SYNTHESE LIBRARY MONOGRAPHS ON EPISTEMOLOGY, LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE,

Transcription

1 MODELS OF DISCOVERY

2 SYNTHESE LIBRARY MONOGRAPHS ON EPISTEMOLOGY, LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE, AND ON THE MATHEMATICAL METHODS OF SOCIAL AND BEHAVIORAL SCIENCES Managing Editor: JAAKKO HINTIKKA, Academy of Finland and Stanford University Editors: ROBERT S. COHEN, Boston University Donald DAVIDSON, University of Chicago GABRIEL NUCHELMANS, University of Leyden WESLEY C. SALMON, University of Arizona VOLUME 114

3 BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE EDITED BY R. S. COHEN AND M. W. WARTOFSKY VOLUME LIV HERBERT A. SIMON Carnegie-Mellon University, Pittsburgh, Penn., U.S.A. MODELS OF DISCOVERY and Other Topics in the Methods of Science D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND / BOSTON-U.S.A.

4 Library of Congress Cataloging in Publication Data Simon, Herbert Alexander, Models of discovery. (Boston studies in the philosophy of science; v. 54) (Synthese library; v. 114) Includes bibliographical references and indexes. 1. Science - Philosophy. 2. Science - Methodology. I. Title. II. Series. Q174.B67 vol. 54 [Q175] 501' ISBN-13: e-isbn-13: DOl: / 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 , U.S.A. All Rights Reserved Copyright 1977 by D. Reidel Publishing Company, Dordrecht, Holland and copyright holders as specified on appropriate pages within. 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.

5 To the memory o/my teachers, RUDOLF CARNAP and HENRY SCHULTZ, who insisted that philosophy should be done scientifically, and science philosophically

6 EDITORIAL PREFACE We respect Herbert A. Simon as an established leader of empirical and logical analysis in the human sciences while we happily think of him as also the loner; of course he works with many colleagues but none can match him. He has been writing fruitfully and steadily for four decades in many fields, among them psychology, logic, decision theory, economics, computer science, management, production engineering, information and control theory, operations research, confirmation theory, and we must have omitted several. With all of them, he is at once the technical scientist and the philosophical critic and analyst. When writing of decisions and actions, he is at the interface of philosophy of science, decision theory, philosophy of the specific social sciences, and inventory theory (itself, for him, at the interface of economic theory, production engineering and information theory). When writing on causality, he is at the interface of methodology, metaphysics, logic and philosophy of physics, systems theory, and so on. Not that the interdisciplinary is his orthodoxy; we are delighted that he has chosen to include in this book both his early and little-appreciated treatment of straightforward philosophy of physics - the axioms of Newtonian mechanics, and also his fine papers on pure confirmation theory. But, of course, here too Herbert Simon is a bit beyond the norm: he found all concepts of mass messy, not sufficiently empirical, too vague in their linkage of the empirical and the theoretical, so he went directly from the physics to its logical analysis, not too patient with Mach and his aftermath. And in confirmation theory, he sees the link to decision theory promptly, and by several connections, and we in turn see his beautiful bias for heuristics as preferable to validation: what is the heuristic worth of a bit of validation? Coming to terms with Herbert Simon should occupy the world of scientists, philosophers, engineers, and policy officials. In the much discussed age of the technological and scientific revolution, Western, Eastern and world-wide, Herbert Simon"s disciplined imagination seems to us central, whether he be right, wrong, or just plainly provocative. This book of his general methodological reflections upon specific natural and social scientific

7 VI11 EDITORIAL PREFACE puzzle-solving will lead his readers to Professor Simon's other works; and to a deepening of methodology itself. Center for Philosophy and History of Science Boston University ROBERT S. COHEN MARX W. WARTOFSKY

8 T ABLE OF CONTENTS ACKNOWLEDGMENTS EDITORIAL PREFACE GENERAL INTRODUCTION Xl VII XIII SECTION 1 - TESTING THEORIES OF EMPIRICAL PHENOMENA Introduction to Section 1 3 Chapter 1.1. Symmetric Tests of the Hypothesis That the Mean of One Normal Population Exceeds That of Another 7 Chapter 1.2. Statistical Tests as a Basis for 'Yes-No' Choices 14 Chapter 1.3. Prediction and Hindsight as Confirmatory Evidence 20 Chapter 1.4. On Judging the Plausibility of Theories 25 SECTION 2 - CAUSES AND POSSIBLE WORLDS Introduction to Section 2 49 Chapter 2.1. Causal Ordering and Identifiability 53 Chapter 2.2. On the Definition of the Causal Relation 81 Chapter 2.3. Spurious Correlation: A Causal Interpretation 93 Chapter 2.4. Cause and Counterfactual (with Nicholas Rescher) 107 SECTION 3 - THE LOGIC OF IMPERATIVES Introduction to Section 3 Chapter 3.1. The Logic of Rational Decision Chapter 3.2. The Logic of Heuristic Decision Making

9 x TABLE OF CONTENTS SECTION 4 - COMPLEXITY Introduction to Section Chapter 4.1. Theory of Automata: Discussion 182 Chapter 4.2. Aggregation of Variables in Dynamic Systems (with Albert Ando) 183 Chapter 4.3. The Theory of Problem Solving 214 Chapter 4.4. The Organization of Complex Systems 245 SECTION 5 - THEORY vf SCIENTIFIC DISCOVERY Introduction to Section Chapter 5.1. Thinking by Computers 268 Chapter 5.2. Scientific Discovery and the Psychology of Problem Solving 286 Chapter 5.3. The Structure of Ill-Structured Problems 304 Chapter 5.4. Does Scientific Discovery Have a Logic? 326 Chapter 5.5. Discussion: The Meno Paradox 338 SECTION 6 - FORMALIZING SCIENTIFIC THEORIES Introduction to Section Chapter 6.1. The Axioms of Newtonian Mechanics 349 Chapter 6.2. Discussion: The Axiomatization of Classical Mechanics 370 Chapter 6.3. Definable Terms and Primitives in Axiom Systems 376 Chapter 6.4. A Note on Almost-Everywhere Definability 387 Chapter 6.5. The Axiomatization of Physical Theories 388 Chapter 6.6. Ramsey Eliminability and the Testability of Scientific Theories (with Guy 1. Groen) 403 Chapter 6.7. Identifiability and the Status of Theoretical Terms 422 NAME INDEX 441 SUBJECT INDEX 445

10 ACKNOWLEDGMENTS I am grateful to Nicholas Rescher, Albert Ando and Guy Groen for permission to republish, as Chapters 2.4, 4.2 and 6.6, respectively, papers that we wrote jointly. The assistance of many friends and colleagues who reviewed and commented upon individual chapters is acknowledged in the notes to those chapters, as is the generous research support that I.~.~... received from a number of sources. Finally, I wish to thank Robert S.,ohen and Marx W. Wartofsky for their generous help in preparing this book for publication, and for their editorial preface to it. Whatever merit may be found in these pages owes much to these friends and this support. Finally, I want to thank the following journals and publishers for permission to reprint the papers from the original sources: The Annals of Mathematical Statistics, Chapter 1.1; The Journal of the American Statistical Association, Chapters 1.2 and 2.3; Philosophy of Science, Chapters 1.3,2.4,5.4,5.5,6.2 and 6.5; The North-Holland Publishing Company, Chapters 1.4,4.3,5.3, and 6.3; The Yale University Press, Chapter 2.1; The Journal of Philosophy, Chapter 2.2; The British Journal for the Philosophy of Science, Chapters 3.1 and 6.6; The University of Pittsburgh Press, Chapters 3.2,5.1 and 5.2; Econometrica, Chapters 4.1 and 4.2; G. Braziller, Chapter 4.4; Artificial Intelligence, Chapter 5.3; The Philosophical Magazine, Chapter 6.1 ; The Journal of Symbolic Logic, Chapter 6.4; D. Reidel Publishing Company, Chapter 6.7.

11 GENERAL INTRODUCTION It is no new thing for a practicing scientist to be seduced into thinking and writing about the methodology and philosophy of his subject - or the philosophy of science in general. A large number of predecessors have set the example for me. My own seduction took place at an early age. I had forgotten how early until, just this morning, I recovered from my files a three-page outline dated July 28, 1937 and titled, 'The Logical Structure of a Science of Administration'. Inspection showed it to be a progenitor of the project that emerged five years later as my dissertation, 'The Theory of Administrative Decision, and ten years later as Administrative Behavior. 1 Successive reformulations of the project squeezed much of the abstract methodology out of it, and transformed it into a more substantively oriented essay on the social science of decision making. What remained of the original methodological content can be seen mainly in Chapter 3 of the dissertation and Chapter 4 of Administrative Behavior. These later documents failed to make good the promise of the original outline to provide answers to the following three questions (among others): What is the logical structure of sentences in Newton's Principia? What is the logical structure of the sentences of economic price theory? What is the logical structure of the sentences of Aristotle's Ethics? Evidently the unkept promises lodged somewhere in my subconscious, for throughout my scientific career I have continued to occupy a portion of my time and thoughts with methodological and philosophical issues - most of which turn out to be closely related to these three questions. In particular, Section 3 of this book is much concerned with the logics of economics and ethics, and Section 6 with the logic of physics. Thus the papers reprinted in this volume, though their dates of publication extend over more than thirty years, are not isolated fragments. Instead, they celebrate the periodic illuminations - a little less than one a year - that fitfully brightened a continuously sustained state of murky puzzlement. Of course, even if a practicing scientist has no special interest in

12 XlV GENERAL INTRODUCTION methodology as such, he cannot avoid taking positions on methodological issues. Substantive and methodological concerns form the warp and woof of every scientific fabric; and advances in methodology are as likely to lead to important scientific discoveries as are advances in substantive concepts. What distinguishes the scientist-turned-philosopher from his fellows is that he abstracts from the specific methodological issues that are intrinsic to his scientific work, and seeks to understand and discuss these issues in a more general context. That is what I have tried to do in this book. 1. APPLICATION AS A SOURCE OF PROBLEMS The papers I have selected for this volume address general issues in the philosophy of science, somewhat detached from specific applications. This does not mean that these issues were generated in a vacuum, or even that they were mainly derived froy? the mainstream literature of philosophy of science. On the contrary, most of them had their origins in specific problems that I encountered in my substantive work, and were then pursued further because they appeared to have interest and significance beyond the immediate needs of application. This strategy reflects my belief that the comparative advantage of the practicing scientist, when he invades the field of philosophy of science, lies in his constant exposure to the concrete realities of scientific endeavor. His contacts with the 'real world' of science may bring questions to his attention, or suggest ways of framing questions, that would be less likely to occur to someone living in the purer air of methodology and theory. In the philosophy of science, as in other theoretical fields, the areas of application are an indispensable source of new problems and new ideas. And the failure of a theoretically oriented field to touch base frequently with the world of application may lead it sometimes to descend into triviality and distract it into the pursuit of formal elegance. One responsibility, then, of the practicing scientist is to try to rescue philosophy and theory, from time to time, from excessive formalism. I shall undertake to provide some examples in later chapters of this book - some having to do with statistical tests, some with modal logic, some with scientific discovery, and some with the axiomatization of scientific theories - of cases where a closer look at the actual practice of science suggests a reformulation of the questions asked by philosophy.

13 GENERAL INTRODUCTION xv 2. THE USES OF MATHEMATICS Readers of this book will fmd that some of the chapters (e.g., Chapters 1.1, 2.2, 4.2, and 6.6) contain arguments that are expressed in the languages of mathematics or mathematical logic. In other chapters mathematical symbolism is nowhere to be found. My attitude toward mathematics and rigor is wholly pragmatic: an argument should be as formal and technical as it needs to be in order to achieve clarity in its statement of issues and in its arguments - and no more formal than it needs to be. Nor do I believe that an argument is always best stated at the greatest achievable levels of generality and abstraction. I recognize that tastes differ widely in these matters, and I despair of persuading others to preter my own tastes. I do find it ironic that, having done much missionary work for mathematics in fields that had been largely innocent of it, I now fmd myself reacting to a surfeit of formalism more often that to a deficit ofit, especially in economics, statistics, and logic. The uses of mathematics in this book will themselves illustrate a general bias that I confess to holding, and on which I will comment further below: a bias toward the processes of discovery rather than the processes of verification. Mathematics is sometimes treated as a body of technique for guaranteeing the validity of propositions that may have been arrived at without its help. Of course, mathematics does have this function, but it has another use that, on balance, is probably far more important: to guide and facilitate the discovery process itself. For the person who thinks in mathematics, and does not simply translate his verbal thoughts or his images into mathematics, mathematics is a language of discovery as well as a language of verification. At the present stage of our knowledge of the psychology of discovery (see Chapter 5.2), I would be hard-pressed to state specifically and operationally what I mean by 'thinking in mathematics' as distinguished from thinking in words, or thinking in some other way. Nevertheless, I am confident, from introspective evidence, that such a distinction exists, and I believe my faith is shared by most applied mathematicians. I doubt that I could have discovered most of the results reported in this book (note that I say 'discovered', not 'proved') without representing the problem situations in mathematical form. However, when conclusions have been reached by mathematical thinking, they are sometimes more readily communicated after thay are translated out of mathematics into ordinary language. In almost all cases, I have tried to provide such interpretations. Hence, the direction of translation between

14 XVl GENERAL INTRODUCTION mathematics and English in this book tends to run in the opposite direction from that found in highly formal treatises that stress verification rather than discovery and understanding. 3. ORGANIZATION OF THE BOOK The papers brought together here have been grouped by topic into six sections, each introduced by a brief essay outlining its central issues and showing the mutual relations among its chapters. The six topics are: (1) the validation and discovery of scientific hypotheses, (2) causal ordering, (3) the logic of imperatives, (4) complex systems, (5) the theory of scientific discovery, and (6) the formalization of scientific theories. Each of these topics deals with a set of issues that has been important in the literature of the philosophy of science. In my approach to them, however, the six topics are not mutually independent, but are closely intertwined with each other by virtue of their sharing a few major themes. These themes run through the entire volume and give it coherence. In the remainder of this introduction, I should like to comment upon them The Processes of Discovery The philosophy of science has for many years taken as its central preoccupation how scientific theories are tested and verified, and how choices are made among competing theories. How theories are discovered in the first place has generally been much neglected, and it is sometimes even denied that the latter topic belongs at all to the philosophy of science. Although in the past few years there has been some challenge to this classical position (e.g.. in the work of Hanson, Kuhn and Lakatos, to mention just three examples), the logic of discovery is still a grossly underdeveloped domain. This emphasis upon verification rather than discovery seems to me a distortion of the actual emphases in the practice of science. As I look about at my own scientific activity and that of my colleagues, we seem to devote much more time to seeking out possible regularities in phenomena than simply to proving that regularities we have noted are really there, and are not products of our imaginations. The history and philosophy of science have been excessively fascinated with the drama of competition between theories: the wave theory of light versus the particle theory, classical mechanics versus relativity theory, phlogiston versus oxygen, and so on. Such competition occurs only occasionally. Much more often, scientists are faced with a set of

15 GENERAL INTRODUCTION xvii phenomena and no theory that explains them in even a minimally acceptable way. In this more typical situation, the scientific task 1s not to verify or falsify theories, or to choose between alternative theories, but to discover candidate theories that might help explain the facts. Researchers in psychology and some of the other behavioral sciences, where there is often a severe deficit of good candidate theories, have sometimes been misled by the literature on philosophy and methodology to exhibit in research and publication an exaggerated concern with verification, accompanied by uncritical application of statistical tests of hypotheses to situations where they don't properly apply. I would be pleased if these essays made some small contribution to stamping out these undesirable practices. The papers in Sections 1 and 5 are particularly concerned with questions of verification and discovery of theories (more or less in that order), and serve to illustrate the progression of my own thinking on these matters. Chapters 1.1 and 1.2 argue that tests of hypotheses must be chosen in a context that takes into consideration the decisions that are to be reached and the consequences of those decisions. The position of these chapters on decision theory is crudely but distinctly Bayesian. Chapter 1.3, taking a more explicitly Bayesian viewpoint, argues that hypotheses cannot be tested without considering the processes that generated them initially - i.e.. the discovery processes. Chapter 1.4 carries this argument further, emphasizing that data precede theories more often than theories precede data. This chapter serves as a transition to the explicit examination in Section 5 of the processes of discovery. Section 5 argues for a close relation between the psychology of scientific discovery and its logic; surveys what is known of the psychological processes of discovery, and applies that knowledge to philosophical and methodological issues Model Theory and Modal Logics Since the turn of the century, logicians and philosophers have been struggling to extend modern symbolic logic to reasoning about the modalities: causality, possibility, necessity, obligation, imperatives, and the like. The initial path that was followed was to define special logics that admitted statements like: 'A causally implies B', 'A is possible', 'A is necessary,' 'If A, then B is obligatory', 'X ought to do Y'. The standard rules of inference were then modified and extended to encompass such statements as well as ordinary declaratives and implications. The use of specially defined modal logics to handle the modalities has been

16 xviii GENERAL INTRODUCTION beset with difficulties, not the least of them being a proliferation of alternative systems of inference, each claiming some plausibility but each failing to handle some of the dilemmas that are taken care of by others. A different approach to the modalities, through the application of model theory, has had great success and has gained wide acceptance? Model theory treats sentences and sets of sentences semantically, in terms of the set of possible worlds in which they are valid. In the hands of Kripke and Kreisel, contemporary model theory reached a high state of technical development, and Richard Montague 3 made important contributions toward its application to the modalities. A model-theoretic treatment of causality is provided in Section 2 of this book, and a similar treatment of the imperative mode and obligation is provided in Section 3. These analyses, arrived at independently of the technical advances in symbolic logic mentioned above, require a much less formidable apparatus than is commonly deployed by model theorists. The papers in Sections 2 and 3 demonstrate, I think, that the central idea of expressing modal concepts in terms of models can be handled in a relatively simple and straightforward way with the aid of the standard predicate calculus and some conventional, and quite elementary, mathematics. Model-theoretic ideas also play an important role in the papers of Section 6, and particularly in the demonstration (Chapter 6.6) that theoretical terms (terms denoting non-observables) are eliminable from axiomatized scientific theories Identifiability and Definability A central issue in modern econometrics has been the identification problem: how to use observational data to estimate the parameters of a theory, and the conditions under which such estimation is possible. A central issue in axiomatizing empirical theories has been the definition problem: determining which terms in a theory are to be defined, and which are to be treated as primitives. Section 2, and particularly Chapter 2.1, demonstrates that there is a very close relation between identification and causal ordering. Section 6 shows that there is also a very close relation between identifiability and the standard logical concept of defmability (as that term has been used by Tarski 4 ). Specifically, identifiability can be regarded as a weakened form of definability. Several chapters of Section 6 (in particular, Chapters 6.3,6.4,6.5 and 6.7) develop the idea that it is identifiability, rather than definability, that is wanted for theoretical terms in axiomatization of empirical theories.

17 GENERAL INTRODUCTION XIX 3.4. Complexity It is widely believed that the methods of analysis that have been so successful in treating 'simple' phenomena in the physical sciences may be inadequate for handling complex biological and social systems. The chapters of Section 4 explore this issue by trying to characterize the special properties that distinguish complex from simple systems. One of these properties is hierarchy, and we will see in Chapter 4.2 that causally ordered systems have a hierarchic structure that makes them amenable to analysis even when they are very large and complex. The topic of complexity is interesting both in its own right, and also as a basis for understanding the phenomena of problem solving by heuristic search, and hence of scientific discovery. Thus, the discussion of complexity in Section 4, based in turn upon the treatment of causal ordering in Section 2, provides an introduction to the topic of scientific discovery, which is dealt with in the chapters of Section Summary These, then, are some of the threads connecting the major sections of this book: concern for the processes of discovery and deemphasis of verification, treatment of the modalities in terms of model theory, use of the notion of identifiability in the interpretation of theoretical terms, a characterization of complexity, and an application of that characterization to the study of scientific discovery. Each of the six sections can be read independently of the others, but their arrangement in the book is neither accidental nor random. As we have seen, Sections 1 and 4 provide some conceptual foundations for Section 5, while Sections 2 and 3 provide underpinnings for Sections 4, 5 and 6. Apart from these ordering constraints, the sequence of topics corresponds, roughly, to the temporal sequence in which they occupied my thoughts. Where necessary, however, temporal order has been sacrified to topical coherence in arranging the chapters and sections. NOTES 1 New York: The Free Press, Third Edition, It is an unfortunate accident that the English language distinguishes orthographically between the very different notions of 'modal' and 'model' by only a single letter. 3'Logical Necessity, Physical Necessity, Ethics, and Quantifiers', Chapter 1 in Formal Philosophy (New Haven: Yale University Press, 1974). 4 'Some Methodological Investigations on the Definability of Concepts', in Logic, Semantics, and Metamathematics (Oxford: The Clarendon Press, 1956).