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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’). -
Montague Meets Markov: Deep Semantics with Probabilistic Logical Form
Montague Meets Markov: Deep Semantics with Probabilistic Logical Form Islam Beltagyx, Cuong Chaux, Gemma Boleday, Dan Garrettex, Katrin Erky, Raymond Mooneyx xDepartment of Computer Science yDepartment of Linguistics The University of Texas at Austin Austin, Texas 78712 x beltagy,ckcuong,dhg,mooney @cs.utexas.edu [email protected],[email protected] g Abstract # » # » sim(hamster, gerbil) = w We combine logical and distributional rep- resentations of natural language meaning by gerbil( transforming distributional similarity judg- hamster( ments into weighted inference rules using Markov Logic Networks (MLNs). We show x hamster(x) gerbil(x) f(w) that this framework supports both judg- 8 ! | ing sentence similarity and recognizing tex- tual entailment by appropriately adapting the Figure 1: Turning distributional similarity into a MLN implementation of logical connectives. weighted inference rule We also show that distributional phrase simi- larity, used as textual inference rules created on the fly, improves its performance. els (Turney and Pantel, 2010) use contextual sim- ilarity to predict semantic similarity of words and 1 Introduction phrases (Landauer and Dumais, 1997; Mitchell and Tasks in natural language semantics are very diverse Lapata, 2010), and to model polysemy (Schutze,¨ and pose different requirements on the underlying 1998; Erk and Pado,´ 2008; Thater et al., 2010). formalism for representing meaning. Some tasks This suggests that distributional models and logic- require a detailed representation of the structure of based representations of natural language meaning complex sentences. Some tasks require the ability to are complementary in their strengths (Grefenstette recognize near-paraphrases or degrees of similarity and Sadrzadeh, 2011; Garrette et al., 2011), which between sentences. -
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 ................................................................................................. -
APA Newsletter on Philosophy and Computers, Vol. 14, No. 2
NEWSLETTER | The American Philosophical Association Philosophy and Computers SPRING 2015 VOLUME 14 | NUMBER 2 FROM THE GUEST EDITOR John P. Sullins NOTES FROM THE COMMUNITY ON PAT SUPPES ARTICLES Patrick Suppes Patrick Suppes Autobiography Luciano Floridi Singularitarians, AItheists, and Why the Problem with Artificial Intelligence is H.A.L. (Humanity At Large), not HAL Peter Boltuc First-Person Consciousness as Hardware D. E. Wittkower Social Media and the Organization Man Niklas Toivakainen The Moral Roots of Conceptual Confusion in Artificial Intelligence Research Xiaohong Wang, Jian Wang, Kun Zhao, and Chaolin Wang Increase or Decrease of Entropy: To Construct a More Universal Macroethics (A Discussion of Luciano Floridi’s The Ethics of Information) VOLUME 14 | NUMBER 2 SPRING 2015 © 2015 BY THE AMERICAN PHILOSOPHICAL ASSOCIATION ISSN 2155-9708 APA NEWSLETTER ON Philosophy and Computers JOHN P. SULLINS, GUEST EDITOR VOLUME 14 | NUMBER 2 | SPRING 2015 but here we wish to celebrate his accomplishments in the FROM THE GUEST EDITOR fields of philosophy and computing one last time. John P. Sullins To accomplish that goal I have compiled some interesting SONOMA STATE UNIVERSITY pieces from an autobiography that Pat wrote some years ago but that he added to a bit for an event held in his honor November 17, 2014, marked the end of an inspiring at Stanford. In this document he explains his motivations career. On that day Patrick Suppes died quietly at the and accomplishments in various fields of study that are age of ninety-two in his house on the Stanford Campus, of interest to our community. In that section you will see which had been his home both physically and intellectually just how ambitious Pat was in the world of computer since 1950. -
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. -
Operators in the Paradox of the Knower I
PATRICK GRIM OPERATORS IN THE PARADOX OF THE KNOWER I ABSTRACT. Predicates are term-to-sentence devices, and operators are sentence-to- sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modatities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom. A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities need not raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient to escape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense. Predicates are term-to-sentence devices: functions that take the terms of a language as input and render sentences (or open formulae) as output. Sentential operators or connectives, on the other hand, are sentence-to-sentence devices: they take sentences (or open formulae) as input and render sentences (or open formulae) as output. Such at least is the current wisdom. Quine's 'Nec' is intended as a predicate. The familiar '[2' of modal logic, in contrast, is an operator. 2 Another claim that appears as part of the current wisdom is this: that what Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic. -
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. -
Leibniz's Lingua Characteristica and Its Contemporary Counterparts
Anna Pietryga LEIBNIZ’S LINGUA CHARACTERISTICA AND ITS CONTEMPORARY COUNTERPARTS Originally published as ”Leibniza << lingua characteristica >> i jej współczesne odpowiedniki,” Studia Semiotyczne 27 (2010), 293–305. Translated by Lesław Kawalec. There is no need to introduce Gottfried Wilhelm Leibniz, a great philoso- pher, theologian, diplomat, creator (independently of Isaac Newton) of the infinitesimal calculus and founder of the Academy of Sciences in Berlin. He also planned the development of the so-called Lingua characteristica (the plan shared by other 17 th century scholars). Literally taken, the name of the language means a language of letters , a graphic language , also called a characteristica universalis . It was meant to be a way of expressing meanings, as modeled after methods used in arithmetic and geometry (Leibniz also mentions logicians) and having unusual properties. 1. Like mathematical methods, such as written multiplication, lingua characteristica is supposed to enable an assessment of the reasoning correctness on the basis of the notation alone, which would prevent disputes between followers of opposing ideas and thus eliminate such disputes at the outset. Agreement would be reached by means of performing calculations in public, as encouraged by the Latin motto: calculemus (Murawski 1994: 93, 97). 2. Lingua characteristica will shut the mouths of ignoramuses as in the new language it will be possible to write about and discuss those topics only that one understands; otherwise the mistake will be noticeable for everyone, the author included (Murawski 1994: 95). (The text fails to mention authors of utopian designs, but these have not yet been expressed in a magical language). 241 Leibniz’s lingua characteristica and its contemporary counterparts 3. -
Arabic Between Formalization and Computation
International Journal of Languages, Literature and Linguistics, Vol. 1, No. 1, March 2015 Arabic between Formalization and Computation Haytham El-Sayed model for semantic processing for Arabic and even no Abstract—This paper provides an attempt to apply a formal existing formal theory is capable to provide a complete and method (Montague grammar) to Arabic, as a pre-step towards consistent account of all phenomena involved in Arabic its computation. Since semantic representation has to be semantic processing. compositional on the level of semantic processing, formalization based on Montague grammar can be utilized as a helpful and This paper is an attempt to provide a syntactic-semantic practical technique for the semantic construction of Arabic in formalization of a fragment of Modern Standard Arabic Arabic understanding systems. As efforts of Arabic (MSA) as a pre-step towards its computation. I do so using syntactic-semantic formalization are very limited, I hope that Montague grammar (henceforth MG) as a formal method. this approach might be a further motivation to redirect research MG is a well-known mathematically motivated logical to modern formal interpretation techniques for developing an method that treats natural languages semantic and of its adequate model of semantic processing for Arabic. relation with syntax. In general, the syntactic component of Index Terms—Arabic NLP, formalization of Arabic, MG is formulated in terms of a categorial system. The Montague grammar, syntax-semantics connectivity. semantic component of