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Ancient Logic and Its Modern Interpretations Synthese Historical Library ANCIENT LOGIC AND ITS MODERN INTERPRETATIONS SYNTHESE HISTORICAL LIBRARY TEXTS AND STUDIES IN THE HISTORY OF LOG IC AND PHILOSOPHY Editors: N. KRETZMANN, Cornell University G. NUCHELMANS, University of Leyden L. M. DE RIJK, University of Leyden Editorial Board: J. BERG, Munich Institute of Technology F. DEL PUNT A, Linacre College, Oxford D. P. HENRY, University of Manchester J. HINTIKKA, Academy of Finland and Stan/ord University B. MATES, University of California, Berkeley J. E. MURDOCH, Harvard University G. PA TZIG, University of Gottingen VOLUME 9 ANCIENT LOGIC AND ITS MODERN INTERPRETATIONS PROCEEDINGS OF THE BUFFALO SYMPOSIUM ON MODERNIST INTERPRETATIONS OF ANCIENT LOGIC. 21 AND 22 APRIL, 1972 Edited by JOHN CORCORAN State University o[ New York at Buffalo D. REIDEL PUBLlSHING COMPANY DORDRECHT-HOLLAND / BOSTON-U.S.A. Library of Congress Catalog Card Number 73-88589 ISBN-13: 978-94-010-2132-6 e-ISBN-13: 978-94-010-2130-2 001: 10.1007/978-94-010-2130-2 Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht-Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Ine. 306 Dartmouth Street, Boston, Mass. 02116, U.S.A. All Rights Reserved Copyright © 1974 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint ofthe hardcover I st edition 1974 No part of thisbook may be reproduced in any form, by print, photoprint, microfilm or any other means, without written permission from the publisher to Lynn with love TABLE OF CONTENTS PREFACE IX PART ONE Andent Semantics NORMAN KRETZMANN / Aristotle on Spoken Sound Signi1icant by Convention 3 RONALD ZIRIN / Inarticulate Noises 23 NEWTON GARVER / Notes for a Linguistic Reading of the Categories 27 PART TWO Modern Research in Andent Logic IAN MUELLER / Greek Mathematics and Greek Logic 35 JOHN MULHERN / Modem Notations and Ancient Logic 71 PART THREE Aristotle's Logic JOHN CORCORAN / Aristotle's Natural Deduction System 85 MAR y MULHERN / Corcoran on Aristotle's Logical Theory 133 PART FOUR Stoic Logic JOSIAH GOULD / Deduction in Stoic Logic 151 JOHN CORCORAN / Remarks on Stoic Deduction 169 VIII T ABLE OF CONTENTS PART FIVE Final Session of the Symposium JOHN CORCORAN / Future Research on Ancient Theories or Communication and Reasoning 185 A Panel Discussion on Future Research in Ancient Logical Theory 189 INDEX OF NAMES 209 PREFACE During the last half century there has been revolutionary progress in logic and in logic-related areas such as linguistics. HistoricaI knowledge of the origins of these subjects has also increased significantly. Thus, it would seem that the problem of determining the extent to which ancient logical and linguistic theories admit of accurate interpretation in modern terms is now ripe for investigation. The purpose of the symposium was to gather logicians, philosophers, linguists, mathematicians and philologists to present research results bearing on the above problem with emphasis on logic. Presentations and discussions at the symposium focused themselves into five areas: ancient semantics, modern research in ancient logic, Aristotle's logic, Stoic logic, and directions for future research in ancient logic and logic-related areas. Seven of the papers which appear below were originally presented at the symposium. In every case, discussion at the symposium led to revisions, in some cases to extensive revisions. The editor suggested still further revisions, but in every case the author was the finaljudge of the work that appears under his name. In addition to the seven presented papers, there are four other items included here. Two of them are papers which originated in discussions folIowing presentations. Zirin's contribution is based on comments he made folIowing Kretzmann's presentation. My 'Remarks on Stoic De­ duction' is based on the discussion whieh followed Gould's paper. A third item contains remarks that I prepared in advance and read at the opening of the panel discussion which was held at the end of the sympo­ sium. The panel discussion was tape-recorded and the transcript proved of sufficient quality to merit inclusion in these proceedings with a mini­ mum of editing. Funds for the symposium were provided by a grant to the Philosophy Department of the State University of New York at Buffalo from the University's Institutional Funds Committee. Departments of Mathe­ maties, Clas sies and Linguistics cooperated in the planning and in the x PREFACE symposium itself. Professors Richard Vesley (Mathematics), Ronald Zirin (Classies), Madeleine Mathiot (Linguistics) and Wolfgang Wolck (Linguistics ) deserve thanks, as do the folIowing Professors ofPhilosophy: William Parry, John Kearns, and John GlanviIIe. Special thanks goes to Professor Peter Hare who conceived of the idea for the symposium, aided in obtaining funds for it, and gave help in many other ways as well. David Levin, Terry Nutter, Keith Ickes, William Yoder, Susan Wood, Sule Elkatip, and Alan Soble, all students in Philosophy, aided in various ways. Levin was especiaIly conscientious and generous with his time. JOHN CORCORAN Buffalo, N. Y., November 1972 PART ONE ANCIENT SEMANTICS NORMAN KRETZMANN ARISTOTLE ON SPOKEN SOUND SIGNIFICANT BY CONVENTION A few sentences near the beginning of De interpretatione (I6a3-8) con­ stitute the most influential text in the history of semantics. The text is highly compressed, and many translations, including the Latin translation in which it had its greatest influence, have obscured at least one interesting feature of it. In this paper I develop an interpretation that depends on taking seriously some details that have been negleeted in the countless discussions of this text. The sentence with which De interpretatione begins, and which imme­ diately precedes the text I want to examine, provides (as Ackrill remarks 1) the program for Chapters 2-6. ... we must settle what a name is [Chapter 2] and what a verb is [Chapter 3], and then what a negation [Chapters 5 and 6], an affirmation [Chapters 5 and 6], a statement [Chapten, 4 and 5] and asentence [Chapters 4 and 5] are. (16al-2)2 But Aristotle says "First we must settle what a name is ... ", and that is what he does in Chapter 2. The remainder of Chapter I, then, may be thought of as preparatory to the main business of those chapters. And since their main business is to establish definitions, it is only natural to preface them with a discussion of the defining terms. At the beginning of Chapter 2, for instance, Aristotle defines 'name' in these terms: 'spoken sound', 'significant by convention', 'time', and 'parts significant in sepa­ ration'. These terms continue to serve as defining terms beyond Chapter 2, and the remainder of Chapter 1 (I 6a3-18) is devoted to clarifying them. The special task of the text I am primarily concerned with is the clari­ fication of the proximate genus for the definitions in Chapters 2-6: "spoken sound significant by convention".3 "Emt ~i;v ouv .li EV Tij q>rovfj .mv Now spoken sounds are symbols EV .fj 'l'Uxfj 1tu8rll.Ul"trov m)~~oA.u, of affections in the soul, and writ- J. Corcoran (ed.). Ancient Logic and Its Modem Interpretations, 3-21. All Rights Reserved Copyright © 1974 by D. Reidel Publishing Company, Dordrecht-Holland 4 NORMAN KRETZMANN Kai. 'til 'Ypaep6J.lEVa 'trov sv 'ttl eprovtl. ten marks symbols of spoken Kai. 6l<rnep 0088 'YpuJ.lJ.la'ta 7tiim. 'til sounds. And just as written marks ao'tu, 0088 ep rova! ai ail'tai' rov are not the same for all men, neither j.låV'tOl 'ta()'ta O11J.lEia 7tpo)'tro~, 4 are spoken sounds. But what these 'tao'tll 7tiim. 7ta9iJJ.la'ta die; 'Vuxi'ie;, are in the first place signs of - af­ Kai. rov 'ta()'ta 6J.101IDJ.l'ta 7tpu'YJ.la'ta fections of the soul - are the same fj811 'tao'tu. for all; and what these affections are likenesses of - actual tbings­ (16a3-8) are also the same. Ignoring the claims about sameness or difference to begin with, we can pick out four elements and three relations. (I am going to use 'mental impression' only because it is handier than Ackrill's 'affection in [or of] thesoul'.) Elements Relations actual thing is a likeness of mental impression is a sign of spoken sound is a symbol of written mark Aristotle makes four claims in wbich these elements and relations are combined. (1) Written marks are symbols of spoken sounds. (2) Spoken sounds are symbols of mental impressions. (3) Spoken sounds are (in the first place) signs of mental impressions. (4) Mental impressions are likenesses af actual things. I shaH begin by pointing out some obvious features of these claims. (In the long history of this text even what is obvious has aften been overlooked.) There is nothing explicit in these four claims relating spoken sounds or written marks to actual things, nor is there any apparent implicit c1aim about such a relationship. 5 When we are told that spoken sounds are symbols and signs of mental impressions and that mental impressions are likenesses of actual tbings, we are given no license to infer anythlng at all about a relations hip between spoken sounds and actual tbings. Yet tbis is ARISTOTLE ON SPOKEN SOUND 5 just what commentators on this text have regularly done, usually remark­ ing (as if it were obvious) that Aristotle maintains that words stand di­ rectly for thoughts and indireetly for things. l think they have been led to do so beeause they have approaehed this text in the belief that it contains Aristotle's general theory ofmeaning. But, as we shaH see, this text makes better sense and fits its context better if it is interpreted as playing a more modest role. If it contains no claim at all, explicit or implicit, about a re­ lationship of spoken sounds to aetual things, then it is not even a sketch of a general theory of meaning.
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