Table Of ContentTHEORETICAL 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,
