An Introduction to Late Mediaeval Logic and Semantic Theory
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Aristotle's Assertoric Syllogistic and Modern Relevance Logic*
Aristotle’s assertoric syllogistic and modern relevance logic* Abstract: This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic. Keywords: Aristotle, Syllogism, Relevance Logic, History of Logic, Logic, Relevance 1. -
Bibliography on Medieval Logic: General Works a - K
Bibliography on Medieval Logic: General Works A - K https://www.historyoflogic.com/biblio/logic-medieval-biblio.htm History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: [email protected] Selected Bibliography on Medieval Logic: General Studies. (First Part: A - K) BIBLIOGRAPHY 1. Amerini, Fabrizio. 2000. "La Dottrina Della Significatio Di Francesco Da Prato O.P. (Xiv Secolo). Una Critica Tomista a Guglielmo Di Ockham." Documenti e Studi sulla Tradizione Filosofica Medievale no. XI:375-408. 2. Angelelli, Ignacio. 1993. "Augustinus Triumphus' Alleged Destructio of the Porphyrian Tree." In Argumentationstheorie. Scholastische Forschungen Zu Den Logischen Und Semantischen Regeln Korrekten Folgerns, edited by Jacobi, Klaus, 483-489. Leiden: Brill. 3. Bertagna, Mario. 2000. "La Dottrina Delle Conseguenze Nella "Logica" Di Pietro Da Mantova." Documenti e Studi sulla Tradizione Filosofica Medievale no. 11:459-496. 4. Beuchot, Mauricio. 1979. "La Filosofia Del Lenguaje De Pedro Hispano." Revista de Filosofia (Mexico) no. 12:215-230. 5. Boh, Ivan. 1964. "An Examination of Some Proofs in Burleigh's Propositional Logic." New Scholasticism no. 38:44-60. 6. ———. 1984. "Propositional Attitudes in the Logic of Walter Burley and William Ockham." Franciscan Studies:31-59. 7. ———. 1991. "Bradwardine's (?) Critique of Ockham's Modal Logic." In Historia Philosophiae Medii Aevi. Studien Zur Geschichte Der Philosophie Des Mittelalters. Festschrift Für Kurt Flasch Zu Seinem 60. Geburtstag. (Vol. I), edited by Mojsisch, Burkhard and Pluta, Olaf, 55-70. Amsterdam, Philadelphia: B. R. Grüner. 8. Braakhuis, Henk Antonius. 1977. "The Views of William of Sherwood on Some Semantical Topics and Their Relation to Those of Roger Bacon." Vivarium no. -
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 Philosophical and Historical Roots of Evolutionary Tree Diagrams
Evo Edu Outreach (2011) 4:515–538 DOI 10.1007/s12052-011-0355-0 HISTORYAND PHILOSOPHY Depicting the Tree of Life: the Philosophical and Historical Roots of Evolutionary Tree Diagrams Nathalie Gontier Published online: 19 August 2011 # Springer Science+Business Media, LLC 2011 Abstract It is a popularly held view that Darwin was the were the result of this blend would, from the nineteenth first author to draw a phylogenetic tree diagram. However, century onward, also include the element of time. The as is the case with most popular beliefs, this one also does recognition of time would eventually lead to the recognition not hold true. Firstly, Darwin never called his diagram of of evolution as a fact of nature, and subsequently, tree common descent a tree. Secondly, even before Darwin, tree iconographies would come to represent exclusively the diagrams were used by a variety of philosophical, religious, evolutionary descent of species. and secular scholars to depict phenomena such as “logical relationships,”“affiliations,”“genealogical descent,”“af- Keywords Species classification . Evolutionary finity,” and “historical relatedness” between the elements iconography. Tree of life . Networks . Diagram . Phylogeny. portrayed on the tree. Moreover, historically, tree diagrams Genealogy. Pedigree . Stammbaum . Affinity. Natural themselves can be grouped into a larger class of diagrams selection that were drawn to depict natural and/or divine order in the world. In this paper, we trace the historical roots and cultural meanings of these tree diagrams. It will be Introduction demonstrated that tree diagrams as we know them are the outgrowth of ancient philosophical attempts to find the In this paper, we focus on the “why” of tree iconography. -
John Duns Scotus's Metaphysics of Goodness
University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 11-16-2015 John Duns Scotus’s Metaphysics of Goodness: Adventures in 13th-Century Metaethics Jeffrey W. Steele University of South Florida, [email protected] Follow this and additional works at: http://scholarcommons.usf.edu/etd Part of the Medieval History Commons, Philosophy Commons, and the Religious Thought, Theology and Philosophy of Religion Commons Scholar Commons Citation Steele, Jeffrey W., "John Duns Scotus’s Metaphysics of Goodness: Adventures in 13th-Century Metaethics" (2015). Graduate Theses and Dissertations. http://scholarcommons.usf.edu/etd/6029 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. John Duns Scotus’s Metaphysics of Goodness: Adventures in 13 th -Century Metaethics by Jeffrey Steele A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Philosophy College of Arts and Sciences University of South Florida Major Professor: Thomas Williams, Ph.D. Roger Ariew, Ph.D. Colin Heydt, Ph.D. Joanne Waugh, Ph.D Date of Approval: November 12, 2015 Keywords: Medieval Philosophy, Transcendentals, Being, Aquinas Copyright © 2015, Jeffrey Steele DEDICATION To the wife of my youth, who with patience and long-suffering endured much so that I might gain a little knowledge. And to God, fons de bonitatis . She encouraged me; he sustained me. Both have blessed me. “O taste and see that the LORD is good; How blessed is the man who takes refuge in Him!!” --Psalm 34:8 “You are the boundless good, communicating your rays of goodness so generously, and as the most lovable being of all, every single being in its own way returns to you as its ultimate end.” –John Duns Scotus, De Primo Principio Soli Deo Gloria . -
The Aristotelian Curriculum in Arabic and Hebrew
1 The Aristotelian Curriculum (Excluding Mathematics) In Arabic and Hebrew (occasionally also Greek, Syriac, Persian, Latin) Handout for “Aristotle in the Middle Ages,” James Robinson, U. Chicago, Winter 2013 General background: Christina d’Ascona, “Greek Sources in Arabic and Islamic Philosophy,” Stanford Encyc. of Philosophy Online: http://plato.stanford.edu/entries/arabic-islamic-greek/ M. Zonta, “The Influence of Arabic and Islamic Philosophy on Judaic Thought,” Stanford Encyc. of Philosophy: http://plato.stanford.edu/entries/arabic-islamic-judaic/ Dag Hasse, “The Influence of Arabic and Islamic Philosophy on the Latin West,” Stanford Encyc. of Philosophy: http://plato.stanford.edu/entries/arabic-islamic-influence/ Tony Street, “Arabic and Islamic Philosophy of Language and Logic,” Stanford Encyc. of Philosophy: http://plato.stanford.edu/entries/arabic-islamic-language/ J. McGinnis, “Arabic and Islamic Natural Philosophy and Natural Science,” Stanford Encyc. of Philosophy: http://plato.stanford.edu/entries/arabic-islamic-natural/ Alfred Ivry, “Arabic and Islamic Psychology and Philosophy of Mind,” Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/arabic-islamic-mind/ Amos Bertolacci, “Arabic and Islamic Metaphysics,” Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/arabic-islamic-metaphysics/ Useful Resources: Arist. semitico-latinus: http://www.brill.com/publications/aristoteles-semitico-latinus Online dictionary of Arabic philosophical terms: http://www.arabic-philosophy.com/dict Hans Daiber -
The Peripatetic Program in Categorical Logic: Leibniz on Propositional Terms
THE REVIEW OF SYMBOLIC LOGIC, Page 1 of 65 THE PERIPATETIC PROGRAM IN CATEGORICAL LOGIC: LEIBNIZ ON PROPOSITIONAL TERMS MARKO MALINK Department of Philosophy, New York University and ANUBAV VASUDEVAN Department of Philosophy, University of Chicago Abstract. Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such as reductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titled Specimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule of reductio ad absurdum in a purely categor- ical calculus in which every proposition is of the form AisB. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule of reductio ad absurdum,but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic ¬ known as RMI→ . From its beginnings in antiquity up until the late 19th century, the study of formal logic was shaped by two distinct approaches to the subject. The first approach was primarily concerned with simple propositions expressing predicative relations between terms. -
Logic: a Brief Introduction Ronald L
Logic: A Brief Introduction Ronald L. Hall, Stetson University Chapter 1 - Basic Training 1.1 Introduction In this logic course, we are going to be relying on some “mental muscles” that may need some toning up. But don‟t worry, we recognize that it may take some time to get these muscles strengthened; so we are going to take it slow before we get up and start running. Are you ready? Well, let‟s begin our basic training with some preliminary conceptual stretching. Certainly all of us recognize that activities like riding a bicycle, balancing a checkbook, or playing chess are acquired skills. Further, we know that in order to acquire these skills, training and study are important, but practice is essential. It is also commonplace to acknowledge that these acquired skills can be exercised at various levels of mastery. Those who have studied the piano and who have practiced diligently certainly are able to play better than those of us who have not. The plain fact is that some people play the piano better than others. And the same is true of riding a bicycle, playing chess, and so forth. Now let‟s stretch this agreement about such skills a little further. Consider the activity of thinking. Obviously, we all think, but it is seldom that we think about thinking. So let's try to stretch our thinking to include thinking about thinking. As we do, and if this does not cause too much of a cramp, we will see that thinking is indeed an activity that has much in common with other acquired skills. -
Thomas Aquinas & John Duns Scotus
THOMAS AQUINAS AND JOHN DUNS SCOTUS: NATURAL THEOLOGY IN THE HIGH MIDDLE AGES Continuum Studies in Philosophy Series Editor: James Fieser, University of Tennessee at Martin, USA Continuum Studies in Philosophy is a major monograph series from Continuum. The series features first-class scholarly research monographs across the whole field of philosophy. Each work makes a major contribution to the field of philosophical research. Aesthetic in Kant, James Kirwan Analytic Philosophy: The History of an Illusion, Aaron Preston Aquinas and the Ship of Theseus, Christopher Brown Augustine and Roman Virtue, Brian Harding The Challenge of Relativism, Patrick Phillips Demands of Taste in Kant’s Aesthetics, Brent Kalar Descartes and the Metaphysics of Human Nature, Justin Skirry Descartes’ Theory of Ideas, David Clemenson Dialectic of Romanticism, Peter Murphy and David Roberts Hegel and the Analytic Tradition, edited by Angelica Nuzzo Hegel’s Philosophy of Language, Jim Vernon Hegel’s Philosophy of Right, David James Hegel’s Theory of Recognition, Sybol Cook Anderson The History of Intentionality, Ryan Hickerson Kierkegaard, Metaphysics and Political Theory, Alison Assiter Kierkegaard’s Analysis of Radical Evil, David A. Roberts Leibniz Re-interpreted, Lloyd Strickland Metaphysics and the End of Philosophy, HO Mounce Nicholas Malebranche, Susan Peppers-Bates Nietzsche and the Greeks, Dale Wilkerson Origins of Analytic Philosophy, Delbert Reed Philosophy of Miracles, David Corner Platonism, Music and the Listener’s Share, Christopher Norris Popper’s Theory of Science, Carlos Garcia Role of God in Spinoza’s Metaphysics, Sherry Deveaux Rousseau and the Ethics of Virtue, James Delaney Rousseau’s Theory of Freedom, Matthew Simpson Spinoza and the Stoics, Firmin DeBrabander Spinoza’s Radical Cartesian Mind, Tammy Nyden-Bullock St. -
Obligations, Sophisms and Insolubles∗
Obligations, Sophisms and Insolubles∗ Stephen Read University of St Andrews Scotland, U.K. March 23, 2012 1 Medieval Logic Medieval logic inherited the legacy of Aristotle: first, the logica vetus, Aristo- tle's Categories and De Interpretatione, which together with some of Boethius' works were all the logic the Latin West had to go on around 1100. Subse- quently, over the following century, came the recovery of the logica nova: the rest of Aristotle's Organon, all of which was available in Latin by 1200. The medievals' own original contribution began to be formulated from around 1150 and came to be known as the logica modernorum. It consisted of a theory of properties of terms (signification, supposition, appellation, ampli- ation, restriction etc.); a theory of consequences; a theory of insolubles; and a theory of obligations. This development was arguably stimulated by the theory of fallacy, following recovery of De Sophisticis Elenchis around 1140.1 It reached fulfilment in the 14th century, the most productive century for logic before the 20th. In this paper, I will concentrate for the most part on the theory of obligations|logical obligations. My focus will be on some logicians at the University of Oxford, mostly at Merton College, in the early fourteenth century, in particular, Walter Burley (or Burleigh), Richard Kilvington, Roger Swyneshed and William Heytesbury. I will contrast three different approaches to the theory of obli- gations found in these authors, and some of the reasons for these contrasts. The standard theory of obligations, the responsio antiqua, was codified by Burley in a treatise composed in Oxford in 1302. -
DEMONSTRATION and Scientific KNOWLEDGE in WILLIAM OF
Longeway-000.FM 11/8/06 2:29 PM Page iii Demonstration and Scientific knowledge in william of ockham ATranslation of Summa Logicae III-II: De Syllogismo Demonstrativo, and Selections from the Prologue to the Ordinatio JO HN LEE LO NGEWAY University of Notre Dame Press Notre Dame, Indiana © 2007 University of Notre Dame Press Longeway-000.FM 11/8/06 2:29 PM Page iv Copyright © 2007 by University of Notre Dame Notre Dame, Indiana 46556 www.undpress.nd.edu All Rights Reserved Manufactured in the United States of America Library of Congress Cataloging-in-Publication Data Longeway, John. Demonstration and scientific knowledge in William of Ockham : a translation of Summa Logicae III-II : De Syllogismo Demonstrativo, and selections from the Prologue to the Ordinatio / John Lee Longeway. p. cm. Includes bibliographical references and index. isbn-13: 978-0-268-03378-1 (cloth : alk. paper) isbn-10: 0-268-03378-1 (cloth : alk. paper) 1. Knowledge, Theory of. 2. Science —Methodology. 3. Logic. 4. Aristotle. Posterior analytics. 5. William, of Ockham, ca. 1285– ca. 1349. Summa logicae. 6.William, of Ockham, ca. 1285– ca. 1349. I. Title. bd161.l66 2006 160 —dc22 2006032380 ∞This book is printed on acid-free paper. © 2007 University of Notre Dame Press Longeway-01.Intro 11/8/06 2:28 PM Page 1 introduction The medievalist needs no convincing that William of Ockham (ca. 1285–1347) is worthy of study. At one time Ockham’s views might have been regarded as a clever but uninstructed sign of the decay of Scholastic discourse, but, with the work of such scholars as Philotheus Boehner, Ernest Moody, and Marilyn McCord Adams, those days are now receding into the past. -
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’).