The Logic of Conditionals An Application of Probability to Deductive
Of the four chapters in this book, the first two discuss (albeit in consider ably modified form) matters previously discussed in my papers 'On the Logic of Conditionals' [1] and 'Probability and the Logic of Conditionals' [2], while the last two present
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SYNTHESE LIBRARY MONOGRAPHS ON EPISTEMOLOGY LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE. AND ON THE MA THEMA TICAL METHODS OF SOCIAL AND BEHAVIORAL SCIENCES
Managing Editor: JAAKKO HINTIKKA,
Academy of Finland and Stanford University
Editors: ROBER T S. COHEN, DONALD DAVIDSON,
Boston University
Rockefeller University and Princeton University
GABRIEL NUCHELMANS, WESLEY C. SALMON,
University of Leyden
University of Arizona
VOLUME 86
ERNEST W. ADAMS
THE LOGIC OF CONDITIONALS An Application of Probability to Deductive Logic
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging in Publication Data Adams, Ernest Wilcox, 1926The Logic of conditionals. (Synthese library; v. 86) Bibliography: p. Includes indexes. 1. Conditionals (Logic) 2. Probabilities. 3. Counterfactuals (Logic) I. Title. 75-20306 BC199.C56A3 160 ISBN 978-90-481-8343-2 ISBN 978-94-015-7622-2 (eBook) DOI 10.1007/978-94-015-7622-2
Copyright © 1975 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company,Dordrecht, Holland in 1975 Softcover reprint of the hardcover 1st edition 1975 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 infoimational storage and retrieval system, without written permission from the copyright owner
To Anne, Jimmy, and Billy
TABLE OF CONTENTS
PREFACE
IX
I. THE INDICATIVE CONDITIONAL
1. A Probabilistic Criterion of Soundness for Deductive Inferences 2. Conditionals and Conditional Probabilities 3. Informal Assessment of Some Patterns of Conditional Inference 4. Partial Soundness and Conversational Implicature Considerations Relating to Contraposition and Inferences of Conditionals from Disjunctions 5. The Hypothetical Syllogism and Aspects of Hypothetical Reasoning 6. The Scope of Antecedent Restrictability 7. A Difficulty about Conditionals with Disjunctive Antecedents 8. The Problem of Compounds of Conditionals 9. A Probabilistic Concept of Consistency: Denials and Contraries of Conditionals
1 3
9
18 21 25 28 31 37
II. MATHEMATICAL THEORY OF PROBABILISTIC CONSISTENCY AND UNIVERSAL PROBABILISTIC SOUNDNESS
1. 2. 3. 4.
Introduction Preliminary Definitions Probabilistic Consistency Probabilistic Entailment
43 45
51 56
III. MOTIVES FOR WANTING TO ASSURE THE SOUNDNESS OF REASONING: TRUTH AND PROBABILITY AS DESIRABLE ATTRIBUTES OF CONCLUSIONS REACHED IN REASONING
1. Introduction: Aims and Methods
69
VIII
TABLE OF CONTENTS
2. A Motive for Wanting to Reach True Conclusions about Certain Particular Matters of Fact 3. Acting on Estimated Probabilities; the Expected Utility Theory 4. A Motive for Wanting to Arrive at Correct Probability Estimates 5. Acting on Beliefs about the Results of Possible Actions 6. Acting on Estimates of the Probabilities of the Possible Consequences of Actions 7. Best Estimates of the Probabilities of Possible Results of Actions
72 76 81 88 92 97
IV
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