ALGEBRA OF CONSCIENCE

ALGEBRA OF CONSCIENCE

THEORY AND DECISION LIBRARY General Editors: W. Leinfellner (Vienna) and G. Eberlein (Munich) Series A: Philosophy and Methodology of the Social Sciences Series B: Mathematical and Statistical Methods Series C: Game Theory, Mathematical Programming and Operations Research SERIES A: PHILOSOPHY AND METHODOLOGY OF THE SOCIAL SCIENCES VOLUME30 Series Editor: W. Leinfellner (Technical University ofvienna), G. Eberlein (Technical University of Munich); Editorial Board: R. Boudon (Paris), M. Bunge (Montreal), J. S. Coleman (Chicago), J. Gotsch! (Graz), L. Kern (Pullach), I. Levi (New York), R. Mattessich (Vancouver), B. Munier (Cachan), J. Nida-Ri.imelin (Giittingen), A. Rapoport (Toronto), A. Sen (Cambridge, U.S.A.), R. Tuomela (Helsinki), A. Tversky (Stanford). Scope: This series deals with the foundations, the general methodology and the criteria, goals and purpose of the social sciences. The emphasis in the Series A will be on well-argued, thoroughly analytical rather than advanced mathematical treatments. In this context, particular attention will be paid to game and decision theory and general philosophical topics from mathematics, psychology and economics, such as game theory, voting and welfare theory, with applications to political science, sociology, law and ethics.

ALGEBRA OF CONSCIENCE Revised Edition with a Second Part with a new Foreword by Anatol Rapoport by VLADIMIR A. LEFEBVRE University of California, Irvine, U.S.A. SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-5751-8 ISBN 978-94-017-0691-9 (ebook) DOI 10.1007/978-94-017-0691-9 Printed on acid-free pa per AlI Rights Reserved 2001 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2001 Softcover reprint of the hardcover 2nd edition 2001 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.

CONTENTS FOREWORD by Anatol Rapoport ACKNOWLEDGMENTS to the second edition ACKNOWLEDGMENTS to the first edition PREP ACE to the second edition INTRODUCTORY CHAPTER 1 PART ONE. ETHICAL SYSTEMS 17 Prologue to Part One 19 Introduction to Part One 21 Chapter I. Moral Cognition 36 Chapter II. Ethical Systems and Boolean Algebra 43 Chapter III. Boolean Algebra, Exponent, Logarithm 46 Chapter IV. Individuals, Reflexion, and Interaction 50 Chapter V. Automata with Semantics and Ethical Status 55 Chapter VI. A Formal Representation of Doubts and Feelings 63 Chapter VII. A Formal Comparison of Ethical Systems: Guilt, Condemnation, Doubt 68 Chapter VIII. A Formal Comparison of Ethical Systems: Doubts and Ethical Status 74 Chapter IX. Ethical Analysis of Artistic and Propagandistic Literature 82 Chapter X. Experimental Analysis of Normative Individuals 88 Chapter XI. The Principle of Maximization of the Ethical Status of One's Image of Oneself 94 Chapter XII. Feelings and Sacrifices 98 Chapter XIII. Formal Connections between Modules oflnner Structures and Individuals 109 Chapter XIV. Interaction. Activity and Its Measure 112 IX xi xii xiii v

vi CONTENTS Chapter XV. Ethical Typology in the Novel Crime and Punishment by Dostoevsky 116 Chapter XVI. Ideology, Morality, and Political Organization 126 Chapter XVII. Generalization. Proof of Existence of Ethically Non-Measurable Situations 135 Conclusion. The Problem of Substantiating Initial Axioms 143 Epilogue to Part One 148 PART TWO. MORAL CHOICE 151 Prologue to Part Two 153 Introduction to Part Two 155 Chapter I. The Three-Faced Janus: An Initial Metaphor for the Model ofthe Subject 160 Chapter II. A Boolean Model of Bipolar Choice 165 Chapter III. Metachoice 174 Chapter IV. Modeling of Awareness 184 Chapter V. The Prisoner's Dilemma 192 Chapter VI. The Morality of Results and the Morality of Means 198 Chapter VII. A Boolean-Linear Model of the Subject 203 Chapter VIII. Examples of Modeling the Process of Choice 214 Chapter IX. Imitation of the Other 222 Chapter X. The Subject Controlling His Relationships with Another Subject 228 Chapter XL Two Aspects of Choice 232 Chapter XII. Generalization of Classical Game Theory of 2x2 Zero-Sum Game 235 Chapter XIII. Risk and Caution 242 Chapter XIV. The Non-Linear Model of the Subject 245 Chapter XV. Subject with a Quadratic Model of the Situation 249 Chapter XVI. Streams of Consciousness and Difference Equations 252 Chapter XVII. Streams of Consciousness and Acts of Awareness 256 Epilogue to Part Two 261 APPENDICES 263 Appendix 1. Construction of Judgments about the Correctness of Images and Judgments 265

CONTENTS vii Appendix 2. Ethical Systems and Multivalued Logics 269 Appendix 3. Self-Generation of Environments 291 Appendix 4. A Method of Calculating Mean Ethical Statuses 298 Appendix 5. Types of Adequacy ofreflexion 307 Appendix 6. Schemas of Empirical Procedures 311 Appendix 7. Tables 316 Appendix 8. Problems of Substantiating the Initial Axioms in an Arbitrary Environment 321 Appendix 9. Another Method of Representing Individuals 327 Appendix 10. Representation of Completed Graphs with Polynomials 329 Appendix 11. The Principle of Complementarity and the Phenomenon of Interference in the Algebraic Model ofethical Cognition 339 REFERENCES 349 INDEX OF NAMES 353 SUBJECT INDEX 355

FOREWORD TO THE SECOND EDITION Almost twenty years have elapsed since the publication of this book. While the approach reflected in Part I differed substantially from the main current of research on moral choices of humans, it appears that the main current has moved toward the author's approach, apparently reflecting an influence of The Algebra of Conscience. Evidence of this process can be seen in the increasing interest in the models formulated in the first edition of this book. Special issues of two journals were devoted to those models: Journal of Social and Biological Structures (vol. 10/2, 1987) and Applied Ergonomics, No. 1, 1994. The contents of a conference devoted to the author's work were published in Proceedings of the Workshop on Multi-Reflexive Models of Agent Behavior (Army Research Laboratory, Fuller Lodge, Los Alamos, NM, 1998). Specifically, the approach is based on a quite simple model of a "manikin," making a decision rather than on analysis of human choices among alternatives as such. Besides the ability of making a choice, this mannikin is supposed to possess an internal world and thus to be able to generate subjective intentions. In this way "freedom of will," as well as the mannikin's ability to make intentional actions are included in the model, whereby intention corresponds to a particular variable in the model. In this respect, the author's model differs substantially from other models, in which, although intentional choice is mentioned, it remains on the level of external verbal description rather than being included in the formalism of the model. In the first edition of this book, the mannikin established his relationship to another mannikin. This led to a distinction between two ethical systems. In Part II of the present edition the mannikin is faced with the choice between good and evil. In other words, he must make a moral choice. The author applies his model to the classical theory of the (2 x 2) constantsum game. The main idea of this connection is supplementing the payoff matrix by a Boolean matrix, where the ix

X FOREWORD outcomes of the games and the strategies ofthe players (manikins) are represented as "good" and "evil. " In this way, choice of strategy can be regarded as a moral choice. The author emphatically points out that the model generates no answer to the question how one should behave. That is, the model does not reflect the normative aspect of the game. It serves another purpose, namely, how the player will behave in the framework of specific assumptions. The introduction of a supplementing Boolean matrix allows us to analyze Prisoner's Dilemma in the case the players are endowed not only with rationality but also with a morality. It turns out that when the actor describes the situation by anon-linear model, his behavior becomes chaotic. Some time ago, drawing the consequences described in detail in Part II, the author made predictions about frequencies of choices between positive and negative poles in simple psychological experiments (Lefebvre, V.A., A Psychological Theory of Bipolarity and Reflexivity. Lewiston: The Edwin Mellen Press, 1992). Relevant experiments have been since carried out and the predictions essentially realized (Adams-Webber, J., Self-Reflexion in Evaluating Others. American Journal of Psychology, Vol. 110: 527-41, 1997). However, much more experimental work is required to the determine the range of applicability of this model. Anatol Rapoport Toronto, June 6, 2000

ACKNOWLEDGMENTS TO THE SECOND EDITION For the past twenty five years I have been lucky to have the opportunity to continual contacts with Anatol Rapoport. His advice and comments have always been invaluable. I am deeply grateful to Victorina Lefebvre, a professional psychologist, for clear and specific suggestions; in addition, she took upon herself the entire burden of preparing this manuscript for print. I am thankful to Harold Baker, Dudley Miller, Sergei Petrov, and Vladimir Reitman for a number of useful recommendations concerning the second Part of this book, and I appreciate advice of Werner Leinfellner in regard to preparation of a new bibliography. I have to note also the suggestions given to me by the late Karl Popper in 1992. My long conversation with him at that time convinced me that I was right in trying to construct my theory based on intuitive insight. In my mind's eye I see my late friend Yulius Schreider, an eminent mathematician and philosopher. I mentally spoke to him throughout the writing of this book. Xl

ACKNOWLEDGMENTS TO THE FIRST EDITION I am indebted to many colleagues and friends for their help and support, without which I probably would not have been able to write this book. With Anatol Rapoport I discussed the main idea of the book, and in great measure I owe its empirical orientation to him. Moreover, he kindly performed the final editing. To William Batchelder I am indebted for many germane discussions while the book was being written. He also edited many sections. Through the good offices of William Batchelder and the former dean of the School of Social Sciences, Christian Werner, I was able to carry out this work at the University of California at Irvine. All the experiments were conducted together with my wife, Victorina Lefebvre, who also put together the computer program employed in Appendix 2. Additionally, she translated the entire work from Russian to English, a task in which Ronald Walter gave her invaluable aid. I am thankful to the editor of this series, Werner Leinfellner, for his attentiveness and support. I received important comments on various aspects ofthe work from Ronald Walter, Russell Ackoff, Max Black, Thomas Schwartz, Lev Levitin, Mark Schafer, and Steven Hall. I would also like to thank Jan P. Wasilewsky for many interesting discussions and his willingness to read the galley proofs. Finally, I thank Kathy Alberti for her professional virtuosity and splendid attitude toward the technical preparation of the manuscript. Parts of Chapters I-VI, VIII, X-XII, Conclusion, and Appendix 1 appeared in 'An Algebraic Model of Ethical Cognition', Journal of Mathematical Psychology 22, 2, 83-120, October 1980, and is used here by permission of the publisher. Academic Press, Inc. quotation from Bukovsky, V. K., 1979, To Build a Castle, p. 135, is used by permission ofviking Penguin, Inc., copyright 1978. Quotations from Dostoevsky, F. M., 1953, Crime and Punishment, translated by Jessie Coulson (1953), reprinted by permission of Oxford University Press. Quotations from Niels Bohr, 1958, Atomic Physics and Human Knowledge, reprinted by permission of John Wiley & Sons, Ltd., copyright 1958 by Niels Bohr. xii

PREFACE TO THE SECOND EDITION The crucial difference between this edition and the first is the addition of a Part Two, expanding on the conclusions of the first edition in the light of new research and continued analysis. The new structure is as follows: Introductory Chapter, Part One, Part Two, Appendices. The Introductory Chapter describes the approach and main ideas common to both parts. Part One, entitled "Ethical systems", includes the main text of the first edition with minor, chiefly editorial changes. In accord with the model described in this part, an individual's choice of his relationship with another individual (either union or confrontation) is determined by the individual's self-esteem, as this is automatically generated by his cognitive system. The existence of two ethical systems is a formal implication of the model. Within the framework of the First ethical system, self-evaluation is favored by the choice of 'union', and in the Second ethical system it is higher with 'confrontation'. As a result, in the First ethical system, the dominant relationship is 'union', and in the Second ethical system, the dominant relationship is 'confrontation', a state of affairs which is not affected either by practical utility or by moral evaluations performed by the 'other'. In Part Two, entitled "Moral Choice," the model described in Part One is elaborated in detail. We assume that the cognitive system of the subject, faced with a bipolar choice between the alternatives good and evil is functioning automatically in two 'dimensions'. On the one hand, the subject's cognitive system performs 'moral computations' which can be described in the terms of Boolean models; on the other hand, it computes utility-measures for the alternatives, which can then be described with continuous models. Then results of both types of computations are brought together in the act of moral choice. The experimental, applicational, and epistemological aspects of the model described in the first edition of this book along with subsequent publications by the author have been discussed by a number of researchers. I would like to mention the following works: Jack Adamsxiii

xiv Webber (1987; 1995; 1997), Harold Baker (1999), William Batchelder (1987), Louis Kauffman (1990), Vladimir Kry1ov (1994), Lev Levitin (1987), Ernst McClain (1990), Dudley Miller & Marc Sulkosky (1999a), Anatol Rapoport (1990; 1996), Julius Schreider (1994; 1998), Tatiana Taran (1999), James Townsend (1983; 1990), Harvey Wheeler (1987), Robert Zajonc (1987), and Karl Popper (1992).