Subjunctive Reasoning

Subjunctive Reasoning John L. Pollock SUBJUNCTIVE REASONING PHILOSOPHICAL STUDIES SERIES IN PHILOSOPHY Editors: WILFRIDSELLARS, University of Pittsburgh KEITHLEHRER, University of Arizona Board of Consulting Editors: JONATHANBENNETT, University of British Columbia ALANGIBBARD, University of Pittsburgh ROBERTSTALNAKER, Cornell University ROBERTG. TURNBULL,Ohio State University VOLUME 8 JOHN L. POLLOCK University of Rochester SUBJUNCTIVE REASONING D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND/BOSTON-U .S.A. Library of Congress Cataloging in Publication Data Pollock, John L Subjunctive reasoning. (Philosophical studies series in philosophy ; v. 8) Bibliography: p. Includes index. 1. Conditionals (Logic) 2. Reasoning. 3. Counter- factuals (Logic) 4. Probabilities. I. Title. BC199.C56P64 160 76-19095 ISBN 90-277-0701 -4 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, Inc. Lincoln Building, 160 Old Derby Street, Hingham, Mass. 02043, U.S.A. All Rights Reserved Copyright @ 1976 by D. Reidel Publishing Company, Dordrecht, Holland 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 informational storage and retrieval system, without written permission from the copyright owner Printed in The Netherlands TO CAROL who puts up with me TABLE OF CONTENTS PREFACE I. INTRODUCTION 1. Subjunctive Reasoning 2. The Linguistic Approach 3. The 'Possible Worlds' Approach 4. Conclusions Notes 11. FOUR KINDS OF CONDITIONALS 1. Introduction 2. The Four Kinds 3. 'Even if Subjunctives 4. 'Might Be' Conditionals 5. Necessitation Conditionals 6. Simple Subjunctives 7. The Axiomatization of Simple Subjunctives 8. Conclusions Notes 111. SUBJUNCTIVE GENERALIZATIONS 1. Introduction 2. Rudiments of an Analysis 3. Strong Generalizations 4. Weak Generalizations 5. Conclusions Notes IV. THE BASIC ANALYSIS OF SUBJUNCTIVE CONDITIONALS 1. Introduction 2. The Analysis of M 3. Simple Propositions VIII TABLEOFCONTENTS 4. Counter-Legal Conditionals 5. Subject Preference Notes V. QUANTIFICATION, MODALITIES, AND CONDITIONALS 104 1. Referential Opacity 2. Transworld Identity 3. Kripke's Observation 4. Quantified Modal Logic 5. Conditionals Notes VI. THE FULL THEORY 1. Syntax 2. Semantics 3. Infinitary Operators 4. The Introduction of Sets 5. Some Consequences of the Analysis Note VII. CAUSES 1. Introduction 2. The Ontology of Causes 3. Some Causal Relations 4. Causal Sufficiency 4.1. Nomic Subsumption 4.2. Contingently Sufficient Conditions 4.3. Causal Sufficiency and Subjunctive Conditionals 5. Remarks on the Analysis 6. The Logic of Causes Notes VIII. PROBABILITIES 1. Introduction 2. Indefinite Probabilities 2.1. Relative Frequencies 2.2. Subjunctive Indefinite Probabilities TABLE OF CONTENTS 2.3. Strong Indefinite Probabilities 2.4. Weak Indefinite Probability Statements 3. The Redefinition of M 3.1. Strong and Weak Definite Probability 3.2. Probabilistic Laws 3.3. The Analysis of M 4. Simple Subjunctive Probability 4.1. The Variety of Probabilities 4.2. Simple Subjunctive Probability 4.3. A Probability Algebra 4.4. Simple Subjunctive Probability and Simple Sub- junctive Conditionals 4.5. Simple Indefinite Probabilities Notes IX. DISPOSITIONS 1. Introduction 2. Absolute Dispositions 3. Probabilistic Dispositions Notes BIBLIOGRAPHY INDEX PREFACE I am indebted to many people for the help they gave me in the writing of this book. I owe a large debt to David Lewis and Robert Stalnaker, on both general and specific grounds. As becomes apparent from reading the notes, the book would not have been possible without their pioneering work on subjunctive conditionals. In addition, both were kind enough to provide specific comments on earlier versions of different parts of the book, and Stalnaker read and commented on the entire manuscript. Closer to home, I am indebted to my colleagues Rolf Eberle and Henry Kyburg, Jr., my erstwhile colleague Keith Lehrer, and numerous graduate students for their helpful comments on various parts of the manuscript. Some of the material contained herein appeared first in the form of journal articles, and I wish to thank the journals in question for allowing the material to be reprinted here. Chapter One contains material taken from 'The "Possible Worlds" Analysis of Counter-factuals', published in Phil. Studies 29 (1976), 469 (Reidel); Chapter Two contains material much revised from 'Four Kinds of Conditionals', Am. Phil. Quarterly 12 (1975), and Chapter Three contains much revised material from 'Subjunctive Generaliza- tions', Synthese 28 (1974), 199 (Reidel). CHAPTER I INTRODUCTION There exists quite a variety of statements which are in some sense 'subjunctive'. The best known of these are the so-called 'counterfactual conditionals' which state that if something which is not the case had been the case, then something else would have been true. An example is 'If Kennedy had been president in 1972, the Watergate scandal would not have occurred'. Ordinary people use counterfactuals all the time, and philosophers use them freely in ordinary situations. However, when they are being careful, philosophers have traditionally felt uncomfort- able about counterfactuals and eschewed their employment in philosophical analysis. Such philosophical squeamishness is on the whole meritorious and results from the recognition that counterfactual conditions have themselves stubbornly resisted philosophical analysis. Although counterfactual conditionals constitute the kind of subjunctive statement which comes most readily to the mind of a philosopher, it is far from being the only philosophically important kind of subjunctive statement. Philosophers have long recognized that laws of nature cannot really be formulated using universally quantified material conditionals, but they have not usually been prepared to go the extra distance of admitting that statements expressing such laws are really subjunctive. It turns out that laws of nature must be formulated using a special kind of subjunctive statement, herein called a 'subjunctive generalization'. Subjunctive generalizations prove to be of pre-eminent importance in discussing inductive confirmation. Causal statements constitute another category of statements which are in the requisite sense 'subjunctive'. The analysis of causal statements has always been recognized to be an extraordinarily difficult philosophical problem, but I think it has rarely been appreciated that the main source of this difficulty lies in the subjunctive nature of causal statements. 2 CHAPTER I A traditional philosophical problem is the analysis of probability statements. There are in fact a number of different concepts equally deserving of being called 'probability'. There is not just one legitimate concept of probability. Philosophers have succeeded in sorting out and distinguishing between a number of different probability concepts, including 'degree of confirmation', 'degree of belief', 'degree of ra- tional belief', and others. However, there are many probability statements which cannot be formulated using any of these recognized 'indicative' probability concepts. It will turn out that there are some extremely important probability concepts that are in essential ways 'subjunctive' and which have been almost entirely overlooked by philosophers bent upon the avoidance of suspicious (to them) subjunctive reasoning. A problematic concept which has usually been recognized to have a subjunctive core is that of a disposition. Dispositions constitute an important tool of philosophical analysis. Particularly in the philosophy of mind, philosophers have felt that through the use of dispositions they could clarify the structure of interesting concepts. But, of course, the extent of such clarification has been strictly limited by the apparent need for clarifying dispositions themselves. These various subjunctive concepts map out areas of what might be called 'subjunctive reasoning'. Subjunctive reasoning in general has been deemed philosophically problematic because it seems to presup- pose a strange metaphysically suspicious sort of logically contingent necessity. To say that the Watergate scandal would not have occurred had Kennedy been president in 1972, seems to be to assert some kind of necessary connection between those two states of affairs. If there were no such connection, how could the occurrence of the one possibly effect the occurrence of the other? This same kind of necessity rears its ugly head repeatedly throughout subjunctive reasoning. The necessity in question is clearly not logical necessity, but what other kind is there? Surely this is a very suspicious notion, and philosophers would be well advised to avoid subjunctive concepts at all cost! But upon sober reflection, it must be admitted that this attitude is preposterous. Subjunctive concepts do make sense - we use them all the time. The problem cannot be whether they make sense, but what sense they INTRODUCTION 3 make. The real issue must be how they are to be analyzed, and not their legitimacy. We cannot in good conscience deny that there is this logically contingent kind of necessity which is involved in subjunctive reasoning. We cannot expunge it from our conceptual framework without leaving that framework seriously impoverished. What we must seek is an understanding of subjunctive reasoning, an analysis of subjunctive

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