THEORETICAL CONCEPTS AND HYPOTHETICO-INDUCTIVE INFERENCE SYNTHESE LIBRARY MONOGRAPHS ON EPISTEMOLOGY, LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE, AND ON THE MATHEMATICAL METHODS OF SOCIAL AND BEHA VIORAL SCIENCES Editors: DONALD DAVIDSON, The Rocke/eller UniversityandPrinceton University JAAKKO HINTIKKA, Academy 0/ Finland and Stan/ord University GABRltiL NUCHELMANS, University 0/ Leyden WESLEY C. SALMON, Indiana University THEORETICAL CONCEPTS AND HYPOTHETICO-INDUCTIVE INFERENCE by ILKKA NIINILUOTO Humanities Research Council, Academy 0/ Finland and RAIMO TUOMELA Department 0/ Phi/osophy, University 0/ He/sinki D. REIDEL PUBLISHING COMPANY DORDRECHT-HOLLAND / BOSTON-U.S.A. Library of Congress Catalog Card Number 73-83567 ISBN -13: 978-94-010-2598-0 e-ISBN -13: 978-94-010-2596-6 DOI: 10.1007/978-94-010-2596-6 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, Ine. 306 Dartmouth Street, Boston, Mass. 02116, U.S.A. All Rights Reserved Copyright © 1973 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover Ist edition 1973 No part of this book rnay be reproduced in any form, by print, photoprint, microfilm or any other means, without written perrnission from the publisher To Jaakko Hintikka CONTENTS PREFACE IX CHAPTER 1. THEORETICAL CONCEPTS AND INDUCTIVE INFERENCE 1 1. Problems of Inductive Systematization: the Transitivity Dilemma 1 2. Inductive Systematization Established by Theories 7 3. A Logical Framework for the Dynamies of Conceptual Change and Induction 13 CHAPTER 2. HINTIKKA'S TWO-DIMENSIONAL CONTINUUM OF INDUCTIVE LOGIC 22 1. Summary of Hintikka's Two-dimensional Continuum 22 2. The Treatment of Incomplete Evidence 27 CHAPTER 3. INDUCTIVE PROBABILITIES OF WEAK GENERALIZATIONS 30 1. Probabilities in the Observational Language 30 2. Evidential Theoretical Concepts 31 3. Non-Evidential Theoretica1 Concepts 43 CHAPTER 4. INDUCTIVE PROBABILITIES OF STRONG GENERALIZATIONS 51 CHAPTER 5. PIECEWISE DEFINABLE THEORETICAL CONCEPTS 57 CHAPTER 6. EPISTEMIC UTILITIES AND INDUCTIVE SYSTEMATIZATION 64 1. Measures of Information and Systematic Power 64 2. Expected Epistemic Utilities of Generalizations 70 3. Competing Generalizations 78 VIII THEORETICAL CONCEPTS AND INDUCTIVE INFERENCE CHAPTER 7. THEORETICAL CONCEPTS AND INDUCTIVE EXPLANATION 88 1. Explanatory Power of Theories 88 2. Inductive Explanation Illustrated 93 3. Positive Inductive Relevance, Supersessance, and Screening Off 96 4. Inductive Explanation within Hintikka's System 107 CHAPTER 8. CORROBORATION AND THEORETICAL CONCEPTS 118 1. Theoretical and Observational Support 118 2. Measures of Corroboration Based on Positive Inductive Relevance 120 3. Hintikka's Measure of Corroboration 128 CHAPTER 9. THE LOGICAL INDISPENSABILITY OF THEORETICAL CONCEPTS WITHIN INDUCTIVB SYSTEMA TIZATION 141 1. The Theoretician's Dilemma: MethodologicalInstrumentalism Refuted 141 2. Logical Indispensability and Positive Inductive Relevance 144 3. Logical Indispensability and Rules of Acceptance 148 CHAPTER 10. LINGUISTIC VARIANCE IN INDUCTIVE LOGIC 165 1. Linguistic Invariance and Linguistic Variance 165 2. Probability Kinematics 180 3. Goodman's New Riddle of Induction 186 CHAPTBR 11. TOWARDS A NON-INDUCTIVIST LOGIC OF INDUCTION 196 1. Deductivism and Inductivism 197 2. Hypothetico-Deductive and Hypothetico-Inductive Inference 205 3. The Atheoretical Thesis 212 4. Converse Deduction and Indirect Support 219 5. Conjectures 234 BIBLIOGRAPHY 246 SUBJECT INDEX 255 PREFACE Conceptual change and its connection to the development of new seien tific theories has reeently beeome an intensively discussed topic in philo sophieal literature. Even if the inductive aspects related to conceptual change have already been discussed to some extent, there has so far existed no systematic treatment of inductive change due to conceptual enrichment. This is what we attempt to accomplish in this work, al though most of our technical results are restricted to the framework of monadic languages. We extend Hintikka's system of inductive logic to apply to situations in which new concepts are introduced to the original language. By interpreting them as theoretica1 concepts, it is possible to discuss a number of currently debated philosophical and methodological problems which have previously escaped systematic and exact treatment. For instance, the role which seientific theories employing theoretical con cepts may play within inductive inference can be studied within this framework. From the viewpoint of seientific realism, sueh a study gives outlines for a theory of what we call hypothetico-induetive inference. Some parts of this work which are based on Hintikka's system of in ductive logic are fairly technical. However, no previous knowledge of this system is required, but, in general, acquaintance with the basic ideas of elementary logic and probability theory is suffieient. This work is part of a project, originated by Professors Jaakko Hintikka and Raimo Tuomela, concerning the role of theoretical concepts in science. Within this project, the study of the inductive aspects of this role was started in 1970 by Ilkka Niiniluoto. Works by Niiniluoto in which this study has been reported include the following: 'Can We Accept Lehrer's Inductive Rule?', Ajatus 33 (1971) 254-265; 'Inductive System atization: Definition and a Critical Survey', Synthese 25 (1972) 25-81; 'Inductive Systematization and Empirically Trivial Theories', in Logic, Language and Probability, A Selection 0/ Papers Contributed to Sections 4,6, and 11 o/the IVth International Congress 0/ Logic, Methodology and Philosophy o/Science, Bucharest, 1971 (ed. by R. Bogdan and I. Niiniluoto), X THEORETICAL CONCEPTS AND INDUCTIVE INFERENCE D. Reidel, 1973; andjointly with Jaakko Hintikka, 'On Theoretical Terms and Their Ramsey-Elimination: An Essay in the Logic of Science' (in Russian), Filosoftkiye Nauki 1 (1973) 49-61. Tuomela has discussed the oretical concepts within induction in 'The Role of Theoretical Concepts in Neobehavioristic Theories', Reports /rom the Institute 0/ Philosophy, University 0/ Helsinki, No. 1, 1971; and in Theoretical Concepts, Library of Exact Philosophy, vol. 10, Springer-Verlag, 1973. The latteris a systema tic study of theoretical concepts and their role within scientific theorizing. The study which led to this monograph was started in 1971 by the authors. This work, especially its philosophical and methodological con tent, was developed by means of intense discussions and detailed mutual criticism between the authors. As this work is a result of a joint attempt, in many cases it is not easy to distinguish the individual contributions of the authors. This applies at least to Chapters 1.2, 8.1, 8.3, and 11.5. Of the remaining part, Nüniluoto can be regarded as primarily responsible for Chapters 2-6, Chapter 7.4, Chapter 9, Chapter 10.1, and Chapter 11.1~, and Tuomela for the rest. We dedicate this work to Professor Jaakko Hintikka. This is not only a token of our deep gratitude for the encouragement we have received from him in completing this project, and in our philosophical work in general. In writing this monograph, Hintikka's studies in inductive logic and in semantic information theory have formed an indispensable starting point for uso An attempt to extend Hintikka's inductive system to cover a so far unexplored field is the best tribute we can pay to his fertile ideas on induction. During the writing of the present work, Niiniluoto has held a research assistantship at the Humanities Research Council (Valtion humanistinen toimikunta) in the Academy of Finland. Much of Tuomela's work was done in Montreal while he was on leave from his professorship at the University of Helsinki, and held a Killam postdoctoral fellowship granted by Canada Council. This study has partly been supported by the Emil Aaltonen Founda tion (Emil Aaltosen säätiö), which is gratefully acknowledged. We wish to thank Mr. Fred A. Fewster for checking the language of the present work. ILKKA NIINILUOTO He/sinki, December 1972 RAIMO TUOMELA CHAPTER 1 THEORETICAL CONCEPTS AND INDUCTIVE INFERENCE This work represents an attempt to clarify the role which theoretical con cepts may play within inductive scientific inference or inductive system atization. A study is made of some of the possible gains that accrue from the introduction of theories employing new theoretical concepts. We are especially interested in gains for which theoretical concepts are logically indispensable, as they provide us with strong methodological reasons for the introduction and employment of theoretical concepts. We have re stricted ourselves to dealing with relatively simple kinds of theories, which may be taken to exemplify theories from the primarily non-quantitative sciences. The role of theoretical terms within hypothetico-deductive theorizing has recently been discussed rather intensively. However, so far, no sys tematic account has existed of their function within inductive inference. Even the very possibility of such an account has been questioned. In contrast with this, our work is an attempt to develop a framework for discussion of the role of theoretical concepts within what will be termed hypothetico-inductive inference. Such a framework has to cope with a number of problems not present in deductive inference. Perhaps the best known of these problems are those resulting from the lack of reasonable transitivity properties of inductive inference. As an introduction to the problems discussed in this study, we begin by showing how a 'transitivity dilemma' arises in connection with theoretical concepts and inductive inference. Another related problem discussed in this introductory chapter is how one can account for the efIect of conceptual change on induction. 1. PROBLEMS OF INDUCTIVE SYSTEMATIZATION: THE TRANSITIVITY DILEMMA 1.1. In his well-known article 'The Theoretician's Dilemma', of 1958, Carl G. Hempel argued that even if theoretical concepts may be logically dispensable for the deductive systematization of observational statements,