THE CATHOLIC UNIVERSITY of AMERICA Logic and Intentionality
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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. -
John P. Burgess Department of Philosophy Princeton University Princeton, NJ 08544-1006, USA [email protected]
John P. Burgess Department of Philosophy Princeton University Princeton, NJ 08544-1006, USA [email protected] LOGIC & PHILOSOPHICAL METHODOLOGY Introduction For present purposes “logic” will be understood to mean the subject whose development is described in Kneale & Kneale [1961] and of which a concise history is given in Scholz [1961]. As the terminological discussion at the beginning of the latter reference makes clear, this subject has at different times been known by different names, “analytics” and “organon” and “dialectic”, while inversely the name “logic” has at different times been applied much more broadly and loosely than it will be here. At certain times and in certain places — perhaps especially in Germany from the days of Kant through the days of Hegel — the label has come to be used so very broadly and loosely as to threaten to take in nearly the whole of metaphysics and epistemology. Logic in our sense has often been distinguished from “logic” in other, sometimes unmanageably broad and loose, senses by adding the adjectives “formal” or “deductive”. The scope of the art and science of logic, once one gets beyond elementary logic of the kind covered in introductory textbooks, is indicated by two other standard references, the Handbooks of mathematical and philosophical logic, Barwise [1977] and Gabbay & Guenthner [1983-89], though the latter includes also parts that are identified as applications of logic rather than logic proper. The term “philosophical logic” as currently used, for instance, in the Journal of Philosophical Logic, is a near-synonym for “nonclassical logic”. There is an older use of the term as a near-synonym for “philosophy of language”. -
Logic, Argumentation & Reasoning
Logic, Argumentation & Reasoning Interdisciplinary Perspectives from the Humanities and Social Sciences Volume 24 General Editor Shahid Rahman (Lille, UMR 8163) Managing Editor Juan Redmond (Universidad de Valparaiso, Chile) Area Editors Argumentation and Pragmatics Frans H. van Eemeren (Amsterdam) Zoe McConaughey (Lille, UMR 8163) Tony Street (Faculty of Divinity, Cambridge) John Woods (British Columbia/King’s College) Argumentation and Rhetoric Gabriel Galvez-Behar (Lille, UMR 8529) Leone Gazziero (Lille) André Laks, (Princeton/Panamericana) Ruth Webb (Lille, UMR 8163) Decision Theory, Mathematics, Economy Jacques Dubucs (IHPST-Paris 1) Karine Chemla (CNRS, SPHERE UMR7219, Université de Paris) Sven Ove Hansson (Stockholm) Cognitives Sciences. Computer Sciences Yann Coello (Lille) Eric Gregoire (CRIL-Lens) Henry Prakken (Utrecht) François Recanati (ENS, Paris) Epistemology and Philosophy of Science Gerhard Heinzmann (Nancy) Sonja Smets (ILLC, Amsterdam) Göran Sundholm (Leiden) Logic Michel Crubellier (Lille, UMR 8163) Dov Gabbay (King’s College) Tero Tulenheimo (Lille, UMR 8163) Political Science and Sociology Jean-Gabriel Contamin (Lille) Franck Fischer (Rutgers) Josh Ober (Stanford) Marc Pichard (Lille, MESHS-Nord Pas de Calais) Logic, Argumentation & Reasoning (LAR) explores links between the Humanities and Social Sciences, with theories (including decision and action theory) drawn from the cognitive sciences, economics, sociology, law, logic, and the philosophy of science. Its main ambitions are to develop a theoretical framework -
THE CONDEMNATION of 1277 the First Known Case of Academic
CHAPTER TWO THE CONDEMNATION OF 1277 Th e fi rst known case of academic condemnation at Oxford occurred in 1277. On March 18th of that year Robert Kilwardby, Archbishop of Canterbury, condemned as erroneous a series of propositions that were being upheld in the arts faculty involving grammar, logic, and natural philosophy.1 Th is event and its sequels, the Condemnation of 1284 and the Condemnation of Richard Knapwell, form the most examined ele- ment in the history of academic condemnation at Oxford, with the possible exception of the events around the condemnation of John Wyclif and the Oxford Lollards in 1381–82. Th ere is a large body of literature on this topic, and various aspects of it have been hotly debated over the past century.2 1 Th e condemnation, including the propositions, can be found in Chartularium Universitatis Parisiensis, ed. H. Denifl e and E. Chatelain, (Paris, 1889–97), 1:558–60. It also exists (with minor variations in the wording of the propositions) in the Collectio errorum in Anglia et Parisius condemnatorum; see Henryk Anzulewicz, “Eine weitere Überlieferung der Collectio errorum in Anglia et Parisius condemnatorum im Ms. Lat. Fol. 456 der Staatsbibliothek Preussicher Kulturbesitz zu Berlin,” in Franziskanische Studien 74 (1992), pp. 375–99, at pp. 380–81. Th ere also exists a letter from Kilwardby to Peter of Confl ans in which he defends his action; Franz Ehrle, “Ein Schreiben des Erzbishofs von Canterbury Robert Kilwardby zur Rechtfertigung seiner Lehrverurtheilung vom 18. Marz 1277,” in Archiv für Literatur- und Kirchengeschichte des Mittelalters, ed. H. -
Kilwardby, Robert 00
K 16/5/05 4:13 pm Page 33 KILWARDBY, ROBERT 00 appearing in Muslim Spain within his lifetime. Here, his Arab Civilization: Challenges and Response. Edited by original tables were studied by *Maslama of Madrid and G.N. Atiyeh and I.M. Oweiss. 98–111. Albany: SUNY his pupils whose adaptation, more accurate than the Press, 1988. original, adjusted the tables to make them useful to Van Dalen, Benno. “Al-Khwarismi’s Astronomical Tables astronomers in the West. This version was then translated Revisited.” In Samso and Casulleras, I: 195–252. MICHAEL C. WEBER by *Adelard of Bath and *Pedro Alfonso, and it is only this Latin version that survives complete whereas in Arabic only selections from the original survive. Al-Khwarizmi’s two other surviving works are the Geography and the Extraction of the Jewish Calendar. It KILWARDBY, ROBERT appears that the Geography represents an important Robert Kilwardby died at the papal court in Viterbo, advance over *Ptolemy’s work of the same name. It has Italy, on September 11, 1279. Although aspects of his been speculated that al-Khwarizmi’s work was based on career as an intellectual and churchman are known, noth- a world map constructed by a collection of scholars for ing is really known about his early life except that he al-Ma’mun; the Geography represents superior knowl- studied at Paris. It would be nice to know if he studied edge of the Islamic lands and the areas visited by Muslim with the natural philosopher Richard Fishacre at Oxford traders and merchants. The work on the Jewish calendar in the early 1240s, for instance: it is possible and some of is curious. -
Concrete Possible Worlds (Final)
CONCRETE POSSIBLE WORLDS Phillip Bricker 1. INTRODUCTION. Open a book or article of contemporary analytic philosophy, and you are likely to find talk of possible worlds therein. This applies not only to analytic metaphysics, but to areas as diverse as philosophy of language, philosophy of science, epistemology, and ethics. Philosophers agree, for the most part, that possible worlds talk is extremely useful for explicating concepts and formulating theories. They disagree, however, over its proper interpretation. In this chapter, I discuss the view, championed by David Lewis, that philosophers’ talk of possible worlds is the literal truth.1 There exists a plurality of worlds. One of these is our world, the actual world, the physical universe that contains us and all our surroundings. The others are merely possible worlds containing merely possible beings, such as flying pigs and talking donkeys. But the other worlds are no less real or concrete for being merely possible. Fantastic? Yes! What could motivate a philosopher to believe such a tale? I start, as is customary, with modality.2 Truths about the world divide into two sorts: categorical and modal. Categorical truths describe how things are, what is actually the case. Modal truths describe how things could or must be, what is possibly or 1 The fullest statement of Lewis’s theory of possible worlds is contained in his magnum opus, Lewis (1986), On the Plurality of Worlds. Lewis’s view is sometimes called “modal realism.” 2 Historically, it was the attempt to provide semantics for modal logic that catapulted possible worlds to the forefront of analytic philosophy. -
David Lewis's Place in Analytic Philosophy Scott Soames by The
David Lewis’s Place in Analytic Philosophy Scott Soames By the early 1970s, and continuing through 2001, David Lewis and Saul Kripke had taken over W.V.O. Quine’s leadership in metaphysics, epistemology, philosophy of language, and philosophical logic in the English-speaking world. Quine, in turn, had inherited his position in the early 1950s from Rudolf Carnap, who had been the leading logical positivist -- first in Europe, and, after 1935, in America. A renegade positivist himself, Quine eschewed apriority, necessity, and analyticity, while (for a time) adopting a holistic version of verificationism. Like Carnap, he placed philosophical logic and the philosophy of science at the center of philosophy. While not entirely avoiding metaphysics and epistemology, he tried to “naturalize” both. By contrast, Lewis and Kripke embraced the modalities Quine rejected.1 They also had no sympathy for his early verificationism, or his twin flights from intension and intention. As for philosophy of science, it was transforming itself into specialized philosophies of the several sciences, and did not lend itself to unified treatment. Although Lewis had deep interests in scientific issues, and was commendably realist about science in general, science itself was not the center of own distinctive approach to philosophy. Despite similarities in their opposition to Quine, the differences between Lewis and Kripke were large – especially in the semantics and metaphysics of modality. They also had different philosophical styles. Whereas Lewis was a wide-ranging thinker who pieced together a systematic philosophical world view, Kripke gave little thought to system, focusing instead on a few central topics. There is, therefore, no conflict between the two on many of the issues on which Kripke was silent. -
The Legacy of Andre Vauchez's Sainthood in the Later Middle Ages
The Legacy of André Vauchez � Sainthood in the Later Middle Ages Thomas Head Hunter College and the Graduate Center, CUNY It is the appearance of a translation entitled Sainthood in the Later Middle Ages (trans. Jean Birrell [Cambridge, 1987]) which provides us the excuse this afternoon to consider the André Vauchez � masterwork and its legacy in shaping the hagiographic scholarship over the course of almost two decades. Vauchez originally published his thèse d �état in 1981. It became on its publication, and remains today, the benchmark for all study of hagiography and the cult of saints in the later middle ages. The book is a systematic examination of the records of the formal processes initiated for the canonization of saints between 1198 and 1431. Vauchez thus implicitly took up the challenge issued in 1965 by Frantisek Graus Volk, Herrscher und Heiliger im Reich der Merowinger: Studien zur Hagiographie der Merowingerzeit (Prague, 1965), that is to use neglected genres of hagiographic works as sources for the social history of western Christianity. Given the importance that has come to be accorded Graus � pioneering study among scholars �particularly Anglophone scholars �who examine hagiography more for social historical than for philological or theological reasons, it is natural to link the work of the French Catholic to that of the Czech Marxist. Our chair this afternoon, Richard Kieckhefer �himself one of the most distinguished Anglophone scholars of late medieval sanctity �made exactly that connection on the opening page (p. xix) of the foreword which he provided for the English translation. Vauchez himself invoked Graus on the first page of his own introduction, but in a much more limited manner, as one among a group of scholars of the Merovingian and Carolingian periods who have "made it possible to bring within the �territory of the historian � the terra incognita which the history of sanctity has long represented." (p. -
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. -
Topics in Philosophical Logic
Topics in Philosophical Logic The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Litland, Jon. 2012. Topics in Philosophical Logic. Doctoral dissertation, Harvard University. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:9527318 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA © Jon Litland All rights reserved. Warren Goldfarb Jon Litland Topics in Philosophical Logic Abstract In “Proof-Theoretic Justification of Logic”, building on work by Dummett and Prawitz, I show how to construct use-based meaning-theories for the logical constants. The assertability-conditional meaning-theory takes the meaning of the logical constants to be given by their introduction rules; the consequence-conditional meaning-theory takes the meaning of the log- ical constants to be given by their elimination rules. I then consider the question: given a set of introduction (elimination) rules , what are the R strongest elimination (introduction) rules that are validated by an assertabil- ity (consequence) conditional meaning-theory based on ? I prove that the R intuitionistic introduction (elimination) rules are the strongest rules that are validated by the intuitionistic elimination (introduction) rules. I then prove that intuitionistic logic is the strongest logic that can be given either an assertability-conditional or consequence-conditional meaning-theory. In “Grounding Grounding” I discuss the notion of grounding. My discus- sion revolves around the problem of iterated grounding-claims. -
Uni International 300 N
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