THE LOGIC OF ESSENTIALISM

Transcription

1 THE LOGIC OF ESSENTIALISM

2 The New Synthese Historical Library Texts and Studies in the History of Philosophy VOLUME 43 Managing Editor: SIMO KNUUTIILA, University of Helsinki Associate Editors: DANIEL ELLIOT GARBER, University of Chicago RICHARD SORABJI, University of London Editorial Consultants: JAN A. AERTSEN, Free University, Amsterdam ROGER ARIEW, Virginia Polytechnic Institute E. JENNIFER ASHWORTH, University of Waterloo MICHAEL AYERS, Wadham College, Oxford GAIL FINE, Cornell University R. J. HANKINSON, University of Texas JAAKKO HINTIKKA, Boston University, Finnish Academy PAUL HOFFMAN, University of California, Riverside DAVID KONSTAN, Brown University RICHARD H. KRAUT, University of Illinois, Chicago ALAIN DE LIBERA, Ecole Pratique des Hautes Etudes, Sorbonne JOHN E. MURDOCH, Harvard University DAVID FATE NORTON, McGill University LUCA OBERTELLO, Universita degli Studi di Genova ELEONORE STUMP, St. Louis University ALLEN WOOD, Cornell University The titles published in this series are listed at the end of this volume.

3 THE LOGIC OF ESSENTIALISM An Interpretation of Aristotle's Modal Syllogistic by PAULTHOM The Australian National University, Department of Philosophy, Faculty of Arts, Canberra, ACT, Australia KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

4 A C.I.P. Catalogue record for this book is available from the Library of Congress. lsbn-13: e-1sbn-13: DOl: / Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. Printed on acid-free paper All Rights Reserved 1996 Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 1996 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.

5 PREFACE Aristotle's modal syllogistic has been an object of study ever since the time of Theophrastus; but these studies (apart from an intense flowering in the Middle Ages) have been somewhat desultory. Remarkably, in the 1990s several new lines of research have appeared, with series of original publications by Fred Johnson, Richard Patterson and Ulrich Nortmann. Johnson presented for the first time a formal semantics adequate to a de re reading of the apodeictic syllogistic; this was based on a simple intuition linking the modal syllogistic to Aristotelian metaphysics. Nortmann developed an ingenious de dicto analysis. Patterson articulated the links (both theoretical and genetic) between the modal syllogistic and the metaphysics, using an analysis which strictly speaking is neither de re nor de dicto. My own studies in this field date from 1976, when my colleague Peter Roeper and I jointly wrote a paper "Aristotle's apodeictic syllogisms" for the XXIInd History of Logic Conference in Krakow. This paper contained the disjunctive reading of particular affirmative apodeictic propositions, which I still favour. Nonetheless, I did not consider that paper's results decisive or comprehensive enough to publish, and my 1981 book The Syllogism contained no treatment of the modal syllogism. The paper's ideas lay dormant till 1989, when I read Johnson's and Patterson's initial articles. I began publishing on the topic in Gradually my thoughts acquired a certain comprehensiveness and systematicity, till in 1993 I was able to take a semester's sabbatical to write up a draft of this book. The book has developed to its present form under the watchful gaze of a select band of correspondents, prime among them Fred Johnson, but also including Ignacio Angelelli, Friedemann Buddensiek, Storrs McCall, Ulrich Nortmann, Richard Patterson, Peter Roeper, Klaus Schmidt, Robin Smith and Steve Thomason. There have been many others too who have helped improve the work by discussing it, whether in the Philosophy Program of the Research School of Social Sciences at the Australian National University, or the Australasian Society for Ancient Philosophy, or the Ancient Philosophy Colloquium at the University of Texas at Austin. I wish to thank all these for the critical attention they have given my work. Finally, it is a pleasure to record my thanks to the Philosophy Department of the University of Melbourne who gave me the status of Visiting Fellow for a very happy and productive semester in P.T. Canberra January 1996

6 TABLE OF CONTENTS O Entering the Realm of Darkness INTRODUCTION CHAPTER ONE. ELEMENTARY SYNTAX 1 Elementary forms 7 2 Modal opposition Necessity- and possibility-forms Necessity- and contingency-forms 15 3 Transformation rules: Substitution, Permutation, Reductio and Cut Substitution Permutation Indirect Reduction Cut 21 4 Transformation rules: Contraction, Ecthesis Contraction Ecthesis 25 5 Transformation rules: modal reductio 26 CHAPTER TWO. AXIOMS 6 Axioms: X and L axioms 6.1 X axioms 6.2 L axioms Pure L axioms L-X axioms 7 Axioms: Q axioms 7.1 Pure Q axioms 7.2 Q-X axioms 7.3 Q-L axioms 8 Axioms: Q', M and X' axioms 8.1 Q' axioms 8.2 M axioms 8.3 'Unqualified' assertoric axioms

7 viii CHAPTER THREE. THESES 9 Necessity moods 9.1 Pure L theses 9.2 L-X theses 10 Unampliated contingency moods 10.1 Q-X theses 10.2 Q-L theses First Figure Second Figure Third Figure 11 Ampliated contingency moods 12 Possibility moods 12.1 First Figure 12.2 Second Figure 12.3 Third Figure 13 'Unqualified'moods 13.1 First Figure 13.2 Second Figure 13.3 Third Figure CHAPTER FOUR. REJECTIONS 14 Necessity moods 14.1 Rejected L-X moods: First Figure 14.2 Rejected L-X moods: Second Figure 14.3 Rejected L-X moods: Third Figure 15 Unampliated contingency moods 15.1 Rejected l-premissed Q moods 15.2 Rejected 2-premissed Q-X moods Rejected Q-X moods: First Figure Rejected Q-X moods: Second Figure Rejected Q-X moods: Third Figure 15.3 Rejected Q-L moods Rejected Q-L moods: First Figure Rejected Q-L moods: Second Figure Rejected Q-L moods: Third Figure

8 ix 16 Ampliated contingency moods 16.1 Rejected Q' moods: First Figure 16.2 Rejected Q' moods: Second Figure 16.3 Rejected Q' moods: Third Figure 17 Possibility and 'unqualified' moods CHAPTER FIVE. FLAWS IN THE FABRIC 18 Incidental mistakes Barbara XLL and the Hintikka Formulae Datisi XLL, Disamis LXL and necessarily awake bipeds QiLo-l, QoLo-l and necessarily non-white men QaLaLo-2, QeLaLo-2 and negative conclusions from affirmative premisses QaLe-3, QeLe-3 and necessarily sleeping horses Barbara X'QM and 'unqualified' assertorics Substantial mistakes QaLaXe-2 and negative conclusions from affirmative premisses Barbara XQM and ephemeral contingencies Inconsistencies Baroco XLL, Bocardo LXL and ecthesis Q-opposition and Qi-conversion 135 CHAPTER SIX. SYSTEM AL 21 Assertoric forms 22 Necessity forms 22.1 Formal semantics 22.2 The Sun set Theorcm 22.3 Validity of the axioms 22.4 Invalidity of the axiomatic rejections 22.5 Corollaries 23 Adding C, K, U and T 24 Reduction to assertoric syllogistic 25 Alternative de re approaches: base 25.1 Existence assumptions 25.2 Sun set assumptions

9 x 26 Alternative de re approaches: superstructure 26.1 Superstructure A 26.2 Superstructure AA 26.3 Superstructure C 26.4 Superstructure CC 27 Alternative approaches: de dicto theories 27.1 Pure de dicto theories 27.2 Mixed de dicto/de re theories CHAPTER SEVEN. SYSTEMS AQ AND AQ' 28 Unampliated contingency-forms 28.1 Formal semantics 28.2 Validity of the axioms 28.3 Invalidity of the axiomatic rejections First Figure Second Figure Third Figure 28.4 Corollaries 29 Ampliated contingency-forms 29.1 Formal semantics 29.2 Validity of the axioms 29.3 In validity of the axiomatic rejections 29.4 Corollaries 30 The relation of ampliated to unampliated systems 31 Reduction to assertoric syllogistic 32 Alternative de re approaches 32.1 Superstructure A 32.2 Superstructure AA 32.3 Superstructure C 32.4 Superstructure CC 32.5 Comparing superstructures 33 Alternative approaches: de dicto theories CHAPTER EIGHT. SYSTEM AX' 34 Unqualified assertorics 35 System AX' 36 Reduction to assertoric syllogistic 37 A reprieve for modal reductio

10 XI CHAPTER NINE. SINGULAR MODAL SYLLOGISTIC 38 System AEL Syntactic base 38.2 Formal semantics 38.3 Provability of AL' s base 39 Systems AEQ5 and AEQ'5 40 Alternative de re approaches 40.1 A-style singular modal syllogistic 40.2 AA-style singular modal syllogistic 40.3 C-style singular modal syllogistic 40.4 CC-style singular modal syllogistic 41 Reduction to assertoric syllogistic 41.1 System EQO 41.2 Alternative superstructures 41.3 Alternative bases CHAPTER TEN. ESSENTIALISM 42 Varieties of essentialism 42.1 Essentialism 42.2 Examples of essentialist theory 42.3 Aristotelian essentialism: generalities 42.4 Aristotelian essentialism: specifics 43 The essentialism of the modal syllogistic 43.1 A metaphysical interpretation of the modal syllogistic 43.2 Interpreting the base 43.3 Interpreting the superstructure La-propositions Le-propositions Li-propositions Lo-propositiions Q-propositions 44 Aristotle's static essentialism 45 Aristotle's dynamic essentialism 46 The metaphysics of unqualified assertorics 47 Aristotelian vs. Platonic essentialism 48 Conclusions

11 xii REFERENCES AND INDEXES References Index locorum Index of axioms Index of rules Index of systems General index