Supposition Theory S 1229 Elements in Suhrawardı¯’S Writings
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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. -
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. -
Existence and Reference in Medieval Logic
GYULA KLIMA EXISTENCE AND REFERENCE IN MEDIEVAL LOGIC 1. Introduction: Existential Assumptions in Modern vs. Medieval Logic “The expression ‘free logic’ is an abbreviation for the phrase ‘free of existence assumptions with respect to its terms, general and singular’.”1 Classical quantification theory is not a free logic in this sense, as its standard formulations commonly assume that every singular term in every model is assigned a referent, an element of the universe of discourse. Indeed, since singular terms include not only singular constants, but also variables2, standard quantification theory may be regarded as involving even the assumption of the existence of the values of its variables, in accordance with Quine’s famous dictum: “to be is to be the value of a variable”.3 But according to some modern interpretations of Aristotelian syllogistic, Aristotle’s theory would involve an even stronger existential assumption, not shared by quantification theory, namely, the assumption of the non-emptiness of common terms.4 Indeed, the need for such an assumption seems to be supported not only by a number of syllogistic forms, which without this assumption appear to be invalid, but also by the doctrine of Aristotle’s De Interpretatione concerning the logical relationships among categorical propositions, commonly summarized in the Square of Opposition. For example, Aristotle’s theory states that universal affirmative propositions imply particular affirmative propositions. But if we formalize such propositions in quantification theory, we get formulae between which the corresponding implication does not hold. So, evidently, there is some discrepancy between the ways Aristotle and quantification theory interpret these categoricals. -
The History of Logic
c Peter King & Stewart Shapiro, The Oxford Companion to Philosophy (OUP 1995), 496–500. THE HISTORY OF LOGIC Aristotle was the first thinker to devise a logical system. He drew upon the emphasis on universal definition found in Socrates, the use of reductio ad absurdum in Zeno of Elea, claims about propositional structure and nega- tion in Parmenides and Plato, and the body of argumentative techniques found in legal reasoning and geometrical proof. Yet the theory presented in Aristotle’s five treatises known as the Organon—the Categories, the De interpretatione, the Prior Analytics, the Posterior Analytics, and the Sophistical Refutations—goes far beyond any of these. Aristotle holds that a proposition is a complex involving two terms, a subject and a predicate, each of which is represented grammatically with a noun. The logical form of a proposition is determined by its quantity (uni- versal or particular) and by its quality (affirmative or negative). Aristotle investigates the relation between two propositions containing the same terms in his theories of opposition and conversion. The former describes relations of contradictoriness and contrariety, the latter equipollences and entailments. The analysis of logical form, opposition, and conversion are combined in syllogistic, Aristotle’s greatest invention in logic. A syllogism consists of three propositions. The first two, the premisses, share exactly one term, and they logically entail the third proposition, the conclusion, which contains the two non-shared terms of the premisses. The term common to the two premisses may occur as subject in one and predicate in the other (called the ‘first figure’), predicate in both (‘second figure’), or subject in both (‘third figure’). -
Denoting Concepts, Reference, and the Logic of Names, Classes As As Many, Groups, and Plurals
Denoting Concepts, Reference, and the Logic of Names, Classes as as Many, Groups, and Plurals Nino B. Cocchiarella Abstract Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his sub- sequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter complex as well as simple common names. Names, proper or com- mon, and simple or complex, occur as parts of quanti…er phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capaci- ties that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quanti…er phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’stheory, there is no empty class as many. -
Philosophy May 20, 2013
Outline of Philosophy May 20, 2013 Contents SOCI>Philosophy .............................................................................................................................................................. 3 SOCI>Philosophy>Aesthetics ....................................................................................................................................... 3 SOCI>Philosophy>Aesthetics>Beauty .................................................................................................................... 4 SOCI>Philosophy>Aesthetics>Theory .................................................................................................................... 4 SOCI>Philosophy>Epistemology ................................................................................................................................. 5 SOCI>Philosophy>Epistemology>Possibility ......................................................................................................... 6 SOCI>Philosophy>Epistemology>World ................................................................................................................ 6 SOCI>Philosophy>Epistemology>Object Properties .............................................................................................. 6 SOCI>Philosophy>Epistemology>System Properties ............................................................................................. 6 SOCI>Philosophy>Epistemology>Representation ................................................................................................. -
Handbook-Of-Semiotics.Pdf
Page i Handbook of Semiotics Page ii Advances in Semiotics THOMAS A. SEBEOK, GENERAL EDITOR Page iii Handbook of Semiotics Winfried Nöth Indiana University Press Bloomington and Indianapolis Page iv First Paperback Edition 1995 This Englishlanguage edition is the enlarged and completely revised version of a work by Winfried Nöth originally published as Handbuch der Semiotik in 1985 by J. B. Metzlersche Verlagsbuchhandlung, Stuttgart. ©1990 by Winfried Nöth All rights reserved No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage and retrieval system, without permission in writing from the publisher. The Association of American University Presses' Resolution on Permissions constitutes the only exception to this prohibition. Manufactured in the United States of America Library of Congress CataloginginPublication Data Nöth, Winfried. [Handbuch der Semiotik. English] Handbook of semiotics / Winfried Nöth. p. cm.—(Advances in semiotics) Enlarged translation of: Handbuch der Semiotik. Bibliography: p. Includes indexes. ISBN 0253341205 1. Semiotics—handbooks, manuals, etc. 2. Communication —Handbooks, manuals, etc. I. Title. II. Series. P99.N6513 1990 302.2—dc20 8945199 ISBN 0253209595 (pbk.) CIP 4 5 6 00 99 98 Page v CONTENTS Preface ix Introduction 3 I. History and Classics of Modern Semiotics History of Semiotics 11 Peirce 39 Morris 48 Saussure 56 Hjelmslev 64 Jakobson 74 II. Sign and Meaning Sign 79 Meaning, Sense, and Reference 92 Semantics and Semiotics 103 Typology of Signs: Sign, Signal, Index 107 Symbol 115 Icon and Iconicity 121 Metaphor 128 Information 134 Page vi III. -
In Ockham's Theory of Supposition
The Role of ‘Denotatur’ in Ockham’s Theory of Supposition Catarina Dutilh Novaes University of Groningen Abstract In the scholarship on medieval logic and semantics of the last decades, Ockham’s the- ory of supposition is probably the most extensively studied version of such theories; yet, it seems that we still do not fully understand all its intricacies. In this paper, I focus on a phrase that occurs countless times throughout Ockham’s writings, but in particu- lar in the sections dedicated to supposition in the Summa logicae: the phrase ‘denotatur’. I claim that an adequate understanding of the role of the concept of denotatur within Ockham’s supposition theory shall yield a deeper understanding of the theory as a whole. Here, I first examine a few uses of the term ‘denotatur’ and its variants by other authors. I then turn to Ockham: first I briefly mention some uses of the term in contexts other than his theory of supposition. Following that, I focus on his supposition theory, in particular on how ‘denotatur’ allows him to deal with two crucial puzzles, namely the supposition of empty terms and the supposition of terms in false affirmative proposi- tions. The treatment of these two puzzles suggests that Ockham’s theory of supposition must be understood as a theory chiefly intended for the generation of the meanings of propositions. Keywords Ockham, supposition theory, denotatur, empty terms, affirmative false propositions 1. Introduction Ockham’s theory of supposition is probably still the most extensively studied of such medieval theories. Interest in Ockham’s theory in particular can be traced back to the pioneering works of E.A. -
Challenges and Opportunities from the Perspectives of Contemporary Philosophy and Religion
Cultural Heritage and Contemporary Change Series IV, Western European Philosophical Studies, Volume 12 Re-Learning to be Human in Global Times: Challenges and Opportunities from the Perspectives of Contemporary Philosophy and Religion Edited by Brigitte Buchhammer The Council for Research in Values and Philosophy Copyright © 2018 by The Council for Research in Values and Philosophy Gibbons Hall B-20 620 Michigan Avenue, NE Washington, D.C. 20064 All rights reserved Printed in the United States of America Library of Congress Cataloging-in-Publication Names: Buchhammer, Brigitte, editor. Title: Re-learning to be human in global times : challenges and opportunities from the perspectives of contemporary philosophy and religion / edited by Brigitte Buchhammer. Description: first [edition]. | Washington DC : Council for Research in Values and Philosophy, 2018. | Series: Cultural heritage and contemporary change. Series IV, Western European philosophical studies ; Volume 12 | Includes bibliographical references and index. Identifiers: LCCN 2018010133 | ISBN 9781565183339 (pbk. : alk. paper) Subjects: LCSH: Philosophical anthropology. | Humanism. | Persons. | Religion and philosophy. | Globalization. Classification: LCC BD450 .R346 2018 | DDC 128--dc23 LC record available at https://lccn.loc.gov/2018010133 Stephen O’Connor, BA (Hons.), Ph.D.: Proofreading Michael Stork: Copy editing, formatting and indexing Ε-mail: [email protected] http://independent.academia.edu/MichaelStork Table of Contents Foreword v Herta Nagl-Docekal Preface vii Kurt Appel Introduction 1 Brigitte Buchhammer 1. Biblical Traces of the Guest 5 Kurt Appel 2. The Search for Lost Intimacy: Georges Bataille on Religion as 13 Immanent Human Experience Thomas M. Schmidt 3. Transformations of Doctrine as Cases of Mutual Learning between 25 Religions and Cultures: Schleiermacher’s Proposal for Translating Christology in Modernity Maureen Junker-Kenny 4. -
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. -
History of Renaissance and Modern Logic from 1400 to 1850
History of Renaissance and Modern Logic from 1400 to 1850 https://www.historyoflogic.com/logic-modern.htm History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: [email protected] History of Renaissance and Modern Logic from 1400 to 1850 INTRODUCTION: LOGIC IN CONTINENTAL EUROPE "At the end of the fourteenth century there were roughly three categories of work available to those studying logic. The first category is that of commentaries on Aristotle's 'Organon'. The most comprehensive of these focussed either on the books of the Logica Vetus, which included Porphyry's Isagoge along with the Categories and De Interpretatione; or on the books of the Logica Nova, the remaining works of the 'Organon' which had become known to the West only during the twelfth century. In addition there were, of course, numerous commentaries on individual books of the 'Organon'. The second category is that of works on non-Aristotelian topics. These include the so-called Parva logicalia, or treatises on supposition, relative terms, ampliation, appellation, restriction and distribution. To these could be added tracts on exponibles and on syncategorematic terms. Peter of Spain is now the best-known author of parva logicalia, but such authors as Thomas Maulvelt and Marsilius of Inghen were almost as influential in the late fourteenth and fifteenth centuries. Another group of works belonging to the second category consists of the so-called 'tracts of the moderns', namely treatises on consequences, obligations and insolubles. A third group includes treatises on sophisms, on the composite and divided senses, and on proofs of terms, especially the well-known Speculum puerorum by Richard Billingham.