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Studies in the Methodology and Foundations of Science Synthese Library STUDIES IN THE METHODOLOGY AND FOUNDATIONS OF SCIENCE 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 Editors: DONALD DAVIDSON~Princeton University J AAKKO HINTIKKA, University of Helsinki and Stanford University GABRIEL NUCHELMANS, University of Leyden WESLEY C. SALMON, Indiana University PATRICK SUPPES STUDIES IN THE METHODOLOGY AND FOUNDATIONS OF SCIENCE Selected Papers from 1951 to 1969 SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. ISBN 978-90-481-8320-3 ISBN 978-94-017-3173-7 (eBook) DOI 10.1007/978-94-017-3173-7 1969 All rights reserved No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher Softcover reprint ofthe hardcover 1st edition 1969 TO ERNEST NAGEL AND ALFRED TARSKI PREFACE The twenty-three papers collected in tbis volume represent an important part of my published work up to the date of this volume. I have not arranged the paper chronologically, but under four main headings. Part I contains five papers on methodology concerned with models and measurement in the sciences. This part also contains the first paper I published, 'A Set of Independent Axioms for Extensive Quantities', in Portugaliae Mathematica in 1951. Part 11 also is concerned with methodology and ineludes six papers on probability and utility. It is not always easy to separate papers on probability and utility from papers on measurement, because of the elose connection between the two subjects, but Artieles 6 and 8, even though they have elose relations to measurement, seem more properly to belong in Part 11, because they are concerned with substantive questions about probability and utility. The last two parts are concerned with the foundations of physics and the foundations of psychology. I have used the term foundations rather than philosophy, because the papers are mainly concerned with specific axiomatic formulations for particular parts of physics or of psychology, and it seems to me that the termfoundations more appropriately describes such constructive axiomatic ventures. Part 111 contains four papers on the foundations of physics. The first paper deals with foundations of special relativity and the last three with the role ofprobability in quantum mechanics. I regret not ineluding some of the earlier work with J. C. C. McKinsey on the foundations of elassical mechanics, but I already have given an account in general terms of that work in the last chapter of my Introduction to Logic. The largest number of papers is in the final part on the foundations of psychology. The greater concentration of papers here correct1y refiects my interests over the past decade. In fact, the bulk of my papers that I think are of some conceptual importance and that are not ineluded in tbis volume are papers that lie strict1y within mathematical psychology as a VIII PREFACE scientific discipline, and are consequently not really appropriate for inc1usion in the present volume. Because so many of the papers in Part IV are concerned with the psychological foundations of mathematics in one form or another, it would almost have been appropriate to have so labeled Part IV. But I have inc1uded several papers that have nothing directly to do with his subject, and so I have kept the more general title. Two of the papers in this collection were written with co-authors. The fourth paper, 'Foundational Aspects of Theories of Measurement', was writtenjointly with Dana Scott. The eighth paper, 'An Axiomatization of Utility Based on the Notion of Utility Differences', was written jointly with Murie1 Winet. The appearance of these two papers here has been generously agreed to by them. Two of the papers have not previously been published. These are the papers, 'Behaviorism' and 'On the Theory of Cognitive Processes' . The first of these two papers was written between 1963 and 1965, and was given in various revised forms at Swarthmore College and at the University of Illinois. The second of the two papers was written in 1967 and was given as an Arnold Isenberg Memorial Lecture at Michigan State University. Acknowledgments for permission to publish the various papers are given at the bottom of the first page of each artic1e, but thanks are extended here to the many editors and publishers who generously granted this permission. No substantive or real stylistic changes have been made in any of the artic1es; only the manner of referring to published artic1es and books has been standardized, as has the formatting of seetion headings. Footnotes in the original articles are numbered, beginning anew with each artic1e; the bibliographie footnotes that originate with this publication are indicated by a dagger following the number. Same introduetory remarks about eaeh article and subsequent pertinent lit­ erature are to be found at the beginning of each part. The publication of aseries of papers spanning more than 18 years of work seems an appropriate occasion to acknowledge some of the intel­ lectual debts I have ineurred during those years. For my initial intro­ duction to the philosophy of science and for continual intellectual counsel and advice, I owe a great deal to Ernest Nagel. Shortly after my arrival at Stanford University in 1950, J. C. C. McKinsey joined the faculty of the Department of Philosophy, and I learned from hirn the set-theoretical PREFACE IX tools that have been one of my main stocks in trade over the years. Various collaborative work that we planned beyond the several articles we originaHy published was abruptly halted by his untimely death in 1953. McKinsey acknowledged that the greatest influence on his scientific career had been Alfred Tarski. Both through McKinsey and also through direct acquaintance with Tarski, inc1uding attendance at his seminars at Berkeley during the years when I was first at Stanford and through his published works as well, I learned much of what I know ab out intellectual c1arity and precision. And so, I take this occasion to acknowledge how much I owe to Tarski. I am indebted to William K. Estes for my first introduction to the conceptual and foundational problems of psychology, especially mathematical learning theory. We worked together intensively during 1955-56 when we were both Fellows at the Center for Advanced Study in the Behavioral Sciences at Stanford. In more recent years I have also learned much from Duncan Luce about both mathematical psychology and the theory of measurement. It is important to record that I owe a very considerable debt to my younger colleagues as well. I mention especiaHy Dana Scott and Richard C. Atkinson. The idea of putting this volume together originated with Donald Davidson and Jaakko Hintikka. To both ofthem I owe a further debt for enlightening and penetrating conversations about philosophical matters. This is especially true of Davidson, who was my colleague at Stanford for many years. Finally, I want to acknowledge the dedicated and able editorial assistance of Miss Diana Axelson and Mrs. Lillian O'Toole, as weH as the excellent help of Miss Anne Fagot in preparing the indexes and that of Mrs. Maria Jedd in preparing the illustrations. PATRICK SUPPES Stanford, California, January 1969 CONTENTS PREFACE VII PAR TI: METHODOLOGY: MODELS AND MEASUREMENT 1. A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences (1960) 10 2. Models of Data (1962) 24 3. A Set of Independent Axioms for Extensive Quantities (1951) 36 4. Foundational Aspects of Theories of Measurement (1958) (with Dana Scott) 46 5. Measurement, Empirical Meaningfulness, and Three-Valued Logic (1959) 65 PART Il: METHODOLOGY: PROB ABILITY AND UTILITY 81 6. The Role of Subjective Probability and Utility in Decision- Making (1956) 87 7. The Philosophical Relevance of Decision Theory (1961) 105 8. An Axiomatization of Utility Based on the Notion of Utility Differences (1955) (with Muriel Winet) 115 9. Behavioristic Foundations of Utility (1961) 130 10. Some Formal Models of Grading Principles (1966) 148 11. Probabilistic Inference and the Concept of Total Evidence (1966) 170 PART In: FOUNDATIONS OF PHYSICS 189 12. Axioms for Relativistic Kinematics with or without Parity (1959) 194 13. Probability Concepts in Quantum Mechanics (1961) 212 14. The Role of Probability in Quantum Mechanics (1963) 227 XII CONTENTS 15. The Probabilistic Argument for a Nonc1assical Logic of Quantum Mechanics (1966) 243 PART IV: FOUNDATIONS OF PSYCHOLOGY 253 16. Stimulus-Sampling Theory for a Continuum ofResponses (1960) 261 17. On an Example of Unpredictability in Human Behavior (1964) 285 18. Behaviorism (1965) 294 19. On the Behavioral Foundations of Mathematical Concepts (1965) 312 20. Towards a Behavioral Foundation of Mathematical Proofs (1965) 355 21. The Psychological Foundations of Mathematics (1967) 371 22. On the Theory of Cognitive Processes (1966) 394 23. Stimulus-Response Theory of Finite Automata (1969) 411 REFERENCES 445 INDEX OF NAMES 454 INDEX OF SUBJECTS 457 PART I METHODOLOGY: MODELS AND MEASUREMENT The five papers in this part examine some of the many issues surrounding the general use of models in empirical science, and also the conceptual foundations of the theory of measurement. In discussing both the general use of models and the particular case of measurement, I have tried to show in these papers how set-theoretical tools standard in modern mathematics can also be used to good advantage
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