MEDIEVAL FORMAL LOGIC

MEDIEVAL FORMAL LOGIC

The New Synthese Historical Library Texts and Studies in the History of Philosophy VOLUME49 Managing Editor: SIMa KNuuTTILA, University of Helsinki Associate Editors: DANIEL ELLIOT GARBER, University of Chicago RlCHARD SORABß, University of London Editorial Consultants: ]AN A. AERTSEN, Thomas-Institut, Universität zu Köln, Germany RoGER ARIEW, Virginia Polytechnic Institute E. JENNIFER ASHWORTH, University ofwaterloo MICHAEL AYERS, Wadharn College, Oxford GAIL FINE, Comell University R. J. HANKINSON, University oftexas 1AAKKO HINTIKKA, Boston University, Finnish Academy PAUL HOFFMAN, University of Califomia, Riverside DAVID KONSTAN, Brown University RICHARD H. KRAUT, Northwestem University, Evanston ALAIN DE LIBERA, Ecole Pratique des Hautes Etudes, Sorbonne JOHN E. MURDOCH, Harvard University DAVID FATE NORTON, McGill University LucA ÜBERTELLO, Universita degli Studi di Genova ELEONORE STUMP, St. Louis University ALLEN Wooo, Comell University The titles published in this series are listed at the end of this volume.

MEDIEVAL FORMAL LOGIC Obligations, Insolubles and Consequences Edited by MIKKO YRJÖNSUURI University of Jyväskylä, Finland and Academy of Finland, Helsinki, Finland SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

Library of Congress Cataloging-in-Publication Data ISBN 978-90-481-5604-7 ISBN 978-94-015-9713-5 (ebook) DOI 10.1007/978-94-015-9713-5 Printed on acid-free paper All Rights Reserved 2001 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcoverreprint ofthe hardcoverist edition 2001 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

TABLE OF CONTENTS PREFACE vii PART I OBLIGATIONSAND INSOLUBLES 1 MIKKO YRJÖNSUURI I Duties, Rules and Interpretations in Obligational Disputations 3 HENRIK LAGERLUND AND ERIK J. OLSSON I Disputation and Change of Belief-Burley's Theory of Obligationes as a Theory of Belief Revision 3 5 CHRISTOPHER J. MARTINI Obligationsand Liars 63 F ABIENNE PIRONET I The Relations between Insolubles and Obligations in Medieval Disputations 9 5 PART II CONSEQUENCES 115 PETER KING I Consequence as Inference: Mediaeval Proof Theory 1300-1350 117 NAN BOH I Consequence and Rules of Consequence in the Post- Ockham Period 14 7 STPEHEN READ I Self-reference and Validity Revisited 183 PART 111 1RANSLATIONS 197 ANONYMOUS I The Emmeran Treatise on False Positio 199 ANONYMOUS I The Emmeran Treatise on Impossible Positio 21 7 PSEUDO-SCOTUS I Questions on Aristotle's Prior Analytics Opposite of the Consequent? 225 INDEXOFNAMES 235 V

PREFACE One of the most important cornerstones of logic is the relation of consequence. This relation is something that is supposed to obtain between the premises and the conclusion of a valid inference. However, spelling out this relation in any further detail has proved to be extremely difficult. In fact, logicians of various times who have tried to provide a comprehensive account of what an inference is have always found themselves in serious difficulties. The purpose of this book is to Iook more closely at medieval discussions of inference. The authors of the various essays aim at bringing the field of medieval logic closer to the concerns of contemporary philosophers and logicians. Thus, although the papers do represent the peak of present-day scholarship, they are not primarily designed t o further specialist research in medievallogic. Instead, the purposes of the book follow from the present situation of medieval scholarship: historical research has advanced quite quickly, but the general philosophical audience still has rather outdated views of the medieval developments o f philosophy in general and of logic in particular. At present, there is a need for presentations that bring the results of historical research to a wider audience. This book is intended to serve such a purpose, and accordingly it should also be suited to the needs of courses in the history of logic. The essays are independent, but they are organized in a way that should make their argumentation easy to follow. As the case often is in historical research, one of the major problems in our understanding of medieval logic derives from fundamental conceptual differences. Most modern logicians have understood their subject as something with close connections to mathematics. On the other hand, medieval scholars often thought that the account of an inference is best given against the framework of a disputation. Medieval university life was strongly dependent on dialectical practices. Academic argumentation and consequently, practically all intellectual reasoning was understood to take place in contexts where someone is trying to convince another person by presenting a sequence of sentences. Such a conception of logic vii

viii PREFACE was of course deeply embedded in the ancient tradition. Aristotle's Topics, for example, put logic in the context of an encounter between an opponent and a respondent. In this context, an inference became a structure by which the opponent can force the respondent to accept something because of what he has already granted to the opponent. The topics covered by the papers in this collection can be defined with reference to three genres of the so-called logica moderna arising in the thirteenth century: obligationes, insolubilia and consequentiae. Part one of this volume is dedicated to obligationes and insolubilia, while part two concerns consequentiae. The third part provides three medieval texts in translation. The two first ones belong together and provide an early representative of the theory of obligationes. The last one is taken from a commentary on Aristotle's Prior Analytics, but can be classified into the genre of consequentiae because of its subject matter. The paper by Mikko Ytjönsuuri provides a general historical survey of the medieval theories of obligationes. Although the name of the genre of logic comes from the word obligatio (an obligation, or a duty), the issues discussed have little to do with deontic logic. More accurately, the genre can be described as a logical theory of a special kind of dialectical encounter similar to that discussed by Aristotle in his Topics. The name comes from the idea that in a disputation the respondent may be given special duties that he or she must follow during the disputation. The treatises on obligationes discuss the logical issues arising in such special disputations. At the focus of attention, we find the rules that the respondent must follow in his answers during the disputation. In his paper, Ytjönsuuri provides a systematic account of three main medieval versions of such rules (by Walter Burley, Richard Kilvington and Roger Swineshed), and gives some guidelines for the variety of interpretations that seem possible for disputations following these rules. In their paper, Henrik Lagerlund and Erik J. Olsson compare W alter Burley's theory of obligations with certain modern techniques of beliefrevision. This is not to say that Burley would have been aiming at the systems that were successfully construed by modern logicians. Rather, the comparison provides the modern reader with an intelligent way of looking at the logical structures employed in Burley's procedures. In essence, the problems encountered and tackled both by Burley's theory of obligationes and modern theories of belief revision concern the ways in which formal inferential techniques can be applied to epistemic contexts with the inherent aim of consistency.

PREFACE ix Lagerlund and Olsson have used Walter Burley's Treatise on obligations from 1302. Modem scholars have often taken it as the paradigm example of an obligational treatise. It indeed seems that the set of rules and practical tricks presented in Burley' s text were rather widely taken as the starting point in the fourteenth century. Further, Burley's theory differs little in its essential features from the system presented in the early thirteenth century anonymous text translated in this volume. As Yrjönsuuri shows in his paper, Duns Scotus can be credited for a central generally accepted revision of the standard approach, and Richard Kilvington and Roger Swineshed provided two alternative approaches to obligations. Nevertheless, it seems that for the most part the central philosophical problems discussed in treatises on obligationes can be tackled with reference to Burley's text. The basic structure of obligational disputations resembled closely but not completely the way in which Aristotle described dialectical encounters in his Topics. This is of course no accident: Topics had a strong effect on the formation of medievallogic. Nevertheless, it seems equally clear that treatises on obligations developed certain themes of Aristotle's Topics in an original way not intended or thought about by Aristotle. These themes are further discussed by Yrjönsuuri in his paper, but let us here pay some attention to one specific development that seems to have taken logicians actually outside the theory of obligationes. It was connected to the Aristotelian idea that in all disputations the opponent aims at forcing the respondent to grant a contradiction. This may, of course, result from either of two mistakes. Bither the respondent has taken an incoherent position from the beginning, or he defends his position badly. It seems that quite early in the development of the theory of obligationes, a third and even more problematic mistake was recognized. This was that the position from which the respondent starts might be paradoxical. If, for example, the respondent has as the positum "the positum is false," he will be led into rather similar inconsistencies as those encountered in the so-called liar' s paradox. When the respondent is asked whether the positum is true or false, he cannot give either answer. N onetheless, he may have to answer because of the general requirements of the game. In medieval parlance, these paradoxes were called insolubilia. Not all medieval solutions devised for them were dependent on the obligational or even disputational context. Nevertheless, even in such cases it pays to recognize the dialectical setting in which medieval logicians worked.

X PREFACE In her paper, Fabienne Pironet Iooks at William Heytesbury's ways of dealing with insolubilia. His solutions are strongly dependent on disputational and obligational techniques, and thus they provide a good vantage point from which to survey the ways in which the disputational setting is relevant to the paradox. The relation between obligationes and insolubilia is perhaps at its clearest in Heytesbury's text. Christopher J. Martin's paper takes the reader further down to the early stages of the medieval traditions of obligationes and insolubilia. The primary aim of his paper is to reconstruct the early histories of these two logical genres in a more comprehensive way. As Martin shows, the origins of the medieval discussions of the Liar may be found within the theory of obligationes. This, in turn, seems to come down from late ancient discussions located at the borderlines of possibility and conceptual imaginability. Thus, the theory of obligations seems to have been developed in order to treat problems connected with imaginability within disputational contexts. As Martin shows, early medieval authors developed many of their central logical concepts within such contexts. From his discussion of obligationes, we achieve a better grasp of how early medieval logicians dealt with concepts that have to do with how two or more statements stand together-that is, concepts like consistency, cotenability and compossibility. On the other hand, in Martin' s discussion of insolubilia we can see many interesting ways in which the medieval conceptions of assertion ( as distinct from mere utterance) were developed against a disputational background, and in a technical sense within the context of an obligational disputation. The general aim of the papers of the second part, dedicated t o consequences, is to give the reader a grasp ofthe ways in which medieval logicians explicitly tackled problems arising from the theory of inference. On the one hand, the papers give a picture of the historical development in logic in the fourteenth century, which was the time when medievallogic was at its peak. On the other hand, the papers cover the field in a systematic sense: What is an inference? How is it related to conditionals? What makes an inference valid? What is the role played by logical form in inferences? Why did the medieval authors Iook at inferences especially from an epistemic perspective? Peter King takes up the distinction between conditionals and inferences. It has been claimed that medieval logicians confused the two, and thus their central concept of consequentia may be variously translated into English as conditional or as inference. King has looked at

PREFACE xi all the available texts from the crucial period 1300-1350, and argues that in these texts the confusion is very rare and always insignificant from the logical point of view. The important thing to come out of this discussion is an interesting picture of the proof theories in the period considered. According to King's conclusion, far from being confused with conditionals, inferences were seen as the heart of logic in the fourteenth century. Furthermore, King also rejects the idea that logic was exclusively understood as a discipline concemed with formal validity. As King sees it, as far as formal validity was considered, it was generally taken as one specific kind of validity, and medieval logicians thought that they must consider validity in general. Some recent studies have suggested that epistemic or psychological considerations were developed in the late Middle Ages to substitute for attention to the formal properties of inferences when evaluating their validity. If this is so, late medievallogic paved the way for Descartes' criticism of scholastic logic and his idea of deduction as a chain of clear and distinct intuitions. Ivan Boh's paper tackles this problern in a systematic fashion. His idea is to look closely at the epistemic, doxastic and disputational rules given in treatises on consequences in the post-ockham period. While confirming the thesis that there was an interesting historical change in the ways of describing the idea of validity, Boh also challenges the main formulations of the thesis. Boh opposes the idea that there are psychological overtones in the ways in which late fourteenth-century authors defined the validity of inferences. As he sees it, the development went into a more mentalistic direction without being straightforwardly naturalistic in the psychologistic sense. According to Boh, such a mentalistic approach can already be seen in John Buridan, who was perhaps the most important logician of the early fourteenth century. He was looking at inference from a mentalistic viewpoint although it is clear that he was not in any interesting sense psychologistic in his discussion of the validity of an inference. Indeed, he relied quite heavily on the concept of logical form in his account of validity. Thus, the fourteenthcentury "mentalistic turn" ought not to be understood as something opposed to an approach based on formal considerations. Boh's investigations make it clear that the main representatives of medieval logic did not understand inference as obtaining between formulas, but rather between conceptual representations of what is the case. Stephen Read's paper tests an interesting hypothesis adopted by an anonymous author from the early fourteenth century, who is usually

xii PREFACE called Pseudo-Scotus. According to the hypothesis, the inferential analogue of the Liar paradox (an argument inferring from a single necessary premise that it itself is invalid) proves paradoxical to the socalled classical account of validity. Pseudo-Scotus thought that the paradox forced him to qualify his account of inferential validity: in his discussion we can, in fact, see many central features of his conception of validity. Thus, Read's discussion also provides a look at how Pseudo Scotus treated the concept of validity. This seems especially interesting if the reader keeps in mind that Pseudo-Scotus was one of the most elaborate late medieval logicians to lean on considerations of logical form in the definition of validity. In this sense, Read's discussion also sheds light on the debate treated by Boh. The text used by Read is included in Question 10 of Pseudo-Scotus' commentary on the Prior Analytics (Super librum primum et secundum Priorum Analyticorum Aristotelis quaestiones), and it is provided here as the third text of the Appendix. The text has traditionally been printed in collections of Duns Scotus' works, but it is now well known that he is not its author. For want of a better name, the author has been called Pseudo-Scotus. In his paper, Read discusses who this Pseudo-Scotus might have been and when he most probably wrote his commentary. He concludes by dating the treatise into approximately two decades after 1331, which provides a rather definite post quem. As for finding out the author's name, Read is more pessimistic than some other scholars: he rejects the view that Pseudo-Scotus would have been John of Cornwall and thus leaves us with no other name than Pseudo-Scotus. In any case, severa1 modern commentators have discussed his questions of the Prior Analytics, and therefore they qualify as one central source for students of medievallogic. The two first texts of the Appendix occur together in the manuscript from which they originate. We know little about their author, and even the dating of them in the early thirteenth century is considerably less exact than is the case for Pseudo-Scotus. They have been known as the 'Emmeran' treatises because of their geographical origin since L. M. de Rijk edited them in Vivarium (vol. 12/1974 and vol. 13/1975). Together, these early treatises provide a simple but philosophically elaborated picture of the rules and practices of different obligational disputations. Y:rjönsuuri and Martin discuss in their respective papers these texts in further detail. All three texts have been translated by Mikko Y:rjönsuuri.