III De Falsa Sapientia Philosophorum") • Cosmas Indicopleustes' "Topographia Cristiana" (6th c AD): the Earth is a disc 3 What the Middle Ages knew • Before the Scholastics – Plato's creation by the demiurge in the Timaeus very similar to the biblical "Genesis" – Christian thinkers are raised by neoplatonists • Origen was a pupil of Ammonius Sacca (Plotinus' teacher) • Augustine studied Plotinus 4 What the Middle Ages knew • Preservation of classical knowledge – Boethius (6th c AD) translates part of Aristotle's "Organon" and his "Arithmetica" preserves knowledge of Greek mathematics – Cassiodorus (6th c AD) popularizes scientific studies among monks and formalizes education ("De Institutione Divinarum" and "De artibus ac disciplinis liberalium litterarum") with the division of disciplines into arts (grammar, rhetoric, dialectic) – and disiplines (arithmeitc,geometry, music, astronomy) – Isidore of Sevilla (7th c AD) preserves Graeco- Roman knowledge in "De Natura Rerum" and "Origines" 5 What the Middle Ages knew • Preservation of classical knowledge – Bede (8th c AD) compiles an encyclopedia, "De Natura Rerum" – St Peter's at Canterbury under Benedict Biscop (7th c AD) becomes a center of learning – Episcopal school of York: arithmetic, geometry, natural history, astronomy.