18253-Thom_Logic 5/31/12 10:24 AM Page i the logic of the trinity 18253-Thom_Logic 5/31/12 10:24 AM Page ii 18253-Thom_Logic 5/31/12 10:24 AM Page iii Medieval Philosophy texts and studies series editor Gyula Klima Fordham University editorial board Richard Cross Brian Davies Peter King Brian Leftow John Marenbon Robert Pasnau Giorgio Pini Richard Taylor Jack Zupko 18253-Thom_Logic 5/31/12 10:24 AM Page iv 18253-Thom_Logic 5/31/12 10:24 AM Page v The Logic of the Trinity Augustine to Ockham paul thom Fordham University Press (cid:129) New York (cid:129) 2012 18253-Thom_Logic 5/31/12 10:24 AM Page vi Frontispiece: Image of Knight in emblematic armor. Peraldase Summa of Vice© The British Literary Board. Harley 3244, f.Z8r. Copyright © 2012Fordham University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means— electronic, mechanical, photocopy, recording, or any other—except for brief quotations in printed reviews, without the prior permission of the publisher. Fordham University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet websites referred to in this publication and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Fordham University Press also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Thom, Paul. The logic of the Trinity : Augustine to Ockham / Paul Thom. — 1st ed. p. cm. — (Medieval philosophy) Includes bibliographical references (p. ) and index. ISBN 978-0-8232-3476-9(cloth : alk. paper) 1. Trinity—History of doctrines. 2. Philosophy, Medieval. I. Title. BT109.T45 2011 231'.0440902—dc23 2011019591 Printed in the United States of America 14131254321 First edition 18253-Thom_Logic 5/31/12 10:24 AM Page vii contents List of Definitions ix List of Rules xi List of Figures xiii Preface xv 1. Background 1 2. Augustine 19 3. Boethius 42 4. Abelard 62 5. Gilbert of Poitiers 78 6. Peter Lombard 94 7. Bonaventure 104 8. Albert 118 9. Aquinas 129 10. Scotus 143 11. Ockham 161 Appendix: Ontological Systems 181 Notes 185 Bibliography 229 Index 235 vii 18253-Thom_Logic 5/31/12 10:24 AM Page viii 18253-Thom_Logic 5/31/12 10:24 AM Page ix definitions 1.1 univ(A) iff for some B: A de B 14 1.2 acc(A)iff for some B: A in B 14 1.3 subst(A) iff not acc(A) and for no B: A ab B 14 1.4 indiv(A) iff not univ(A) and for no B: A ab B 14 2.1 subst(A) iff not acc(A) and for no B(B ≠ A) : A ab B 40 5.1 A in* Biff B ab A 82 5.2 A in Biff for some C: A adest Cand C in* B 83 5.3 acc(A) iff for some B: A adestB 92 5.4 subst(A) iff not acc(A) and for no B: both A adest B and A in* B 92 5.5 quo(A) iff for some B: A in* B 92 5.6 quod(A) iff for no B: A in* B 92 5.7 subsistent(A) iff subst(A) and quod(A) 92 7.1 A opp Biff for some C,D: C ab Aand D ab B and C ad D 115 7.2 A in** Biff for some C: A in* Cand C est B 115 ix