a. f. kuipers - from instrumentalism to constructive realism - on some relations between...

FROM INSTRUMENTALISM TO CONSTRUCTIVE REALISM

SYNTHESE LIBRARY

STUDIES IN EPISTEMOLOGY,

LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE

Managing Editor:

JAAKKO HINTIKKA, Boston University

Editors:

DIRK VAN DALEN, University of Utrecht, The Netherlands DONALD DAVIDSON, University of California, Berkeley

THEO A.F. KUIPERS, University of Groningen, The Netherlands PATRICK SUPPES, Stanford University, California

JAN WOLENSKI, iagiellonian University. Krakow, Poland

VOLUME 287

FROM INSTRUMENTALISM TO CONSTRUCTIVE REALISM

On Some Relations between Confirmation, Empirical Progress, and Truth Approximation

by

THEO A.F. KUIPERS University of Groningen, The Netherlands

SPRINGER-SCIENCE+BUSINESS MEDIA, B.Y.

A catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-5369-5 ISBN 978-94-017-1618-5 (eBook) DOI 10.1007/978-94-017-1618-5

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Originally published by K1uwer Academic Publishers in 2000 No part of the material protected by this copyright notice may be reproduced

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TABLE OF CONTENTS

FOREWORD ix

CHAPTER 1: GENERAL INTRODUCTION: EPISTEMOLOGICAL POSITIONS

1.1. Four perspectives on theories 1 1.2. The four main epistemological questions 3 1.3. The main epistemological and methodological claims 8 1.4. Preliminaries and a survey of cognitive structures 10

PART I: CONFIRMATION

INTRODUCTION TO PART I 15

CHAPTER 2: CONFIRMATION BY THE HD-METHOD 17 2.1. A qualitative theory of deductive confirmation 21 2.2. Ravens, emeralds, and other problems and solutions 27 2.3. Acceptance of hypotheses 38

CHAPTER 3: QUANTITATIVE CONFIRMATION, AND ITS 43 QUALITATIVE CONSEQUENCES

3.1 . Quantitative confirmation 44 3.2. Qualitative consequences 55 3.3. Acceptance criteria 65 Appendix 1: Corroboration as inclusive and impure 68

confirmation Appendix 2: Comparison with standard analysis of the raven 70

paradox

CHAPTER 4: INDUCTIVE CONFIRMATION AND INDUCTIVE 73 LOGIC

4.1. Inductive confirmation 4.2. The continuum of inductive systems 4.3. Optimum inductive systems 4.4. Inductive analogy by similarity and proximity 4.5. Universal generalizations

v

74 77 79 80 83

vi TABLE OF CONTENTS

PART II: EMPIRICAL PROGRESS

INTRODUCTION TO PART II 91

CHAPTER 5: SEPARATE EVALUATION OF THEORIES BY THE 93 HD-METHOD

5.1. HD-evaluation of a theory 95 5.2. Falsifying general hypotheses, statistical test implications, 103

and complicating factors

CHAPTER 6: EMPIRICAL PROGRESS AND PSEUDOSCIENCE 111 6.1. Comparative HD-evaluation of theories 111 6.2. Evaluation and falsification in the light of truth 120

approximation 6.3. Scientific and pseudoscientific dogmatism 126

PART III: BASIC TRUTH APPROXIMATION

INTRODUCTION TO PART III 137

CHAPTER 7: TRUTH LIKENESS AND TRUTH APPROXIMATION 139 7.1. Actual truthlikeness 142 7.2. Nomic truthlikeness 146 7.3. Actual and nomic truth approximation 154 7.4. Survey of bifurcations 165 7.5. Novel facts, crucial experiments, inference to the best 166

explanation, and descriptive research programs

CHAPTER 8: INTUITIONS OF SCIENTISTS AND PHILOSOPHERS 173 8.1. Conceptual foundations of nomic truth approximation 173 8.2. Truthlikeness and the correspondence theory of truth 190 8.3. Explicating dialectical concepts 198

CHAPTER 9: EPISTEMOLOGICAL STRATIFICATION OF NOMIC 208 TRUTH APPROXIMATION

9.1. Theoretical and substantial nomic truth approximation 209 9.2. Referential truth approximation 219 9.3. Rules of inference, speculations, extensions, and 228

explanatory research programs 9.4. Epistemological positions reconsidered 236

TABLE OF CONTENTS

PART IV: REFINED TRUTH APPROXIMATION

INTRODUCTION TO PART IV

CHAPTER 10: REFINEMENT OF NOMIC TRUTH APPROXIMATION

vii

243

245

10.1. Structurelikeness 246 10.2. Refined nomic truthlikeness and truth approximation 249 10.3. Foundations of refined nomic truth approximation 262 10.4. Application: idealization & concretization 268 to.5. Stratified refined nomic truth approximation 272

CHAPTER 11: EXAMPLES OF POTENTIAL TRUTH 278 APPROXIMATION

11.1. The old quantum theory 278 11.2. Capital structure theory 288

CHAPTER 12: QUANTITATIVE TRUTHLIKENESS AND TRUTH 299 APPROXIMATION

12.1. Quantitative actual truth likeness and truth approximation 301 12.2. Quantitative nomic truthlikeness 302 12.3. Quantitative nomic truth approximation 308

CHAPTER 13: CONCLUSION: CONSTRUCTIVE REALISM 317 13.1. Main conclusions 317 13.2. Three types of induction 320 13.3. Formation of observation terms 322 13.4. Direct applicability of terms 324 13.5. The metaphysical nature of scientific research 325 13.6. Portraits of real and fictitious scientists 327 13.7. Reference and ontology 329 13.8. Truth definitions and truth criteria 330 13.9. Metaphors 331

NOTES 334

REFERENCES 347

INDEX OF NAMES 355

INDEX OF SUBJECTS 359

FOREWORD

Over the years, I have been working on two prima facie rather different, if not opposing, research programs, notably Carnap's confirmation theory and Popper's truth approximation theory. However, I have always felt that they were compatible, even smoothly synthesizable, for all empirical scientists use confirmation intuitions, and many of them have truth approximation ideas. Gradually it occurred to me that the glue between confirmation and truth approximation was the instrumentalist or evaluation methodology, rather than the falsificationist one. By separate and comparative evaluation of theories in terms of their successes and problems, hence even if already falsified, the evaluation methodology provides in theory and practice the straight route for short-term empirical progress in science in the spirit of Laudan. Further analysis showed that this sheds also new light on the long-term dynamics of science and hence on the relation between the main epistemological positions, viz., instrumentalism, constructive empiricism, referential realism, and theory real-ism of a non-essentialist nature, here called constructive realism. Indeed, thanks to the evaluation methodology, there are good, if not strong, reasons for all three epistemological transitions "from instrumentalism to constructive realism".

To be sure, the title of the book is ambiguous. In fact it covers (at least) three interpretations. Firstly, the book gives an explication of the mentioned and the intermediate epistemological positions. Secondly, it argues that the successive transitions are plausible. Thirdly, it argues that this is largely due to the instrumentalist rather than the falsificationist methodology. However, to clearly distinguish between the instrumentalist methodology and the instru-mentalist epistemological position, the former is here preferably called the evaluation methodology. In the book there arises a clear picture of scientific development, with a short-term and a long-term dynamics. In the former there is a severely restricted role for confirmation and falsification, the dominant role is played by (the aim of) empirical progress, and there are serious prospects for observational, referential and theoretical truth approximation. Moreover, the long-term dynamics is enabled by (observational, referential and theoretical) inductive jumps, after 'sufficient confirmation', providing the means to enlarge the observational vocabulary in order to investigate new domains of reality.

This book presents the synthesis of many pieces that were published in various journals and books. Material of the following earlier publications or publica-tions to appear has been used, with the kind permission of the publishers:

IX

x FOREWORD

'The qualitative and quantitative success theory of confirmation" Part 1 and 2, to appear in Logique et Analyse. (Chapter 2, 3).

"The Carnap-Hintikka programme in inductive logic", in Knowledge and Inquiry: Essays on laakko Hintikka's epistemology and philosophy of science, ed. Matti Sintonen, Poznan Studies, Vol. 51, 1997, pp. 87-99. (Chapter 4).

"Explicating the falsificationist and the instrumentalist methodology by decomposing the hypothetico-deductive method", in Cognitive patterns in sci-ence and common sense, eds. T. Kuipers and A.R. Mackor, Poznan Studies, Vol. 45, Rodopi, Amsterdam, 1995, pp. 165-186. (Chapter 5).

"Naive and refined truth approximation", Synthese, 93, 1992, 299- 341. (Chapter 7, 9, 10).

"The dual foundation of qualitative truth approximation", Erkenntnis, 47.2, 1997,145-179. (Section 8.1., Chapter 10).

"Truthlikeness and the correspondence theory of truth", Logic, Philosophy of Science and Epistemology, Proc. 11th Wittgenstein Symp. 1986, Wenen, 1987, 171-176. (Section 8.2.).

"Structuralist explications of dialectics", in: Advances in scientific philosophy. Essays in honour of Paul Weingartner on the occasion of the 60-th anniversary of his birthday, eds. G. Schurz and G. Dorn, Poznan Studies, Vol. 24, Rodopi, Amsterdam, 1991,295-312. (Section 8.3.).

"Comparative versus quantitative truthlikeness definitions. Reply to Mormann", Erkenntnis, 47.2, 1997, 187- 192. (Chapter 10).

"Sommerfeld's Atombau: a case study in potential truth approximation", together with H. Hettema, in Cognitive patterns in science and common sense, eds T. Kuipers and A.R. Mackor, Poznan Studies, Vol. 45, Rodopi, Amsterdam, 1995, pp. 273-297. (Section 11.1.)

"Truth approximation by concretization in capital structure theory", together with K. Cools and B. Hamminga, in: Idealization VI: Idealization in economics, eds B. Hamminga and N.B. de Marchi, Poznan Studies, Vol. 38, Amsterdam, Rodopi, 1994, pp. 205- 228. (Section 11.2.).

Many people have contributed over the years to my writing and teaching about these subjects. To begin with the PhD-students who were engaged in related research: Roberto Festa, Bert Hamminga, Hinne Hettema, Yao-Hua Tan, Henk Zandvoort and Sjoerd Zwart. I profited a lot from interaction with them. Moreover, I gratefully acknowledge the permission of the co-authors Hinne Hettema, and Kees Cools and Bert Hamminga to use for CHAPTER 11 the main parts of two earlier joint publications on applications of truthlikeness ideas in physics and economics, respectively.

I would also like to thank many others who have critically commented upon underlying research and previous versions of chapters: David Atkinson, Wolfgang Balzer, Johan van Benthem, Anne Boomsma, Roger Cooke, Domenico Costantini, Anton Derksen, Igor Douven, Job van Eck, Arthur Fine, Kenneth Gemes, Carl Hempel, Johannes Heidema, Jaakko Hintikka, Richard

FOREWORD Xl

Jeffrey, Otto Kardaun, Erik Krabbe, David Miller, Ivo Molenaar, Hans Mooij, Thomas Mormann, Ulises Moulines, Wim Nieuwpoort, Ilkka Niiniluoto, Leszek Nowak, Graham Oddie, David Pearce, Karl Popper, Hans Radder, Hans Rott, Willem Schaafsma, Gerhard Schurz, Abner Shimony, Brian Skyrms, Wolfgang Spohn, Peter Urbach, Nicolien Wierenga, Andrzej Wisniewski, Sandy Zabell, Gerhard Zoubek, and Jan Zytkow.

The opportunity to write this book was provided by three important factors. First, I got a sabbatical year (96/97) from my home university, the University of Groningen, the Netherlands. Second, I was, after fourteen years, again invited as a fellow for a year at the Dutch work-paradise for scholars, the Netherlands Institute for Advanced Study of the Royal Dutch Academy of Sciences (NIAS, in Wassenaar, near Leiden). The support of the staff was in various respects very pleasant and efficient. I am especially grateful to Anne Simpson and Jane Colling for editing my English. Third, and finally, three colleagues and friends were willing to read and comment upon the entire manuscript: Roberto Festa, Ilkka Niiniluoto, Andrzej Wisniewski, and some others were willing to comment upon one or more chapters: Kenneth Gemes and Hans Radder. Of course, the responsibility for any shortcomings is mine.

Theo A.F. Kuipers, September 1999, Groningen, The Netherlands

1 GENERAL INTRODUCTION:

EPISTEMOLOGICAL POSITIONS

Introduction We will start by sketching in a systematic order the most important epistemo-logical positions in the instrumentalism-realism debate, viz., instrumentalism, constructive empiricism, referential realism and theory realism. They will be ordered according to their answers to a number of leading questions, where every next question presupposes an affirmative answer to the foregoing one. The survey is restricted to the investigation of the natural world and hence to the natural sciences. It should be stressed that several complications arise if one wants to take the social and cultural world into account. However, the present survey may well function as a point of departure for discussing episte-mological positions in the social sciences and the humanities.

We will not only include the different answers to the standard questions concerning true and false claims about the actual world, but also the most plausible answers to questions concerning claims about the nomic world, that is, about what is possible in the natural world. Moreover, we will include answers to questions about 'actual' and 'nomic' truth approximation. At the end we will give an indication of the implications of the results of the present study of confirmation, empirical progress and truth approximation for the way the epistemological positions are related. The main conclusions are the following: there are good reasons for the instrumentalist to become a con-structive empiricist; in his turn, in order to give deeper explanations of success differences, the constructive empiricist is forced to become a referential realist; in his turn, there are good reasons for the referential realist to become a theory realist of a non-essentialist nature, here called a constructive realist.

1.1. FOUR PERSPECTIVES ON THEORIES

The core of the ongoing instrumentalism-realism debate is the nature of proper theories, that is, theories using theoretical terms, or rather the attitude one should have towards them. Proper theories arise from the two-level distinction between observational and theoretical terms, as opposed to observational laws and theories, which only use, by definition, observation terms. The resulting two-level distinction between observational laws and proper theories gives rise

2 GENERAL INTRODUCTION: EPISTEMOLOGICAL POSITIONS to a short-term dynamics in the development of scientific knowledge. That is, as we will elaborate in Part I, observational hypotheses are tested and may be falsified or 'sufficiently' confirmed such that they become accepted. On the other hand, as we will elaborate in Part II, proper theories are, before and after falsification, evaluated and compared in terms of the observational laws they contradict or are able to successfully explain and predict. The survey of positions will primarily be presented in terms of this short-term dynamics. However, from time to time we will also take the long-term dynamics into account generated by the transformation of proper theories into observation theories and giving rise to a multi-level distinction according to which proper theories may not only explain or predict a lower level observational law, but also be presupposed by a higher level one. For the main positions the view on the nature of proper theories implies also a view on the nature of the indicated short-term and long-term dynamics.

For most of the positions it makes sense to distinguish four possible perspec-tives on the nature of theories in general. First, we may distinguish two versions or modes of the natural world, the one called the actual world, that is, the natural world of the past, the present and the future, the other called the nomic world, that is, the natural world in the sense of all conceivable possibilities that are physically possible. The actual world is of course in some sense part of the nomic world. The two versions will lead to two modes of each position, that is, the 'actualist' version, merely pertaining to the actual world, and the nomic version, which primarily pertains to the nomic world. Second, one's primary focus may be the truth-value of claims about the (actual or nomic) natural world, or claims about truth approximation, that is, claims of the form that one theory is closer to the (actual or nomic) truth than another.

In sum, there are four possible (primary) perspectives on the nature of observational and proper theories, depicted in Table 1.1, in which we mention some leading authors representing the realist tradition! . Below we will see that anti-realist authors such as Van Fraassen usually subscribe to the standard, actualist and truth-value oriented, perspective, restricted to observational theo-ries, of course.

Table 1.1. Four (realist) perspectives on theories

Mode

Focus

Truth-value Truth approximation

Actual

Standard/traditional Peirce/ Niiniluoto

Nomic

Giere Popper

Taking the variety of (versions of) positions seriously, implies that the notions of 'true' and 'false' are assumed to have adapted specifications, that is, 'true' and 'false' may refer to the actual or the nomic world and may concern observationally, referentially, or theoretically true and false, respectively. The

GENERAL INTRODUCTION: EPISTEMOLOGICAL POSITIONS 3

same holds for the notion of 'the truth', but it should be stressed in advance that it will always be specified in a domain-and-vocabulary relative way. Hence, no language independent metaphysical or essentialist notion of 'THE TRUTH' is assumed. With this in mind, let us start with the successive questions.

The first question really is not an epistemological question, but a preliminary ontological question.

Question 0: Does a natural world that is independent of human beings exist?

The question of whether there is a human-independent natural world is to some extent ambiguous. If one thinks in terms of a conceptualized natural world, that is, a world that in some way or other brings one or more conceptual-izations with it, then one has to assume either a kind of essences underlying the natural world, or one has to assume a non-human designer of the natural world, or some human intervention. We take the question in the other sense, that is, does a non-conceptualized natural world independent of human beings exist? If one answers this question negatively one takes the position of (straight-forward) ontological idealism. If one answers it positively we will speak of ontological realism. It is certainly questionable (Rescher 1992) whether so-called idealists, like Berkeley, really subscribed to ontological idealism. However this may be, and this is our main argument, it is highly implausible and not taken seriously by natural scientists. The positive answer may be plausible in the actualist version, it is not evident in the nomic version. To speak meaningfully about physical or, more generally, nomic possibilities seems to require at least some conceptualization. However, in the same way, to say something specifi-cally about the actual world presupposes some conceptualization. Hence, as far as the role of conceptualizations is concerned, it can be argued that if one believes in an unconceptualized actual world, which can be conceptualized in different ways, one may equally well believe in an unconceptualized nomic world, which can be conceptualized in at least as many ways. To be precise, there are more, because in order to conceptualize the nomic world it is plausible to take also dispositions into account which do not seem to be of any use in characterizing the actual world. Apart from the comparable (epistemological!) role of conceptualizations, it is clear that nomic ontological realism makes a stronger ontological claim than actual ontological realism. In the following, it will be clear when the nomic version is presupposed and when the actual version suffices.

1.2. THE FOUR MAIN EPISTEMOLOGICAL QUESTIONS

The first really epistemological question is:

Question 1: Can we claim to possess true claims to knowledge about the natural world?

4 GENERAL INTRODUCTION: EPISTEMOLOGICAL POSITIONS

Again it is important to first eliminate some ambiguities in this question. A positive answer to this question does not presuppose that true claims can be known to be true with certainty in some fundamental sense, nor that they can be verified or can be recognized as true or can be obtained in some other way. Moreover, a positive answer evidently does not presuppose that the true claims the question refers to do not depend on a conceptualization, for the formulation of claims requires a vocabulary. What is intended is only that the claim that we can have good reasons for assuming that certain claims, by definition phrased in a certain vocabulary, about the natural world are true in some objective sense, whereas others are false. The negative answer amounts to the position of epistemological relativism, the positive answer may be called epi-stemological realism, with an actual and a nomic version, depending on whether all of these claims are just claims about the actual world or some about the nomic world. As with the position of ontological idealism, the position of epistemological relativism is hard to take seriously in some straightforward, consistent way when dealing with scientific knowledge and knowledge develop-ment, despite the fact that it has played a dominant role in the history of epistemology in the form of skepticism of one kind or another. The main forms of skepticism are experiential skepticism, that is, skepticism with respect to claims about sensory and introspective experiences and inductive skepticism, that is, skepticism merely with respect to inductive extrapolations in the sense of inductive predictions or inductive generalizations. Scientists can escape skepticism by always taking the possibility of experiential illusions and induc-tive mistakes seriously. As a consequence, although skepticism still plays an important role in philosophical curricula and, as a matter of fact, recently became fashionable in certain, so-called postmodern, circles, it does not concern the core issue between realism and instrumentalism.

The next question brings us to the heart of the distinction between observa-tional and theoretical terms. Assuming a certain definition of observability and hence of the border between observational and theoretical terms, the following question arises:

Question 2: Can we claim to possess true claims to knowledge about the natural world beyond what is observable?

In other words, the question is whether more than observational knowledge, that is, knowledge in observation terms, is possible. A negative answer only makes sense, of course, if the notion of observability is relatively fixed. Our human observation possibilities might be extended, or just change, due to some evolutionary or artificial change of our physiological abilities. Moreover, they might be extended by accepting some observational laws, that enable the definition of new concepts. However, in case of the negative answer, one has to exclude the possibility of extension of the observable on the basis of the acceptance of proper theories. In other words, the transformation process of

GENERAL INTRODUCTION: EPISTEMOLOGICAL POSITIONS 5 proper theories into observation theories, such as the atomic theory of matter became for nuclear physics, has then to be conceived as merely a way of speaking, giving rise to other kinds of as-if-behavior. A positive answer to the present question amounts to so-called scientific realism, according to which proper theories, or at least theoretical terms, have to be taken seriously. A negative answer might be said to reflect observational realism or just empiricism.

As a matter of fact, there are two well-known types of the negative answer to Q2. According to the first type, usually called instrumentalism, talking about reference of theoretical terms does not make sense, let alone talking about true or false (proper) theories. This way of talking reflects according to the instru-mentalist a kind of category mistake by mistakenly extrapolating meaningful terminology for the observational level to the theoretical level. The only func-tion of proper theories is to provide good derivation instruments, that is, they need to enable the derivation of as many true observational consequences as possible and as few false observational consequences as possible. Hence, the ultimate aim of the instrumentalist is the best derivation instrument, if any. Well-known representatives of the instrumentalist position among philosophers are Schlick (1938) and Toulmin (1953). Although Laudan (1977,1981) admits that theories have truth-values, he is frequently called an instrumentalist because of his methodology, according to which theories are not disqualified by falsification as long as they cannot be replaced by better ones. Moreover, although debatable, the physicist Bohr is a reputed instrumentalist, at least as far as quantum mechanics is concerned. Notice that it is plausible to make the distinction between an actual and a nomic version of instrumentalism depend-ing on whether the relevant true and false observational consequences all pertain to the actual world or at least some to the nomic world.

According to the second type of negative answer to Q2, called (constructive) empiricism by its inventor and main proponent Van Fraassen (1980, 1989), there is no category mistake, that is, the point is not whether or not theoretical terms can refer and whether proper theories can be true or false. In fact, such terms mayor may not refer and such theories are true or false, but the problem is that we will never know this beyond reasonable doubt. Hence, what counts is whether such theories are empirically adequate or inadequate or, to use our favorite terminology, whether they are observationally true or false. Again there are two versions, actual and nomic empiricism, depending on whether the theories are supposed to deal all with the actual world or at least some with the nomic world. Although Van Fraassen is clear about his non-nomic intentions, the nomic analogue has some plausibility of its own. That is, it makes perfect sense to leave room for observational dispositions, without taking theoretical terms of other kinds seriously. In other words, if one conceives dispositions in general, hence including observational dispositions, as theoreti-cal terms, one may well reserve a special status for observational dispositions. In both versions, it makes sense to talk about the observational truth in the sense of the strongest true observational hypothesis about a certain domain of

6 GENERAL INTRODUCTION: EPISTEMOLOGICAL POSITIONS the natural world within a certain vocabulary. Assuming that it is also possible to make sense of the idea that (the observational theory following from) one theory is closer to the observational truth than another, even convergence to the observational truth is possible. As suggested, Van Fraassen is a strong defender of empiricism in the traditional, that is, actualist and truth-value oriented, perspective, where it should be remarked that his attitude is strongly influenced by his interest in quantum mechanics. Although Van Fraassen extrapolates this attitude to other proper theories, there are also scientists, in fact there are many, who take advantage of the fact that there may be examples of proper theories towards which an empiricist attitude is the best defensible one, whereas there are other examples towards which a realist attitude is the best defensible one. This gives rise to what Dorling (1992) has aptly called local positivist versus realist disputes, as opposed to the global dispute about whether it is a matter of yes or no for all proper theories at the same time. In this respect the empiricist attitude is usually identified with a position in the global dispute, the realist positions that follow usually leave room for local empiricist deviations from the globally realist attitude, as a kind of default heuristic rule.

As remarked already, for both types of empiricists, the long-term dynamics in science, according to which proper theories transform into observation theories, has to be seen as an as-if way of speaking. The question even arises whether this is really a coherent way of deviating from scientific practice where it seems totally accepted that the concept of observation is stretched to the suggested theory-laden interpretation.

Hence, it is time to turn to the positive answer to Q2, that is, to the position called scientific realism. Since the books by Hacking (1983) and Cartwright (1983) there is a weaker version of realism than the traditional one, which is suggested by the next question.

Question 3: Can we claim to possess true claims to knowledge about the natural world beyond (what is observable and) reference claims

concerning theoretical terms?

Whereas Hacking and Cartwright, when answering this question in the negative sense, primarily think of reference of entity terms, and call their position entity realism, it is highly plausible to extrapolate that position to attribute terms, in some plausible sense of reference, and speak of referential realism.2 According to referential realism, entity and attribute terms are intended to refer, and frequently we have good reasons to assume that they do or do not refer. Again it is possible to distinguish an actual and a nomic version, not only with respect to observational consequences, but also with respect to theoretical terms. For instance, when one takes the existence of atoms in the actual world seriously, which goes beyond empiricism, it is also defensible to take the existence of physically possible atoms seriously, even if they do not (yet) exist in the actual


world. In a sense this is just a definition of (existence in) the nomic world, as encompassing the actual world. Moreover, in both versions it is possible that one theory is observationally and referentially closer to the truth than another, as soon as we assume, in addition to the previous assumptions for observational truth approximation, that it is possible to define the idea that (the total referential claim of) one theory can be closer to the referential truth than another. Here, the referential truth is of course the strongest true referential claim which can be made within a certain vocabulary about a certain domain. However, since referentialists do not want to take theoretical induction seriously, that is, deciding to further assume that a certain proper theory is true (see further below), the transformation of proper theories into observation theories is for them no more open than for empiricists, i.e., it is open only in some as-if-reading. Referential realism seems, however, more difficult to defend than constructive empiricism, in particular when one takes the possibility of truth approximation into account. That is, as long as one is only willing to think in terms of true and false claims about theoretical terms when they are supposed to refer, one may be inclined to hold that most of these claims, past and future ones, are false. However, as soon as one conceives of sequences of such claims that may approach the truth, it is hardly understandable that the truth would not be a worthwhile target, at least in principle. Hence, let us turn to the suggested stronger position.

The positive answer to Q3 brings us to so-called theoretical or theory realism, in some version or another advocated by, for instance, Peirce (1934), Popper (1963), and Niiniluoto (1987a)3. Theory realism shares with referential realism the claim that theoretical terms are supposed to refer, and that, from time to time, we have good reasons to assume that they refer, including the correspond-ing truth approximation claims. It adds to this the claim that theories are claimed to be true, and that we have from time to time good reasons to further assume that they are true, that is, to carry out a theoretical induction. Moreover, proper theories can converge to the theoretical truth, that is, the strongest true claim that can be made, in a given vocabulary, about a specific domain, again leaving room for an actual and a nomic version. Although the truth to be approached is again domain-and-vocabulary relative, this does not exclude, of course, the possibility of comparison and translation of theories. Moreover, theoretical induction is always a matter for the time being, a kind of temporal default rule: as long as there is no counter-evidence, it is assumed to be true. This default-assumption not only implies that the theoretical terms of the theory then are assumed to refer, but also that the proper theory can from then on be used as an observation theory. Hence, the transformation process and the corresponding long-term dynamics are possible.

The last question to be considered is the following:

Question 4: Does there exist a correct or ideal conceptualization of the natural world?

8 GENERAL INTRODUCTION: EPISTEMOLOGICAL POSITIONS In contrast to the positive answers on the questions Q1 to Q3, a posItive answer to the fourth question brings us to a position that is not purely epistemologically built on the positive answer to QO (i.e., ontological realism), viz., it amounts to an extreme kind of metaphysical realism which we like to call essentialistic realism. The reason to call it this is, of course, that if there is an ideal conceptualization then the natural world must have essences of a kind. For instance, there must be natural kinds, not only in some pragmatic sense, but in the sense of categories in which entities in the actual or the nomic world perfectly fit. Philosophers of science like Boyd (1984) and Harre (1986) seem to come close to this point of view. According to this extreme form of realism, the challenge of science is to uncover the ideal conceptualization, that is, to discover and extend the ideal vocabulary, on the basis of which perfect observa-tional, referential and theoretical truths can be formulated. Refinement of this vocabulary is not so much directed at more precise and deeper truths, but at additional truths. Of course, it is possible to restrict the idea of an ideal vocabulary to an observational vocabulary, but there do not seem to be representatives of this kind of 'essentialistic empiricism'. It will also be clear that there is again an actual and a nomic version, but if one is an essentialist, the nomic version seems to be the most plausible one.

The negative answer to Q4 gives rise to what we call constructive realism.4 The term was already used by Giere (1985) in more or less the same way. The difference is that Giere does not take truth approximation into account. Peirce, Popper and Niiniluoto, however, do take truth approximation into account. Moreover, whereas Peirce and Niiniluoto focus on the actual version, Popper and Giere seem to have primarily the nomic version in mind, without excluding the actual version. In our view, the nomic version of constructive realism is the best fit to scientific practice. The adjective 'constructive' is used for more or less the same reason as it is used by Van Fraassen, in his case restricted to the observational level. Vocabularies are constructed by the human mind, guided by previous results. Of course, one set of terms may fit better than another, in the sense that it produces, perhaps in cooperation with other related vocabularies, more and/or more interesting truths about the domain than another. The fruitfulness of alternative possibilities will usually be comparable, at least in a practical sense, despite the possibility of fundamental incommensu-rability. There is however no reason to assume that there comes an end to the improvement of vocabularies.

We summarize the preceding survey in Figure 1.1.

1.3 . THE MAIN EPISTEMOLOGICAL AND METHODOLOGICAL CLAIMS

We consider instrumentalism, constructive empiricism, referential realism, and constructive realism to be the main epistemological positions. With the empha-sis on their nomic interpretation, they will be further characterized and com-pared in the light of the results of the analysis of confirmation, empirical


00: independent natural world?

yes D ontological realism 01: true claims about natural world?

yes D epistemological realism 02: beyond the observable?

yes D scientific realism 03: beyond reference?

yes D theory realism 04: ideal conceptualization?

yes D essentialistic realism

c:=::::::=> no

> no

~ no

:> no

> no

Figure 1.1. The main epistemological positions

ontological idealism

epistemological relativism 'experiential skepticism 'inductive skepticism

empiricism (observational realism) , instrumentalism

, constructive empiricism

referential realism => entity realism

constructive realism

progress and truth approximation in the rest of this book. The main results will come available at the end of Chapter 2, 6, 9, and finally in Chapter 13. A brief indication of the results is the following.

There are good reasons for the instrumentalist to become a constructive empiricist; in his turn, in order to give deeper explanations of success differences, the constructive empiricist is forced to become a referential realist; in his turn, there are good reasons for the referential realist to become a theory realist. The theory realist has good reasons to choose for constructive realism, since there is no reason to assume that there are essences in the world. Notice that the road to constructive realism amounts to a pragmatic argumentation for this position, where the good reasons will mainly deal with the short-term and the long-term dynamics generated by the nature of, and the relations between, confirmation, empirical progress and truth approximation.

Besides these epistemological conclusions, there are some general methodologi-cal lessons to be drawn. There will appear to be good reasons for all positions not to use the falsificationist but the instrumentalist or 'evaluation(ist), methodol-ogy. That is, the selection of theories should exclusively be guided by more empirical success, even if the better theory has already been falsified. Hence, the methodological role of falsifications will be strongly relativized. This does not at all imply that we dispute Popper's claim that aiming at falsifiable theories is characteristic for empirical science, on the contrary, only falsifiable theories can obtain empirical success. Moreover, instead of denouncing the hypothetico-deduc-tive method, the evaluation methodology amounts to a sophisticated application


of that method. As suggested, the evaluation methodology may also be called the instrumentalist methodology, because the suggested methodology is usually asso-ciated with the instrumentalist epistemological position. The reason is, of course, that from that position it is quite natural not to consider a theory as seriously disqualified by mere falsification. However, since we will argue that that methodol-ogy is also very useful for the other positions, we want to terminologically separate the instrumentalist methodology from the instrumentalist epistemological posi-tion, by calling the former the evaluation methodology, enabling to identify 'instru-mentalism' with the latter.

We close this section with a warning. The suggested hierarchy of the heuristics corresponding to the epistemological positions is, of course, not to be taken in a dogmatic sense. That is, when one is unable to successfully use the constructive realist heuristic, one should not stick to it, but try weaker heuristics, hence first the referential realist, then the empiricist, and finally the instrumentalist heuris-tic. For, as with other kinds of heuristics, although not everything goes always, pace (the suggestion of) Feyerabend, everything goes sometimes. Moreover, after using a weaker heuristic, a stronger heuristic may become applicable at a later stage: "reculer pour mieux sauter".

1.4. PRELIMINARIES AND A SURVEY OF COGNITIVE STRUCTURES

The book is written in terms of three background assumptions. They concern cognitive structures, research programs, and the structuralist view on theories. These and many other topics are elaborated in a twin book, entitled Structures in Science (Kuipers (SiS, consciously alluding to Ernest Nagel's seminal The Structure of Science.

In our view, the main aim of philosophy of science is to uncover (cognitive) structures in knowledge and knowledge development. The underlying assump-tion is, of course, that there is system in them. Research programs in the spirit of Lakatos are a kind of macro-structures and can be classified into four ideal-types: descriptive, explanatory, design and explication research programs. Although they have different goals, they have similar fine-structures, provided they are centered around a strong idea. This book deals with some explication programs, notably, around confirmation in the spirit of Carnap and Hempel, empirical progress in the spirit of Laudan and truth approximation in the spirit of Popper. Such explication programs may be seen as conceptual design pro-grams. The subject of our explication activities concerns the nature of develop-ment in descriptive and explanatory research programs.

The following survey of the parts focuses on the main specific cognitive structures that will be uncovered.

In Part I, entitled "Confirmation": - The qualitative and quantitative conceptual systems of confirmation


and falsification of hypotheses, together with disconfirmation and verifi-cation (the 'deductive confirmation matrix' and the 'confirmation square', respectively).

- Systems of inductive probability, representing inductive confirmation, among which optimum systems, systems with analogy and systems with non-zero probability for universal statements.

In Part II, entitled "Empirical progress": - 'The evaluation report' of a theory in terms of general successes and

(individual) counter-examples, and a systematic survey of the factors complicating theory testing and evaluation.

- The nature of comparative theory evaluation, giving rise to the 'rule of success', characterizing 'empirical progress', prescribing to select the theory, if any, that has so far proven to be the most successful one.

- The symmetric 'evaluation matrix' for the comparison of the relative success of two theories.

In Part III, entitled "Basic truth approximation": - The, domain and vocabulary relative, definitions of 'the actual truth'

and 'the nomic truth', the basic definitions of 'closer to the nomic truth' or 'nomically more truthlike', the success theorem, according to which 'more truthlikeness' guarantees 'more successfulness'. With the conse-quence that scientists following the rule of success behave functionally for truth approximation, whether they like it or not.

- The detailed reconstructions of intuitions of scientists and philosophers about truth approximation, the correspondence theory of truth, and dialectical patterns.

- The epistemological stratification of these results, including definitions of reference, the referential truth, and referential truthlikeness, enabling the detailed evaluation of the three transitions from instrumentalism to constructive realism.

In Part IV, entitled "Refined truth approximation": - The basic definitions do not take into account that theories are fre-

quently improved by replacing mistaken models by other mistaken ones. Roughly the same patterns arise as in Part III by refined definitions that take this phenomenon into account.

- Specifically idealization and concretization become in this way func-tional for (potential) truth approximation, which will be illustrated by three examples, two illustrating the specific pattern of 'double concretiza-tion', viz., the law of Van der Waals and capital structure theory, and one illustrating the pattern of 'specification followed by concretization', viz., the old quantum theory.

The book concludes with a sketch of the resulting favorite epistemological position, viz., constructive realism, which may be seen as a background pattern


of thinking, guiding many, if not most, scientists when practicing the instrumen-talist methodology.

This brings us to the use-value of cognitive structures. They always concern informative patterns, which seem useful in one way or another. We briefly indicate five kinds of possible use-value, with some particular references to structures disentangled in this book

(a) they may provide the 'null hypothesis of ideal courses of events', which can playa guiding role in social studies of science; e.g., the cognitive justification of non-falsificationist behavior, following from the nature of theory evaluation (Section 6.3.).

(b) they may clarify or even solve classical problems belonging to abstract philosophy of science; e.g., the intralevel explication of the correspon-dence theory of truth (Section 8.2.).

(c) they may be useful as didactic instruments for writing advanced text-books, leading to better understanding and remembrance; e.g., the comparative evaluation matrix (Section 6.1.).

(d) they may playa heuristic role in research policy and even in science policy; e.g., confirmation analysis suggests redirection of drugs testing (Section 2.2.).

(e) last but not least, they may playa heuristic role in actual research; e.g., when explanatorily more successful, the theory realist may have good reasons to hypothesize theoretical truth approximation despite some extra observational problems (Chapter 9).5

A final remark about the technical means that will be used. Besides some elementary logic and set theory, some of the main ideas of the structuralist approach of theories will be used. Where relevant, starting in Part III, what is strictly necessary will be explained. However, for detailed expositions the reader is referred to (Balzer 1982) and (Balzer, Moulines and Sneed 1987). For a general survey the reader may consult (Kuipers 1994), also to appear in (Kuipers SiS).

PART I

CONFIRMATION

INTRODUCTION TO PART I

The first part is in many respects a systematic exposition of well-known ideas on deductive, non-deductive, and inductive confirmation. However, we present these ideas in a non-standard way and refine and revise several standard solutions of problems associated with these ideas. This part consists of three chapters, the first one dealing with qualitative (deductive) confirmation as resulting from applying the hypothetico-deductive (HD-)method, and the second one dealing with quantitative (deductive and non-deductive) confirm-ation and its qualitative consequences. The third one explicates the idea of (quantitative) inductive confirmation and gives a brief survey of the main systems of inductive confirmation in the Carnap-Hintikka tradition of so-called inductive logic. The main non-standard aspect is the approach of confirmation from the 'success perspective', according to which confirmation is equated with evidential success, more specifically, with an increase of the plausibility of the evidence on the basis of the hypothesis. Hence, in contrast to standard exposi-tions, confirmation is not equated with an increase of the plausibility of the hypothesis by the evidence. This is merely an additional aspect of confirmation under appropriate conditions and epistemological assumptions.

Chapter 2 starts from the classical idea that testing of a hypothesis by the HD-method aims at establishing the truth-value (of the observational conse-quences) of a hypothesis, and results in confirmation or falsification. A qualita-tive (classificatory and comparative) theory of deductive confirmation is presented, as well as its (in details) non-standard solutions of Hempel's raven paradoxes and Goodman's grue paradox. It is called a pure theory of confirm-ation because it is based on the principle that equally successful hypotheses are equally confirmed by the relevant evidence, that is, independent of the initial plausibility of the hypotheses.

In Chapter 3 the corresponding quantitative, i.c., probabilistic Bayesian, theory of confirmation is presented, with a decomposition in deductive and non-deductive confirmation. It is pure, and inclusive, hence non-standard, in the sense that it leaves room for the confirmation of hypotheses with probability zero. The qualitative theory of (general) confirmation, including the one for deductive confirmation, generated by the quantitative theory, is also formulated. In Appendix 1 it is argued that Popper's ideas about corroboration basically amount to an inclusive and impure variant of the Bayesian approach to confirmation. Appendix 2 elaborates some details of the quantitative treatment of the raven paradoxes.

15

16 INTRODUCTION TO PART I Deductive and non-deductive confirmation mayor may not have extrapolat-

ing or inductive features. The last chapter of this part (Chapter 4) deals with the program of inductive confirmation or inductive logic, set up by Carnap and significantly extended by Hintikka. It is a special explication program within the Bayesian program of confirmation theory. It is governed by the idea of extrapolating or learning from experience in a rational way, to be expressed in terms of 'inductive probabilities' as opposed to 'non-inductive probabilities'.

In later chapters the role of falsification and confirmation will be relativized in many respects. However, it will also become clear that they remain very important for particular types of hypotheses, notably, for general observational (conditional) hypotheses, and for several kinds of (testable) comparative hypotheses, e.g., hypotheses claiming that one theory is more successful or (observational, referential and theoretical) truthlike than another.

A recurring theme in this part, and the other ones, will be the localization and comparison of the main standard epistemological positions, as they have been presented in Chapter 1, viz., instrumentalism, constructive empiricism, referential realism, and constructive (theory) realism.

2 CONFIRMATION BY THE HD-METHOD

Introduction According to the leading expositions of the hypothetico-deductive (HD-)method by Hempel (1966), Popper (1934/1959) and De Groot (1961/1969), the aim of the HD-method is to answer the question whether a hypothesis is true or false, that is, it is a method of testing. On closer inspection, this formulation of the aim of the HD-method is not only laden with the epistemological assumption of theory realism according to which it generally makes sense to aim at true hypotheses, but it also mentions only one of the realist aims. One other aim of the HD-method for the realist, an essentially more refined aim, is to answer the question of which facts are explained by the hypothesis and which facts are in conflict with it. In the line of this second aim, we will show in Part II that the HD-method can also be used to evaluate theories, separately and in comparison with other theories, among others, in terms of their general successes and individual problems, where theories are conceived as hypotheses of a strong kind. In Part III and IV we will argue that the methodology of (comparative) HD-evaluation of theories is even functional for truth approximation, the ultimate aim of the realist.

For the moment we will restrict attention to the HD-method as a method of testing hypotheses. Though the realist has a clear aim with HD-testing, this does not mean that HD-testing is only useful from that epistemological point of view. Let us briefly review in the present connection the main other epistemo-logical positions that were described in Chapter 1. Hypotheses mayor may not use so-called 'theoretical terms', besides so-called 'observation terms'. What is observational is not taken in some absolute, theory-free sense, but depends greatly on the level of theoretical sophistication. Theoretical terms intended to refer to something in the nomic world mayor may not in fact refer. For the (constructive) empiricist the aim of HD-testing is to find out whether the hypothesis is observationally true, i.e., has only true observational conse-quences, or is observationally or empirically adequate, to use Van Fraassen's favorite expression. For the instrumentalist the aim of HD-testing is still more liberal: is the hypothesis observationally true for all intended applications? The referential realist, on the other hand, adds to the aim of the empiricist to find out whether the hypothesis is referentially true, i.e., whether its referential claims are correct. In contrast to the theory realist, he is not interested in the

17

18 CONFIRMATION BY THE HD-METHOD question whether the theoretical claims, i.e., the claims using theoretical terms, are true as well. Recall that claims may pertain to the actual world or to the nomic world (of physical possibilities). However, this distinction will not play an important role in the first part of this book.

Methodologies are ways of answering epistemological questions. It will turn out that the method of HD-testing, the test methodology, is functional for answering the truth question of all four epistemological positions. For this reason, we will present the test methodology in fairly neutral terms, viz., plausibility, confirmation and falsification.

The expression 'the plausibility of a hypothesis' abbreviates the informal qualification 'the plausibility, in the light of the background beliefs and the evidence, that the hypothesis is true', where 'true' may be specified in one of the four main senses: (1) observationally as far as the intended applications are concerned, (2) observationally, in all possible respects, (3) and, moreover, referentially, (4) and, even, theoretically. Admittedly, despite these possible qualifications, the notion of 'plausibility' remains necessarily vague, but that is what most scientists would be willing to subscribe to. 1 At the end of this chapter we will further qualify the exposition for the four epistemological positions when discussing the acceptance of hypotheses. When talking about 'the plausibility of certain evidence', we mean, of course, 'the (prior) plausibility of the (observational) hypothesis that the test will result in the reported out-come'. Hence, here 'observationally true' and 'true' coincide by definition of what can be considered as evidential statements.

Regarding the notions of 'confirmation' and 'falsification' the situation is rather asymmetric. 'Falsification' of a hypothesis simply means that the evidence entails that the hypothesis is observationally false, and hence also false in the stronger senses. However, what 'confirmation' of a hypothesis precisely means, is not so clear. The explication of the notion of 'confirmation' of a hypothesis by certain evidence in terms of plausibility will be the main target of this and the following chapter. It will be approached from the success perspective on confirmation, equating confirmation with an increase of the plausibility of the evidence on the basis of the hypothesis, and implying that the plausibility of the hypothesis is increased by the evidence.

The variety of empirical hypotheses is large. To stress this we mention a number of examples:

- Mozart was poisoned by Salieri, - Dutch is more similar to English than to German, - When people have bought something they have selective attention for

information justifying their choice, - People tend to choose that action which maximizes their expected utility, - The function of lungs is to supply oxygen to the organism, - The average rainfall per year gradually increased in the 20th century, - The universe originated from the big bang,

CONFIRMATION BY THE HD-METHOD 19

- Action is minus reaction, - Dalton's theory of the atom. The last example will be used a couple of

times for illustrative purposes in this part of the book.

A general characterization of an empirical hypothesis is the following: an empirical hypothesis is a tentative statement which, in some way or other, is about the nomic world and which is testable. Statements about the nomic world claim to tell something about the world, how it is or was (not), how it will (not) be, how it can (not) be. They are supposed to have, or may acquire a sufficiently clear meaning such that they are true or false in a sense which has to be specified, preferably such that a false statement may, nevertheless, be approximately true in some plausible sense. The above characterization of an empirical hypothesis still leaves room for hypotheses with nonsensical or other-wise redundant additions. Instead of trying to exclude such additions, which is not easy, it will become clear that such additions are relatively harmless.

A test for a hypothesis may be experimental or natural. That is, a test may be an experiment, an active intervention in nature or culture, but it may also concern the passive registration of what is or was the case, or what happens or has happened. In the latter case of a so-called natural test the registration may be a more or less complicated intervention, but is nevertheless supposed to have no serious effect on the course of events of interest.

According to the HD-method a hypothesis H is tested by deriving test implications from it, and checking, if possible, whether they are true or false. Each test implication has to be formulated in terms that are considered to be observation terms. A test implication mayor may not be of a general nature. Usually, a test implication is of a conditional nature, if C then F (C -> F). Here C denotes one or more initial conditions which can be, or have been realized, by nature or artificially, i.e., by experiment. F denotes a potential fact (event or state of affairs) predicted by Hand C. If C and F are of an individual nature, F is called an individual test implication, and C -> F a conditional one. When C is artificially realized, it is an experimental test, otherwise it is a natural test.

As is well-known, the basic logic of HD-testing can be represented by some (valid) applications of Modus (Ponendo) Ponens (MP), where 'F' indicates logical entailment:

Hl=l H

1

Scheme 2.1.1.

HI=(C-+F) H,C

F

Scheme 2.1.2.

It should be stressed that H /= I and H /=(C -> F) are supposed to be deductive claims, i.e., claims of a logico-mathematical nature.

The remaining logic of hypothesis testing concerns the application of Modus (Tollendo) Tollens (MT). Neglecting complications that may arise, if the test

20 CONFIRMATION BY THE HD-METHOD implication is false, the hypothesis must be false, it has been falsified, for the following arguments are deductively valid:

HFI -,1

Scheme 2.2.1.

HF(C-+F) C, -,F

-,H

Scheme 2.2.2.

When the test implication turns out to be true, the hypothesis has of course not been (conclusively) verified, for the following arguments are invalid, indi-cated by '-/- /-':

HFI HF(C-+F) I C,F

- j- j- - j- j- j- j- j-H? H?

Scheme 2.3.). Scheme 2.3.2.

Since the evidence (I or C&F) is compatible with H, H may still be true. However, we can say more than that. Usually it is said that H has been confirmed. It is important to note that such confirmation by the HD-method is in the strong sense that H has obtained a success of a (conditional) deductive nature; by entailing the evidence, H makes the evidence as plausible as possible. This will be called the success perspective on conditional) deductive) corifirmation.

Falsification and confirmation have many complications, e.g., due to auxiliary hypotheses. We will deal with several complications, related to general and individual test implications, at the end of Chapter 5. There is however a great difference between falsification and confirmation. Whereas the 'logical gram-mar' of falsification is not very problematic, the grammar of confirmation, i.e., the explication of the concept of confirmation, has been a subject of much dispute.

One of the most influential theories of confirmation is the so-called Bayesian theory (Howson and Urbach 1989; Earman 1992), which is of a quantitative nature. Unfortunately, quantitative formal methods necessarily have strong arbitrary elements. However, a quantitative theory may have adequate qualita-tive features. The rest of this chapter deals with a qualitative theory of confirm-ation which is in agreement with the qualitative features of the corresponding version of the Bayesian theory. The presentation and analysis of the Bayesian theory, and the proof that it has these features, will be postponed to the next chapter. Since the main ideas of Carnap and Hintikka about confirmation concern a special form of the Bayesian theory (see Chapter 4), there is also qualitative agreement with them. Finally, there is largely agreement with Popper, for it will be argued in Appendix 1 of Chapter 3 that Popper's


qualitative ideas about confirmation (or corroboration, to use his favorite term) are basically in agreement with the Bayesian approach.

However, there is at least one influential author about confirmation, viz., Glymour, whose ideas do not seem to be compatible with the qualitative theory to be presented. In Note 11 to Subsection 2.2.3. we will briefly discuss Glymour's project, and question it as a project of explication of the concept of confirm-ation, rather than of theoretical measurement, which it surely is.

Guided by the success perspective on confirmation, Section 2.1. gives an encompassing qualitative theory of deductive confirmation by adding a compar-ative supplement to the classificatory basis of deductive confirmation. The comparative supplement consists of two principles. In Section 2.2. several classical problems of confirmation are dealt with. First, it is shown that the theory has a plausible solution of Hempel's raven paradoxes, roughly, but not in detail, in agreement with an influential Bayesian account. Second, it is shown that the theory has a plausible, and instructive, solution of Goodman's problem with 'grue' emeralds. Third, it is argued that further arguments against 'deduc-tive confirmation' do not apply when conditional deductive confirmation is also taken into account. Section 2.3. concludes with some remarks about the problem of acceptance of well-confirmed hypotheses.

2.1. A QUALITATIVE THEORY OF DEDUCTIVE CONFIRMATION Introduction

Traditionally, a qualitative theory of deductive confirmation is conceived as merely a classificatory theory. However, we conceive it from the outset as a combination of classificatory and comparative principles. In general, in this book the term 'qualitative theory' should not be interpreted as referring to merely a classificatory theory, but to a non-quantitative theory with classifica-tory and comparative aspects. We will use this terminology also for the theories of theory evaluation and truth approximation to be presented in later chapters. Regarding the qualitative theory of confirmation, the subject of this chapter, we start with its classificatory principles.

2.1.1. Classificatory basis The classificatory notions of evaluation of a hypothesis H by evidence E, are generated by considering the four possible, mutually exclusive (except for some extreme cases), deductive relations (1=) in a systematic order, assuming that H is consistent and E is true. They are depicted in the following (Deductive) Confirmation Matrix (Figure 2.1.). The names will first be elucidated. To speak of falsification of H by E in the case H entails -, E, H 1= -, E, which is equivalent to E 1= -, H, and of (conclusive) verification of H by E in the case -, H entails -, E, -, H 1= -, E, which is equivalent to E 1= H, will be plausible enough. The other names are suggested by the success perspective on confirmation, that is,


E (true) 'E (false)

H HI=E ('E/='H) H/='E (EI='H) Deductive Confirmation Falsification DC(E,H) F(E,H)

'H 'Ht=E ('E I=H) 'H /='E (E F=f1) Deductive Disconfirmation Verification DD(E,H) V(E,H)

Figure 2.1. The (Deductive) Confirmation Matrix

confirmation amounts to a success of a hypothesis. The first case, H FE, is a paradigm case in which scientists speak of confirmation, viz., when E is a (hypothetico-)deductive success of H, for that reason called (the principle of) deductive (d-)confirmation. Note that only in this case E is a test implication of H (which came true). Just as verification (of H) amounts to falsification of --, H, the remaining case, --, H F E, amounts to a deductive success of --, H, hence to deductive confirmation of --, H. However, speaking, by way of short-hand, precisely in this case of deductive disconfirmation seems also very plausi-ble. Hence, whereas philosophers and scientists sometimes use the term disconfirmation as an euphemism for falsification, we use the formal opportu-nity to qualitatively distinguish sharply between (deductive) disconfirmation and falsification.

The Confirmation Matrix specifies the basic cognitive structure governing hypothesis testing. However, although it gives the core of the classificatory part of the qualitative success theory of confirmation, it does not yet reflect standard scientific practice in detail. Recall that there occur as premises in hypothetico-deductive (HD-)prediction and deductive-nomological (DN-)explanation of individual events, besides the hypothesis, the so-called 'initial conditions'. The above definition of 'deductive confirmation', as confirmation by a deductive success, directly suggests the notion of 'conditional deductive (cd-)confirmation', i.e., confirmation of H by E, assuming a certain condition C, defined as follows:

H &C F E conditional Deductive Confirmation: DC(E,H; C) Here it is assumed that Hand C are logically independent (U(H, C, for reasons becoming clear in Subsection 2.2.3., and that C does not entail E,

CONFIRMATION BY THE HD-METHOD 23 whereas C mayor may not be entailed by E. Hence, in view of the fact that hypotheses and initial conditions usually are logically independent, successful HD-prediction and ON-explanation of individual events form the paradigm cases of cd-confirmation, for they report 'conditional deductive successes'.2

When dealing with specific examples, several expressions related to cd-confirmation will be used with the following interpretation:

"E C-confirms H": E cd-confirms H on the condition (indicated by) C, "E cd-confirms H": there is a (non-tautological) condition C, such that E entails C and E C-confirms H, "E is deductively (d-)neutral (evidence) for H": Hand E are logically independent (i.e., none of the four deductive relations holds), "E is conditional deductively (cd-)neutral (evidence) for H": E is d-neutral for H and in addition E does not cd-confirm H nor -, H.

Note that 'cd-neutrality' trivially implies 'd-neutrality', but not vice versa. Of course, 'conditionalization' of the other three deductive relations between

E and H, by just adding C as a premise, is also possible and more realistic, leading to the corresponding conditional (Deductive) Confirmation Matrix.

2.1.2. Comparative supplement As announced, we explicate 'confirmation by the HD-method', in this chapter, as (conditional) deductive confirmation including some crucial comparative principles. However, in order to do so it is useful to introduce first some main principles of general confirmation, that is, confirmation of deductive and non-deductive nature. The success perspective on confirmation in general may be explicated by the following definition of (general) confirmation:

SDC: Success definition of cmifirmation: E confirms H iff (E is a success of H in the sense that) H makes E more plausible

This definition is satisfied by d-confirmation in the extreme sense that E is made true, hence maximally plausible, by (the truth of) H. The second principle deals with increasing the plausibility of hypotheses by confirming evidence:

RP P: Reward principle of plausibility E makes H more plausible3 iff E confirms H

For d-confirmation the reward principle implies an increase of the plausibility of the hypothesis.

Note that the two general principles imply the

PS: Principle of symmetry H makes E more plausible iff E makes H more plausible

Note, moreover, that the combination of the first two principles makes comparative expressions of the form "E* confirms H* more than E confirms


H" essentially ambiguous. It can express that the plausibility increase of E* by H* is higher than that of E by H, or that the plausibility increase of H* by E* is higher than that of H by E. However, we exclude this ambiguity by adopting as the third and last general principle, now of a comparative nature:

pes: Principle of comparative symmetry E* confirms H* (much) more than (as much as) E confirms H iff H* increases the plausibility of E* (much) more than (as much as) H increases the plausibility of E iff E* increases the plausibility of H* (much) more than (as much as) E increases the plausibility of H

For our purposes, the three principles SOC, RPP (together implying PS) and PCS of general confirmation are sufficient. From now on in this chapter, comparative confirmation claims will always pertain to (conditional) deductive success and (conditional) deductive confirmation.

Now we are able to propose two comparative principles concerning d-confirmation, one (P.l) for comparing two different pieces of evidence with respect to the same hypothesis, and one (P.2) for comparing two different hypotheses in the light of the same piece of evidence.

P.l if E and E* d-confirm H then Ed-confirms H more than E* iff E is less plausible than E* in the light of the background beliefs

P.2 if Ed-confirms Hand H* then Ed-confirms H* as much as H

To be sure, P.l and P.2 are rather vague, but we will see that they have some plausible applications, called the special principles. Hence, if one finds the general principles too vague, it is suggested that one primarily judges the special principles.

The motivation of the plausibility principles is twofold. First, our claim is that P.l and P.2 are roughly in agreement with scientific common sense concerning confirmation by successes obtained from HO-tests. For P.l this is obvious: less expected evidence has more 'confirmation value' than more expected evidence. P.2 amounts to the claim that hypotheses should be equally praised for the same success, which is pretty much in agreement with (at least one version of) scientific common sense.

The second motivation of the principles P.I and P.2 will be postponed to the next chapter, where we will show that they result, with some qualifications, from certain quantitative confirmation considerations of a Bayesian nature applied to HO-tests, Bayesian considerations for short, when 'more plausible' is equated with 'higher probability'.

P.2 amounts to the claim that the 'amount of confirmation', more specifically, the increase of plausibility by evidence E is independent of differences in initial plausibility between Hand H* in the light of the background beliefs. In the

CONFIRMATION BY THE HD-METHOD 25 next chapter we will also deal with some quantitative theories of confirmation for which holds that a more probable hypothesis profits more than a less probable one. This may be seen as a methodological version of the so-called Matthew-effect, according to which the rich profit more than the poor. It is important to note, however, that P.2 does not deny that the resulting posterior plausibility of a more plausible hypothesis is higher than that of a less plausible one, but the increase does not depend on the initial plausibility. For this reason, P.2 and the resulting theory are called neutral with respect to equally successful hypotheses or, simply, pure4 , whereas theories having the Matthew-effect, or the reverse effect, are called impure. The first type of impure theories are said to favor plausible hypotheses, whereas theories of the second type favor implau-sible hypotheses. In Subsection 2.2.1 . of the next chapter, we will give an urn-model, hence objective probabilistic, illustration and defence of P.2.

The condition 'in the light of the background beliefs' in P.l is in line with the modern view (e.g., Sober 1988, p. 60, Sober 1995, p. 200) that confirmation is a three place relation between evidence, hypothesis and background beliefs, since without the latter it is frequently impossible to make differences between the strength of confirmation claims. As a matter of fact, it would have been better to include the background beliefs explicitly in all formal representations, but we have refrained from doing so to make reading the formulas more easy.

This does not mean that background beliefs always playa role. For instance, they do not playa role in the following two applications of the principles, that is, the first two special principles (for non-equivalent E and E*):

S.l if H 1= E 1= E* then Ed-confirms H more than E* S.2 if H* 1= H 1= E then Ed-confirms H* as much as H

These special principles obviously are applications of the corresponding general principles. For S.2 it is trivial and for S.l it is only necessary to assume that (logically) weaker evidence is more plausible than stronger evidence. Hence, they can be motivated in the same two ways as the general principles themselves: indirectly, by showing later that they result from certain Bayesian considera-tions as soon as 'logically weaker' guarantees a higher prior probability, and directly, by referring to scientific common sense around HD-tests. S.l states, in line with the success perspective, that a (logically) stronger deductive success of a hypothesis confirms that hypothesis more than a weaker success. S.2 states that a logically stronger hypothesis is as much confirmed by a deductive success as a weaker one which shares that success.

Since S.l and S.2 directly pertain to the rebuttal of two standard objections in the literature against deductive confirmation, we will deal already now with these objections, but postpone the treatment of some other ones to Subsection 2.2.3. It is easily checked that deductive confirmation has the so-called 'converse consequence property' with respect to the hypothesis (CC-H) and the 'consequence property' with respect to the evidence (C-E). The first property amounts to:

26 CONFIRMATION BY THE HD-METHOD CC-H: converse consequence property with respect to H: if Ed-confirms H then it also d-confirms any stronger H*

This property generates the 'irrelevant conjunction objection', i.e., CC-H has the prima facie absurd consequence that if H F E then Ed-confirms H &H', for any H', which is compatible with H, but not entailed by H (Hempel 1945jI965); Glymour 1980ajb). From the cIassificatory-cum-comparative point of view, this consequence is not at all absurd as soon as we are aware of all relevant (qualitative) confirmation aspects, which we like to call the proper (conjunction) connotation:

if Ed-confirms H then - Ed-confirms H&H', for any H' compatible with H - even as much as H (due to S.2) - but E does not at all necessarily d-confirm H' - hence, the d-confirmation remains perfectly localizable

If one finds it strange that E confirms H&H' as much as H, it is important to realize that the prior plausibility of H&H' will be less than that of H, and hence, because of PCS and S.2, this will hold for the corresponding posterior plausibilities. Hence, if H' is nonsensical or otherwise implausible, e.g., the moon is made of cheese, H&H' will be implausible as well, a priori as well as a posteriori. For this reason, nonsensical additions to empirical hypotheses are relatively harmless.

The situation is to some extent similar for the standard objection against the second property, C-E, the consequence property with respect to the evi-dence. This property amounts to:

C-E: consequence property with respect to the evidence: if Ed-confirms H, then also any weaker E*

This property generates what might be called the "irrelevant disjunction objec-tion", i.e., C-E has the prima facie absurd consequence that if H F E then EvE' d-confirms H, for any E' (Grimes 1990). Again, from our point of view this consequence is not at all absurd as soon as we are aware of all relevant (qualitative) confirmation aspects, i.e., the proper (disjunction) connotation:

if Ed-confirms H then - EVE' d-confirms H, for any E' compatible with E - though (much) less (due to S.l) - but E' does not at all necessarily d-confirm H - hence, the d-confirmation remains perfectly localizable

It will be useful to conditionalize the general and special principles:

P.lc if E C-confirms Hand E* C*-confirms H then E C-confirms H more than E* C*-confirms H iff E* is, given C*, more plausible than E, given C, in the light of the background beliefs


S.lc if H FC -+ E FC* -+ E* then E C-confirms H more than E* C*-confirms H

P.2c if E C-confirms Hand H* then E C-confirms H* as much as H S.2c if H F C -+ E, H* F C -+ E and H* F H then E C-confirms H* as

much as H

Later we will introduce two other applications of the principles, more specifi-cally of P.lc and P.2c, or, if you want, new special principles. They will provide the coping-stones for the solution of the raven paradoxes and the grue problem. In contrast to S.l and S.2, they presuppose background beliefs and concern conditional (deductive) confirmation. Moreover, they deal with special types of hypotheses, pieces of evidence and conditions. They will be indicated by S#.lc(-ravens) and SQ.2c(-emeralds), respectively.

2.2. RAVENS, GRUE EMERALDS, AND OTHER PROBLEMS AND SOLUTIONS

Introduction In this section it will be shown how the qualitative theory of deductive confirm-ation resolves the famous paradoxes of confirmation presented by Hempel and Goodman. Moreover, we will deal with the main types of criticism in the literature against the purely classificatory theory of deductive confirmation, that is, when a comparative supplement is absent.

In view of the length of the, relatively isolated, subsection (2.2.2.) about Goodman's grue problem, the reader may well decide to skip that subsection in first reading.

2.2.1. The raven paradoxes Hempel (1945/1965) discovered two paradoxes about confirmation of the hypothesis "all ravens are black" (RH) on the basis of two prima facie very plausible conditions. Assuming that a black raven confirms RH (so-called Nicod's criterion (NC) and that the logical formulation of RH may not matter (equivalence condition (EC), Hempel derived not only that a non-black non-raven (the first paradox), but, even more counter-intuitive, also a black non-raven (the second paradox) confirms RH in the same sense as a black raven. First, according to NC, a non-black non-raven confirms "all non-blacks objects are non-ravens" and hence, according to EC, RH itself. Second, again according to NC, a black non-raven confirms "all objects are non-ravens or black" and hence, according to EC, RH itself.

It is easy to check that the previous section leads to the following classifica-tory results:

(1) a black raven, a non-black non-raven and a black non-raven are all deductively (d-)neutral evidence for RH

28 CONFIRMATION BY THE HD-METHOD (2) a black raven and a non-black non-raven both cd-confirm RH,

more specifically, a black raven on the condition of being a raven and a non-black non-raven on the condition of being non-black

(3) a black non-raven is even cd-neutral evidence for RH, i.e., not only just deductively, but even conditional deductively, for a black non-raven does not cd-confirm RH on the condition of being a non-raven, nor on the condition of being black.

All three results are in agreement with scientific common sense, provided the following comparative claim can also be justified:

(4) a black raven cd-confirms RH (much) more than a non-black non-raven

However, assuming that the background beliefs include or imply the assumption:

A-ravens: the number of ravens is much smaller than the number of non-black objects

the desired result, i.e., (4), immediately follows from the third special principle, viz., the following general application of P.lc. Though the symbols are suggested by the raven example (e.g., an RB may represent a black raven, i.e., a raven which is black), they can get any other interpretation. Let #R indicate the number of R's, etc.

S#.lc(-ravens): an RB R-confirms "all Rare B" more than an R8 8-confirms it iff the background beliefs imply that #R

CONFIRMATION BY THE HD-METHOD 29 of RB's among the R's is (relatively speaking) much lower than the percentage of RB's among the R's. Precisely because typical applications of S#.lc concern such cases, it is defensible to call it a qualitative application and principle, despite its explicit reference to numbers of individuals and the reference to percentages in the motivation.6

In sum, cd-confirmation solves the raven paradox concerning black non-ravens by (3) and the one concerning non-black non-ravens by (4), which is guaranteed by applying P.lc, or its application S#.lc-ravens, to the background assumption (A-ravens) that the number of ravens is much smaller than the number of non-black objects.

There remains the question of what to think of Hempel's principles used to derive the paradoxes of confirmation. It is clear that the equivalence condition was not the problem, but Nicod's criterion that a black raven confirms RH unconditionally. Whereas Nicod's criterion is usually renounced uncondition-ally, we may conclude that it is (only) right in a sophisticated sense: a black raven is a case of cd-confirmation, viz., on the condition of being a raven.

2.2.2. Grue emeralds

The qualitative theory of deductive confirmation generates an instructive analy-sis of the other famous riddle of confirmation, i.e., the problem with 'grue' emeralds, discovered by Goodman (1955). This problem is also called the grue 'paradox', for the same reason as one speaks about the raven paradoxes. They both concern counter-intuitive consequences of certain principles of confirmation.

The problem with grue emeralds is that a green emerald found before the year 3000 seems to confirm not only the hypothesis that all emeralds are green but also that all emeralds are 'grue', where grue is defined as the following queer predicate: green if examined before 3000, and blue if not examined before 3000. Goodman's generally accepted account roughly is as follows: the predicate 'grue' is not weB-entrenched in predictively successful scientific generalizations, hence, as it stands, it is below the mark of scientific respectability to be used in generalizations that can be confirmed, i.e., to use Goodman's other favorite expression, the 'grue-hypothesis' is not (yet) projectible. We will give a related, but more detailed diagnosis of the problematic aspect. It may well be conceived as a formal explication and justification of Goodman's informal account. It can best be presented by using from time to time a formally similar, but less queer, definition of 'grue', which is only applicable to living beings, say, eagles: 'being male and green, or being female and blue'. This wiB be called the 'gender' reading, as opposed to the former 'temporal' reading.

Recall that we use the abbreviation: " .. . C-confirms ... " as a shorthand for " ... cd-confirms ... on the condition (indicated by) C". We add the abbreviations: E: emerald/eagle (in this subsection not to be confused with 'evidence'), M: (known to be) examined before 3000/male, M: not (known to be) examined before 3OOO/female, G: green, B: blue, and Q: grue (queer), i.e., MG or MB. G


and B are supposed to be mutually exclusive, but they are not supposed to be exhaustive.

We will first specify in detail to what extent 'green' and 'grue' are similar, and show that additional assumptions are needed to create the intuitively desirable asymmetry. More specifically, it will be shown that not only a strong, but also a weak irrelevance assumption is suitable for this purpose. Both are in line with the entrenchment analysis of Goodman.

The basic intuition The basic intuition of Goodman is, of course, that, though a green emerald investigated before 3000 confirms 'the green hypothesis' ("all E are G"), it does not confirm 'the grue hypothesis' ("all E are Q"). It postulates an asymmetry in confirmation behavior between 'green' and 'grue'. However, from the uncon-ditional version of Nicod's criterion, 'Nicod-confirmation', we not only get

(1) an EMG Nicod-confirms "all E are G" but also, as is easy to check,

(2) an EMG Nicod-confirms "all E are Q" Hence Nicod's criterion excludes an account of the asymmetric intuition, which shows an additional problematic feature of that criterion.

As may be expected, from the straightforward, that is, unconditional deduc-tive point of view, both cases are invalid, for in both cases the evidence is deductively neutral for the hypothesis. Hence, unconditional deductive con-firmation also fails to account for the basic intuition, but it does not exclude a 'conditional deductive' account. So, what about conditional deductive confirmation?

Cd-confirmation, however, is also in conflict with the intuition, for it is easy to check that the following classifications obtain:

(3) an EMG EM-confirms "all EM are G" (4) an EMG EM-confirms "all E are G" (5) an EMG EM-confirms "all E are Q"

Note first that (3) is an unproblematic formal analogue of the equally valid claim that an EG E-confirms "all E are G", where E is replaced by EM. More importantly, whereas (4) fits the basic intuition, (5) is in conflict with it. However, before rejecting cd-confirmation because of (5), it is important to study the validity of (5) in detail. To begin with, it is important to note that the following claim is invalid:

(6*) an EMG EM-confirms "all EM are B" The invalidity of (6*) amounts to the claim that a green object does not confirm the hypothesis "all EM are B" on the condition that it is an emerald investigated before 3000. In this light, we suggest that the problem with (5) derives from


the wrong impression that it implies (6*) and the intuition that it would indeed be absurd if (6*) were to obtain. In other words, we take the invalidity of (6*) as the proper interpretation of the confirmation-rejecting side of the basic intuition, instead of the originally, but wrongly, suggested invalidity of (5).

It is interesting to see in more detail how (5), (6*), and (3) are related. Note that the following equivalence holds:

(7) "all E are Q".;;. "all EM are G" & "all EM are B" which makes clear, by the way, that "all E are Q" may be less strange than the temporal reading suggests, for in the

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