EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association 9048132622, 9789048132621

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Mauricio Suárez Mauro Dorato Miklós Rédei Editors Volume 1

EPSA Epistemology and Methodology of Science Launch of the European Philosophy of Science Association

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EPSA Epistemology and Methodology of Science

Mauricio Suárez

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Mauro Dorato

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Miklós Rédei

Editors

EPSA Epistemology and Methodology of Science Launch of the European Philosophy of Science Association

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Editors Prof. Mauricio Suárez Universidad Complutense de Madrid Fac. Filosofía Depto. Lógica y Filosofía de la Ciencia 28040 Madrid Planta Sótano, Edificio B Spain [email protected]

Mauro Dorato Via Ostiense 234 00144 Rome Italy [email protected] Miklós Rédei Houghton Street WC2 2AE London United Kingdom

ISBN 978-90-481-3262-1 e-ISBN 978-90-481-3263-8 DOI 10.1007/978-90-481-3263-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009941460 c °Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: Boekhorst Design b.v. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Contents

Introduction . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . ix 1

Naturalism and the Scientific Status of the Social Sciences . . .. . . . . . . . . . . Daniel Andler

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Reconsidering Gilbert’s Account of Social Norms . . . . . . . . . . . . .. . . . . . . . . . . 13 Caroline M. Baumann

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Theories for Use: On the Bearing of Basic Science on Practical Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 23 Martin Carrier

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Structural Realism as a Form of Humility . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 35 Angelo Cei

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Approaching the Truth via Belief Change in Propositional Languages . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 47 Gustavo Cevolani and Francesco Calandra

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Can Graphical Causal Inference Be Extended to Nonlinear Settings? .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 63 Nadine Chlaß and Alessio Moneta

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Towards a Grammar of Bayesian Confirmation . . . . . . . . . . . . . . .. . . . . . . . . . . 73 Vincenzo Crupi, Roberto Festa, and Carlo Buttasi

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Epistemic Accuracy and Subjective Probability . . . . . . . . . . . . . . .. . . . . . . . . . . 95 Marcello D’Agostino and Corrado Sinigaglia

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Interpretation in the Natural Sciences . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .107 Jan Faye

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10 Multiple Realizability and Mind-Body Identity .. . . . . . . . . . . . . . .. . . . . . . . . . .119 Simone Gozzano 11 Why Should Philosophers of Science Pay Attention to the Commercialization of Academic Science? .. . . . . . . . . . . . . .. . . . . . . . . . .129 G¨urol Irzik 12 Some Consequences of the Pragmatist Approach to Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .139 Tarja Knuuttila 13 The Gray Area for Incorruptible Scientific Research . . . . . . . . .. . . . . . . . . . .149 Theo A.F. Kuipers 14 Epistemic Replacement Relativism Defended . . . . . . . . . . . . . . . . . .. . . . . . . . . . .165 Martin Kusch 15 Models and Truth .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .177 Uskali M¨aki 16 Theory Change, Truthlikeness, and Belief Revision . . . . . . . . . . .. . . . . . . . . . .189 Ilkka Niiniluoto 17 Mechanisms: Are Activities up to the Job? .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .201 Johannes Persson 18 Why the Model-Theoretic View of Theories Does Not Adequately Depict the Methodology of Theory Application . .. . . . . . . . . . .211 Demetris Portides 19 A Deflationary, Neo-Mertonian Critique of Academic Patenting .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .221 Hans Radder 20 ‘I Want to Look Like a Lady, Not Like a Factory Worker’ Rose Rand, a Woman Philosopher of the Vienna Circle . . . . . .. . . . . . . . . . .233 Maria Rentetzi 21 Natural Kind Theory as a Tool for Philosophers of Science . .. . . . . . . . . . .245 Thomas A.C. Reydon 22 Whence Ontological Structural Realism? .. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .255 Juha Saatsi

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23 Local, General and Universal Prediction Methods: A Game-Theoretical Approach to the Problem of Induction . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .267 Gerhard Schurz 24 Multiple Contraction Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .279 Wolfgang Spohn 25 Statistical Inference Without Frequentist Justifications . . . . . .. . . . . . . . . . .289 Jan Sprenger 26 Carnap and the Perils of Ramseyfication . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .299 Thomas Uebel 27 Naturalizing Meaning Through Epistemology: Some Critical Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .311 Nicla Vassallo and Claudia Bianchi 28 What Games Do Scientists Play? Rationality and Objectivity in a Game-Theoretic Approach to the Social Construction of Scientific Knowledge . . . . . . . . . . . .. . . . . . . . . . .323 Jes´us Zamora-Bonilla Index . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .333

Introduction

These two volumes contain a selection of the papers delivered at the first conference of the European Philosophy of Science Association (EPSA) which took place in Madrid, at Complutense University, from 14 to 17 November 2007. The first volume is entitled Epistemology and Methodology, and includes papers mainly concerned with general philosophy of science, rationality, and method. The second volume, devoted to Philosophical Issues in the Sciences, includes papers concerned with philosophy of the sciences, particularly physics, economics, chemistry and biology. Overall the selection has been very severe and took place in two stages. The 30-strong conference programme committee chaired by Mauro Dorato and Mikl´os R´edei first selected 160 papers for presentation out of 410 abstracts submitted. After the conference the three of us went on to further select 60 papers among those delivered. The selection was made on the recommendation of the members of the programme committee and the chairs of the conference sessions, who were invited to nominate their favourite papers and provide reasons for their choices. Every paper included in these volumes has been independently nominated by at least two referees. There are thus good grounds to the claim that these essays constitute some of most significant and important research presently carried out in the philosophy of science throughout Europe. The two volumes also represent the first tangible outcome of the newly born EPSA. Together with the conference they in effect constitute the launching of the Association. The resounding success of the conference and its call for papers bears testimony to the strong demand for an Association of this nature. EPSA was established in anticipation of such demand and it intends to be an institution that helps cultivate philosophy of science across Europe, where modern philosophy of science was born in the first half of the twentieth century. While based in Europe, EPSA is an association that welcomes members of any nationality – just like its more established, successful older sister, the Philosophy of Science Association. The varied range and outstanding quality of the papers in the present two volumes constitute a powerful signal of the healthy state and bright future of philosophy of science across Europe. EPSA07, the Founding conference of EPSA, was organised by Mauricio Su´arez and the members of his research group at Complutense. Mauricio Su´arez would like

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to personally thank them for their help and work during the long and unnerving months before and after the conference. Thanks also to Julian Reiss for his support during the first few months of planning. Financial help is acknowledged from the Spanish Ministry of Science and Education (grant HUM2007–29190-E), and the Vice-Rectorate of Research at Complutense University (programme OC36/07). Some of the funds allocated by the Government of Madrid’s Autonomous Community (grant 930370–2007) were diverted to cover some unexpected last minute conference expenses too. Thanks are also due to the Faculty of Philosophy at Complutense for its unconditional support. In particular the Dean of the Faculty of Philosophy, Juan Manuel Navarro Cord´on, lent us the Faculty building and all its audiovisual facilities free of charge. This greatly reduced the cost of the conference, which a newly born association like EPSA would not have been able to cover. In compiling these volumes we were fortunate to be able to rely on I˜naki San Pedro, who has been an efficient and responsible editorial assistant. In the last few months he has almost become a ‘fourth editor’ in the background – we are very grateful to him. Springer backed us up from the very beginning. Lucy Fleet was the always friendly and supportive first port of call at Springer. Ties Niejssen was a supportive editor in the last few stages. But our greatest debt is to Charles Erkelens, the lead Humanities editor at Springer. The level of support we have found in Charles is difficult to overemphasise. He contacted the conference organiser well ahead of the event, and made sure that there would be a strong Springer presence at EPSA07. He himself attended the conference in its entirety and continued to support us throughout the editorial work. Afterwards he responded with invariable efficiency to all kinds of requests, related not only to these volumes, but also the planned-for journal, the European Journal of Philosophy of Science, where these papers were originally intended to appear. It was the good fortune of EPSA to come across such a devoted Editor – at just the right time, and just the right place. Madrid, Rome and London 25 May 2009

Mauricio Su´arez Mauro Dorato Mikl´os R´edei

Chapter 1

Naturalism and the Scientific Status of the Social Sciences Daniel Andler

The purpose of this paper is to characterize a dichotomous view of the current situation in the sciences of man and show it to be fallacious. On the view to be rejected, the sciences of man are undergoing the first serious attempt in history to thoroughly naturalize their subject matter and thus to put an end to their separate status. Progress has (on this view) been quite considerable in the disciplines in charge of the individual, while in the social sciences the outcome of the process is moot: the naturalistic social sciences are still in their infancy, and whether they will eventually engulf or at least profoundly transform the field of social science is unclear. The dichotomous conception pits two camps against one another. On the one hand, the advocates of the naturalistic social sciences maintain that they hold the key to the long-awaited realization of the unity of science program and are set to put the social sciences on equal footing with the natural sciences as we know them today. On the other, the mainstream in social science is strongly opposed to the very idea of naturalizing the field. The impartial observer is then asked to wait and see: either the current attempts at naturalization succeed, and the goals of unified science are attained; or they fail, in which case the prospect of developing a social science which is truly scientific recedes in the distant future. But this view is based on too narrow a concept of science, and thus fails to do justice to the situation, or so I’ll argue.

1.1 Unity of Science, Yesterday and Today Unity of science, a program propounded by the Vienna Circle, under a label coined by Otto Neurath, has had a curious posterity. On the one hand, it has been all but rejected by the ‘post-positivist’ philosophers of science. Unity of science is seen as part of the ‘Legend’,1 a philosophers’ rational reconstruction of science, a misplaced D. Andler () Philosophy, Universit´e Paris-Sorbonne, Cognitive Studies, Ecole normale sup´erieure, Institut universitaire de France e-mail: [email protected] 1

As P. Kitcher puts it in Kitcher (1993).

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 1, c Springer Science+Business Media B.V. 2010 

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attempt to force upon actual science a normative stance based on presuppositions, both ontological and epistemic, which are no longer even remotely plausible. On the other hand, unity of science is conspicuously used as an overall justification for a number of research programs in a number of disciplines. It serves them as warrant and as value: because we have every reason to believe, according to proponents of such a program, that science will eventually reach unification, the success of our particular program has some prima facie plausibility as the only, or the winning, game in town; and because science should aim for unification, it is our duty to pursue this program, as long at least as it looks promising. This eschatological form of unitarianism is encountered not only in the sciences of man, but also in particle physics, in dynamical systems theory, in complexity theory, in logical modeling, in game theory. Of course, the unity to be achieved is not the same across the various programs. But the combination of putative support and recommendation provided by the idea of unification works in every case. There is in every case the implicit, or explicit reference to the positivists’ ideal of unity of science, of which the present efforts are seen as a straightforward implementation. I shall limit myself from now on to unification programs in the sciences of man. In order to bring to light the spurious character of their claim of perfect continuity with the Unity of Science program, it will help to introduce some terminology. Rather than ‘monism’, which can cause some misunderstanding, I will use ‘unitarianism’ as a label for the doctrine, principle or thesis of the unity of science, and rather than ‘bifurcationism’, which is too limited, I will use ‘regionalism’ to name the opposing view. Unitarianism can be reductive, i.e. propose the in-principle reduction of all particular sciences to one single science; physics being the only plausible candidate, reductive unitarianism is often called physicalism. Note than physicalism is often defined as an ontological thesis, while unitarianism is at first an epistemic thesis. However, the reductive version of unitarianism seems to imply either agnosticism about the ontology, or adherence to ontological monism. There is another kind of unitarianism, which does not to my knowledge possess a canonical label, and which I will take the liberty therefore of calling organic unitarianism, according to which the various sciences can maintain their autonomy, while fated to eventually develop intelligible interconnections, rather than leaving forever some slack between them, so that science as a whole aims at the heterogeneous unity of a complex organism. Whether organic unitarianism is a stable position, which need not eventually collapse into reductive unitarianism is a genuine question which I will leave untouched. Regionalism also comes in two flavors. According to weak regionalism, the sciences as we know them are as a matter of fact disjointed: there simply is no systematic interconnections between them, nor a method which can be relied on to eventually provide such links. Strong regionalism claims an in-principle separation of the sciences, whether based on some specific purported disconnections (as in the familiar arguments in favor of the separateness of the Geistes- and the Naturwissenschaften), on some burden-of-proof argument taking as premise the chaotic state of the scientific landscape, or on an inference from the disunity of nature.

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One might wonder whether there is a real difference between weak regionalism and organic unitarianism. A definite answer would require a more precise characterization of the two positions. The weak unitarian might contemplate as a distant possibility some form of organic unification; on the other hand she might find such speculation on such poorly grasped ideas quite otiose. Suffice it here to point to two historical examples: Poincar´e clearly defends an organic unitarianism, while Comte seems to go for weak regionalism (he quite explicitly rejects reductive unitarianism, in terms which seem to rule out the intermediate position which Poincar´e would defend half a century later).2 Be that as it may, we are now in a position to contrast two very different dialectical situations. In the heydey of (neo) positivism, reductive unitarianism was pitted against regionalism, both weak and strong. In our postpositivist age, it is organic unitarianism which takes on strong regionalism. Moreover, both parties to the first debate appear to have granted an assumption which is rejected by many today. When the Unity of science movement was launched, the issue was bifurcationism, the doctrine of an absolute separation between the so-called moral (Geistes) and natural sciences. What Neurath and his friends wanted to tear down is what they saw as a protective wall which the sciences of man had built around themselves to prevent the natural sciences (and more broadly the associated stringent form of critical rationality) from interfering: We cannot make a division between ‘natural science’ and ‘mental science’; even less can we make a division between ‘natural philosophy’ and a ‘philosophy of mental science’.3

The physical sciences seemed to have achieved, against all odds (as they would have been assessed up to the late eighteenth century), what seemed at the time as a very high degree of unification. Further, the life sciences were not then in a position to suggest the possibility of, and the need for a weaker form of unitarianism. It was thus perfectly obvious to the Vienna Circle that the proper way of countering bifurcationism was to extend to the entire repertory of the sciences the demand which had seemed to yield such a positive outcome for the physical sciences. The assumption which was common ground then was the unity of the natural sciences, a unity construed as reductive: although the reduction to physics had clearly not been completed, it was I think the majority view (or perhaps the default view, one which few cared to challenge) that it would eventually be shown to be achievable in principle. Symmetrically, the moral sciences were supposed to share a common crucial feature which functioned as a principle of unity. If necessary, exceptions could be dealt with by dividing a field (such as geography or anthropology) into a natural-scientific component and a social-scientific, historical, cultural or hermeneutic component.

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Compare e.g. (Comte 1848) and (Poincar´e 1902). Neurath, Sociology and physicalism, 1931, repr. as chap. 6 in (Neurath 1983), p. 69.

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The assumption of the unity of the natural sciences is now clearly rejected, or at least strongly questioned, by nearly everyone today.4 If the natural sciences themselves display some form of disunity, the situation is no longer necessarily one in which two solid blocks of disciplines are to either be kept completely apart, or completely joined together. The loosening of the ties previously thought to tightly bond together the various natural sciences provides some slack which can allow some natural sciences to come closer to some sciences of man, without forcing the fusion of the entire two blocks. Thus a new direction opens up, which strict neo-naturalism (variously also called scientific naturalism or philosophical naturalism5 ) as well as dissenting, liberalized forms of contemporary naturalism,6 are exploring: organic unitarianism, bordering, in the liberalized forms, on weak regionalism, with no other opponent than strong regionalism.

1.2 Neo-naturalist Unification The professed goal of neo-naturalism is to bring the sciences of man at a distance of the natural sciences as a whole no greater than that which separates some of the natural sciences amongst themselves. In other words, the neo-naturalist aims at no more than to show that the topics of psychology, linguistics, sociology, anthropology and so forth stand to disciplines such as biology, logic, statistical physics, in a relation comparable to that between say biology, chemistry, geology and physics. This can be achieved by brute force, i.e. through a complete reconstruction of the sciences of man in a naturalistic framework; or in a more subtle way, by mooring them to the natural sciences by way of a dense network of empirical and conceptual links. A hybrid strategy might combine the two approaches: partial reconstruction, completed by specially fashioned new links between the old and the new corpus. Eventually, the natural (or naturalistic) social sciences would either directly absorb the social sciences as we know them, or force them into a partial reconceptualization making such an absorption possible. How do the neo-naturalists propose to carry out such a program? They rely, first, on an attitude, a stance, and second, on certain recent research traditions. The naturalistic stance is, in its simplest and most stable form, a passion for looking, looking at ways things in the world really are, how they really work. In a more contemporary vocabulary, naturalists want scientific knowledge to be thoroughly evidence-based, rather than resting on conceptualizations and beliefs originating in commonsense, philosophical tradition, or armchair speculation. Neo-naturalists believe that the social sciences have remained, by and large, stuck in the prescientific stage characterized by over-reliance on commonsense or speculation, and want to deploy instead some research programs which have emerged over the last 50–70 years. 4

See, e.g., Galison and Stump (1996), Kitcher (1993), Dupr´e (1993), Kellert, Longino and Waters (2006). E.O. Wilson (Wilson 1998) and friends of the ‘consilience’ view he defends are exceptions. 5 See, e.g Papineau (1993). 6 See De Caro and Macarthur (2004).

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These are the various cognitive sciences7 , evolutionary biology, suitably updated and extended8, and philosophy itself9 , transformed as a result of the naturalistic turn ushered by Quine10 and other ‘postpositivist’ thinkers. These three strands combine into something like a cognitive-evolutionary ‘paradigm’, which has already very much refashioned the field of study centered on the individual agent.11 The issue now is whether and to what extent it will reach into the social sciences proper. Anthropology, economics, sociology, social psychology all now have a ‘cognitive’ (or, in the case of economics, ‘behavioral’) wing, but these wings are at best small shacks leaned against their respective mansions. The common thread running through the research programs in the various cognitive/behavioral social sciences is a simple idea: the individual human being is a complex entity whose behavior is to be studied naturalistically, rather than modeled from first principles. No strong methodological individualism need be presupposed: the mere fact that mainstream theorizing in the social sciences is based on some assumptions, however minimal and often implicit (such as the blank-slate ‘theory’ of the mind12 ), regarding the behavior of individuals, is enough to justify the naturalist’s demand. It may turn out that some collective phenomena are insensitive to the details, or even to large-scale features of individual behavior, but the burden of proof rests on the social scientist. She cannot take as her starting point a blanket invariance hypothesis based on nothing more than a holistic dogma. But how is one supposed to form a correct representation of the individual? This is where cognitive science and evolutionary biology are recruited, as well as philosophy which, in true naturalistic fashion, is understood as working in tandem with the relevant sciences, especially when new frontiers are being explored, which is very much the case for cognition. However, in actual practice, most so-called cognitive models of social phenomena make shallow use of concepts from cognitive science, and invoke evolutionary theory in highly speculative form. There are as yet not many research programs which combine deep results from cognitive science and evolutionary biology to produce novel insights.13 Thus the ‘naturalistic social sciences’ are at present barely rising from limbo. Optimists see these attempts as a highly significant beginning. But this view is far from universally shared. In fact, there is widespread doubt, within the social sciences, that the naturalistic approaches (even of the weak kind) can go much beyond the restricted area in which they have some relevance. Moreover, many oppose the prospect for reasons which are basically those advanced in favor of bifurcationism: normativity, intentionality, interpretation, historicity or again free will, are the 7

Turing (1950), Chomsky (2000). Sperber (2000), Margolis and Lawrence (2003). 9 Fodor (1983), Dretske (1995), Searle (1995), Kim (1998). 10 Quine (1969). 11 I do not mean to imply that naturalism has won the day in the sciences of the individual human being. What seems to me uncontroversial is that it has become a major force in those fields. The emphasis here is on the prospects for a similar naturalistic turn in the social sciences. 12 See, e.g. Pinker (2002). 13 Dan Sperber (1997) labels the first (most common) kind of work ‘weakly cognitive’ and the second ‘strongly cognitive’. See also his 2006. 8

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familiar challenges which any naturalistic theory must meet, and they claim that the new cognitive-evolutionary paradigm is in no better position to do this than previous forms of naturalism. Of course, this is exactly what neo-naturalists deny, and a large majority of the efforts of naturalistic philosophers of mind is devoted to outlining possible solutions. Finally, it is often stressed by skeptics that cognitive science itself is threatened by deep conceptual problems, whose resolution even sympathetic philosophers of mind increasingly view as doubtful. This is the context in which the question arises. Will the social sciences finally yield to the neo-naturalist approach and thus at long last earn their place in the realm of genuine scientific thought, or will they resist and thus remain unscientific? That, according to the neo-naturalist, is the issue. Her opponent sees it differently: the social sciences need not and should not heed the call of the cognitive sirens; they have already earned their scientific accreditation; to become natural science, they would need to lose their soul, to cease to be genuine social science. This, I claim, is a false dichotomy. It will probably not be news to the informed philosopher of science; but I believe that within the social sciences and the cognitive sciences, many people, some philosophers included, are convinced that the issue as I have presented it is correctly posed. As Neil Levy puts it succinctly, “For many of its adherents, evolutionary psychology holds out the promise of bringing the study of humanity within the ambit of science.”14 The same can be said more broadly of many adherents of cognitive science, more particularly philosophers of mind.

1.3 The Forgotten Party: QFSS To present the neo-naturalistic approaches in social science (briefly, NSS) as the first, one and only properly or strictly scientific player in the field is a mistake. From their nineteenth century beginnings, the social sciences have harbored a set of research programs which I propose to group together under the heading of quantitative and formal social science (QFSS). It includes a large part of economics, as well as the partly overlapping fields of decision theory, game theory, rational choice theory, political science and sociology. Formal models of emergence and interaction in populations of more or less sophisticated agents, as developed in artificial intelligence and artificial life, lay the foundations of a form of general theoretical sociology. And of course the social sciences have always heavily relied on quantitative methods. Social systems are now viewed as ‘complex systems’, which implies a commitment to an open-ended collection of methods which are all at least in part mathematical in nature.15 The existence, and persistence, of QFSS completely changes the picture. First, QFSS can reasonably claim to be far more important, in terms of results, manpower and resources, than NSS. It constitutes a considerably larger (strictly) 14 15

Levy (2004). Auyang (1998).

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scientific enclave in the social sciences than NSS. The first and foremost mode of naturalization is by way of methods. Second, QFSS is the ‘official’ representative, within social science, of natural science. The serious methodological controversies within SS pit the interpretative, constructivist and historicist currents against QFSS, not NSS, and the resulting dialectic sets the agenda for SS. Third, and perhaps most importantly, QFSS is truly about the social realm, which is more than can be said, without further evidence, of NSS. Broadening the perspective, for a moment, to the sciences of man at large (the human and social sciences, or HSS), this is a point worth elaborating, for it is precisely this difference which explains the greater resistance of the mainstream to neo-naturalistic HSS. It is one thing to discover formal-mathematical structure in human affairs; quite another is to treat the sciences of man as a mere province of biology (to put it dramatically). Formalism may be limited in scope, or outright sterile (as the critics insist), at least it doesn’t altogether pull the rug from under HSS’s feet. For uncovering the ontology of the human order remains a daunting task which only HSS are competent to achieve. Quantitative social science, even buttressed by complexity theory, may perhaps predict how things will turn out, in favorable cases; they have nothing to say about what it is whose outcome is of interest. Compare: mathematicians may help meteorologists set up forecasting models; but only meteorologists can tell us what scientific ontology the study of weather and climate calls upon. The basic categories of HSS will never come out of complexity’s hat: they have to be put there in the first place. The distinction is especially clear when the denizens of the task domain misbehave – in other words, when they fail to conform to their assigned role in the model. So if winds, currents, tides, clouds, etc. don’t quite conform to their specifications in the model, only a meteorologist can fix the problem. This is of little import in the case of meteorology: mathematics is so deeply embedded in the natural sciences that nothing much hangs on the precise distribution of labor. When it comes to HSS however, it’s a different matter. Humans tend to resist in all sorts of ways to externally imposed categories, and only the finest skills and the long experience of the social scientist can be of any help in preventing the modeling enterprise from going hopelessly off track. So while meteorology and say sociology or demography play the lead role in such junctures, with mathematics (or complex systems theory) retrograded to their traditional function of obedient toolbox, the kind of adjustment which the leading discipline needs to make is, in the case of meteorology, naturalistic by definition, in the case of sociology or demography, it is deemed to be of a deeply different nature: bifurcation all over again. Thus it appears that formal-quantitative, complexity-theory based approaches in HSS preserve, after all, the latter’s specificities. By contrast, bio (neuro-cognoevolutionary) naturalism may seem to want to impose the one true scientific ontology to HSS. In other words, while formalism does not imply reductionism, let alone eliminativism, bio-naturalism may carry reductive and even eliminative implications. For should bio-naturalistic research programs eventually show (or be allowed

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to falsely convince us) that we humans are ordinary biological creatures subject to both distal (evolutionary) and proximal (physiological and mechanical) causation which leave no room for any other type of fundamental determination, then indeed, or so the critics argue, the age-old images of man on which HSS are based would be discredited, and mainstream HSS would soon be displaced by biology, suitably extended. Fourth, QFSS is unproblematically scientific in the strict sense, inasmuch as its strictly scientific character is based solely on its mathematical methodology. By contrast, NSS’s (strict) scientific status is predicated on its naturalism, which in turn is incomplete or flawed, due to the uncertain status of the intentional or semantic (or more broadly normative) concepts which it constantly deploys. QFSS has its own criteria of validation and success, regarding both scientific status and relevance to social science, and these criteria do not rest on dubious claims regarding the proper extension of ‘nature’ or ‘naturalistic methodology’. These arguments in favor of QFSS are themselves not above dispute of course. But they are not without force either and they rather deeply refashion the problem situation. In a sense, the rivalry between QFSS and NSS is the latest episode in the longstanding dispute between the Platonists and the Mechanists, between those who view mathematics as the universal, unifying matrix and those who view mechanistic causal explanations as the connecting factor, as the ‘glue’ holding together the scientific worldview. It can also be viewed as a replica of the quake which shook analytic philosophy in the 1960s and the 1970s as its Young Turks rebelled against the established anti-psychologistic, anti-naturalistic stance recommended by Husserl, Frege and the logical positivists.16 But is it right to think of the relation between the two approaches as an instance of rivalry? This, I think, is the central question. It is viewed differently by the two parties. Within QFSS, it is fair to say that a majority is indifferent or hostile to NSS, siding quite naturally with mainstream social science within which it enjoys the status of a mostly welcome minority. But there is also a minority within this established minority which is well disposed towards NSS, for both strategic and conceptual reasons. The strategic reasons are a felt need to forge an alliance in order to resist what the ‘minority-squared’ senses as the rise of an intolerant version of interpretativist, constructivist and historicist social science, which rise in turn may be a reaction to the pretensions of NSS. The conceptual warrant for the alliance rests on two premises. One is the basic dual-aspect assumption of cognitive functionalism which allows, at the level of the individual mind, for both a formal and a mechanistic account, with mechanisms ‘realizing’ or ‘implementing’ functions which are fully characterized by their formal properties. The other is that collective phenomena can be accounted for by applying formal, quantitative or more broadly complex-theoretical methods to populations of individuals under the descriptions provided by cognitive science, with the possible help of evolutionary considerations. 16 See Kitcher (1992) for a detailed account of the ‘return’ of naturalism in philosophy, and Kusch (1995) for a historical account of the rise and triumph of anti-psychologism at the turn of the twentieth century.

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Combining these approaches is by no means trivial, and judging from the ongoing attempts it requires additional assumptions or schemata such as social cognition, mind-reading, massive modularity, gene-culture co-evolution, niche construction, generative entrenchment, epidemiology etc.17 Within NSS, the situation is the reverse. In the cognitive-scientific community, the mainstream view, which is still a majority, albeit an embattled one, is favorable to QFSS, for the same conceptual reasons for which the minority within QFSS has embraced NSS. What some regard as ‘orthodoxy’ in cognitive science, and which certainly can claim historical precedence, holds that mechanisms implement computations, which in turn constitute the appropriate level of description for cognitive processes. Thus it is not only conceivable, but actually obligatory, to have or aim for both formal characterizations and mechanical accounts of cognition. The ascent to social phenomena requires a naturalistic basis in the form of the appropriate conceptual equipment in the individual, supplemented, as we just saw, by the extra level of complexity of collective phenomena. But an increasingly vocal minority within NSS rejects the ‘formalistic’ approaches of historical cognitive science associated to figures such as Turing, Simon, Chomsky, Marr, or Fodor, and tend to be suspicious of QFSS. In this discussion, it should be said, the ‘Q’ and the ‘F’ components tend to come apart: while formal accounts are in dispute, the quantitative dimension is welcomed by both sides within NSS, as an indisputable reinforcement of the strictly scientific methodology of the field. The precise way in which NSS and FQSS would, in the fullness of time, and provided they meet with continued success, complement one another is very much of an open question. There is a continuum of hypotheses, ranging from complete integration, as sketched above, to a theoretically much less ambitious, loose form of complementarity, with NSS and FQSS each providing certain constraints and heuristics to social science, without claiming to exhaust the field but helping it, through gradual reconceptualizations, on the path to a never-completed unification. Most current proposals belong to the latter type: they start from a formal account, and submit some of its assumptions to empirical testing on individuals or groups of agents, in the hope of making the initial model more realistic, or again in order to arbitrate between rival accounts. This movement within the social sciences parallels, and is buttressed on the new wave of experimental philosophy, which challenges the exclusive reliance of traditional analytic philosophy on conceptual analysis, and claims that we need to confront our assumptions about how people reason, what they mean by the words they use, what their moral or epistemic standards really are, etc., to the ‘tribunal of experience’.18

17 See Tooby and Cosmides (1992), Hirschfeld and Gelman (1994), Sperber (1996), Carruthers (2006), Richerson and Boyd (2005), Durham (1991), Aunger (2000), Wimsatt (2007), Sterelny (2003), Nichols and Stich (2003), Goldman (2008). 18 See Knobe and Nichols (2008), Jackson (1998).

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1.4 A Return to Neurath? To conclude, it may be worth returning briefly to the source. As we reminded ourselves at the beginning, Neurath is the one, within the Vienna Circle, who coined the phrase ‘Unity of Science’. As has now been rediscovered19 (nor was it an arduous task: it was enough to read some of his papers, which are quite explicit about it), the unity he was proposing as a reasonable demand had little to do with reductive unitarianism, nor even with organic unitarianism. His was a realistic vision of science as it actually proceeds (Neurath ‘invented’ descriptive philosophy of science several decades before post-positivists philosophers of science decided to renounce or tone down the normative attitude prevalent among the founders of the field). One of Neurath’s conclusions was that all the sciences except possibly fundamental physics make ineliminable use of ‘hybrid concepts’ (Ballungen) which have a component belonging to the formal apparel of the science under consideration, and other components foreign to it, belonging as they do to common parlance or to other, possibly higher-level disciplines: Complex (messy) statements –‘Ballungen’– are the basic material of the sciences.20

The impurity of concepts leads to an impurity of methods, making all speculations about eventual reduction otiose. This skeptical view was complemented by a rejection of the notion of science as an enterprise on its way to completion: Pseudorationalism will time and again try to reach, in roundabout ways, the ‘one real world’ (‘the one mass of statements distinguished by certain characteristics’), for example, by putting forward the doctrine of a perfection, perhaps ‘infinitely far away’ to which science gets closer and closer.21

Science as Neurath sees it is more like a series of lighting bolts in the dark, throwing a temporary light and moving on to another location, with few stable connections established between the partial views obtained at successive moments of scientific development. But these views, which in retrospect seem to go against contemporary trends such as neo-naturalism, were also effectively deployed, as we reminded ourselves earlier, against bifurcationism, the Circle’s avowed target. Neurath was after a knock-down argument against any justification of an ‘apartheid’ view of the ‘society’ of research programs. What he wanted to promote instead was a state which was neither apartheid nor unification under the banner of physics, but rather ‘orchestration’22 : research programs were somewhat like musicians who contributed to a harmonious, dynamic flux of understanding, explaining, forecasting and reforming.

19

See Cartwright et al. (1996), Andler (in press). Neurath (1935), repr. as chap 10 in Neurath (1983), p. 128. 21 Neurath (1936), repr. as chap 11 in Neurath (1983), p. 137. 22 Cf. the title of a 1946 paper: The orchestration of the sciences by the encyclopedism of logical empiricism, repr. as chap. 22 in Neurath (1983). 20

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Perhaps ‘orchestration’ can still serve as an inspiring metaphor for the social sciences and more broadly the sciences of man, in an age where neo-naturalism brings to light solid empirical data and novel conceptual tools to a collection of research programs which are already partly governed by strictly scientific methodologies, yet retain elements which seem resistant to naturalization. This cannot be the last word, for Neurath was elaborating his views in a world which has undergone immense changes. The history of ideas moves not in cycles, but in helices. This paper ends by merely stating the real challenge: Where in the helix do we stand at present?

References Andler D (in press) Unity without myths. In: Symons J, Torres JM, Pombo O (eds), New Approaches to the Unity of Science, vol. 1, Otto Neurath and the Unity of Science, Springer Aunger R (ed) (2000) Darwinizing culture: the status of memetics as a science. Oxford University Press, New York Auyang SY (1998) Foundations of complex-system theories in economics, evolutionary biology, and statistical physics. Cambridge University Press, Cambridge Carruthers P (2006) The architecture of the mind: massive modularity and the flexibility of thought. Clarendon, Oxford Cartwright N, Jordi C, Lola F, Uebel Th (1996) Otto Neurath: philosophy between science and politics. Cambridge University Press, Cambridge Chomsky N (2000) New horizons in the study of mind and language. Cambridge University Press, Cambridge Comte A (1848) Discours sur l’ensemble du positivisme. L. Mathias, Paris De Caro M, Macarthur D (eds) (2004) Naturalism in question. Harvard University Press, Cambridge, MA Dretske F (1995) Naturalizing the mind. MIT, Cambridge, MA Dupr´e J (1993) The disorder of things – metaphysical foundations of the disunity of science. Harvard University Press, Cambridge, MA Durham WH (1991) Coevolution: genes, culture and human diversity. Stanford University Press, Stanford, CA Fodor J (1983) The modularity of mind. MIT Press, Cambridge, MA Galison P, Stump DJ (eds) (1996) The disunity of science. Stanford University Press, Stanford, CA Goldman A (2008) Simulating minds: the philosophy, psychology, and neuroscience of mindreading. Oxford University Press, New York Hirschfeld LA, Gelman SA (eds) (1994) Mapping the mind: domain specificity in cognition and culture. Cambridge University Press, Cambridge Jackson F (1998) From metaphysics to ethics. a defense of conceptual analysis. Oxford University Press, Oxford Kellert SH, Longino H, Waters CK (eds) (2006) Scientific pluralism. Minneapolis: University of Minnesota Press Kim J (1998) Mind in a physical world. MIT Press, Cambridge, MA Kitcher P (1992) The naturaiists return. Philos Rev 101(1):53–114 Kitcher P (1993) The advancement of science. Oxford University Press, New York Kusch M (1995) Psychologism. Routledge, London Knobe J, Nichols S (eds) (2008) Experimental philosophy. Oxford University Press, Oxford Levy N (2004) Evolutionary psychology, human universals, and the standard social science model. Biol Philos 19:459–472

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Margolis E, Lawrence S (2003) Should we trust our intuitions? Proc Aristotelian Soc 103:299–323 Neurath O (1983) Philosophical papers 1913–1946. Reidel, Dordrecht Nichols S, Stich S (2003) Mindreading: an integrated account of pretence, self-awareness, and understanding other minds. Oxford University Press, New York, Oxford Papineau D (1993) Philosophical naturalism. Blackwell, Oxford Pinker S (2002) The blank slate: the modern denial of human nature. Penguin, New York Poincar´e (1902) La science et l’hypoth`ese; transl. Science and Hypothesis, Dover, New York (1952) Quine WVO (1969) Ontological relativity and other essays. Columbia University Press, New York Richerson PJ, Boyd R (2005) Not by genes alone: how culture transformed human evolution. University of Chicago Press, Chicago, IL Searle J (1995) The construction of social reality. Penguin, London Sperber D (1997) Individualisme m´ethodologique et cognitivisme. In: Boudon R, Chazel F, Bouvier A (eds) Cognition et sciences sociales. Presses Universitaires de France, Paris, pp 123–136. Available (as well as an unpubl. English translation) at http://sperber.club.fr/ index.htm Sperber D (2006) Why a deep understanding of cultural evolution is incompatible with shallow psychology. In: Nick E, Stephen L (eds) Roots of human sociality. Berg, Oxford, pp 431–449 Sperber D (1996) Explaining culture: a naturalistic approach. Blackwell, Oxford Sperber D (ed) (2000) Metarepresentations. A multidisciplinarity perspective. Oxford University Press, Oxford Sterelny K (2003) Thought in a hostile world. Blackwell, Oxford Tooby J, Cosmides L (1992) The psychological foundations of culture. In: Barkow J, Cosmides L, Tooby J (eds) The adapted mind. evolutionary psychology and the generation of culture. Oxford University Press, New York Turing AM (1950) Computing machinery and intelligence. Mind LIX(236):433–460 Wilson EO (1998) Consilience: the unity of knowledge. Alfred A. Knopf/Random House, New York Wimsatt WC (2007) Re-Engineering philosophy for limited beings. Piecewise approximations to reality. Harvard University Press, Cambridge, MA

Chapter 2

Reconsidering Gilbert’s Account of Social Norms Caroline M. Baumann

2.1 Introduction How are we to account for social norms and their normativity? Why do we believe that in certain situations that we ought to act honestly or politely or that we ought to cooperate with others? The phenomenon of social norms represents a serious challenge for individualistic social theories. Trying to cope with the weaknesses of these accounts, alternative proposals have been offered. This paper evaluates Margaret Gilbert’s theory of social norms. Focusing on the social rationality of individuals, Gilbert tries to explain the normativity of social norms in the ways individuals are part of a social setting. Her account has been considered as a promising alternative to rational-choice approaches (see, for example, Elisabeth Anderson 2000). Nevertheless, while Gilbert’s general account of social phenomena has been widely discussed, her account of social norms has not been analysed thoroughly. In the following, I argue that Gilbert does not adequately capture the phenomena of social norms and their normativity.

2.2 Social Norms and Joint Commitments Gilbert’s analysis of social norms is part of her broad project to provide a conceptual analysis of certain group concepts such as group belief, group intention, and group agency. According to Gilbert, these social phenomena are grounded in joint commitments. A joint commitment (JC) is a commitment of two or more people. Two people might be jointly committed to paint a house or to go for a walk together. JCs involve obligations and rights (see, for example, Gilbert 1989, 2002a, b). Most importantly, the parties to the JCs have the obligation to act in conformity with the JC unless or until the JC is rescinded, where a JC can only be rescinded by all parties involved. C.M. Baumann () European Association of Philosophy of Science, Founding Conference, Madrid, Spain e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 2, c Springer Science+Business Media B.V. 2010 

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For example, if individuals A and B are jointly committed to paint the house together, A has the obligation to paint the house together with B until both A and B change their mind and rescind or abandon the JC. A cannot just stop painting without violating a right B has toward A to continue paint the house. What are the conditions for the existence of a JC? Gilbert holds that JCs are formed when individuals openly express their willingness or readiness to participate in the relevant JCs. There are three basic conditions for the creation of a JC (Gilbert 1989: 222–223). First, there need to be an intention to participate in the JC (Gilbert 2002b: 81). Second, to enter a JC there need be an open expression or manifestation of one’s intention to participate. In other words, potential parties to a JC must, for the JC to be created, communicate in some way their intention to participate in the JC. Consider the following example given by Gilbert (2002b: 88): Bob says to Lily “shall we dance?” and Lily responds “Yes! Let’s”. According to Gilbert, during this interchange, Bob and Lily express explicitly their readiness to dance together. Third, Gilbert posits a common knowledge condition: the manifestation of willingness must be common knowledge to all participants of the JC. To summarise, individuals A and B are jointly committed to paint the house together if it is common knowledge among them that both have expressed that they intend to be jointly committed to paint the house together. Having clarified the concept of a JC inherent in group phenomena in general, let me turn to Gilbert’s account of social norms. Note first that Gilbert prefers using the notion of ‘social rule’ or ‘social convention’ instead of ‘social norm’. However, I think that Gilbert’s view of social conventions applies also to social norms. This suggestion does not seem controversial. Anderson (2000: 193) takes Gilbert’s account of social conventions to apply to social norms without even arguing her case. Nevertheless, let me quickly elaborate on why we may treat social norms by analogy to social conventions here. What might provoke unease about this analogy is the sharp distinction which is commonly drawn between social conventions and social norms. At least in the economic literature, social conventions (such as traffic rules) are generally distinguished from social norms (such as rules of etiquette or norms of cooperation) by the way they are enforced: while, following David Lewis’s discussion in his book Convention (1969), social conventions are considered by definition to be self-enforcing, social norms are thought to be enforced by way of a social sanctioning system. Jon Elster (1991: 111) specifies social norms as norms which are “shared by other people and partly sustained by their approval and disapproval”. Whatever the worth of the distinction between conventions and social norms, the way Gilbert uses the notion of social convention suggests that what she has in mind are not merely Lewisian conventions but also social norms as commonly defined in the economic literature. First, in line with the objective to provide an account for plural-subject phenomena in general, Gilbert explicitly holds that her analysis does not only apply to social conventions but to social rules in general (1998, 2007). The notion of a social rule is commonly considered to be a general term, covering not only Lewisian conventions and moral rules but also social norms. Second, Gilbert’s (1989: 315–316) understanding of a social convention is explicitly based on pre-theoretic and everyday intuitions which does not only go beyond Lewisian

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conventions but invokes rules which, according to the common definition in the economic literature, count as social norms. Actually, her rejection of Lewis’ understanding of social conventions builds at least partly on examples, such as dress codes and rules of etiquette, which are definitely not Lewisian social conventions but are generally considered to be social norms. In the following I shall ignore the differences between the notions ‘social rule’, ‘social convention’ and ‘social norm’ and use them interchangeably. According to Gilbert, a key characteristic of social norms is that they are essentially normative: social norms tell us how we ‘ought’ to act. Typical manifestations of the normativity of social norms are reactions of social approval and disapproval (Gilbert 1989: 349–351). Further, social norms are special in that their normativity is essentially grounded in the attitudes people take towards them; social norms exist only to the extent that they are supported by a group of people (Gilbert 1989: 351–352). Based on this understanding of social norms, Gilbert argues that their normativity is grounded in JCs. More precisely, on Gilbert’s (1989: 377, 1998) account our everyday concept of a social norm is that of a jointly accepted principle of action or rule. A social norm exists in a population if and only if all members of the population have openly manifested their willingness to be jointly committed to accept the norm or simply to jointly accept the norm (1989: 373). The normativity of a social norm is that of the binding nature of the JC to accept the norm: someone is bound by a social norm if and only if he has openly expressed his readiness to jointly accept the norm. A party to the joint acceptance of a social norm ought to act accordingly unless he is released from being bound by the norm by all parties to the joint acceptance. While Gilbertian JCs may well be able to make sense of the normative force of some social norms, I think that they are not applicable to social norms in general. I wish to draw attention to four problems.

2.3 Over-voluntarisation Gilbert’s account over-intellectualises and, more precisely, over-voluntarises the process by which one becomes subject to social norms. Others have attacked Gilbert’s theory of social phenomena the grounds of over-intellectualisation. Deborah Tollefsen (2004: 11) criticises that Gilbert assumes that individuals who form a plural subject have an understanding of the notions of JC and plural subject. Considering that these terms are very technical, it seems psychologically implausible that everyday folk have an explicit or implicit understanding of them. Ulrich Baltzer (2002) argues that while Gilbert’s account may be fine for joint actions involving a few people, it cannot adequately deal with large social groups. Particularly the common knowledge condition underlying JCs is problematic when it comes to make sense of large social groups. My criticism focuses on Gilbert’s voluntaristic or intentionalist understanding of the normativity of social norms.

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Remember, Gilbert holds that for someone to be subject to a social norm one must have expressed one’s intention to jointly accept the social norm. This condition is too strong. People may be subject to social norms simply to the extent that they participate in a practice governed by these norms; and participating in a practice need not involve a JC to accept all norms governing the practice. There are many cases where we join in a social practice without subscribing to all the rules governing the practice; however, insofar as we participate in the practice, we are subject to the governing rules. Consider a person who starts studying at university. When registering as a student he subscribes to a set of rules governing the practice, such as rules on the duration of his programme, requirements for obtaining a degree or library regulations. There are many informal and unwritten rules governing the student life on campus he may have no idea about when starting his programme. For example, he comes to learn the rules regulating workshops, behaviour on College ground or student interaction only by and by. Even if he cannot be said to have expressed his intention to act according to these rules when he joins university, as a participant in the university life, he is subject to the rules. Or take someone who goes ice-skating on a skating rink. When paying the entrance fee she does indeed subscribe to some rules governing the practice of skating on that particular rink. However, there are unwritten rules, as for example the rule that when there are many people around everybody ought to ice-skate in anticlockwise direction or the rule that one ought to stop only in the centre of the rink or close to the board. Nevertheless, when starting to ice-skate, she is subject to these rules whether or not she expressed her acceptance of them. Actually, participants in a practice who disobey its rules are socially disapproved of and generally accept or grant the disapproval as warranted irrespective of whether they subscribed to the rules or not. The ice-skater who starts skating on the rink in clockwise direction will soon learn about her mistake by being bumped into, by being looked at strangely or by being informed by other ice-skaters; she will normally accept others’ rebuke right away and grant that on that rink she ought to skate in the same direction as everybody else. It is important to note that being subject to a rule is compatible with one’s rejection of the rule. It may well be that someone is participating in a social practice while rejecting some of its governing rules. The non-acceptance of some of the rules governing the practice one is participating in does not undermine the fact that one is bound by these rules in the sense that one is subject to social disapproval in case of nonconformity to the rules. Gilbert might counter that these examples build on an underlying presumption, namely the presumption that, when joining a social practice, people enter a JC to accept the rules and norms of the practice, whatever these rules might be.1 To the

1 Gilbert (1987: 199–200) argues on these lines when it comes to attibuting collecive beliefs: when we say “the United States believes that the invasion of Afghanistan was an unconscionable act” based on the acceptance of this judgment by the government and despite the fact that most people of the United States have no idea of the invasion of Afghanistan, we assume that the citizens of the United States have endorsed the idea that they may be regarded as jointly accepting whatever proposition the government itself accepts.

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extent that we entered such a general commitment, we are bound by all rules of the practice. I’m not convinced by this move. Entering a JC is a very strong engagement that implicates serious obligations. It can hardly be assumed that when we join a social practice we jointly commit ourselves ‘blindly’, that is, that we commit ourselves to rules whatever these rules might be. When starting to participate in a practice, such as entering a programme at university or ice-skating on a skating rink, even if we are subject to the underlying rules we did not explicitly subscribe to, we seem to remain free to jointly commit us to them or not.

2.4 A Different Type of Normativity I argue that the normativity of social norms is not necessarily of the type of normativity underlying JCs. Remember, a party to a JC is obliged to act accordingly as long as the other parties to the JC do not release her from the commitment. It would follow that we are subject to social norms as long as we are not granted permission to be no longer bound by them. I think that while there are situations where the ‘ought’ of social norms is binding until or unless one has been released from it, there are cases where the termination of the mandatory force of social norms does not depend on the permission by others to be released from being bound by them. This view builds on the intuition that we may stop participating in a social practice (and thereby stop being subject to its norms) without the need to be granted permission to do so. My objection goes against what Gilbert (2003: 42–46) calls the permission point. Several authors have criticised Gilbert’s permission point with respect to joint actions. Gilbert defines joint actions in terms of a goal endorsed by all parties to a joint action. Whatever the relation between the notions of joint action and social practice, I think that we are safe to assume that in most cases, joint actions are constituted (at least in part) by social practices. Joint actions involve participating in a social practice, that is, in a practice governed by rules and norms. Consider typical Gilbertian joint actions, such as dancing together or going for a walk together: to the extent that they are governed by certain rules to which the parties are subject, they involve participating in a social practice. With respect to joint actions Robert Sugden (2000: 190) holds that the more we move away from cases of explicit agreement, the more problematic the insistence on the relevant rights and obligations becomes. Consider a teenager living in her family and taking herself to be a member of the family. Sugden thinks that it is not at all intuitively straightforward that the teenager has an obligation to participate in the family unless she is released from this obligation by the other members. In line with Sugden’s intuition, R¨udiger Bittner (2002) argues that the mere fact of acting together does not by itself imply rights and obligations. Particularly, he holds that Gilbert’s examples of travelling together, walking together, or engaging in a conversation do not imply the obligation for the parties to carry on with the activity unless they are granted permission by the other party or parties to stop the

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activity. According to Gilbert (1989: 357–358), for two people walking together, they have the obligation to walk together unless they are granted permission by the other party to give up the joint walk. Bittner (2002: 38–39) disagrees, holding that it would be merely ‘unusual’ or ‘rude’ if one party would just stride off without asking for permission to do so. Gilbert answers, I think, plausibly. First, the behaviour of striding off without asking for permission is definitely not merely ‘unusual’ (Gilbert 2002b: 96). In these cases, rebukes are standardly uttered by and accepted from the other participants. Second, to claim that such behaviour is only ‘rude’ is merely begging the question (Gilbert 2002b: 96; 2003: 45). If the behaviour is rude it must violate some right in the person to whom it is rude. Gilbert’s point is that it is precisely the right inherent in walking together which is violated. To strengthen Bittner’s stance, let me spin the argument further. Consider the following example. Suppose that Jane and Bill are walking along Oxford Street in London in the same direction but by themselves. As soon as they notice each other they greet and continue their walk together. They do so until Jane says ‘I have to turn right here’ and Bill answers ‘Ok. Good to see you.’ I think in this case, Jane and Bill do not have the obligation to continue their walk until they are granted the permission to leave. Bill does not have a right on Jane to continue to walk with him until he allows her to stride off by herself. Gilbert’s reply might be twofold. First, she might say that my interpretation of the situation is mistaken. The conversation between Bill and Jane when breaking off the joint walk indicates that they are indeed subject to the relevant rights and obligations. Jane gives an ‘excuse’ for breaking of the joint walk by saying ‘I have to turn right’; Bill gives his permission by saying ‘Ok.’ My intuition is that this understanding misconstrues what is going on here. The short conversation indicates that they have indeed an obligation to inform each other in case they wish to stride off – an obligation which might be grounded in a rule of etiquette which governs human interactions. However, to suggest that it indicates that they have the obligation to ask and be granted permission to leave goes too far. Second, Gilbert might counter that even if we accept this description of the situation, it does not undermine that joint actions imply Gilbertian rights and obligations. The above example suggests that there are no Gilbertian rights and obligations only because it is taken out of context. If we reconstruct the situation completely, the relevant Gilbertian rights and obligations become apparent. According to Gilbert (2003: 43–44), some joint actions can be terminated without the need of asking for permission because, in these cases, there is a prior agreement or a convention between the parties that permission need not be granted for interrupting the joint action. Considering the above example, Gilbert might say that Bill’s and Jane’s starting to walk together expresses a JC to walk together with the understanding that the joint walk may be terminated as soon as their routes separate and without the need to grant each other the permission to terminate it. Or it may be said that there is a convention which is jointly accepted by Bill and Jane to the effect that in situations of the type Bill and Jane encounter, neither of them does have to be granted the permission to interrupt the joint walk.

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While this second argument is coherent as it stands, I think it is unconvincing. It fights off apparent counterexamples by reconstructing them to support the theory. While this strategy is not objectionable as such, it is problematic in Gilbert’s case. For the approach to be successful it need not merely suggest the reconstruction as an available but as the best available understanding of the situation. Gilbert’s reconstruction seems highly artificial. For every case of joint action which does not involve the relevant rights and obligations, Gilbert needs to postulate the existence of an agreement or a convention to the effect that one can stop participating in a joint action without the need of being granted permission to stop participating. This suggestion is rather unintuitive and unhelpful. I see no reason why we should postulate the omnipresence of JCs even in cases where they seem to be absent except that it would save Gilbert’s theory. It is more natural to argue that some joint actions involve Gilbertian obligations whereas others do not than to argue that all joint actions involve Gilbertian obligations and those which do not involve Gilbertian obligations involve Gilbertian JCs to the effect that the Gilbertian obligations do not apply.

2.5 Overambitious Strategy Gilbert’s strategy to ground all social rules in JCs seems unwarranted and overambitious. In her analysis of social rules, Gilbert takes the existence of JCs and the underlying obligations as bedrock. However, further analysis suggests that JCs do not merely ground but that they are themselves plural subject phenomena. JCs are best understood as social practices which are governed by certain social rules. The rules which govern JCs involve: (i) rules which regulate the practice of entering and being released from a JC, for example, the rule that if one tacitly or explicitly expresses his intention to be part of a JC one becomes party to the JC; and (ii) rules which define the obligations governing JCs, such as the rule that if one is party to a JC he ought to act accordingly unless he is released from it by the other parties to the JC. This understanding clarifies what is at stake here. If Gilbertian JCs are indeed social practices governed by social rules, what Gilbert’s account of social rules and norms amounts to is to put one social practice over and above any other social practice and to argue that the rules of one social practice are more fundamental than other social rules. It is at least doubtful that such an enterprise can succeed. It might be objected that the rules (i) and (ii) are not social rules, that is, they are not rules whose ‘ought’ grounds in facts about a group of people. The argument might go as follows. The particularity of the rules (i) and (ii) is that they are implied by the notion of JC: (i) the rule that to enter a JC one ought to agree either explicitly or tacitly to be jointly committed defines what entering a JC consists in; (ii) the obligation that one ought to act according to the JC unless one is released from it is conceptually related to being part of a JC. Social rules, such as traffic rules, rules of fashion, and rules of etiquette, however, are not conceptually related to what they

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regulate. The rule that one ought to drive on the left is not conceptually related to driving: one might drive a car even if one does not drive on the left. Or the rule that one ought to shake hands when greeting others is not implied by the notion of greeting: one might not shake hands when greeting others and still greet them. Based on this difference it might be argued that the ‘ought’ of (i) and (ii) is conceptual in the sense that it is grounded in conceptual truths about the notion of JC whereas the ‘ought’ of rules, such as traffic rules, rules of fashion and rules of etiquette, is grounded in facts about people. To the extent that the ‘ought’ of (i) and (ii) is conceptually grounded these rules are not social rules. This argument is obviously mistaken. Even if we grant that the mandatory force of (i) and (ii) is indeed conceptually tied to the notion of JC, it does not follow that (i) and (ii) are not social rules. The difference between the obligations underlying traffic rules and rules of etiquette and the obligations underlying JCs does not lie in the fact that the former type of obligation is grounded in a social rule while the latter originates in a non-social conceptual relation. What the difference amounts to is merely that the former rules are regulative rules while the latter are constitutive rules. Both regulative and constitutive rules may be social rules. Paradigmatic examples of constitutive rules are rules of games such as rules of chess and rules of baseball.2 They do not merely regulate but define or constitute the practice of playing chess or baseball. On the other hand, examples of merely regulative rules are traffic rules or rules of etiquette. Rules of polite table behaviour regulate eating, but eating exists independently of these rules. It is, however, important to note that the difference between regulative and constitutive rules is not considered to lie in the fact that the latter are social while the former are not. Constitutive rules such as rules of chess or rules of baseball are no less social than regulative rules such as traffic rules and rules of etiquette. Rules of chess or rules baseball are social rules which govern social practices, namely the social activity of playing chess or playing baseball. While the ‘ought’ of rules of chess is conceptually tied to the game of chess, the game of chess and its constitutive rules are ultimately grounded in facts about people very much like traffic rules and rules or etiquette. In the light of the distinction between regulative and constitutive rules, the rules (i) and (ii) governing Gilbertian JCs fall straightforwardly under the notion of constitutive rules. These are rules which define or constitute the practice of jointly committing oneself. As the game of chess, the game of baseball, the practice of jointly committing oneself are social games or practices. Similarly to the former, the practice of jointly committing oneself and its underlying rules are ultimately grounded in facts about people, that is, in the attitudes people take towards them. In other words, the rules governing JCs are straightforwardly social rules.

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2.6 Circularity The view that jointly committing oneself is a social practice does not only raise doubts about the plausibility of Gilbert’s project; it weakens Gilbert’s explanation of social rules more seriously. Gilbert’s account of social rules is circular. Other authors have raised the objection of circularity against Gilbert’s proposal of social phenomena in general. Raimo Tuomela (1992: 291) argues that, given that JCs are analysed in terms of individuals expressing their intention to be jointly committed, Gilbert’s account leaves the concept of a JC unanalysed. Tollefsen (2004: 12) counters that expressions of willingness to be committed are conditions for the formation of a JC and not necessarily part of its analysis. If the analysis of JCs does not refer to the notion of JC, the objection falls. Tollefsen (2002: 29), however, maintains the charge of circularity by reformulating it. She holds that the mechanism of forming a plural subject or a JC by individuals presupposes that the individuals have an understanding of the concept of a plural subject or a JC. Remember, for plural subjects to be formed, the individuals must express their readiness to form with others a plural subject or to be jointly committed to do something. Gilbert (1989: 416) agrees that people do indeed need to have a grasp of these notions in order to form a plural subject. She thinks, however, that this circularity is not vicious. It is just the way how group concepts are irreducibly social: the holistic nature of the social leads to a circular analysis but if the circle is large enough the analysis is still illuminating (Tollefsen 2002: 29). Let me point to another type of circularity inherent in Gilbert’s account of social norms. Granted that jointly committing oneself is a social practice, the claim that the normativity of social rules is grounded in JCs amounts to explaining the normativity of social rules in terms of the normativity of other social rules. As a conceptual analysis of social rules, this account seems circular. Remember, if the normativity of social rules is grounded in a JC to accept them, the question arises: what grounds the normativity of the rules constituting JCs? (i) Why should we be subject to the rules governing the entrance to a JC? (ii) And why should we be bound by the rule that we ought to act according to the JC until or unless we are released from it? These questions seem to lead to a vicious regress. Granting that these rules are social rules, one might argue that we are subject to the rules underlying JCs to the extent that we enter a JC to participate in the practice of jointly committing ourselves or to jointly accept the constitutive rules of JCs. Unfortunately this answer presupposes what we are supposed to explain – namely that we participate in the practice of JCs and that we are subject to their constitutive rules. Again the question can be asked: why should we be bound by the JC to participate in the practice of jointly committing ourselves? And again Gilbert would have to postulate a JC to participate in the practice of jointly committing ourselves. This leads to a vicious circle: for every JC which grounds the normativity of a JC there need be another JC. Gilbert cuts the regress short by taking the practice of jointly committing oneself as primitive. With the practice of jointly committing oneself we hit bedrock: jointly committing oneself is a social practice governed by rules which hold independently of whether we are jointly committed to them or not. Under these circumstances,

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Gilbert might further argue that the circularity, that is, the fact that the normativity of social rules is grounded in the normativity of other social rules is not vicious: this circularity is the outcome of the holistic nature of the social and indicates that social norms are irreducibly normative and the normativity of social norms is irreducibly social. Unfortunately, taking the practice of JC as fundamental is unsatisfactory. JC is a too complex and sophisticated notion to figure as a primitive in the debate on social phenomena.

References Anderson E (2000) Beyond homo economicus: new developments in theories of social norms. Philos Public Aff 29(2):170–200 Baltzer U (2002) Joint action of large groups. In: Georg M (ed) Social facts and collective intentionality. Dr. H¨ansel-Hohenhausen AG, Frankfurt Bittner R (2002) An action for two. In: Georg M (ed) Social facts and collective intentionality. Dr. H¨ansel-Hohenhausen AG, Frankfurt Elster J (1991) Rationality and social norms. Archives europ´eens de sociologie 32:109–129 Gilbert M (1983) Notes on the concept of a social convention. New Literary Hist 14(2):225–251 Gilbert M (1987) Modelling collective beliefs. Synthese 73:185–204 Gilbert M (1989) On social facts. Princeton University Press, Princeton, NJ Gilbert M (1998) Social norms. In: Edward C (ed) Routledge encyclopedia of philosophy. Retrieved online on October 18, 2006, from http://www.rep.routledge.com/article/R029 Gilbert M (2002a). Acting together. In: Georg M (ed) Social facts and collective intentionality. Dr. H¨ansel-Hohenhausen AG, Frankfurt Gilbert M (2002b) Considerations on joint commitment: responses to various comments. Social facts and collective intentionality. In: Georg M (ed) Social facts and collective intentionality. Dr. H¨ansel-Hohenhausen AG, Frankfurt Gilbert M (2003) The structure of the social atom: joint commitment as the foundation of human social behavior. In: Frederick FS (ed) Socializing metaphysics. Rowman & Littlefield, Lanham, MD Gilbert M (2007) Collective intentions, commitment, and collective action problems. In: Fabienne P, Hans Bernhard S (eds) Rationality and commitment. Oxford University Press, New York Lewis DK (1969) Convention: a philosophical study. Harvard University Press, Cambridge, MA Rawls J (1955) Two concepts of rules. Philos Rev 64(1):3–32 Searle JR (1964) How to derive “ought” from “is”. Philos Rev 73(1):43–58 Searle JR (1995) The construction of social reality. Penguin Books, London Sugden R (2000) Team preferences. Economics and Philosophy 16:175–204 Tollefsen DP (2002) Collective intentionality and the social sciences. Philos Soc Sci 32(1):25–50 Tollefsen DP (2004) Collective intentionality. The internet encyclopedia of philosophy. Retrieved on October 1, 2007, from http://www.iep.utm.edu/c/coll-int.htm Tuomela R (1992) Group beliefs. Synthese 91:285–318

Chapter 3

Theories for Use: On the Bearing of Basic Science on Practical Problems Martin Carrier

3.1 Science Policy and the Advancement of Technology In the past half-century, scientific research has enjoyed financial support of an unprecedented degree. The reason behind this expenditure is not the hope for clarification of the nature of dark energy, nor the desire to learn more about super symmetry. Rather, underlying public and private sponsoring of research alike is the idea that science is a primary source of technological development which is in turn viewed as a driving force of economic growth. In what follows I will attempt to identify methodological features of research directed at practical goals. Projects of this sort thrive or fail on the appropriateness of distinguishing between kinds of scientific research. The distinction between basic or epistemic research, on the one hand, and applied research, on the other, is of foremost importance in this respect. It is objected that such a distinction cannot be sustained in that applied research, like basic research, produces new knowledge, and in that basic research, like applied research, has an impact on technology. This observation is justified but of a limited bearing on the issue. Namely, it is still possible to conceptually separate basic and applied research by appeal to the goals pursued or, correspondingly, by the success criteria invoked. Epistemic research primarily strives for understanding natural phenomena or processes, applied research aims at practical needs or utility (Stokes 1997: 6–8). Correspondingly, the success of a project in applied research is assessed by economic standards whereas epistemic projects are judged according to the understanding gained. Such standards need not be assumed hypothetically, they are laid open publicly. Attempts to build optical switches or blue light emitting diodes (LEDs), to name just a few technological challenges on the present agenda, are supported by estimates of the future potential market volume. Endeavors like the quest for the Higgs boson, by contrast, are justified by appeal to the human desire to understand nature’s workings. The conceptual boundary between epistemic and applied research is marked by the commitment to understanding and utility,

M. Carrier () Department of Philosophy, Bielefeld University, P.O.B. 100 131, 33501 Bielefeld, Germany e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 3, c Springer Science+Business Media B.V. 2010 

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respectively. However, this distinction does not imply an empirical dichotomy; it does not rule out that a given research project serves both ends simultaneously. Within the framework of this distinction between what is basic and what is applied, the question to be pursued here takes the following form: What is the role of theoretical knowledge or epistemic research in accomplishing technological innovations? In particular, could it be recommended that science policy sponsor thorough and broad theoretical analyses or are technological challenges to be better mastered by concentrating on research that is directly connected to the particulars of the case at hand? The philosophical issue behind this question is the relationship between utility and understanding.

3.2 The Cascade Model Versus Emergentism The Scientific Revolution was fueled by the prospect of technological progress. Uncovering nature’s contrivances was claimed to be the royal road toward the betterment of the human condition. Conversely, seeking utility without understanding was considered a vain attempt. The power of intervention in the course of nature only accrues from disentangling the underlying causal fabric. Francis Bacon is the chief advocate of the principle that systematic basic research or epistemic penetration is the prerequisite of the development of technology. According to this cascade model, research striving for understanding is the chief source of technological change. Practical tasks are best solved by bringing to bear insights into the mechanisms at work and understanding of the fundamentals (Bacon 1620, Bk. I, 3, 110, 117, 129; see Carrier 2006: 16). This traditional position was laid down and renewed in a highly influential way in a report Vannevar Bush delivered in 1945. Bush suggested basic research as the pivot of practical progress. As he argued, technological innovations are not likely to be generated by research narrowly targeted at the problem at hand. A more promising strategy is to conduct fundamental research whose technological fertility can be assumed to be superior for two reasons. First, the solution to a practical problem can arise as an unexpected consequence of a seemingly remote scientific principle. Second, practical progress is often reached through a novel combination of knowledge pieces. The two arguments entail that the theoretical resources apt for clearing up a practical difficulty cannot be established beforehand. Rather, practical success may be made possible by findings that are prima facie unrelated to the problem at hand. Conducting broad epistemic research creates the knowledge capital from which interests in the form of technological accomplishments are drawn (Bush 1945, Chap. 3). However, the intertwinement between basic research and technological development turned out not to be as close as anticipated. Historically speaking, science did not begin to gain significance for engineering purposes prior to the Second Industrial Revolution in the latter part of the nineteenth century, and only in the twentieth

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century did the impact of science on technological change extend to larger parts of industry. Furthermore, it happens that new technologies do not derive from scientific principles but rather build on existing technology or are due to tinkering at the bench. For instance, pharmacological research was for a long time (and in part still is) dominated by a methodology of trial and error. The most widespread procedure used in drug research throughout the twentieth century is schematic screening. A large number of potentially effective substances are administered to model organisms or tissue test systems and their effects are registered. When a successful medication had been tracked down by a procedure of this sort, it was in no way automatically clear how the drug operated. As a matter of fact, this is true of a significant fraction of the drugs in use today. Aspirin successfully relieved headaches for almost a century before its biological mechanism was finally disclosed. In such cases, medical progress does obviously not rely on understanding. The progressive realization that technological change sometimes proceeds independent of progress in basic science generated a major change of attitude in the latter third of the twentieth century. It was no longer assumed that sponsoring pure research would guarantee cutting-edge technology. As a result, funding policies generally switched to sponsoring targeted, short-term research projects which directly address specific problems. In addition, developments in philosophy of science cast doubt upon the cascade model as well. Nancy Cartwright has drawn attention to the failure of universal laws to account for concrete phenomena with their rich details and variegated traits. Such laws and the highbrow theories they form part of are too abstract to capture the more subtle features of nature. They over-generalize and thus lose touch with the richness of detail the phenomena exhibit. If the concrete experiences are supposed to be accounted for, generalizations of non-theoretical origin need to be part of the models (in addition to initial and boundary conditions). Rules of experience and specific assumptions bear the explanatory burden; tailor-made approaches are needed when the experiences are to be addressed in their full complexity. Descriptive adequacy is limited to small-scale accounts (Cartwright 1996: 322–323). Such an approach may be termed “emergentist.” Emergentists feature the specific character of the phenomena at each level of organization and deny that insights about the constituents will have much impact on the clarification of the properties of organized wholes. The emergentist position does not refer to applied science in the first place but rather to “applying science.” The chief claim is that it is highly non-trivial to hook up theory with evidence and that the only way to get a grip on the phenomena is by making use of specific models that are tightly locked onto a particular problem. Still, emergentist approaches are tied up with a particular conception of applied research. The cascade model is abandoned; basic research is said to be largely unsuccessful in solving applied problems. Practical challenges should be addressed by doing research on precisely these challenges rather than elucidating the underlying principles and mechanisms (Carrier 2004: 1–2; 2006: 18–19; Adam et al. 2006: 438). Thus we are faced with two contrary views on the relationship between basic and applied research. The contrast is based on a markedly different assessment of

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the bearing of fundamental theories on the solution of practical problems. The two approaches offer opposing recommendations as to how applied research should proceed.

3.3 Local Models in Applied Research It has been observed that – in contrast to the emergentist position – overarching theories do contribute essentially to explaining concrete phenomena. Yet such theories cannot exclusively bear the explanatory burden; rather, models are needed as “mediators” between theory and evidence. The salient point is that the models typically used for applying theories are more complex than traditionally assumed in the philosophy of science. Such mediating models often do not only contain laws and boundary conditions but additional conceptual elements, such as generalizations from divergent theoretical sources or even without theoretical backing (that is, rules of experience), approximations and correction factors, or parameters that can only be evaluated empirically (that is, read off from the data). Consequently, such models cannot be derived from highbrow theory. They rather rely to a considerable extent on extra-theoretical assumptions and their construction may involve a highly creative process. The “articulation” of a theory, the procedure of bringing to bear theoretical principles on concrete evidence, in no way resembles a deductive chain and needs to resort to additional empirical, conceptual, and mathematical resources (Morrison 1999; Winsberg 2003; see Carrier 2004: 9–13). If the amount of adjustment of a model to the particular case in question is comparatively large, I speak of a “local model.” Just to convey a rough idea, a model of the planetary system within Newtonian celestial mechanics is not local, whereas a model of the spreading of Victoria perch within evolutionary theory is local. Much more empirical information, as inferred from the phenomena, is contained in the evolutionary model than in the mechanical one. Models are typically adjusted to a particular problem situation by parameter evaluations and correction factors, and a model is local if there are lots of specifics to be added and if they are restricted to a narrow scope. My claim is that applied science typically proceeds by constructing local models. The reason is that the variegated details of the phenomena typically escape the grip of a comprehensive theory that merely addresses the generic features of the situation. Yet technological development is bound to take the quantitative particulars into consideration. Descriptive adequacy is often only accomplished by small-scale accounts as provided by local models. However, the conceptual structure of the local models developed in applied research is typically still shaped by general theory. Applied research does not proceed on the exclusive basis of observational generalizations, experience-based regularities, ad-hoc assumptions, or rules of thumb. The conceptual backbone of such models, as a rule, derives from theory; the necessary adjustments are made by way of modifying this theory-based structure.

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Here is an example. “Giant magnetoresistance” is a physical effect discovered in 1988 and quickly explored by industrial research laboratories. The relevant arrays involve a sandwich-like structure in which two ferromagnetic semiconducting layers cover a non-ferromagnetic conductor layer in between. It was found that the electrical resistance of such arrays is liable to large (“giant”) variations, depending on the orientation of the magnetization directions of the two ferromagnetic layers relative to each other. This magnetization direction can be influenced by an outside magnetic field so that the electrical resistance of the array is affected by such a field. Consequently, its electrical resistance indicates the intensity of a surrounding magnetic field. The effect is suitable for building extremely sensitive magnetic field sensors. Giant magnetoresistance underlies the functioning of today’s magnetic read heads; it is used for hard disks or magnetic tapes. The qualitative explanation of the effect was suggested immediately after its discovery. Quantum theory entails for a layered array of this sort that the scattering of electrons should depend on the orientation of the electron spin relative to the prevailing magnetic field. Electron scattering is the mechanism underlying electrical resistance so that a relationship between resistance and field orientation results. Consequently, the basis of giant magnetoresistance is the theoretically well-understood spin-dependent scattering of electrons. However, this qualitative understanding did not automatically furnish the relevant quantitative relations. Knowledge of the precise dependence of the pertinent quantities is necessary for any practical use of the effect. If a read head is to be constructed, the influence of layer thickness, material properties, temperature variations and changes of the magnetic field need to be known exactly. The anticipation of subtle dependencies of this sort transcended the scope of the theoretical account (Wilholt 2006: 72–79). In order to get access to the details of the effect, a local model needs to be built. Its conceptual structure reflects the theoretical account and yields results such that the sensitivity of resistance changes essentially hinges on two parameters, namely, material properties and layer geometry (i.e., the thickness of the layer and the spatial dimensions of the system). The model also entails generic consequences as to the impact of certain such properties and arrays but leaves large room for empirical adjustment. In order to arrive at “design rules” for particular devices, a huge number of parameters need to be evaluated empirically and their impact on the quantities in question be measured. When it came to figuring out the precise relations, as requisite for the construction of reliable contrivances, recourse to empirical adjustment was indispensable (Wilholt 2006: 79, 80).

3.4 Uses of Understanding in Applied Research Yet in spite of the limited grip of theory on the phenomena, theoretical understanding is useful in applied research. It is helpful to bring theory to bear on practical problems although theoretical understanding is often limited to the generic features of the situation whereas reliable intervention often needs to take the details into

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account. Let me sketch three pertinent reasons which have to do with the identification of relevant quantities, the generalization of the results, and with ascertaining their reliability in the face of distortions. The first reason for drawing on theory is the crucial assistance it offers for the identification of the relevant quantities. Theoretical accounts serve to highlight the influential magnitudes and suggest relations among them. In this way they accomplish a figure-ground distinction which is often a prerequisite of fruitful empirical investigation. In the case of giant magnetoresistance, the quantum mechanical (or semi-classical) analysis helped to unfold the space of potentially relevant quantities which could subsequently be studied by measuring the precise relationship that obtains between them. Empirical investigation is facilitated considerably by such a theory-based distinction of potentially relevant factors. Second, the generalization of theory-shaped models is much easier than the transfer of phenomenological models to new cases encountered. Phenomenological models are shaped conceptually by the demands of the problem-situation at hand. They are not necessarily completely independent of theory, but they contain comparatively few elements that transcend the particulars of the explanatory challenge to be dealt with. As a result, each such phenomenon needs to be approached on its own terms. For instance, the prediction of the tidal flow of a particular harbor is not based on the known causal mechanism underlying the phenomenon but is rather achieved by performing a Fourier analysis of the tidal oscillations observed in the past. The reason is that the influence of a multiplicity of factors relevant for the quantitative details of tidal flow (such as coastline, water depth, currents) can hardly be assessed on first principles so that the phenomenological analysis is more accurate. The drawback is that results gained by this method cannot be transferred to different coastal areas; the latter need to be addressed completely afresh. By contrast, theory-based models whose empirical shortcomings are rectified by parameter fitting and correction factors can be used for a whole class of phenomena. This feature comes out clearly in the giant-magnetoresistance case. The standard arrangement is a “current-in-plane” geometry in which the electric current flows parallel to the layers of the sandwich-like structure. A different arrangement is the “current-perpendicular-to-plane” geometry, which underlies the most recent development of computer hard disks since it allows a further shrinking in size. This arrangement can be modeled using the same theoretical approaches as applied to the standard case (Wilholt 2006: 83). By contrast, if this configuration had been approached on a purely experimental basis it would have to be captured completely on its own. This shows that empirical investigation is facilitated considerably by a theory-based distinction of potentially relevant factors. Theoretical accounts serve to highlight the influential quantities and suggest relations among them. Experiments are appealed to, subsequently, in order to examine the models and to fill the lacunae left by them. Third and finally, theories are of outstanding importance when the reliability of a device or procedure is to be secured in the face of distorting factors. Ascertaining reliability typically demands elucidating the underlying causal mechanism. The history of pharmacological research is replete with examples of this sort. Statements

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about the therapeutic efficacy of a certain medical drug are initially phrased as “contextualized causal relations.” Such relations are restricted to typical or normal conditions and leave the pertinent causal processes out of consideration. “Aspirin relieves headache” is a statement of this sort: it usually holds true but possesses exceptions for particular persons or conditions, and it contains nothing as to how the effect is brought about. If the efficiency of the drug is to be improved or pernicious side-effects are to be controlled, the mechanism of action needs to be clarified. If perturbations intrude, upholding the desired operation of a procedure demands theoretical penetration. These considerations suggest that overarching theories rightly continue to conceptually shape models in applied research and thereby structure the account of the phenomena while leaving room for empirical adaptation. In fact, theory structure in applied research is not represented by a scattered collection of isolated accounts. Rather, the local models put to use remain linked up with higher-order accounts (Carrier 2004: 14). Theoretical integration and the understanding thereby generated are essential in applied research although technological devices and inventions need more than theory and eventually draw heavily on empirical adaptation and correction.

3.5 Uses of Understanding in the Development of Technology The first question is where all this leaves us with respect to the contrast between the cascade model and the emergentist approach. In light of the preceding considerations, both positions need to be abandoned and give way to an interactive view which preserves aspects of both positions. This interactive view stresses that nontheoretical factors like unexplained properties and corrections play an important role in the development of technology but also emphasizes that the models used for representing the technologically relevant physical processes are conceptually shaped by higher-order theories. It criticizes the cascade model for failing to recognize the importance of situation-specific factors. The interactive view accepts the emergentist claim that nature is multifaceted in character and cannot be accounted for without qualification by comprehensive principles. Yet the emergentist approach overshoots the goal by denying theoretical analysis an essential role in the generation of useful knowledge. The best way to deal with multifarious experience is by bringing to bear universal principles and to correct for their shortcomings by empirical adjustments. The second question is what kind of relationship between technological change and scientific progress this interactive view suggests. To begin with, the demise of the cascade model implies that there is no monocausal chain leading from a scientific discovery up to a technological innovation. Scientific progress is in no way the only source and stimulus for technological change. First, on the part of the knowledge input, a major part of the development of technology draws on empirical generalizations and ad-hoc adjustments rather than on systematic theory, let alone on cutting-edge research findings. Second, it has been frequently pointed out that

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societal demands and market conditions constitute chief driving forces of technological development and heavily affect pathways of technological change. Institutional structures, social exigencies, market demands, traditions, or perceived weaknesses of existing systems are the determinants of the pathways of technology. Scientific discoveries and scientific progress are conspicuous in their absence. This can be made more explicit by a quick glance at some “radical inventions” of the past which profoundly transformed the technological systems dominant at the time: Alexander Bell and the electric telephone, Henry Ford and the assembly line for automobile production, Ferdinand Graf von Zeppelin and the dirigible airship. The crux to these inventions was not supplied by recent progress in understanding; the knowledge that went into them was fairly standard and well established. They were rather due to an engineering type of creativity: new devices were assembled from existing building blocks and widely available components. These considerations suggest that the technological dynamics proceeds to a considerable extent decoupled from scientific progress. I will add qualifications later but should stress right away that this is no way meant to imply that technological development can proceed without a scientific basis. To be sure, inventions and technological innovations do not, as a rule, draw on more recent scientific discoveries. Still, technological novelties do rest on scientific knowledge. Here is an example. A recent technology invented at the University of South Carolina and developed into a marketable product by a company serves to monitor the composition of substances (like drugs or food) using spectroscopic means. The procedure is based on the separation of the spectrum of the expected active ingredient from the background radiation using filters which transmit light only at some selected frequencies, characteristic of the compounds whose concentration is relevant. The advantage is that this quality control can be performed in real time during the production process and can thus be used for instant correction and adjustment (Nelson et al. 1998). This technology is buttressed by two pillars of established knowledge, namely, spectral analysis in optics and the mathematical procedure of factor analysis. These two received techniques are combined using a particular array of color filters – which is not a spectacularly sophisticated technology either. It is the novel combination of known elements of scientific knowledge that constituted the technological innovation. Moreover, the combination itself was due rather to tinkering than to deduction. Different setups were tried out and the best one retained (Baird 2006). This example shows that the development of technology is, in fact, dependent on science but is not always hot on the heels of scientific progress. The science invoked is of some age but maturity doesn’t make knowledge less scientific. Although this invention did not rely on recent findings in basic research, it is essentially science-based. The body of scientific knowledge constitutes a huge reservoir of technological options which can be tapped at various locations, not alone at the more recent additions (Rosenberg 1991: 337). While the dependence of technological novelties on established knowledge is in accordance with the cascade model, the latter is deficient in a different respect. It fails to take into account the effect of technology on science. First, the development

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of new instruments for registration and experimentation repeatedly contributed to opening up new intellectual horizons for science. Second, applied research is not infrequently faced with challenges of a more fundamental bearing. The adequate treatment of practical problems may require us to address the fundamental challenges as well. In such cases the necessary basic research may be conducted within applied research projects. This feature I call application innovation. It involves the emergence of theoretically significant novelties within the framework of useoriented research projects. A large number of such use-oriented projects in the life sciences address questions of fundamental impact. Consider the revolutionary conception of “retrovirus” which was conceived in the context of identifying infectious chains. The reduplication of a retrovirus involves the reversal of the familiar directedness of transcription from DNA to RNA, a directedness which was formerly supposed to be universal. The initial aim of the pertinent studies was to gain useful knowledge about the spread of diseases but they generated a deep-reaching transformation of biological concepts. Pursuing practical questions can have a revolutionary impact on the fundamentals. Application innovation amounts to a partial vindication of the cascade model. It is true that the cascade model says that the most effective way to foster applied science is to support pure science. The sketched examples suggest to the contrary that stimulation may proceed in the opposite direction. However, the cascade model also says that applied science is in its substance based on basic research. The need to take recourse to theoretical principles in meeting practical challenges is made evident by the formulation of such principles in case they are missing. The temporal relations between science and technology are at odds with the cascade model if application innovation occurs. But the logical relations are yet in agreement with the model.

3.6 Science Policy and Technological Benefits What remains to be clarified is how the interactive view translates into a science policy and a funding strategy. Such policies are usually directed at supporting technological innovations; sponsors typically aim at useful science or theories for use. The impact and success of such policies depend crucially on how science and technology are connected to each other. Bush’s idea that progress in basic research is the prime mover of technology dynamics translates into a funding policy that gives priority to broad basic research. However, the underlying idea is mistaken: technological development is rarely based on cutting-edge basic research. In the short run, technological change is largely independent of progress in fundamental science. On the other hand, technological change hinges essentially on scientific knowledge. Although existing technologies and rules of experience provide another major repository for technological inventions, science constitutes the pivot of the development of technology. Accordingly, it remains true that, in the long run, basic research

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amounts to plowing the field and cultivating the soil so that it bears fruit later. Yet this is a long-term effect whose time-scale is estimated in decades, not years, the usual time-span of science-funding decisions. Application innovation suggests that the basic research necessary for sustaining applied research may grow out of applied research itself. In such cases applied research produces on its own the knowledge basis required for the solution of applied problems. It generates scientific innovations rather than drawing on them. Basic research may be inspired by considerations of use (Rosenberg 1990: 169; Stokes 1997: 74). All the cases I am aware in which cutting-edge research was transformed quickly into a technological novelty are “use-inspired basic research” (to use Stokes’ phrase; Stokes 1997: 93). The spectrum ranges from giant magnetoresistance to the polymerase chain reaction (PCR). Application innovations represent a gain in understanding achieved in pursuing a practical goal. Under such conditions, the new knowledge bears directly on the issues at hand and promotes the rapid transformation of a scientific accomplishment into a technological novelty. This is the qualification indicated earlier (see Section 3.5). In cases of application innovation, the practical relevance of basic understanding tends to come out more quickly and the time lag between scientific discovery and its technological implementation is frequently measured in years, not decades. What does this scheme imply for the initial question of whether science policy should support focused practical research projects or rather broad epistemic research? In contrast to what was suggested by the Bush report, applied research does not detract from the epistemic aspirations and achievements of science. In general, the fear is unfounded that the search for utility drives out the quest for understanding. On the contrary, practical problems often bring theoretical challenges in their train which need to be taken care of by epistemic research if the practical endeavor is supposed to get off the ground. The relationship between epistemic and applied research often transcends a peaceful coexistence and rather approaches mutual reinforcement. What is essential, however, for letting this potential of reciprocal stimulation unfold is to leave room or leisure for hooking up the practical goals with the theoretical framework. Research producing light and fruit at the same time, to use Bacon’s apt phrase, requires the willingness and the freedom to address epistemic challenges as they emerge along the road toward some practical research goal.

References Adam M, Carrier M, Wilholt T (2006) How to serve the customer and still be truthful: methodological characteristics of applied research. Sci Public Policy 33:435–444 Bacon F (1620) In: Krohn W (ed) lat./dt. Neues Organon I. Meiner, Hamburg 1990 Baird D (2006) Engineering reality. Lecture presented at the Conference on Science in the Context of Application: Transformations of Academic Research. ZiF, Bielefeld University, Bielefeld, 27 Oct 2006 Bush V (1945) Science the endless frontier: a report to the President. United States Government Printing Office, Washington, DC. http://www.nsf.gov/od/lpa/nsf50/vbush1945.htm, accessed 12 Sept 2008

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Carrier M (2004) Knowledge gain and practical use: models in pure and applied research. In: Gillies D (ed) Laws and models in science. King’s College Publications, London, pp 1–17 Carrier M (2006) The challenge of practice: Einstein, technological development and conceptual innovation. In: Ehlers J, L¨ammerzahl C (eds) Special relativity: will it survive the next 101 years? Springer, Heidelberg, pp 15–31 Cartwright N (1996) Fundamentalism versus the patchwork of laws. In: Papineau D (ed) The philosophy of science. Oxford University Press, Oxford, pp 314–326 Morrison M (1999) Models as autonomous agents. In: Morgan M, Morrison M (eds) Models as mediators. Perspectives on natural and social sciences. Cambridge University Press, Cambridge, pp 38–65 Nelson MP, et al. (1998) Multivariate optical computation for predictive spectroscopy. Anal Chem 70:73–82 Rosenberg N (1990) Why do firms do basic research (with their own money)?. Research Policy 19:165–174 Rosenberg N (1991) Critical issues in science policy research. Sci Public Policy 18:335–346 Stokes DE (1997) Pasteur’s quadrant. Basic science and technological innovation. Brookings Institution, Washington, DC Wilholt T (2006) Design rules: industrial research and epistemic merit. Philos Sci 73:66–89 Winsberg E (2003) Simulated experiments: methodology for a virtual world. Philos Sci 70: 105–125

Chapter 4

Structural Realism as a Form of Humility Angelo Cei

4.1 Introduction The paper has two main objectives. It will be seen that the idea of a structure of a theory as a theoretical element resistant to deep theory changes in science has been presented ambiguously. The disambiguation will make evident two conceptions of structure. Such disambiguation is my first aim here. Both the views that will emerge are entrenched with a defence of scientific objectivity from scepticism based on radical theory shifts. One view is traditionally associated with scientific structuralism – not necessarily realistically construed – and is based on the emphasis on some form of primacy of the relations over the entities postulated by the theory. On the second view, the focus is rather on those theoretical constituents that retained in modern science also explain the success of the old dismissed theory in the light of the modern one. In other terms, the second view emerges when we focus on the elements of theoretical continuity, no matter if relational or not, with an emphasis on the explanatory role they play in both the older theory and its successor(s).1 I will not concern myself here with the second view. I will just offer a characterization of it and some indications of the possible links with the Ramsey sentence. If appropriately formulated, RS have a role to play in both the views. I will focus on the first view that I will associate with the recently discussed thesis of Humility. To probe the relationship between structuralism and such thesis is my second aim here. The work will proceed as follows: the first section will expose the ambiguity and disentangle the two theses; the second section will argue that in the second reading structural realism can be seen as embracing a form of Humility. It will also be seen that RS not only has a direct role to play in defining structure but it plays also a rather interesting and subtle role in the argument for Humility.

A. Cei Centre for History and Philosophy of Science, University of Leeds, Leeds, UK e-mail: [email protected] 1

I take Worrall (1989) to float between these two views.

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4.2 Problems from the Past and an Ambiguous Solution 4.2.1 Past Troubles There is a family of arguments that exploits the radical changes in natural science in its history to argue against the idea that scientific success is an evidence of truth and our trust in the truth of scientific theories is wrongheaded. The core of the arguments based on radical theory shift is the idea that the shift is so radical that, at the theoretical level, there is no continuity between past and present theories (Laudan 1981; Psillos 1996). Here the upshot would be that progress and accumulation of knowledge are applicable only at the observable level. Not surprisingly then, the realist responses to this issue have tried to show that parts of the theoretical set up resist to the shifts. It is a remarkably widespread phenomenon in physics that the equations of many once successful and now abandoned physical theories are retrieved in present day physics (Saunders 1993). Structural realists have insisted (Worrall 1989; Stein 1989) that such equations prima facie describe relational features that can be conceived as what remains with us in the shift. This position thus aims to show that realistic optimism regarding science can be maintained despite scientific change. In a nutshell, the equations describing a structure in the past theory are preserved because they described the right structure. Since Worrall’s (1989) contribution, the debate on structural realism, intended as the thesis that only structure can be known (ESR henceforth), has been driven by the need of addressing the following core concern: to what exactly amount the theoretical content remaining with us across the shift between two theories? Or more simply what is structure? RS has featured this debate precisely as a device to make the notion of structure precise. The identification between RS and structuralist views has ran so deep in the literature that frequently concerns about RS have been treated straightaway as concerns about ESR. It is my contention that the debate revolving around ESR oscillates between two theses on the nature of structure. Once the two thesis are disentangled, RS will appear to play a further role in relation to ESR.

4.2.2 On a “Structural” Ambiguity: Worrall vs Poincar`e! This section has the purpose to isolate the two different thesis. In order to do so, I will try to indicate the origin of the conflation. It will then be clear not only that they are not equivalent but also that they involve different commitments for the realist that subscribes to them. RS can be seen as relating differently to both views. Here it is where the whole rigmarole began: Roughly speaking, it seems right to say that Fresnel completely misidentified the nature of the light, but nonetheless it is no miracle that his theory enjoyed the empirical predictive success that it did; it is no miracle because Fresnel’s theory, as science later saw it, attributed to light the right structure. (Worrall 1989: 117, second italics mine)

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Despite the fact that it postulated the existence of the Ether, a notoriously false assumption, Fresnel’s optical theory was impressively successful. The predictive success of the elastic Ether theory of light is nonetheless non-mysteriously explainable from the perspective of later science in terms of its structural correctness. There was no elastic Ether. The electric and magnetic fields of Maxwell’s electromagnetic theory are not something that the Ether even approximates. Although he [Fresnel] was quite wrong on what oscillates he was, from this later point of view [Maxwell’s point of view], right, not just about the optical phenomena, but right also that these phenomena depend on the oscillations of something or other at right angles to the light (Worrall 1989: 118)

Looking at the old theory from the perspective of the modern one we can see how wrong we were once, we can see that a lot must go. Nonetheless, we can also see where scepticism must end. Certain genuinely explanatory theoretical acquisitions remain with us. They are still operating in the new theory. Fresnel rightly understood that something was oscillating at right angles to the light and rightly identified the laws of such oscillations. He could, on the basis of this, construct an explanation of optical phenomena of refraction and reflection. Our contemporary explanation still agrees on that point, and only on that point, with Fresnel’s one (Worrall 1994: 340). Now, if we consider the above passage, the structural – in the sense of relational – element is purely contingent. What really matters is the point that we can explain the success of the older theory through the more recent one. If we look at the way in which the new framework explains certain facts, we will retrieve relevant parts of the old explanation. This involves an important retreat from a standard realistic view: we concede that even an impressively successful theory can be wrong to the point of postulating fundamental entities that do not exist. There is a gain though. The theoretical shift is now harmless. It just reminds us that success grants limited reliability to science. A theory is reliable as long as its directly explanatory parts are involved. In this sense, the success of the older theory is not a miracle. Now, the relational aspects might even be prominent in the case in point but the argument would work whatever those elements might be, provided, that they are genuinely explanatory theoretical features.2 Worrall himself nonetheless associated such passages with a quotation from Poincar`e. The aim of the quotation seems that of giving historical ancestry to ESR. Indeed, following Worrall’s lead, Poincar`e could be indicated not only as the founder of the position but also as the one suggesting the appropriate case-study to defend it: [Motions and current displacement are] images that we substituted for the real objects which Nature will hide forever from our eyes. The true relations between these real objects are the only reality we can attain : : :” (Poincar`e quoted in Worrall 1989)

Poincar`e (1905) puts a particular spin on the position. There is something that remains hidden and what remains hidden is kept from our grasp by Nature. It is

2

In other terms, this view can be thought of as a variety of the divide et impera move advocated by Psillos (1996).

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because of the nature of things that something exceeds our grasp. The historical case-study is instantiating a limitation that will always affect the progress of science. We are not wrong simply because we have limited data and we judge mistakenly. There is more, something is “out of reach”. We can indicate what in the world exceeds our grasp and what does not: as the case study shows, the relations captured by the mathematical laws are retained whereas the ontology of a theory is dismissed in the shifts. The relations are the only aspect of the theory that is retained, because they are the only aspect of the world of which we can have knowledge. This is quite different from what has been said above regarding the historical case study. The considerations above about the retained relations are not sufficient to exclude the possibility that there might be different cases of retention. In particular, the idea of explaining the old success through the new theory conflicts with the idea of an a priori restriction of the theoretical content we might retrieve to relational features only. We can put the two theses as follows:  ESR1 : given a successful theory, its structure is expressed by the theoretical

features that are essential to the successful epistemic performance. Such features are the ones we expect to retrieve in successive successful scientific frameworks and the ones to which the realist should be committed. We shift our focus from the entities theories postulate to the theoretical features that allow theories to successfully performing their epistemic task. This is a form of explanatory selective realism.  ESR2 : given a successful scientific theory, its structure is expressed by the rela-

tions it ascribes to the entities the theory postulates. Such structure is held responsible for the empirical success of the theory and constitutes the only unobservable aspect of reality we can access, thus the only one that we are committed to. Structure is what is to be retained in successive science. They are certainly not equivalent views and taken in isolation they project a different image of science. Consider that seen from the perspective of ESR1 a final theory would be simply true, its explanations covering any empirical detail. From the perspective of ESR2 , yet it would be only structurally correct, any of its claims on each intrinsic aspect of the unobservable being purely conjectural. Let me add few more details. First consider ESR1 . Structure is the theoretical content that retained in the change explains from the perspective of modern science the empirical success of the old theory. The commitment is rather to the theoretical features that actually play a direct role in the explanations delivered by the theory. The perspective is backwards, from modern science to the previously accepted theories. Such a structural realist owes us an account of what is intended by explanation and has to carefully elucidate case by case what are the theoretical features essential to the explanation delivered by the theory. Of course there is no particular partition of the theoretical content to which he is supposed rigidly to conform. Consider now ESR2 . Structure is the set of relations that a theory ascribes to its fundamental entities and that in physics is captured by the mathematical formulation

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of the laws. Such content enjoys an epistemic primacy on the theoretical content evidenced in the tendency of physics to retain certain equations even when the new frameworks have completely abandoned the ontology of their predecessors. The advocate of such view is committed to give us a characterization of structure such that the success of science can be explained in terms of the relational features the theory introduces. It would be also desirable to give an account of why reality stands in such a peculiar relation with us qua epistemic agents. ESR1 is a form of fallibilism that credits scientific theories with limited reliability on the grounds of historical evidence. ESR2 , on the other hand, is a thesis on what in the world is accessible. The advocate of ESR1 would probably put the emphasis on the fallibility of our methods and practices but is free to take no definite position on the origin of our failures. The advocate of ESR2 is committed to an argument that explains why he draws a line between relations on one hand and properties and entities on the other. There is a sense in which one can be seen as endorsing both theses: we can think of ESR2 as a special case of ESR1 . Indeed, if the world is knowable only up to certain kind of relational features then our best guess can be at most structurally correct. Having distinguished these two ways to conceive ESR, it is now time to turn to consider where RS sits in this scenario. The suggestion to use the RS of a theory in order to characterize a weak form of realism based on structure dates back to Grover Maxwell’s 1970 realistic interpretation of Carnap’s approach to it3 . Considering the results of this section and the ascertained problems of triviality (the infamous Newman Problem) that affect certain formulations of the RS, the following queries remain open in relation to its adoption in this context: (a) provided that a non trivial formulation of RS is available, would it meet the desiderata of an advocate of a form of ESR? (b) if any, which of the two above theses would be naturally mesh with RS? The answer to the first question can be already found in the literature (Melia and Saatsi, 2006) and I would add that it leaves us with a good candidate for a version of ESR1 . I will not pursue such issues here. I will, instead turn to ESR2 and in that context I will explore some new work for RS. In relation to RS the thesis of Humility will appear as the searched argument for ESR2 .

4.3 The Structural Meets the Humble ESR2 is the view that the structure of a theory has to do with its relational content pre-eminently with the relations between the entities and the laws that are retained across theory change. The view holds that such elements despite their unobservable character are knowable whereas the entities are not. The epistemic priority, if we take face value Worrall (1989) motivating example, is supported by a historical example. Nonetheless, it is not argued for. In the case study mentioned we have 3 In Cei and French (2006), serious reasons of disagreement have been opposed to this way of reading Carnap and to its fruitfulness for the debate on structural realism.

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a case for ESR2 , if we can claim that in the structural correctness it is the structural component that yields the correctness. For the advocate of this view we retain the structure because that is the only thing we can know. The case study does not say why this is our predicament. Indeed this point cannot be argued for in purely historical terms, it requires an argument in principle to the effect that some unobservable elements of the world are not accessible to science whereas others are. It is my contention that the Humility thesis provides such an argument. In the following, I will explore two versions of Humility and take a stand on what I believe could be the most appropriate for ESR2 . The analysis starts with the reconstruction of David Lewis’ contribution on RS, since it is relevant to his argument for Humility. I will then turn to Rae Langton version of Humility that will turn out to be the argument I am after.

4.3.1 Multiple Realizability: Problem or Resource? Perhaps the most important discussion of RS in a realist context, drawn upon by almost all recent commentators, is that due to Lewis (Lewis 1970). In Lewis’s view the neo-positivistic theoretical/empirical distinction is to be rejected. The language of T is understood in natural terms as any other kind of language. The definition of T-terms is formulated via O-terms. O-terms are old terms whose meaning is acquired in scientific practice and non-problematic. The language is made of names under the assumption that it provides enough copulas, thus we have “a has F-hood.” instead of Fa. It is endowed with intensional operators so in its O-vocabulary there are terms like “ because ” or “ is a law that ”. The system of logic chosen to formulate RS (namely, Scott’s denotationless terms tolerant logic) is designed to deal with denotationless4 terms and it will be shortly clear why. Lewis’s RS is based on a modal language and it is thus very different from the versions of RS based on extensional languages an frequently bothered by problems of triviality. Lewis (1970) is concerned with a definition of T-terms. For this reason he is uncomfortable with the fact that the RS can be multiply realizable. If the machinery is designed with a definitional task it has to single out the realizers. Here is how the definition is effected: (1) 9y1 ; : : : ; yn 8 x1 ; : : : ; xn .TŒx1 : : : xn   : y1 D x1 & : : : &yn D xn / ) TŒ£1 : : : £n  (1) states that if T is uniquely realized then it is realized by the items named by £1 : : : £n (2) :9x1 ; : : : ; xn .TŒx1 : : : xn / ) ::9x.x D £1 /& : : : & :9.x D £n / (2) states that if T is not realized, then £1 : : : £n names nothing,

4

See Lewis 1970.

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(3) 9x1 ; : : : ; xn TŒx1 : : : xn  &:9y1 ; : : : ; yn 8 x1 ; : : : ; xn .TŒx1 : : : xn   :y1 D x1 & : : : &yn D xn /: ) :9x.x D £1 /& : : : &:9.x D £n / (3) states that if T is multiply realized then £1 : : : £n do not name anything. The adoption of a modal language does not rule out the character of indeterminacy that is typical of RS qua existential generalisation and it is expressed by its multiple realisability. Lewis constrains it through postulate (3) that makes the theory false in case of multiple realizations. Nonetheless, his argument against multiple realizability is worth our while because it seems too strong. A ‘realization’ of a theory T is simply an n-tuple of entities denoted by the theoretical terms of T and which satisfies the relevant ‘realization formula’ of T (obtained by replacing the theoretical terms by variables). In the case T is multiply realized, the axiomatization of the T-terms (1–2) would name the components of some realization or other. Lewis thinks that this concedes too much to the instrumentalist view even though his Ramsey reconstruction retains much theoretical content. Hence, his demand that the theoretical terms of a multiply realized theory be denotationless (the postulate 3). It is this which motivates the use of Scott’s denotationless term tolerant logic as the underlying formal framework and the prefacing of the relevant Ramsey sentences with the ‘uniqueness’ operator. Now, Lewis suggests that scientists themselves appear to proceed with the expectation that their theories will be uniquely realised. In other terms he seems to think that the exclusion of situations of multiple realizability is in line with scientific practice and anyway required by the realist aims of the account. This seems too strong. The question is, of course, does multiple realizability really concede too much to the anti-realist? In the light of the current debate Lewis preoccupation seems overstated. What realists seem content with is the idea that a theory gives us an approximately true account of how things are in its domain. The possibility that more than one n-tuple of unobservables might be realisers of RS seems perfectly compatible with the idea of approximation to truth. Moreover it seems a natural feature to cash out the structuralist sense in which hidden natures are associated with structure. So postulate (3) above could be dropped without worrying too much of leaning towards antirealism. Lewis himself seems to take this direction elsewhere.

4.3.2 The First Path to Humility and the Structuralist Intuitions Lewis (pre-print) discusses the issue of what we can know on the basis of our theories and his contribution seems to go in a direction that fulfils some of the desiderata of ESR2 . Now multiple realizability will appear as a resource. Lewis (preprint) agrees with Rae Langton’s Humility thesis, regarding our limitations as epistemic agents. I will get into the details of Langton’s interpretation of Kant in terms of Humility in the next section. Lewis argues that the conclusion of the unknowability of the intrinsic properties of objects follows from the principles of his metaphysics as well. The combinatorial principle in particular yields the Humility. Let us see then.

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Assume that T is the Final Theory of Everything. The language of T is formulated as illustrated above but with a meaningful difference: T-terms label only fundamental properties. We further assume that a fundamental property we refer to via a T-term always falls within a category containing at least two such properties. RS is then formulated in the usual way. We have the following situation: the actual realization of T prima facie seems unique but the role-occupancy of the fundamental properties is specified by the RS which has the same empirical success as that of T and is multiply realized. This means that in the case that T could be proved to be multiply realizable there is no empirical evidence that can decide between the different possible realizations. Two factors make this situation inescapable: (a) T and its RS have the same empirical power thus RS can be taken to specify which role the fundamental properties have to play to account for all empirical data and this role is all we need for our epistemic purposes. (b) Since we assume that our fundamental properties belong to classes with at least two members, the combinatorial principle allows us to conclude that the same phenomena would be observable in worlds in which fundamental properties belonging to the same category are swapped. In other words there is room to argue that on this view, even the final T is multiply realizable. We can read the Ramseyan humility as follows: a role is occupied by a fundamental property and this is crucial in order to account for observable data, but we are not in the position to establish which property in a class of fundamental properties occupies it because the observable phenomena would remain the same whatever property in that class is chosen. The RS here plays the crucial role because its empirical equivalence with the original theory tells us precisely that once the role occupancy is granted the empirical outcome would be the same. Our limitation depends upon a metaphysical picture. First of all according to combinatorialism we can take apart the distinct elements of a possibility and rearrange them. There is no necessary connection between distinct existences, so the result of the recombination is another possibility. In general, combinatorialism states that a possibility is preserved under permutation of items and entails that the laws of nature are contingent. Secondly, quidditism is the view that properties have a kind of primitive identity across possible worlds. Thus, different possibilities can differ only on the permutation of fundamental properties. This offers a further way of understanding the ‘hidden’ natures of ESR2 . The quiddities of the properties, their cross-world identity, are further elements that remains unaccessible. Let us now go back to RS. It is indisputable that the RS in Lewis’s own version carries a highly theoretical load and the items featuring in the descriptions that the sentence provides are not only empirical or observational: rooted in the multiple realizability of Lewis’ RS, the thesis of Humility seems to have a strong realist character. What about the consequences for ESR2 ? Can we happily embrace the Lewisian argument as an argument for ESR2 ? First of all, the T-terms correspond just to the intrinsic properties. We know we do not know them but we have no hint on the status of the relations and this view admits in the realm of the knowable a

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considerable amount of non-purely structural features. Secondly, the overall picture relies on combinatorialism which in turn pushes us to abandon a conception of laws of nature as necessary. This in turn means that any articulated set of relational properties captured by the structure of the theory also loses any character of necessity. This may or may not be a heavy cost to bear, depending on one’s attitude to laws and necessity of course. The advocate of ESR2 could adopt some form of regularity view. Nonetheless consider: ESR2 central thesis is that structure is epistemically independent from the underlying, and hidden, ‘natures’. We are after an argument to the effect that this epistemic distinction can be based on metaphysical grounds establishing where to place the threshold between the structural knowable and the non-structural unknowable. In doing so, we rely on evidences from the history of physics that emphasise the retention of law-like relational features. On the other hand, our metaphysical set up denies that such features express any necessary connection. It might not be wrong but it certainly appears strange since it rejects any necessary connection ‘tying together’ the set of properties represented in the laws. A question is in point. Why we are buying into a framework that indeed humbles our original structuralist intuitions? We are not but this story contains a moral about the possibility that the intrinsic nature of the entities might be truly unknowable that is worth taking seriously. Ramseyan Humility springs from a metaphysical background in which relational features are largely reducible to the intrinsic natures of the objects. They enjoy no special status but nonetheless the intrinsic nature of things turns out to be inaccessible. Dialectically this can just reinforce a similar conclusion drawn from more structuralist-friendly presuppositions. Such presuppositions is what we are going to investigate in the contest of Kantian Humility that will conclude our search for an argument to support ESR2 .

4.3.3 The Structure Goes Kantian Let me begin this section dispelling a possible source of confusion. I am not asking the advocate of ESR2 , a realist after all, to make an undesirable conversion to transcendental idealism. In Rae Langton’s highly controversial interpretation of Kant (Langton 1998), the knowledge we have of the world is not due to the constructive activity of the understanding that organizes the data of sensibility in spatiotemporal representations. This is the wisdom (Langton 2004): (i) (ii) (iii) (iv)

Things in the world are substances characterised by their intrinsic properties. They interact with us affecting our perception. Their causal powers are what allow them to affect us. Being affected by them is the only way in which we can know them (receptivity). (v) Their causal powers are relational properties not intrinsic properties. (vi) Causal powers are not reducible to intrinsic properties. (vii) We do not know anything about things in themselves (humility).

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Kantian Humility diverges from Lewis’s view because intrinsic properties play here the exclusive role of characterising the nature of substances. In Lewis’s picture they are the site of causal powers and we do not know about them because as Lewis put it to be the ground of a disposition is to occupy a role, but it is one thing to know that a role is occupied and another thing to know what occupies it (Lewis preprint)

In the Kantian picture, instead intrinsic properties are idlers. We do not know them because they do not act on us (Langton 2004) and our knowledge is based on receptivity, on the fact that the world can affect us. I wish now, to focus on points (v) and (vi), I think that they give to the advocates of ESR2 the sort of Humility that can appeal to their structuralism, and together with receptivity, they grant that we are realist enough in our attitude towards science. Natures are, thus really hidden and there are metaphysical motivations for the fact that we consistently retrieve certain relational features. They are the sole fuel for the engine of our knowledge. Kantian humility has costs as well. We challenge the traditional view that intrinsic properties are the site of causal powers and we subscribe to the view(s) that dispositions are extrinsic and relational. Secondly, we downplay the role of intrinsic properties in natural processes. They are idlers so it is not because of them that certain phenomena occur as they actually do. It is not that all we know is the structure because the structure is all there is but all we know is structure because the structure is all that actively determines natural processes.

4.4 Conclusions I have disambiguated the notion of structure involved in the characterisation of ESR currently debated. I have shown that the disambiguation leads to two views of structure ESR1 and ESR2 . Only ESR2 can be seen as asserting the priority of relations usually captured in physics by equations. I have indicated that such view needs an argument in principle to explain such a priority. I have shown that RS can play a role even in establishing such an argument and have identified the argument in the thesis of Kantian Humility.

References Cei A, French S (2006) Looking for the structure in all the wrong places. Stud Hist Philos Sci 37:633–655 Langton R (1998) Kantian humility. Our ignorance of things in themselves. Oxford University Press, Oxford Langton R (2004) Elusive knowledge of things in themselves. Aus J Philos 82:129–136 Laudan L (1981) A confutation of convergent realism. Philos Sci 48:19–49 Lewis D (1970) How to define theoretical terms. J Philos 67:427–446

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Lewis D (preprint) Ramseyan humility Maxwell G (1970) Structural realism and the meaning of theoretical terms. In: Winkour S, Radker M (eds) Analysis of theories and methods and of physics and psychology: Minnesota studies on the philosophy of science, vol IV. University of Minnesota Press, Minneapolis, MN, pp 181–192 Melia J, Saatsi J (2006) Ramseyfication and theoretical content. Br J Philos Sci 57:561–585 Poincar`e HJ (1905) Science and method. Walter Scott, London Psillos S (1996) Scientific realism and the ‘pessimistic induction’. Philos Sci 63(PSA Proc.): S306–S331 Saunders SW (1993) To what physics corresponds. In: French S, Kaminga H (eds) Correspondence, invariance, and heuristics; Essays in honour of Heinz Post. Kluwer, Dordrecht, pp 295–326 Stein H (1989) Yes but : : : some skeptical remarks on realism and anti-realism. Dialectica 43:47–65 Worrall J (1989) Structural realism: the best of both worlds? Dialectica 43:99–124 Worrall J (1994) How to remain (reasonably) optimistic: scientific realism and the “luminiferous ether”, Philosophy of Science, PSA Proceeding Vol. I, pp 334–342

Chapter 5

Approaching the Truth via Belief Change in Propositional Languages Gustavo Cevolani and Francesco Calandra

Starting from the 1960s of the past century, scientific change has become a main concern of philosophy of science. In particular, a great deal of attention has been devoted to theory change.1 Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (for short: PPV)2 and the AGM theory of belief change (for short: AGM).3 In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, i.e., for achieving the cognitive aim of science pointed out by PPV. PPV and AGM are characterized by strongly different assumptions concerning the aims of science. In fact, while all versions of PPV share the view that verisimilitude is the main cognitive aim of science, the only aims explicitly suggested by

G. Cevolani () Department of Philosophy, University of Bologna, via Zamboni 38, 40126 Bologna (Italy) e-mail: [email protected] F. Calandra University of Trieste, Italy e-mail: [email protected] 

Although we are separately responsible for particular sections (Gustavo Cevolani: Sections 5.1.2, 5.2 and 5.3; Francesco Calandra: Section 5.1.1), we have each benefited from regular discussions and the rereading of each other’s contributions, which produced a unified exposition of all the subjects dealt with in the paper. 1 For a discussion of the problem of rational theory change and its relations with the aims of science, see Cevolani and Festa (2009). 2 In the present paper, the terms “verisimilitude” and “truth approximation” are used as synonymous. The first full-fledged account of verisimilitude was provided by Karl Popper (1963, 1972). Later, David Miller (1974) and Pavel Tich´y (1974) showed that Popper’s account was untenable, thus opening the way to the post-Popperian theories of verisimilitude, emerged since 1975. An excellent survey of the modern history of verisimilitude is provided by Niiniluoto (1998). 3 In the literature, the terms “belief dynamics”, “belief change”, and “belief revision” are used as synonymous. AGM, which is named after Alchourr´on, G¨ardenfors, and Makinson (1985), was developed, starting from the 1970s, by researchers in philosophy of science, logic and Artificial Intelligence. The first monograph devoted to AGM was written by G¨ardenfors (1988), and the first textbook presentation by Hansson (1999).

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AGM are consistency and informative content. In fact, truth and truth approximation play no role at all in AGM, as the following telling quote by G¨ardenfors (1988, p. 20) clearly reveals: Œ: : : the concepts of truth and falsity are irrelevant for the analysis of belief systems. These concepts deal with the relation between belief systems and the external world, which I claim is not essential for an analysis of epistemic dynamics. Œ: : : My negligence of truth may strike traditional epistemologists as heretical. However, one of my aims is to show that many epistemological problems can be attacked without using the notions of truth and falsity.4

In spite of this, one may ask whether the AGM rules for belief change are effective means for approaching the truth (Niiniluoto 1999). In Sections 5.1 and 5.2, the key ideas of PPV and AGM and their application to so called “propositional theories” will be illustrated. In Section 5.3 we will prove that, as far as propositional theories are concerned, AGM belief change is an effective tool for approaching the truth.

5.1 Post-Popperian Verisimilitude for Propositional Theories 5.1.1 Post-Popperian Theories of Verisimilitude The intuitive idea underlying the concept of verisimilitude is that: a theory is highly verisimilar if it says many things about the domain under investigation and many of those things are true, or almost exactly true. One of the best known accounts of verisimilitude has been provided by Ilkka Niiniluoto (1987). Niiniluoto’s approach can be applied to theories stated in many kinds of language, including propositional and first-order languages. In this paper, however, we will only be concerned with theories stated within a propositional language L with n atomic propositions p1 ; p2 ; : : : ; pn . Given an atomic proposition pm we will say that pm and :pm are the basic propositions – or b-propositions – associated to pm . The b-propositions of L form a set B D fp1 ; :p1 ; p2 ; :p2 ; : : : ; pn ; :pn g including 2n members. The most informative propositions of L are called constituents. A constituent Ci is the most complete description of a possible world made by means of the expressive resources of L. In fact, for any atomic proposition pm ; Ci tells whether pm is true or not. Hence, Ci can be written in the following form: ˙ p1 ^ ˙p2 ^ : : : ^ ˙pn ;

4

(5.1)

Quite recently, however, some AGM theorists have criticized the lack of any concern for truth in AGM. For instance, Hans Rott argues that AGM “should worry more about truth” considered as one of the basic aims of scientific inquiry (see Rott 2000, pp 513, 518 and ff., and in particular note 38).

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where “˙” is either empty or the negation symbol “:”. Any b-proposition occurring in Eq. 5.1 will be called a basic claim – or b-claim – of Ci . Moreover, we will say that each b-claim ˙pm of Ci is true in (the possible world described by) Ci . The constituents of L form a set C D fC1 ; C2 ; : : : ; Cq g including q D 2n members. Moreover, one can check that: (i) C1 ; C2 ; : : : ; Cq are mutually exclusive and jointly exhaustive; (ii) there is an unique true constituent, which will be denoted by “C  ”; (iii) any sentence T of L can be expressed in its normal disjunctive form as follows: T  _ Cj

(5.2)

j 2T

where T is the index set of the constituents entailing T . The so called “similarity approach” to verisimilitude is based on the idea that an appropriate measure of verisimilitude Vs.T / should express the similarity between T and “the truth” C  or, equivalently, the closeness of T to C  . The basic intuition underlying Niiniluoto’s version of the similarity approach is that the verisimilitude Vs.T / of a theory T  _ Cj can be defined as a function of the distances between j 2T

the disjuncts Cj of T and C  . The versions of the similarity approach based on this intuition may be called disjunctive versions (or d-versions). In Niiniluoto’s d-version of the similarity approach, Vs.T / is defined as follows. First, a distance function  is defined on the ordered couples .Ci ; Cj / of constituents of C by identifying ij  .Ci ; Cj / with the number of the differences in the ˙-signs between Ci and Cj , divided by n; i.e., with the number of the b-claims on which Ci and Cj disagree, divided by the total number of atomic propositions. This implies that 0  ij  1 and ij D 0 iff i D j . Second, an extended distance function .T; Ci / is defined on all the couples .T; Ci /, where the distance .T; Ci / of T from Ci is a function of the distances ij between the disjuncts Cj of T and Ci . Niiniluoto’s favourite extended distance function .T; Ci / is the so called min-sum distance function: 0

ms .T; Ci /  min .T; Ci / C  0 sum .T; Ci /;

(5.3)

0

with 0 < ”; ” 0  1.5 Since ms is normalized, the similarity s.T; Ci / of T to Ci can be simply defined as: 0

0

 .T; Ci /  1  ms .T; Ci /: sms

5

0

(5.4)

Distance ms is a weighted sum of two simpler (extended) distances, the minimum distance min .T; Ci / and the normalized sum distance sum .T; Ci /. The minimum distance of T from Ci is the distance from Ci of the closest constituent entailing T , defined as: min .T; Ci / D minj 2T ij . The normalized sum distance of T from Ci is the sum of the distances from Ci of all the constituents entailing T normalized with.respect to the sum of the distances of all the elements of C P P from Ci W sum .T; Ci / D j 2T ij Cj 2C ij .

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Finally, the degree of verisimilitude Vsms .T / of T can be defined as the similarity between T and “the truth” C  : 0

0

0

  .T /  sms .T; C  /  1  ms .T; C  /: Vsms

(5.5)

0

One can prove that Vsms satisfies a number of plausible principles. Among them, the following are especially important6: (Vs.1) Among true statements, verisimilitude covaries with information. (Vs.2) Among false statements, verisimilitude does not covary with information. (Vs.3) Some false statements may be more verisimilar than some true statements.

5.1.2 Applying PPV to Propositional Theories According to the d-version of the similarity approach, the verisimilitude Vs.T / of a sentence T depends only on the distances between the states of affairs allowed by T – represented by the constituents Ci which entail T – and the true state of affairs C  . On the other hand, according to a recently proposed version of this approach – which may be called the conjunctive version (or c-version) – Vs.T / depends only on what T says about the “basic features” of the actual world C  , where such features are expressed by the b-claims ˙pm which are true in C  .7 The key concept of the c-version of the similarity approach is the notion of conjunctive proposition – or c-proposition. C-propositions are possibly the simplest kind of “propositional theories”, i.e., of theories stated within a propositional language L.8 While a constituent Ci specifies a complete list of the allegedly true b-propositions of L, a c-proposition T specifies a (possibly) incomplete list of such b-propositions. A c-proposition can be expressed in the following form: ˙ p1T ^ ˙p2T ^ : : : ^ ˙pkT ;

(5.6)

where kT  n. Constituents are nothing but a special kind of c-proposition with kT D n; moreover, a tautology T can be seen as the c-proposition with kT D 0. Any b-proposition ˙pm occurring in Eq. 5.6 will be called a b-claim of T . The set T C of all the b-claims of a c-proposition T will be referred to as the basic content – or b-content – of T . Given a constituent Ci ; T C can be partitioned into two subsets: (1) the subset t.T; Ci / of the b-claims of T which are true in Ci , and 6 There are good reasons to think that any plausible measure of verisimilitude should respect (Vs.1– Vs.3) (see Niiniluoto 1987, pp 232–233). 7 The c-version of the similarity approach presented here has been developed by Festa (2007a,b,c), Cevolani and Festa (2009), and Cevolani et al. (2009) with respect to first-order and propositional languages. 8 C-propositions are essentially identical to “descriptive statements” or “D-statements” (Kuipers 1982, pp 348–349) and to “quasi-constituents” (Oddie 1986, p 86).

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(2) the subset f .T; Ci / of the b-claims of T which are false in Ci. We may say that t.T; Ci / is the true b-content of T w.r.t. Ci , while f .T; Ci / is the false b-content of T w.r.t. Ci . Given a non-tautological c-proposition T , we will say that T is true in the case where t.T; C  / D T C (and f .T; C  / D ¿/ and that T is completely false in the case where t.T; C  / D ¿ (and f .T; C  / D T C /. T is false if some of its b-claims are false. The c-proposition TQ , given by the conjunction of the negations of all T ’s b-claims, will be called the specular of T. It is easy to see that if T is true then TQ is completely false and viceversa, whereas if T is false then TQ too is false. Starting from the qualitative notions of true and false b-content of T w.r.t. Ci , the corresponding quantitative notions of degree of true b-content contt .T; Ci / and degree of false b-content contf (T; Ci) of T w.r.t. Ci can be introduced as follows: contt .T; Ci / D

t.T; Ci / f .T; Ci / and contf .T; Ci / D n n

(5.7)

The similarity s£ .T; Ci / of T to Ci can then be defined as a weighted average of contt .T; Ci / and contf .T; Ci /, where contt .T; Ci/ is construed as the prize attributed to the true b-content of T w.r.t. Ci and contf .T; Ci / as the penalty attributed to the false b-content of T w.r.t. Ci : s .T; Ci / D contt .T; Ci / C .1  /.contf .T; Ci // D contt .T; Ci /  .1  /contf .T; Ci /

(5.8)

where 0 < £  1=2. The verisimilitude of T; Vs£ .T /, is then identified with the similarity between T and the true constituent C  : Vs .T / D s .T; C  /:

(5.9)

In order to state some interesting features of Vs£ , it is useful to introduce the notions of verisimilar sentences and of sentences which are distant from the truth—or t-distant sentences.9 To this purpose, we shall say that a c-proposition T is verisimilar in the case where Vs£ .T / > 0 and that T is t-distant in the case where Vs£ .T / < 0. Some relevant consequences of Eqs. 5.8 and 5.9 can now be proved: Theorem 1. Given a c-proposition T of the form ˙p1T ^ ˙p2T ^ : : : ^ ˙pkT : 1. .£  1/  Vs£ .T /  £. 2. If T is tautological, then Vs£ .T / D 0. 3. If T is true, then T is verisimilar.

9 A similar definition can be given with respect to any verisimilitude measure Vs, by selecting a suitable threshold value ¢ and calling “verisimilar” and “t-distant” those sentences whose verisimilitude is greater or lower than ¢, respectively.

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If T is completely false, then T is t-distant. P Vs .T / D pm 2T C Vs .pm /. Vs£ satisfies principles (Vs.1–Vs.3). Vs .T / < = D = > Vs .TQ / iff contt .T; C  / < = D = > contf .T; C  /.

5.2 AGM Belief Change for Propositional Theories 5.2.1 The AGM Theory of Belief Change Within the AGM theory of belief change, the epistemic state of an ideal agent X is represented by a belief set or theory, i.e., by a deductively closed set of sentences. More precisely, given a language L, an operation of logical consequence Cn defined on L, and a set K of sentences within L, the notion of belief set is defined as follows: K is a belief set if and only if Cn.K/ D K:

(5.10)

Although the notion of belief set in Eq. 5.10 includes also inconsistent belief sets, AGM theorists adopt the following principle of consistency: (C) The belief set K of an ideal agent X should be consistent. Suppose that the epistemic state of X is represented by a consistent belief set K. Then X can have one of the following epistemic attitudes towards a sentence A of L: i X accepts A in the case where A 2 K; ii X rejects A in the case where :A 2 K; iii X suspends the judgment on A – or, equivalently, A is undetermined for X – in the case where both A … K and :A … K. The basic purpose of AGM is to provide a plausible account of how an ideal agent X should update his belief set K in response to certain epistemic inputs coming from some information source. Given a sentence A, two kinds of epistemic input concerning A are considered within AGM: (a) Additive inputs, which can be expressed as orders of the form “Add A to your belief set!”. (b) Eliminative inputs, which can be expressed as orders of the form “Remove A from your belief set!”. Below, the additive input “Add A to your belief set!” and the eliminative input “Remove A from your belief set!” will also be denoted by the shorter expressions “additive input A” and “eliminative input A”, respectively.

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Suppose that X receives the additive input “Add A to your belief set!”. Of course, if A already belongs to K – i.e., if X already accepts A – then X ’s appropriate response is keeping K unchanged. However, there are two more interesting cases where A … K: Expansion. A is compatible with K, i.e., :A … K. In this case, the epistemic operation by which X should update K by the addition of A is called expansion, and the expanded belief set is denoted by “KAC ”. Revision. A is incompatible with K, i.e., :A 2 K. In this case, the epistemic operation by which X should update K by the addition of A is called revision, and the revised belief set is denoted by “KA ”. Below, we will call “addition” the generic operation of updating K by an additive input A. Hence, the addition of A to K will be either the expansion of K by A, in the case where A is compatible with K, or the revision of K by A, in the case where A is incompatible with K. Now suppose that X receives the eliminative input “Remove A from your belief set!”. If A does not belong to K – i.e., X rejects, or suspends the judgment on, A–X’s appropriate response consists is keeping K unchanged. However, the more interesting case where A 2 K may occur: Contraction. If A 2 K, the epistemic operation by which X should update K by the removal of A is called contraction, and the contracted belief set is denoted by “KA ”. AGM theorists have made systematic efforts aiming to show how, given a belief set K and a sentence A, an ideal agent X could specify the updated belief sets KAC ; KA and KA . A basic intuition underlying the AGM approach is expressed by the following general principle of rationality, known as the principle of minimal change: (MC) When the belief set K of an ideal agent X is updated in response to a given epistemic input, a minimal change of K should be accomplished. This means that X should continue to believe as many of the old beliefs as possible and start to believe as few new beliefs as possible. There are many alternative ways of defining KAC ; KA and KA in accordance with the general principles of consistency and minimal change. For this reason, G¨ardenfors (1988) has proposed a number of adequacy conditions – the so called G¨ardenfors postulates – that any appropriate definition of KAC ; KA and KA should satisfy. For instance, the “Success” postulate for revision says that A 2 KA . However, it should be noted that the G¨ardenfors postulates alone cannot fully determine the result of any belief change. Suppose, for example, that an agent X receives the additive input A. If X ’s theory K includes :A, then X has to revise K by A. This means that :A must be removed from K, in order to guarantee both that A 2 KA – as required by the Success postulate – and that KA is consistent – in agreement with (C). Moreover, X has to remove from K not only :A but – due to the definition (Eq. 5.10) of belief set – also any set of sentences entailing :A. Since there are normally many alternative ways to fulfill this task, the choice of one of them will

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depend on the relative “importance” that X attaches to the sentences in K. In this connection, one may assume that the elements of K are ordered with respect to their so called epistemic entrenchment (G¨ardenfors and Makinson 1988). When X has to remove some sentences from K, he will choose the less entrenched in agreement with appropriate selection rules. A well known method for defining the operations of expansion, revision and contraction in accordance with the G¨ardenfors postulates and with entrenchment-based selection rules has been provided by Grove (1988). For the sake of brevity, below we will outline Grove’s method only with reference to expansion and revision.10 Grove shows that, given a propositional language L, any belief set K in L is identical to the set of all the logical consequences of some sentence T of L – i.e., is identical to the so called consequence class Cn.T /. Hence, a generic belief set or “theory” may be identified with the corresponding sentence T of L, expressed in its normal disjunctive form as T  _ Cj . An epistemic entrenchment relation can be defined j 2T

on the sentences of L by ordering the constituents of C with respect to their relative closeness or similarity to the elements of T. Niiniluoto (1999) shows that such an ordering is easily obtained in the case where a suitable distance function  is defined on the constituents of L (see Section 5.1.1). In fact, the distance i .T / of a constituent Ci from a theory T may be defined as i .T / D minj 2T ij D min .Ci ; T /. Moreover, given an epistemic input A,˚the set CT .A/ of the closest  constituents to T entailing A is defined as: CT .A/ D i 2 A W i .T /  j .T / for all j 2 A. By using these notions, Niiniluoto proves the following identities concerning expansion and revision11: Theorem 2. If the additive input A is compatible with T , in the sense that :A … Cn.T /, then TAC is simply given by the conjunction of T and A: TAC D T ^ A D

_ Ci :

i 2T\A

Theorem 3. If the additive input A is incompatible with T , in the sense that :A 2 Cn.T /, then TA is given by TA D _ Ci : i 2CT .A/

5.2.2 Applying AGM to Propositional Theories Now we will show how the basic principles of AGM can be applied to the definition of TAC and TA in the case where both T and A are c-propositions. To this purpose, we have to introduce some preliminary notions concerning T and its logical relations with A. 10 11

See Cevolani et al. (forthcoming) for a discussion of contraction. See Niiniluoto (1999), pp 7–9.

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First of all, recall that T C is the set of all b-claims of T , i.e., the set of all b-propositions occurring in T . The set of the negations of the elements of T C will be denoted by “T  ”, whereas the set of the b-propositions which occur neither in T C nor in T  will be denoted by “T ‹ ”.12 Note that the sets T C ; T  and T ‹ form a partition of the set B of the 2n b-propositions of L. Suppose that the agent X receives the additive input A. In order to understand how X should update his belief set T in response to A, one should note that the logical relations between T and A depend on how AC overlaps the partition fT C ; T  ; T ‹ g. For this reason, it is useful to introduce the notions of the “redundant”, “conflicting” and “extra” part of A with respect to T , as follows. Given two c-propositions T and A, the following related c-propositions are defined: 1. ArT , the conjunction of the elements of AC \ T C , will be called the redundant part of A w.r.t. T. 2. AcT , the conjunction of the elements of AC \ T  , will be called the conflicting part of A w.r.t. T. 3. AxT , the conjunction of the elements of AC \ T ‹ , will be called the extra part of A w.r.t. T. Below, the conflicting and the extra parts of A w.r.t. T will be also referred to as the “non-redundant parts” of A w.r.t. T . Note that the three sets AC \ T C ; AC \ T  and AC \ T ‹ form a partition of AC . Hence, A can be written as ArT ^ AcT ^ AxT and, in the same way, T can be written as TrA ^ TcA ^ TxA . The following properties of the c-propositions ArT ; AcT and AxT defined above are worth noting. First, ArT is identical to TrA , by definition. Moreover, it is easy to see that AcT D TQcA and TcA D AQcT – i.e., that the conflicting part of A w.r.t. T is the specular of the conflicting part of T w.r.t. A, and vice versa. Finally, AxT and TxA share by definition no common conjuncts. The above notions can be used to prove the following theorems concerning expansion and revision13: Theorem 4. If the additive input A is compatible with T , in the sense that AC \ T  D ¿, then TAC D T ^ A. Theorem 5. If the additive input A is incompatible with T , in the sense that AC \ T  ¤ ¿, then TA D A ^ TxA . A consequence of Theorem 4 is worth noting here. First, recalling that ArT D TrA , one can see that the information ArT is already conveyed by T . Second, since A is compatible with T by hypothesis, the conflicting part of A w.r.t. T is empty – i.e., AC \ T  D ¿ and AcT D TcA D T. From these two facts, it follows that the conjunction of T with A is identical to the conjunction of T with the extra part of A w.r.t. T . Hence, Theorem 4 implies that T C A D T ^ AxT . 12 If T is the theory of an agent X, then T C ; T  , and T ‹ can be seen as the set of the b-propositions which X accepts, rejects, and on which suspends the judgment, respectively. 13 These theorems are proved in Cevolani et al. (forthcoming) together with a number of results about contraction.

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5.3 Is AGM Belief Change a Road to Verisimilitude? We can now come back to the question considered at the beginning of the paper, i.e., the question whether the AGM rules for belief change are effective means for approaching the truth. This question may be now rephrased as follows: are AGM expansion and revision effective means for approaching the truth?14 Niiniluoto (1999) investigates this problem with respect to his favored verisimil0 itude measure Vsms , introduced in Section 5.1.1. In particular, Niiniluoto asks in which cases expansion and revision lead our theories closer to the truth or, in other words, in which cases, given a theory T and an additive input A; TAC and TA are more verisimilar than T . In this connection, Niiniluoto can immediately prove the following result15 :  0  0 Theorem 6. Suppose that both T and A are true. Then Vsms TAC  Vsms .T /. 0

It is not difficult to show that this result doesn’t hold only for Vsms but also for most of the existing verisimilitude measures. Indeed Theorem 3 holds for any verisimilitude measure satisfying the principle (Vs.1) according to which, among true statements, verisimilitude covaries with information.16 Unfortunately, Niiniluoto shows that Theorem 3 cannot be extended to more general cases. In particular, Niiniluoto proves that, even in the case where A is true, TAC and TA may be less verisimilar than T 17 : Theorem 7. Suppose that A is true. Then: 1. If T is false, TAC may be less verisimilar than T . 2. TA may be less verisimilar than T. Niiniluoto’s results above concern the expansion and the revision of theories expressed in propositional and first-order languages. Theorem 3 shows that the simple addition of true epistemic inputs to such theories doesn’t necessarily lead them closer to the truth. In this regard, one can say that expansion and revision are not 0 effective means for approaching the truth, at least as far Vsms is concerned. However, a different conclusion can be reached if we restrict our attention to a special kind of propositional theories, i.e., c-propositions. In this case, we can specify various cases where expansion and revision are effective means for approaching the truth. Accordingly, from now on we will assume that both the theory T and the epistemic input A are c-propositions. The following theorems state the conditions under which expansion and revision increase the verisimilitude of a theory T with respect to the verisimilitude measure Vs£ introduced in Section 5.1.2. 14 The problem of the effectiveness of contraction for approaching the truth is considered in Cevolani et al. (forthcoming). 15 See Niiniluoto (1999), Eq. 5.10. 16 One of the few verisimilitude measures violating (Vs.1) has been proposed by Graham Oddie (1986). 17 See Niiniluoto (1999), pp. 10–13, in particular equations 10, 17 and 20.

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Theorem 8. Given a theory T , suppose that A is compatible with T and AC 6 T C .18 Then:   Vs TAC > Vs .T / iff AxT is verisimilar: Theorem 9. Given a theory T , suppose that A is incompatible with T . Then:   Vs TA > Vs .T / iff Vs .AxT / > Vs .AQcT /  Vs .AcT /: In order to grasp the intuitive meaning of Theorem 9, recall that, by hypothesis, A is incompatible with T , i.e., that the conflicting part of T w.r.t. A is not empty. According to Theorem 5, the revision of T by A replaces such conflicting part TcA D AQcT with AcT and adds AxT to T . Now suppose that Vs .AcT / < Vs .AQcT /. Then the difference Vs .AQcT /  Vs .AcT / can be construed as the loss of verisimilitude due to the addition of the conflicting part of A to T . However, if the extra part of A outweighs this loss – i.e., if Vs .AxT / > Vs .AQcT /  Vs .AcT / – then the revised theory TA will still be more verisimilar than T . Recalling that, according to Theorem 1, if A is true then A is verisimilar, whereas if A is completely false then A is t-distant, one can now prove some interesting consequences of Theorems 8 and 9. First, the addition of true inputs to (false) theories always increases their verisimilitude: Theorem 10. Suppose that A is true. Then:   1. Vs TAC > Vs .T /. 2. Vs TA > Vs .T /. Second, if the non-redundant parts of A w.r.t. T are verisimilar, then the addition of A to T leads T closer to the truth: Theorem 11. Suppose that AcT and AxT are verisimilar. Then:   1. Vs TAC > Vs .T /. 2. Vs TA > Vs .T /. To sum up, expansion and revision are effective means for approaching the truth, as far as c-propositions and the verisimilitude measure Vs£ are concerned, in the following sense. First, the addition of true inputs to (false) theories leads to more verisimilar theories. Second, the addition of inputs whose non-redundant parts are verisimilar also increases the verisimilitude of the original theory. Finally, one may consider another aspect of AGM’s effectiveness for approaching the truth which is not discussed by Niiniluoto (1999). In fact, Theorems 10 and 11 concern the expansion and the revision of T by true inputs or by inputs whose nonredundant parts are verisimilar. However, one might ask what happens in the case where T is expanded or revised by inputs which are completely false or whose nonredundant parts are t-distant. In such cases, it seems plausible to expect that the 18

The proviso is needed in order to exclude the trivial case where A is already contained in T , i.e., the case where AxT D T and TAC D T .

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expansion and the revision of T by A leads to theories which are less verisimilar than T . An answer to this question is provided by the following theorems. First, one can prove that the addition of completely false inputs to T leads to a less verisimilar theory, as the following result (which is the counterpart of Theorem 3) states: Theorem 12. Suppose that A is completely false. Then:   1. Vs TAC < Vs .T /. 2. Vs TA < Vs .T /. Moreover, if the non-redundant parts of A are t-distant, the expansion of T by A is less verisimilar than T :   Theorem 13. Suppose that AcT and AxT are t-distant. Then, Vs TAC < Vs .T /. Interestingly, however, this doesn’t hold for revision; in fact: Theorem 14. TA may be more verisimilar than T , even if both AcT and AxT are t-distant. The results illustrated in this paper suggest two further questions. The first is whether similar results may be obtained for the contraction of c-propositions by different kind of eliminative inputs. This problem is analyzed in Cevolani et al. (forthcoming). The second question is whether Theorems 10–14 can be extended to verisimilitude measures different from Vs£ . In this connection, we advance the admittedly bold guess that the results proved in Theorems 10–14 hold for any plausible verisimilitude measure defined on propositional languages. Acknowledgments The authors wish to express their gratitude to Roberto Festa and Theo A. F. Kuipers for commenting on an early draft of the paper.

Proofs. Proof of Theorem 1. 1. The most verisimilar c-proposition T of L is the true constituent itself, i.e., C  . If T D C  , then contt .T; C  / D 1, whereas contf .T; C  / D 0. Then Vs£ .T / D £contt .T; C  / D £ is the verisimilitude of the most verisimilar c-proposition of L. On the other hand, the less verisimilar c-proposition T is the completely false constituent, i.e., the specular CQ  of C  . If T D CQ  , then contt .T; C  / D 0, whereas and contf .T; C  / D 1. Then Vs£ .T / D  .1  £/contf .T; C  / D £  1 is the verisimilitude of the less verisimilar c-proposition of L. 2. Recall that T is tautological iff kT D 0, i.e., T C D ¿. Then, contt .T; C  / D contf .T; C  / D 0 and Vs£ .T / D 0. 3. If T is true (and non-tautological), then t.T; C  /DT C ¤¿ and contt .T; C  / > 0, whereas f .T; C  / D ¿ and contf .T; C  / D 0. Consequently, since £ > 0; Vs£ .T / D £contt .T; C  / > 0.

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4. If T is completely false, then t.T; C  / D ¿ and contt .T; C  / D 0, whereas f .T; C  / D T C ¤ ¿ and contf .T; C  / > 0. Since .1  £/ > 0; Vs£ .T / D .1  £/contf .T; C  / < 0. Note that a b-proposition pm is also a c-proposition, whose unique b-claim is pm . If pm is true, then t.pm ; C  / D fpm g and contt .pm ; C  / D 1=n, whereas f .pm ; C  / D ¿ and contf .pm ; C  / D 0; moreover Vs£ .pm / D £=n. Conversely, if pm is false, then f .pm ; C  / D fpm g and contf .pm ; C  / D 1=n, whereas t.pm ; C  / D ¿ and contt .pm ; C  / D 0; moreover Vs£P .pm / D  .1  £/=n. It contt .pi ; C  / and is now easy to see that, for any T; contt .T; C  / D pi 2t .T;C  / P contf .T; C  / D contf .pj ; C  /. Hence, Vs .T / D    pj 2f .T;C / P P contt .pi ; C  /  .1  /  contf .pj ; C  /, i.e., since  pi 2t .T;C / pj 2f .T;C  / P P Vs .pi / C Vs .pj / t.T; C  / [ f .T; C  / D T C ; Vs .T / D pi 2t .T;C  / pj 2f .T;C  / P D Vs .pm /. pm 2T C

5. Consider two c-propositions A and B such that A is logically stronger than B, i.e., such that A ` B but B `/ A. This means that B C  AC , i.e., that A contains all B’s claims and at least one additional b-proposition ˙pm . First, suppose that A and B are both true; it follows that ˙pm is true and Vs£ .˙pm / D £=n by the lemma above. By the same lemma, Vs£ .A/ D Vs£ .B/ C Vs£ .˙pm /; moreover, since pm is true, Vs£ .˙pm / > 0. Thus, Vs£ .A/ > Vs£ .B/. Consequently, (Vs1) is satisfied: if A is logically stronger than B and both are true, A is more verisimilar than B. Suppose now that A and B are both false. If ˙pm is true, then A will be more verisimilar than B; however, if ˙pm is false, then A will be less verisimilar (but logically stronger) than B. Thus, (Vs2) is satisfied, since verisimilitude doesn’t covary, among false c-propositions, with logical strength. Finally, to see that (Vs3) is satisfied, consider the measure Vs£ with £ D 1=2, defined on the language L with three atomic propositions p, q and r. Suppose that p, q and r are true and consider the two c-propositions A  p and B  p ^ q ^ :r. Although A is true and B is false, Vs£ .A/ D £=n D 1=6, whereas Vs£ .B/ D £2=n  .1  £/1=n D 1=3. Thus, the false c-proposition B is more verisimilar than the true c-proposition A. Q C  / and contf .A; C  / D contt .A; Q C  /. 6. By definition, contt .A; C  / D contf .A; Q iff, by definition (9), £contt .A; C  /  Consequently, Vs£ .A/ < = D = > Vs£ .A/  .1  £/contf .A; C / < = D = > £contf .A; C  /  .1  £/contt .A; C  /, i.e., since £ > 0, iff contf .A; C  / > = D = < contt .A; C  /.   Proof of Theorem 8. Let us prove the following result: Vs TAC > = D = < Vs .T / iff Vs .AxT / > = D = < 0. The expansion of T by A is TAC D T ^ A by Theorem 4. As observed at the end of Section 5.2.2, since AxT D TxA and TcA D AcT D T by hypothesis (since A is compatible with T ), TAC can be written as T ^ AxT .   Consequently, Vs TAC > = D = < Vs .T / iff Vs .T ^ A/ > = D = < Vs .T /.

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  By Theorem 1, Vs£ .T ^ A/ D Vs£ .T / C Vs£ .AxT /. Hence, Vs TAC > = D = < Vs .T / iff Vs .AxT / > = D = < 0.   Proof of Theorem 9. Let us prove the following result: Vs TA > = D = < Vs .T / iff Vs .AxT / > = D = < Vs .AQcT /Vs .AcT /. The revision of T by A is TA D A^TxA by Theorem 5. Recalling from Section 5.2.2 that A D ArT ^ AcT ^ AxT , we have that TA D ArT ^ AcT ^ AxT ^ TxA . Since A is incompatible with T by hypothesis,   i.e., AcT is not empty, T may be expressed as ArT ^ AQcT ^ TxA . Thus, Vs TA > = D = < Vs .T / iff Vs .ArT ^ AcT ^ AxT ^ TxA / > = D = < Vs .ArT ^ AQcT ^ TxA / iff (by Theorem 1) Vs .AcT / C Vs .AxT / > = D = < Vs .AQcT /, i.e., iff Vs .AxT / > = D = < Vs .AQcT /  Vs .AcT /. Proof of Theorem 10. 1. If A is true, AxT is also true (a fortiori) and Vs£ .AxT / is verisimilar by Theorem 1. Thus, Vs TAC > Vs .T / by Theorem 8. 2. If A is true, both AcT and AxT are true (a fortiori). Thus, Vs£ .AxT / > 0 and Vs£ .AcT / > 0 by Theorem 1. We want to prove, according to Theorem 8, that Vs .AxT / > Vs .AQcT /  Vs .AcT /; to this purpose, it is then sufficient to prove that Vs .AQcT /  Vs .AcT /  0, i.e., Vs .AQcT /  Vs .AcT /. By Theorem 1.7, this holds iff contt .AcT ; C  /  contf .AcT ; C  /. To see that this is in fact the case, note that, since AcT is true,cont t .A; C  / > 0 and contf .A; C  / D 0. Consequently, by Theorem 8, Vs TA > Vs .T /. Proof of Theorem 11. 1. Note that since A is compatible with T by hypothesis, the only non-redundant part of A w.r.t. T is AxT . If AxT is verisimilar, then Vs£ .AxT / > 0 by definition and Vs TAC > Vs .T / by Theorem 8. 2. If AcT and AxT are verisimilar, then Vs£ .AcT / > 0 by definition. In order to prove that Vs .AxT / > Vs .AQcT /  Vs .AcT /, it is then sufficient to prove (see the proof of Theorem 10) that contt .AcT ; C  /  contf .AcT ; C  /. To see that this is in fact the case, note that, since Vs£ .AcT / > 0; £contt .AcT ; C  /  .1  £/contf .AcT ; C  / > 0. Consequently, contt .AcT ; C  / > .1  £/= £contf .AcT ; C  /. Since .1  £/=£  1, it follows that contt .AcT ; C  /  contf .AcT ; C  /. It follows from this that Vs .AcT /  Vs .AQcT /, i.e., Q Vs .AQcT /  Vs .AcT /  0, and thus  that Vs .AxT / > Vs .AcT /  Vs .AcT /. Consequently, by Theorem 8, Vs TA > Vs .T /. Proof of Theorem 12. 1. If A is completely false, AxT is also completely false (a fortiori) and Vs£ .AxT / < 0 by Theorem 1. Thus, Vs TAC < Vs .T / by the proof of Theorem 8. 2. If A is completely false, both AcT and AxT are completely false (a fortiori). Thus, Vs£ .AxT / < 0 and Vs£ .AcT / < 0 by Theorem 1. As observed above (see the proof of Theorem 8), to prove that Vs .AxT / < Vs .AQcT /  Vs .AcT / it is sufficient to prove that contt .AcT ; C  /  contf .AcT ; C  /. To see that this is in fact the case, note that, since AcT is completely false, contt .AcT ; C  / D  0 and contf .AcT ; C  / > 0. Consequently, by the proof of Theorem 8, Vs TA < Vs .T /.

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Proof of Theorem 13. Note that since A is compatible with T by hypothesis, the only non-redundant part  of A w.r.t. T is AxT . If AxT is t-distant, then Vs£ .AxT / < 0 by definition and Vs TAC < Vs .T / by Theorem 8. Proof of Theorem 14. Consider the following counterexample to the claim that if  AcT and AxT are t-distant, then Vs TA < Vs .T /. Let p1 ; : : : ; p6 be true atomic propositions of L and let be T  :p1 ^ :p2 ^ :p3 ^ p4 ^ p5 a false theory. Let consider the (false) additive input A  p1 ^ p2 ^ p3 ^ :p4 ^ :p5 ^ :p6 ; the conflicting part of A w.r.t. T is AcT D p1 ^ p2 ^ p3 ^ :p4 ^ :p5 and the extra part of A w.r.t. T is AxT D :p6. The revision of T by A will be, by Theorem 5, TA D p1 ^p2 ^p3 ^:p4 ^:p5 ^:p6 . Now consider a verisimilitude measure Vs£ defined on L with £ D 1=3. It is easy to calculate that Vs£ .T / D 4=3n. Moreover, Vs£ .AcT / D 1=3n and Vs£ .AxT / D  2=3n, i.e., both AcT and AxT are t-distant. This notwithstanding, since Vs TA D 1=n; TA is more verisimilar than T .

References Alchourr´on C, G¨ardenfors P, Makinson D (1985) On the logic of theory change: partial meet contraction and revision functions. J Symbol Logic 50:510–530 Cevolani G, Festa R (2009) Scientific change, belief dynamics and truth approximation. La Nuova Critica 51–52:27–59 Cevolani G, Crupi V, Festa R (2009) The whole truth about Linda: probability, verisimilitude and a paradox of conjunction. In: D’Agostino M, Sinigaglia C (eds) Selected papers from the SILFS07 Conference, College Publications, London, forthcoming Cevolani G, Crupi V, Festa R (forthcoming) Verisimilitude and belief change for conjunctive theories Festa R (2007a) The qualitative and statistical verisimilitude of qualitative theories. La Nuova Critica 47–48:91–114 Festa R (2007b) Verisimilitude, cross classification, and prediction logic. Approaching the statistical truth by falsified qualitative theories. Mind Soc 6:37–62 Festa R (2007c) Verisimilitude, qualitative theories, and statistical inferences. In: Pihlstr¨om S, Sintonen M, Raatikainen P (eds) Approaching truth: essays in honour of Ilkka Niiniluoto. College Publications, London, pp 143–177 G¨ardenfors P (1988) Knowledge in flux: modeling the dynamics of epistemic states. MIT Press/Bradford Book, Cambridge, MA G¨ardenfors P, Makinson D (1988) Revisions of knowledge systems using epistemic entrenchment. In: Vardi MY (ed) Proceedings of the second conference on theoretical aspects of reasoning about knowledge. Morgan Kaufmann, Los Altos, CA, pp 83–95 Grove A (1988) Two modelling for theory change. J Philos Logic 17:157–170 Hansson SO (1999) A textbook of belief dynamics: theory change and database updating. Kluwer, Dordrecht Kuipers TAF (1982) Approaching descriptive and theoretical truth. Erkenntnis 18:343–378 Miller D (1974) Popper’s qualitative theory of verisimilitude. Br J Philos Sci 25:166–177 Niiniluoto I (1987) Truthlikeness. Reidel, Dordrecht Niiniluoto I (1998) Verisimilitude: the third period. Br J Philos Sci 49:1–29 Niiniluoto I (1999) Belief revision and truth likeness. In: Hansson B, Halld´en S, Sahlin N-E, Rabinowicz W (eds) Internet Festschrift for Peter G¨ardenfors. URL http://www.lucs.lu.se/ spinning/

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Oddie G (1986) Likeness to truth. Reidel, Dordrecht Popper KR (1963) Conjectures and refutations: the growth of scientific knowledge. Routledge & Kegan Paul, London Popper KR (1972) Objective knowledge. Clarendon, Oxford Rott H (2000) Two dogmas of belief revision. J Philos 97:503–522 Tich´y P (1974) On Popper’s definitions of verisimilitude. Br J Philos Sci 25:155–160

Chapter 6

Can Graphical Causal Inference Be Extended to Nonlinear Settings? An Assessment of Conditional Independence Tests Nadine Chlaß and Alessio Moneta

6.1 Introduction Graphical models are a powerful tool for causal model specification. Besides allowing for a hierarchical representation of variable interactions, they do not require any a priori specification of the functional dependence between variables. The construction of such graphs hence often relies on the mere testing of whether or not model variables are marginally or conditionally independent. The identification of causal relationships then solely requires some general assumptions on the relation between stochastic and causal independence, such as the Causal Markov Condition and the Faithfulness Condition (Spirtes et al. 2000; Pearl 2000). However, a procedure would require further assumptions to hold. Namely those the independence tests themselves are based on. In continuous settings, Spirtes et al. (2000) suggest causal inference based on a very restrictive formulation of independence, that is, vanishing partial correlations. Such a measure does, however, limit the applicability of causal inference to linear systems. This constitutes a serious drawback especially for the social sciences where an a priori specification of the functional form proves difficult or at odds with linearity. In short: graphical models theoretically reduce specification uncertainty regarding functional dependence, but their implementation in practice deprives them of this virtue. In this paper we investigate how causal structures in continuous settings can be identified when both functional forms and probability distributions of the variables remain unspecified. We focus on tests exploiting the fact that if X and Y are conditionally independent given a set of variables Z, the two conditional densities f .X jY; Z/ and f .X jZ/ must coincide. We start by estimating the conditional densities f .X jY; Z/ and f .X jZ/ via nonparametric techniques (kernel methods). We proceed by testing if some metric expressing the distance between these very conditional densities is sufficiently close to zero. Out of several metrics available in the

N. Chlaß and A. Moneta () Max Planck Institute of Economics, Jena, Germany e-mail: [email protected]; [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 6, c Springer Science+Business Media B.V. 2010 

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literature to express such distance we choose two, the Euclidean, and the Hellinger distance. We investigate in a Monte Carlo study how different tests involving either measure are able to detect statistical independence, conditioned on a small set of variables. One limitation may result from nonparametric density estimation being subject to the curse of dimensionality. As the number of variables increases, the estimated empirical density converges at a slower rate to its population value. To compensate this drawback we use a local bootstrap procedure which consists of resampling the data for each test. While local bootstrap strongly increases the computational time of the test, it succeeds in counterbalancing the curse of dimensionality. Section 6.2 presents the statistical methods used in detail. Section 6.3 describes the simulation design and our results. Section 6.4 concludes.

6.2 Nonparametric Tests for Conditional Independence We want to test the following null hypothesis: X is independent of Y given Z, that is X? ? Y j Z;

(6.1)

where X and Y are continuous random variables, and Z is a (possibly empty) vector of d continuous random variables .Z1 ; : : : ; Zd /. We observe n random realizations .Xt ; Yt ; Zt /; t D 1; : : : ; n. Note that Fisher’s z statistic proposed by Spirtes et al. (2000: 94) to test conditional independence relations in continuous settings, and also incorporated in Tetrad (Scheines et al. 1996), requires normality of the joint probability distribution f .X; Y; Z/. The latter is guaranteed by the linearity assumption if the error terms are also normal. We propose a class of tests based on the estimation and comparison of the following two multivariate distribution h1 ./ and h2 ./: h1 .X; Y; Z/  f .X; Y; Z/f .Z/ h2 .X; Y; Z/  f .X; Z/f .Y; Z/:

(6.2)

This type of tests exploits the fact that under the null hypothesis: f .X jY; Z/ D f .X jZ/; whenever f .Y; Z/ and f .Z/ > 0. Hence, by definition of a conditional density function: f .X; Z/ f .X; Y; Z/ D : f .Y; Z/ f .Z/ It follows that under the null hypothesis: h1 ./ D h2 ./:

(6.3)

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Can Graphical Causal Inference Be Extended to Nonlinear Settings?

65

We estimate h1 and h2 using a kernel smoothing approach (see Wand and Jones 1995: Chapter 4). Both h1 and h2 are of length m D d C 2. In particular, we use the so-called product kernel estimators: hO 1 .x; y; zI b/ 1 D 2 mCd N b hO 2 .x; y; zI b/ 1 D N 2 b mCd

(

n X

 K

i D1

(

n X i D1

 K

Xi  x b

Xi  x b



 K



Yi  y b 

KZ



Zi  z b

 K

Zi  z b

) ( X n i D1

) ( X n

Kp

Zi  z b





i D1

 K



Yi  y b

Kp

)

Zi  z b

) ; (6.4)

where K denotes the kernel function, b indicates a scalar bandwidth parameter, and Q Kp represents a product kernel, i.e., Kp ..Zi z/=b/ D djD1 K..Zji zj /=b/. For our simulations (see next section) we choose the kernel: K.u/ D .3  u2 /.u/=2, with .u/ the standard normal probability density function. We use a “rule-ofthumb” bandwidth: b D n1=8:5 . Having obtained h1 and h2 , we test the null hypothesis (6.1) by verifying whether hO 1 ./ and hO 2 ./ are sufficiently similar. There are several ways to measure distance between two products of estimated density functions (see Su and White 2008). Here, we focus on the following ones: (i) Weighted Hellinger distance proposed by Su and White (2008). In this case the distance is: dH

s ( )2 n h2 .Xt ; Yt ; Zt / 1X 1 D a.Xt ; Yt ; Zt /; n t D1 h1 .Xt ; Yt ; Zt /

(6.5)

where a./ is a nonnegative weighting function. The weighting function a./, as well as the resulting test statistics are specified in Su and White (2008). (ii) Euclidean distance as proposed by Szekely and Rizzo (2004) in their “energy test.” In this case, we have: 1 XX 1 XX 1 XX jjh1i h2j jj jjh1i h1j jj jjh2i h2j jj; n 2n 2n n

dE D

n

i D1 j D1

n

n

i D1 j D1

n

n

i D1 j D1

(6.6) where h1i D h1 .Xi ; Yi ; Zi /; h2i D h2 .Xi ; Yi ; Zi /, and jj  jj is the Euclidean norm. (iii) Euclidean distance as proposed by Baringhaus and Franz (2004) in their “Cramer test.” There is no substantial difference with (ii) in the distance proposed, which is dE =2. There is only some difference in the method to obtain the critical values (see Baringhaus and Franz 2004).

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When Z is empty we obtain p values using (ii) and (iii) as implemented in the R packages energy and cramer respectively. The Hellinger distance test cannot be used in this case, since it has been designed for Z non-empty. When Z is non-empty we obtain p-values for (i), (ii), and (iii) using a local bootstrap procedure, as described in Su and White (2008: 840, 841) and Paparoditis and Politis (2000: 144, 145). Local bootstrap imposes the null hypothesis in the resampling scheme and counts how many times the bootstrap statistic is larger than the statistic calculated on the basis of the real data. More specifically, local bootstrap proceeds as follows: (1) Draw a bootstrap sampling Zt (for t D 1; : : : ; n) P from the estimated kernel density fO.z/ D n1 b d ntD1 Kp ..Zt  z/=b/. (2) For t D 1; : : : ; n, given Zt , draw Xt and Yt independently from the estimated kernel density fO.xjZt / and fO.yjZt / respectively. These functions are defined as follows: 

Pn

sD1 K

fO.xjZt / D

b

sD1 K

b



Pn

Ys y b



Kp 

rD1 Kp



Pn fO.yjZt / D

Pn

Xs x b

Zr Zt b



rD1 Kp

Zs Zt b

 Kp 



Zs Zt b

Zr Zt b







(3) Using Xt ; Yt , and Zt compute the bootstrap statistic Sn using one of the distances defined above. (4) Repeat steps (1) and (2) I times to obtain I statistics ˚  I Sni i D1 . (5) The p-value is then obtained by: PI p

 i D1 1fSni

I

> Sn g

;

where Sn is the statistic obtained from the original data using one of the distances defined above, and 1fg denotes an indicator function taking value one if the expression between brackets is true and zero otherwise.

6.3 Monte Carlo Study 6.3.1 Simulation Design To compare the aforementioned test procedures we assess their performance in both size and power. To identify size properties, the hypothesis H0 of independence or conditional independence must hold everywhere. Data generating processes (DGPs) for which H0 is true are named size-DGPs. The null hypothesis .H0 W X ? ? Y jZ/ may apply for three reasons. Either (i) there is no connection at all between X

6

Can Graphical Causal Inference Be Extended to Nonlinear Settings?

Fig. 6.1 DAG 1

Fig. 6.2 DAG 2

V1

V2

67 V3

V4

V1,(t−1)

V2,(t−1)

V3,(t−1)

V1,t

V2,t

V3,t

and Y , or (ii) there exists a causal relation between X and Y but only via a set of variables Z, or still (iii) Z constitutes a common cause for X and Y in absence of any other connection besides (ii). In these latter two cases Z is said to screen off X from Y (Reichenbach 1956). To illustrate, let us represent the DGP via a Directed Acyclic Graph (DAG).1 In absence of any causal relation between X and Y the corresponding DAG does not contain any edge or path between X and Y . In case of screening-off, there is a path connecting X and Y via variables Z. Take, for instance, the DAG represented in Fig. 6.1. Here, V2 screens off (or d-separates) V1 from V3 such that V1 ? ? V3 jV2 . Analogously, V2 ? ? V4 jV3 and V1 ? ? V4 jV2 ; V3 . While for size DGPs H0 W X ? ? Y jZ holds everywhere, Z may obviously form causal relations with X and/or Y . These causal relations may take on different functional forms and represent the touchstone for the testing procedures emphasized in this work. To systematically vary nonlinearity and its impact we characterize the causal relation between, say, z1 and y, in a polynomial form, i.e., via y D f .z1 /Ce, Pp j where f D j D0 bj z1 . Herein j would reflect the degree of nonlinearity while bj would capture the impact nonlinearity exerts. For polynomials of any degree only bp ¤ 0. An additive error term e completes the specification. In case of p D 1 we also examine the impact of an error entering the causal relation in a multiplicative manner, i.e., y D b1 z1  e. Besides varying the functional form we distinguish an i.i.d. and a time-series case. The latter proves interesting since kernel smoothers generally show notoriously little sensitivity to i.i.d. violations (Welsh et al. 2002). Hence, the alternative procedures put forth before may not be subject to the usual overrejection of H0 entailed by non-i.i.d. structures (Chlaß and Kr¨uger 2007). For the i.i.d. case, realizations fXt ; Yt ; Zt gntD1 are generated from a (serially) independent and identical distribution, i.e., corr.Xt ; Xs / D 0 for s ¤ t. For the time-series case, each element of fXt ; Yt ; Zt gntD1 follows an AR(1) process with coefficient a1 D 0:5 and error term et N.0; 1/, i.e., Xt D a1 Xt 1 C eX;t . For an illustration, take the DAG dis? V2;t jV1;.t 1/ , played in Fig. 6.2 representing such a time series case. Here, V1;t ? since V1;.t 1/ d -separates V1;t from V2;t , while V2;t ? ? V3;s , for any t and s. Within the i.i.d. and AR(1) scenarios we vary the number of variables that may establish conditional independence between Xt and Yt . Either zero, one, but

1

For definition and properties of DAGs see Spirtes et al. (2000: Chapter 2).

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Table 6.1 Simulated cases for size properties No causal relations #Z D 0 #Z D 1 #Z D 2

S0.1 S1.1 S2.1

#Z D 0 #Z D 1 #Z D 2 Note:  Non-additive errors.

S0.2 S1.6 S2.6

fX; Y; Zg  i.i.d.

fX; Y; Zg  AR.1/

Causal relations with screening-off pD1 pD2 pD3 S1.2 S1.5 S2.2 S2.5

S1.3 S2.3

S1.4 S2.4

S1.7 S2.7

Table 6.2 Simulated cases for power properties pD1

pD2

pD3

fX; Y; Zg  i.i.d.

#Z D 0 #Z D 1 #Z D 2

P0.11 P0.22 P0.7 P1.1 P1.4 P2.1 P2.5

P0.31 P0.42 P1.2 P1.5 P2.2 P2.3

P0.51 P0.62 P1.3 P2.4

#Z D 0 #Z D 1 #Z D 2

P1.8

fX; Y; Zg  AR.1/

P1.9 P1.6 P2.6

Note:  Non-additive errors; 1 bp D 0:4, 2 bp D 0:8.

maximally two variables may form the set Z D fZ1 ; : : : ; Zd g of conditioned variables; hence Z has cardinality #Z D f0; 1; 2g. Table 6.1 reviews all cases for which size properties are investigated. Power properties of the tests proposed were assessed using DGPs such that H0 does not hold anywhere, i.e., X ? ? = Y jZ. The latter is guaranteed by either (i) a direct path between X and Y which does not include Z, (ii) a common cause for X and Y which is not an element of Z or (iii) a “collider” between X and Y belonging to Z.2 As before, we vary the functional form f of these causal paths polynomially. In a very stylized manner we design three further phenomena that often arise jointly with nonlinearity. First, we investigate the impact of a non-additive, i.e., multiplicative error term when bj Dp D 0:5 and p D 1. Second, we relinquish the i.i.d. assumption as before and induce Xt and Yt as two time series of the aforementioned AR(1)structure. Xt now furthermore depends on Yt while the functional, i.e., polynomial form of this dependence writes either fbj ¤1 D 0; b1 D 0:5; p D 1g or fbj ¤2 D 0; b2 D 0:5; p D 2g. Third, we investigate different cardinalities #Z D f0; 1; 2g of the set of variables that establishes conditional independence between Xt and Yt . The latter is done to challenge nonparametric procedures in higher dimensional settings where they are known to weakly perform.3 Table 6.2 reviews all cases for which size properties are investigated.

2

An example for a collider is displayed in Fig. 6.2: V2;t forms a collider between V1;.t1/ and ? = V2;.t1/ jV2;t although V1;.t1/ ? ? V2;.t1/ . V2;.t1/ . In this case V1;.t1/ ? 3 For an introduction to the so-called curse of dimensionality see, e.g., Yatchew (2003, p. 676).

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6.4 Results Table 6.3 reports our simulation results for the case where Z is empty .#Z D 0/. Hence, Y and X are marginally independent. Rejection frequencies are reported for three different tests, both at the 0.05 and 0.1 level of significance. Take the first line depicting the case S0.1. Here, X and Y were generated 1,000 times from two independent white noise processes. We find a proportion of rejections that is 0.048 at the 0.05 confidence level and 0.096 at the 0.1 confidence level. In other words, for 48 simulation runs out of 1,000 the p-value was greater than 0.05 and for 96 simulation runs out of 1,000 the p-value was greater than 0.1. The Energy test behaves quite well for all cases, since it tends not to reject H0 when it holds (size DGPs) and it tends to reject H0 when it is violated (power DGPs). Only when X linearly depends upon Y with a low coefficient (case P0.1), the rejection frequency is not as high as in the other cases. The Cramer test does not produce correct results for: P0.1, P0.3, P0.5, P0.8, P0.9. Let us compare these two nonparametric tests with the Fisher test proposed by Spirtes et al. (2000). We find this test to perform well in some nonlinear cases (P0.2, P0.5, P0.6). However, the percentage of rejection is too high for independent time series (S0.2) and too low for several forms of nonlinear dependence (P0.3, P0.4, P0.7, P0.9). To summarize the case without conditioned variables, the Energy test outperforms both the Cramer and the Fisher test. Results for the one-conditioned-variable case (Z consisting of one variable) are reported in Table 6.4. Here, for each simulated realization of the process, we apply the local bootstrap procedure described in Section 6.2. To save computation time, we lower the number of iteration to 200. We assess the nonparametric tests described in Section 6.2 and compare them with the parametric Fisher’s z. The label “Euclid” comprises Energy and Cramer tests based on the Euclidean distance

Table 6.3 Proportion of rejection of H0 (no conditioned variables) Energy Cramer Fisher Energy Level of significance 5% Size DGPs S0.1 (ind. white noises) S0.2 (ind. time series)

0:048 0:065

0:000 0:000

Cramer

Fisher

Level of significance 10%

0:046 0:151

0:096 0:122

0:000 0:000

0:096 0:213

Power DGPs P0.1 (linear, coefficient D 0:4) 0:675 0:024 0:972 P0.2 (linear, coefficient D 0:8) 0:999 0:663 1 P0.3 (quadratic, coef: D 0:4) 0:855 0:023 0:165 P0.4 (quadratic, coef: D 0:8) 0:999 0:598 0:282 P0.5 (cubic, coefficient D 0:4) 0:865 0:025 1 P0.6 (cubic, coefficient D 0:8) 1 0:605 1 P0.7 (non-additive, coef: D 0:5) 1 0:969 0:279 P0.8 (time series linear) 0:959 0:308 0:999 P0.9 (time series non-linear) 0:986 0:255 0:432 Note: Length series .n/ D 100; number of iterations D 1,000.

0:781 1 0:897 1 0:915 1 1 0:981 0:997

0:047 0:821 0:093 0:790 0:105 0:805 0:996 0:462 0:452

0:988 1 0:240 0:383 1 1 0:376 1 0:521

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Table 6.4 Proportion of rejection of H0 (one conditioned variable) Hellinger Euclid Fisher Hellinger Size DGPs S1.1 (ind. white noises) S1.2 (linear) S1.3 (quadratic) S1.4 (cubic) S1.5 (non-additive) S1.6 (time series) S1.7 (time series nonlinear)

Euclid

Fisher

Level of significance 5%

Level of significance 10%

0.035 0.030 0.015 0.000 0.005 0.035 0.040

0.070 0.050 0.015 0.000 0.020 0.090 0.065

0.035 0.025 0.005 0.000 0.545 0.035 0.020

0.053 0.050 0.220 0.375 0.221 0.062 0.048

0.085 0.055 0.005 0.000 0.600 0.060 0.035

Power DGPs P1.1 (linear) 0.735 0.745 0.997 0.825 0.820 P1.2 (quadratic) 0.865 0.870 0.187 0.925 0.925 P1.3 (cubic) 0.995 1 1 1 1 P1.4 (non-additive) 1 1 0.260 1 1 P1.5 (quadratic) 0.965 0.975 0.204 0.995 0.990 P1.6 (time series nonlinear) 0.905 0.895 0.416 0.940 0.950 Note: n D 100; number of iterations D 200; number of bootstrap iterations .I/ D 200.

0.100 0.099 0.315 0.436 0.313 0.103 0.104 1 0.278 1 0.352 0.285 0.504

formulated in equation 6.6. P -values for the Hellinger and Energy/Cramer tests are obtained using the local bootstrap procedure described in Section 6.2 with I D 200. The upper part of the table refers to size DGPs for which the hypothesis of condi? Y jZ/ always holds. For instance, when X, Y, and tional independence .H0 W X ? Z follow independent white noise processes, H0 W X ? ? Y jZ is rejected in 3.5% of all simulation runs using the Hellinger test (same result for the Energy/Cramer test) at the 0.05 level of significance and rejected in 7% of all runs at the 0.1 level of significance. That is, the p-value obtained for this case is greater than 0.05 in 3.5% of all simulations and greater than 0.1 for 7% of the simulations. Our results show that the Hellinger distance test (supported by the local bootstrap) performs quite well in all cases, except for the case of linear dependence. Therein, the frequency of rejection is satisfactory while not as high the one for the Fisher test. Such a result was to be expected since the linear case satisfies the assumptions required by the Fisher test. Both Energy and Cramer test (labeled “Euclid” in the table) perform quite similarly to the Hellinger test. In some cases they even slightly outperform the Hellinger test with somewhat lower rejection frequencies for size DGPs S1.2 and S1.7 and relatively higher rejection frequencies in many power DGPs (P1.1, P1.2, P1.3, P1.5). However, neither Energy nor Cramer test detect conditional independence in case of non-additive errors (S1.5). The results also confirm that we are led astray when applying the Fisher test in presence of nonlinear dependencies. In many of these cases (P1.2, P1.4, P1.5, P1.6) the power of the test turns out unsatisfactory. A better strategy proves to apply the Hellinger or, in case of additive errors, the Energy/Cramer test. Table 6.5 finally displays our results for the case of two conditioned variables .#Z D 2/. As previously, columns “Hellinger”, “Euclid”, and “Fisher” refer to the

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Table 6.5 Proportion of rejection of H0 (two conditioned variables) Hellinger Euclid Fisher Hellinger Size DGPs S2.1 (independent white noises) S2.2 (linear) S2.3 (quadratic) S2.4 (cubic) S2.5 (non-additive) S2.6 (time series linear) S2.7 (time series non-linear)

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Euclid

Fisher

Level of significance 5%

Level of significance 10%

0.040 0.000 0.000 0.000 0.960 0.006 0.000

0.060 0.000 0.000 0.007 0.993 0.033 0.000

0.070 0.007 0.000 0.000 0.253 0.020 0.010

0.059 0.056 0.336 0.028 0.190 0.050 0.035

0.100 0.047 0.000 0.000 0.340 0.046 0.040

Power DGPs P2.1 (linear) 1 1 1 1 1 P2.2 (quadratic) 1 1 1 1 1 P2.3 (quadratic) 0.273 0.573 1 0.320 0.673 P2.4 (cubic) 1 1 0.999 1 1 P2.5 (non-additive) 1 1 0.246 1 1 P2.6 (time series non-linear) 0.170 0.960 0.338 0.250 0.980 Note: n D 100; number of iterations D 150; number of bootstrap iterations .I/ D 100.

0.109 0.108 0.434 0.068 0.268 0.102 0.087 1 1 1 1 0.336 0.411

Hellinger distance test, the Energy/Cramer test, and the Fisher’s z test respectively. The Hellinger and Energy/Cramer tests here are based on four dimensional density functions. To save computational time, we lower the number of test iterations to 150 and the number of bootstrap iterations (I ) to 100. All nonparametric tests perform well except for some cases. The Hellinger distance test fails in presence of nonadditive-errors (S2.5), quadratic dependencies (P2.3) and time series (P2.6). The Energy/Cramer test rejects somewhat less often in the S2.5 case, though still too frequently. Moreover, the power of the Energy/Cramer test outperforms the Hellinger test in the quadratic (P2.3) and time series case (P2.6). Fisher’s z test does not produce satisfactory results for: S2.3, S2.5, P2.5, P2.6. To sum up, in absence of any information about the functional form, using the Energy/Cramer test proves the better strategy.

6.5 Concluding Remarks We have assessed the performance of conditional independence tests to be used for graphical causal inference in continuous settings. Hitherto, the latter was based on parametric formulations of conditional independence, i.e., vanishing partial correlations. Such measures do, however, prove restrictive since they require linearity in the underlying dependencies and normally distributed errors. Here, we stress and compare nonparametric procedures operating on the distances between conditional kernel densities and on a local bootstrap. On one hand, our findings show these tests to reach a performance comparable to Fisher’s z given linearity and normal

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errors. On the other hand, parametric tests perform very poorly given nonlinear data generating processes whereas nonparametric procedures still yield correct results. In continuous settings graphical causal inference hence cannot generally be based on the independence tests used so far. Their results lead astray when the functional form is not known and/or likely to be nonlinear. Any constraint-based causal discovery method, (Spirtes et al. 2000; Pearl 2000; Moneta 2008), can be applied on the basis of the tests proposed in this paper.

References Baringhaus L, Franz C (2004) On a new multivariate two-sample test. J Multivariate Anal 88(1):190–206 Chlaß N, Kr¨uger J (2007) The Wilcoxon signed rank test with discontinuous and dependent observations. Jena Econ Res Pap 032 Moneta A (2008) Graphical causal models and VARs: An assessment of the real business cycles hypothesis. Empirical Econ 35(2):275–300 Paparoditis E, Politis DN (2000) The local bootstrap for Kernel estimators under general dependence conditions. Ann Inst Statist Math 52:139–159 Pearl J (2000) Causality. Models, reasoning, and inference. Cambridge University Press, Cambridge Reichenbach H (1956) The direction of time. University of California Press, Berkeley Scheines R, Spirtes P, Glymour C, Meek C, Richardson T (1996) Tetrad III, tools for causal modeling. Erlbaum, New York Spirtes P, Glymour C, Scheines R (2000) Causation, prediction, and search. MIT Press, Cambridge Su L, White H (2008) A nonparametric Hellinger metric test for conditional independence. Economet Theor 24:829–864 Szekely GJ, Rizzo ML (2004) Testing for equal distributions in high dimension. InterStat November (5) Wand MP, Jones MC (1995) Kernel smoothing. Chapman and Hall, London Welsh AH, Lin X, Carroll RJ (2002) Marginal longitudinal nonparametric regression: Locality and efficiency of spline and Kernel methods. J Am Statis Assoc 97(458):482–492 Yatchew A (2003) Semiparametric regression for the applied econometrician. Cambridge University Press, Cambridge

Chapter 7

Towards a Grammar of Bayesian Confirmation Vincenzo Crupi, Roberto Festa, and Carlo Buttasi

7.1 Introduction A long standing tradition in epistemology and the philosophy of science sees the notion of confirmation as a fundamental relationship between a piece of evidence E and a hypothesis H. A number of philosophical accounts of confirmation, moreover, have been cast or at least could be cast in terms of a formally defined model c.H; E/ involving evidence and hypothesis.1 Ideally, a full-fledged and satisfactory confirmation model c.H; E/ would meet a series of desiderata, including the following: (1) c.H; E/ should be grounded on some simple and intuitively appealing “core intuition”; (2) c.H; E/ should exhibit a set of properties which formally express sound intuitions; (3) it should be possible to specify the role and relevance of c.H; E/ in science as well as in other forms of inquiry. In what follows we will focus on accounts of confirmation arising from the Bayesian framework and we will mainly address issues (1) and (2). Bayesianism arguably is a major theoretical perspective in contemporary discussions of reasoning in science as well as in other domains (Bovens and Hartmann 2003; Howson and Urbach 2006; Oaksford and Chater 2007). As we will see, the Bayesian approach to confirmation includes traditional and well-known proposals along with novel and more recent variants. Despite all this, the exploration of points (1) and (2) still seems

V. Crupi () Department of Philosophy, University of Turin, via Sant’Ottavio 20, 10124 Turin (Italy), e-mail: [email protected] R. Festa and C. Buttasi Department of Philosophy, University of Trieste, Trieste, Italy  Research supported by a grant from the Spanish Department of Science and Innovation (FFI2008-01169/FISO). 1 It should be kept in mind that this relationship is strictly speaking a three-place one, involving a given background of knowledge and assumptions, often denote as K. Such a term will be omitted from our notation for simple reasons of convenience, as it is unconsequential for our discussion.

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 7, c Springer Science+Business Media B.V. 2010 

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to lag behind a fully satisfactory level of detail and completeness. In trying to contribute to a more systematic treatment, we hope to provide some useful conceptual material to effectively tackle issue (3), ultimately bridging philosophical accounts of confirmation back to practice.

7.2 How to Price a Horse: Intuitions Concerning Distance In the 20s of the seventeenth century, Galileo Galilei was consulted by some Florentine gentlemen engaged in a “learned conversation” on the following question: a horse is really worth a hundred crowns, one person estimated it at ten crowns and another at a thousand; which of the two made the more extravagant estimate? A priest named Tolomeo Nozzolini had argued that the higher estimate was more mistaken, since “the excess of a thousand above a hundred is greater than that of a hundred above ten”. In disagreement with that, Galilei submitted that the two estimates were equally extravagant, “because the ratio of a thousand to a hundred is the same as the ratio of a hundred to ten” (see Todhunter 1865, p. 5). The Nozzolini-Galilei controversy reveals different intuitions about the correct way to measure error and, more generally, the distance between quantitative values. In Bayesian confirmation theory, evidence E is seen as possibly increasing or decreasing the initial probability of a hypothesis of concern H . As applied to the departure of the final from the initial probability, Nozzolini’s and Galilei’s diverging notions of “distance” seem to lie behind two of the most widely known Bayesian measures of confirmation, i.e., the so-called probability difference and probability ratio measures (first proposed by Carnap (1950/1962), and Keynes (1921), respectively): cd .H; E/ D p.H jE/  p.H / cr .H; E/ D p.H jE/=p.H / Indeed, a very similar debate involving diverging intuitions has occurred concerning precisely cd .H; E/ and cr .H; E/. Sober (1994) has argued that the probability ratio measure of confirmation conflicts with clear presystematic judgments by means of numerical examples such as the following. Suppose that on one hand p.H1 / D :1 and p.H1 jE1 / D :9, whereas on the other hand p.H2 / D :0001 and p.H2 jE2 / D :001. Then it can be computed that cr .H1 ; E1 / D 9 < 10 D cr .H2 ; E2 /. However, Sober claims, “surely a jump from .1 to .9 reflects a larger change in plausibility than a jump from .0001 to .001”, contrary to what cr .H; E/ implies (Sober 1994, 228). It should be noticed that, as Festa (1999) has pointed out, complaints can be construed which go in exactly the opposite direction. For now suppose that p.H1 / D :000001 and p.H1 jE1 / D :1, whereas p.H2 / D :7 and p.H2 jE2 / D :8. This time, the ratio measure cr .H; E/, in contrast to the difference measure cd .H; E/, ranks the former jump as larger, reflecting the arguably sound judgment that “the initial probability increases from a ridiculously small value to a noticeable one” (Festa 1999, p. 66).

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Although based on different ways to conceive distance, the difference and ratio measures above share a common trait. Measures cd .H; E/ and cr .H; E/ are both meant to provide an answer to the question: how far has the probability of H gone from its initial value (as an effect of E)? However, the probability of a hypothesis enjoys the important property of having a clear-cut limiting case, i.e., certainty – either of H being true or of it being false. As a consequence, one can legitimately conceive confirmation in terms of a measure crd .H; E/ of the “relative reduction of the probability distance (difference) from certainty”, in a sense to be explained immediately. The core intuition underlying a crd -measure is the focus on the question: to what extent is the initial probability distance from certainty concerning the truth (falsehood) of H reduced by a confirming (disconfirming) piece of evidence E? Or, in other terms: how much of such a distance is “covered” by the upward (downward) jump from p.H / to p.H jE/? A rather natural way to formalize crd .H; E/ is the following: 8 p.H jE/  p.H / ˆ ˆ ˆ < 1  p.H / crd .H; E/ D ˆ p.H jE/  p.H / ˆ ˆ : p.H /

if p.H jE/  p.H / if p.H jE/ < p.H /

Previous appearances of crd .H; E/ include Rescher (1958, p 87), Shortliffe and Buchanan (1975) and Mura (2006, 2008). Measure crd .H; E/ has also been advocated by Crupi et al. (2007) as enjoying a set of interesting formal properties, on some of which we will return later on. For the time being, we would like to point out that, as far as we can see, crd .H; E/ is the only Bayesian alternative to cd .H; E/ and cr .H; E/ which emerges as a relatively simple way to assess confirmation on the basis of “distances” involving relevant probability values. In probability theory, odds may work as measures of confidence under uncertainty much as probabilities themselves. Both quantities are strictly related in a perfectly well-known fashion: p.X / D o.X /=Œ1 C o.X / and o.X / D p.X /=Œ1  p.X /. Following an illuminating informal remark made by Joyce (2004), one can conveniently illustrate the correspondence between “probability talk” and “odds talk” as simply analogous to the correspondence between “we are two thirds of the way there” and “we have gone twice as far as we have yet to go”. It so happens, thus, that the difference-based and the ratio-based notions of distance can also be applied to odds, thus having the following further pair of Bayesian confirmation measures: cod .H; E/ D o.H jE/  o.H / cor .H; E/ D o.H jE/=o.H / It is then interesting to notice that the odds ratio cor .H; E/ itself – a largely known notion, famously advocated by Good (1950) and others (e.g., Fitelson 2001) – can

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be seen as a distance-based confirmation measure. The odds difference measure cod .H; E/ has also appeared in the literature, if only occasionally (see Festa (1999, p 59), and Joyce (2004).)2

7.3 The Sharp Edges of Incremental Confirmation: Basic Properties An intuitively neat core intuition is a valuable basis, but still represents too feeble a ground to meet the challenges of a satisfactory philosophical account of confirmation. We will now address various details of a proper “grammar” of (Bayesian) confirmation which are often only separately analyzed (if at all). Indeed, Bayesian confirmation theories are typically introduced in a rather cursory way, e.g., by simply pointing to the large class of functions mapping relevant probability values involving H and E onto a number which is positive, null or negative depending on p.H jE/ being higher, equal or lower as compared to p.H /. Other times a different rather informal characterisation can be found, presumably capturing the “incremental” nature of Bayesian confirmation: c.H; E/ is then called an incremental measure of confirmation when increasing with the final probability p.H jE/, and – as it is sometimes added – decreasing with the initial probability p.H /. This sort of approach may well be often pursued for the sake of simplicity and brevity. It is surprising, however, that no complete formal characterisation of Bayesian incremental confirmation seems to be available so far. In what follows, we will provide such a characterisation as grounded in a small number of conditions, thus labelled basic. A few preliminary assumptions and points of notation will be useful. We will say that a statement X is p-normal iff 0 < p.X / < 1 (see Kuipers 2000, p. 48). Also, we will say that hypothesis H and evidence E represent a p-normal pair iff both are pnormal. Further, we will assume that, for any p-normal pair .H; E/; c.H; E/ maps the joint probability distribution p.˙H ^ ˙E/ onto a real number. Importantly, this requires that c.H; E/ be defined for p-normal pairs, but does not forbid it to be defined for non-p-normal pairs as well.3

2

One can define a rather natural odds counterpart of the measure crd .H; E/ of the relative reduction of probability distance (from certainty). (An earlier occurrence of this measure appears in Heckerman (1986).) As shown in Crupi (2008), however, such an odds counterpart turns out to be ordinally equivalent to the simple odds ratio measure cor .H; E/. 3 There are confirmation measures whose behavior is perfectly defined and identical for any p-normal pair while being divergent for non-p-normal ones. To illustrate, consider the measure advocated by Kuipers (2000), i.e., ck .H; E/ D p.EjH /=p.E/. Since for any p-normal pair p.EjH /=p.E/ D p.H jE/=p.H /, in this class of cases ck .H; E/ is identical to the probability ratio measure cr .H; E/ defined above. However, the latter is not defined whenever p.H / D 0. On the contrary, ck .H; E/ may be defined in this case as well, provided that E is p-normal and a value for p.EjH / can be specified. (For more on this point, see the distinction between “inclusive” and “non-inclusive” accounts of confirmation in Kuipers (2000); also see Festa (1999, pp 67–68).)

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It may be useful to consider that a reader who is familiar with standard presentations of Bayesian confirmation theory may already have expectations that certain statements appear as eminently basic conditions. The following is a case in point:

(IFPD) Initial and Final Probability Dependence For any p-normal pair .H; E/; c.H; E/ is a real-valued function of p.H / and p.H jE/ only. Indeed, to the extent that confirmation is thought of as capturing the direction and amount of a change in the probability of hypothesis H as provided by evidence E, (IFPD) should sound very natural. It will be shown shortly, however, that such a principle needs not be assumed as primitive, as it can be promptly derived from a set of conditions which we see as providing a more convenient theoretical basis. In our proposed reconstruction, the first basic condition defining Bayesian incremental confirmation is the following comparative principle concerning the dependence on the final probability of hypotheses:

(FPI) Final Probability Incrementality For any two p-normal pairs .H1 ; E1 / and .H2 ; E2 / such that p.H1 / D p.H2 /; c.H1 ; E1 / > = D = < c.H2 ; E2 / iff p.H1 jE1 / > = D = < p.H2 jE2 /. Condition (FPI) quite simply says that, for any fixed (non-extreme) value of the initial probability of hypotheses, the degree of confirmation is higher for higher values of the final probability, i.e., a strictly increasing function of the latter. The second basic condition is a somewhat parallel comparative principle concerning the dependence of incremental confirmation on the initial probability of hypotheses.

(IPI) Initial Probability Incrementality For any two p-normal pairs .H1 ; E1 / and .H2 ; E2 /: (1) if p.H1 jE1 / D p.H2 jE2 / 2 0; 1Œ, then c.H1 ; E1 / > = D = < c.H2 ; E2 / iff p.H1 / < = D = > p.H2 /; (2) if p.H1 jE1 / D p.H2 jE2 / 2 f0; 1g, then: (i) if p.H1 / < p.H2 /, then c.H1 ; E1 /  c.H2 ; E2 /; (ii) if p.H1 / D p.H2 /, then c.H1 ; E1 / D c.H2 ; E2 /; (iii) if p.H1 / > p.H2 /, then c.H1 ; E1 /  c.H2 ; E2 /. Condition (IPI.1) requires that, for non-extreme values of the final probability of hypotheses, the degree of confirmation is higher for lower values of the initial probability, i.e., a strictly decreasing function of the latter. On the other hand, (IPI.2) weakens the requirement for extreme values of the final probability of hypotheses,

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implying only that the degree of confirmation is a non-increasing function of the initial probability. The latter caveat is suggested by the remark that, for extreme values of the final probability, the concerned evidence allows full certainty about the truth value of the hypothesis at issue. In such cases, one might arguably want the degree of confirmation to depend on this final state of full certainty only, whatever the initial probability. The third basic condition concerns neutrality, i.e., the case in which the evidence at issue does not affect the credibility of the hypothesis of concern:

(EN) Equineutrality For any two p-normal pairs .H1 ; E1 / and .H2 ; E2 / such that p.H1 jE1 / D p.H1 / and p.H2 jE2 / D p.H2 /; c.H1 ; E1 / D c.H2 ; E2 /. Condition (EN) dictates that all p-normal pairs involving probabilistically independent statements should be assigned a unique numerical value. As compared to principles (FPI) and (IPI) above, equineutrality may appear less transparent in its intuitive basis. It can be defended, however, by the crucial role it plays in the derivation of desirable properties to which we will turn shortly. For the time being, let us point out that Theorem 1. The basic conditions (FPI), (IPI) and (EN) are logically independent.4

7.4 Some Derived Properties of Incremental Confirmation As a consequence of the basic properties specified by the three basic conditions above, incremental confirmation measures share several interesting derived properties. Some of them are established by the following principles, which will thus label derived conditions. A first important derived condition is the following, showing how incremental measures naturally discriminate among confirmation, neutrality and disconfirmation:

(QD) Qualitative Discrimination There exist a real number t such that for any p-normal pair .H; E/: (1) c.H; E/ > t iff p.H jE/ > p.H /; (2) c.H; E/ D t iff p.H jE/ D p.H /; (3) c.H; E/ < t iff p.H jE/ < p.H /.

4

The Appendix provides proofs of this as well as all subsequent theorems.

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Principle (QD) states that the fixed quantity t indicating neutrality acts as a threshold separating cases of confirmation from cases of disconfirmation. The precise value of t is largely a matter of convenience, usual choices being either 0 or 1. It is easy to see that: Theorem 2. (QD) follows from the basic conditions (FPI) and (EN). It should be noticed that (QD) is sometimes taken as an appropriate general definition for Bayesian confirmation measures. Strictly speaking, this is quite unsatisfactory though, as we will now see by discussing a number of further derived properties. To begin with, consider once again the following:

(IFPD) Initial and Final Probability Dependence For any p-normal pair .H; E/; c.H; E/ is a real-valued function of p.H / and p.H jE/ only. It can be shown that: Theorem 3. (IFPD) follows from each of the basic conditions (FPI) and (IPI). Thus, the fulfilment of (IFPD) amounts to an important derived property of Bayesian incremental confirmation measures. However, (IFPD) does not follow from (QD). As a matter of fact, it can be proven that: Theorem 4. (QD) and (IFPD) are logically independent. Furthermore, consider the following principle:

(FPI-H) Final Probability Incrementality with Fixed Hypothesis For any two p-normal pairs .H; E1 / and .H; E2 /; c.H; E1 / > = D = < c.H; E2 / iff p.H jE1 / > = D = < p.H jE2 /. According to Eells and Fitelson (2000, p. 670), “it is not an exaggeration to say that most Bayesian confirmation theorists would accept (FPI-H) as a desideratum for Bayesian measures of confirmation”. For one thing, as Eells and Fitelson (2000) also point out, (FPI-H) is crucially involved in classical Bayesian analyses such as the solution of the ravens paradox provided by Horwich (1982, pp 54–63). Yet (FPI-H) itself can not be derived from (QD), as implied by the following demonstrable fact: Theorem 5. (QD) and (FPI-H) are logically independent. On the contrary, our basic conditions for incremental confirmation do yield (FPIH) as specifying a derived property. Indeed, it is very easy to show that: Theorem 6. (FPI-H) follows from basic condition (FPI).

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Once the “fixed hypothesis” version of final probability incrementality is considered, a natural “fixed evidence” counterpart promptly comes to mind, i.e.:

(FPI-E) Final Probability Incrementality with Fixed Evidence For any two p-normal pairs .H1 ; E/ and .H2 ; E/ such that p.H1 / D p.H2 /; c.H1 ; E/ > = D = < c.H2 ; E/ iff p.H1 jE/ > = D = < p.H2 jE/. It is easy to show that this extremely plausible principle is again no more than a straightforward consequence of the basic condition (FPI), thus indicating a further derived property of Bayesian incremental confirmation: Theorem 7. (FPI-E) follows from basic condition (FPI). It should also be pointed out that – much as with (FPI-H) above – the often mentioned condition (QD) is not sufficient to yield (FPI-E), as implied by the following demonstrable fact: Theorem 8. (QD) and (FPI-E) are logically independent. Further important remarks about incremental measures involve the notion of predictive success. We will say that the predictive success of hypothesis H concerning evidence E amounts to the quantity q.H; E/ D p.EjH /=p.E/. It can be shown that (FPI-H) is logically equivalent to the following condition linking confirmation to the predictive success of a given hypothesis:5

(PS) Dependence on Predictive Success For any two p-normal pairs .H; E1 / and .H; E2 /; c.H; E1 / > = D = < c.H; E2 / iff q.H; E1 / > = D = < q.H; E2 /. Theorem 9. (FPI-H) and (PS) are logically equivalent. From (PS), in turn, the following “surprise bonus” principle for successful deductive prediction of hypotheses can be easily derived:6 (SB) Surprise Bonus for Successful Deductive Predictions For any two p-normal pairs .H; E1 / and .H; E2 / such that H jD E1 ; E2 ; c.H; E1 / > = D = < c.H; E2 / iff p.E1 / < = D = > p.E2 /. Theorem 10. (PS) implies (SB).

5 (PS) essentially amounts to a statement that Steel (2007) labels LP1 and identifies as one among two possible renditions of the “likelihood principle”. While departing from his terminological choices, we concur with Steel’s argument that (PS) is a compelling principle for Bayesians. 6 We borrow the term “surprise bonus” from Kuipers (2000, 55).

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(SB) states that hypothesis H is more strongly confirmed by the occurrence of the most surprising (unlikely) among its deductive consequences, a rather widespread principle in the philosophy of science which is often said to reflect a basic tenet of scientific methodology. In order to appreciate the relevance of the foregoing analysis, it should be noticed that confirmation measures have been proposed in the literature which, although broadly consistent with the Bayesian framework, notably lack some of the basic and derived properties of incremental confirmation. As an illustration, consider the following well-known measure, proposed by Nozick (1981, 252): cn .H; E/ D p.EjH /  p.Ej:H / It can be easily shown that such a measure does satisfy the basic equineutrality condition (EN). As far as the derived properties above are concerned, it also satisfies the qualitative discrimination condition (QD) along with condition (FPI-E). Yet it does not generally satisfy the basic incrementality conditions (FPI) and (IPI), and it ends up violating all other derived conditions as well, i.e., (IFPD), (FPI-H), (PS) and (SB).7

7.5 Sorting Out the Grammar: from Basic to Structural Properties 7.5.1 The Ordinal Versus Quantitative Level By definition, all incremental confirmation measures share the basic and derived properties presented above. Yet one or more specific incremental measures may be characterized by further interesting features to be called structural properties, as specified by appropriate structural conditions. Once the class of structural properties of incremental confirmation is so identified, it may serve for grounding a thorough and unified discussion of a variety of issues already addressed or touched upon in the literature in a less systematic fashion. We will outline such a discussion shortly, soon after introducing a further useful distinction, i.e., that between ordinal level and quantitative level structural properties. For our purposes, two confirmation measures c.H; E/ and c  .H; E/ will be said ordinally equivalent iff, for any two p-normal pairs .H1 ; E1 / and .H2 ; E2 /; c.H1 ; E1 / > = D = < c.H2 ; E2 / iff c  .H1 ; E1 / > = D = < c  .H2 ; E2 /. Isotone transformations of a given confirmation measure yield measures whose detailed quantitative behavior (including domain and neutrality value) may vary widely, but such that rank-order (for p-normal pairs) is strictly preserved. To

7 Detailed proofs are omitted here, but see Steel (2003, 219–221), Crupi et al. (2007, 246), and Tentori et al. (2007, 109), for relevant remarks.

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illustrate, the measures in the following list are all ordinally equivalent variants:8 cr .H; E/ D p.H jE/=p.H / cr .H; E/ D

p.H jE/  p.H / p.H jE/ C p.H /

cr .H; E/ D

p.H jE/  p.H / p.H /

cr .H; E/ D

p.H jE/ p.H jE/ C p.H /

domain W Œ0; C1/

neutrality value W 1

domain W Œ1; 1/

neutrality value W 0

domain W Œ1; C1/ neutrality value W 0 domain W Œ0; 1/

neutrality value W 1=2

Both Fitelson (1999) and Festa (1999) emphasized that probabilistic confirmation measures are not generally ordinally equivalent – not even properly incremental ones. As a consequence, at the ordinal level of analysis of the notion of confirmation one can already find conceptually remarkable properties that are, in our current terms, structural and not basic. Ordinal level structural properties are simply invariant upon classes of ordinal equivalence, i.e., c.H; E/ will enjoy the property at issue if and only if any ordinally equivalent c  .H; E/ does. If that is not the case, then the property at issue posits constraints operating at a more fine-grained quantitative level, thus being sensitive to the quantitatively different behavior of ordinally equivalent measures. In this section, we will mainly address a sample of significant ordinal level structural properties. As a final point, we will also touch upon the quantitative level of analysis by reference to one illustrative example.

7.5.2 “Laws” of Likelihood A widely known and discussed principle in probabilistic analyses of confirmation is the so-called “law of likelihood” (or “likelihood principle”), whose rendition in our present framework is the following:

(LL) Law of Likelihood For any two p-normal pairs .H1 ; E/ and .H2 ; E/; c.H1 ; E/ > = D = < c.H2 ; E/ iff p.EjH1 / > = D = < p.EjH2 /.9 Principle (LL) certainly amounts to an important structural property of incremental confirmation. Structural, and not basic, for many incremental confirmation measures are well-known not to satisfy (LL). More generally, it can be shown that: For cr .h; e/ and cr .h; e/ see Festa (1999, 64) and Finch (1960), respectively. (LL) essentially amounts to a statement that Steel (2007) labels LP2 and identifies as the second possible renditions of the “likelihood principle”. (See footnote 5.) 8 9

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Theorem 11. (LL) is logically independent from incrementality, i.e., from the set of basic conditions (FPI), (IPI) and (EN). (LL) is also a principle concerning the ordinal level of analysis. Indeed, it has been seen by Bayesian confirmation theorists as isolating (incremental) confirmation measures ordinally equivalent to the probability ratio measure (see Milne 1996) as well indicating some significant limitations of this very class of measures (see Fitelson 2007). Interestingly, despite being independent from incrementality, (LL) is a sufficiently powerful and committing principle to imply by itself conditions appearing above as derived for incremental measures: Theorem 12. (LL) implies the derived condition (FPI-E). Now consider the following claim: (WLL) For any two p-normal pairs .H1 ; E/ and .H2 ; E/, if p.EjH1 / > p.EjH2 / and p.Ej:H1 / < p.Ej:H2 /, then c.H1 ; E/ > c.H2 ; E/. “WLL” stands for “weak law of likelihood”, according to the following fact: Theorem 13. (LL) implies (WLL). Joyce (2004) has argued that (WLL) “must be an integral part of any account of evidential relevance that deserves the title ‘Bayesian”’. In a similar vein, according to Fitelson (2007, 479), “(WLL) captures a crucial common feature of all Bayesian conceptions of relational confirmation”. In light of these statements, it is thus of interest to point out that the following also holds: Theorem 14. (WLL) is logically independent from incrementality, i.e., from the set of basic conditions (FPI), (IPI) and (EN). As a consequence we submit that, as plausible as it may seem in a Bayesian perspective, (WLL) – just as (LL) – counts as a properly structural (not basic) condition for Bayesian theories of incremental confirmation. Joyce’s and Fitelson’s statements are only contingently supported in the sense that, to the best of our knowledge, all incremental confirmation measures which have been historically proposed and seriously defended do in fact satisfy (WLL).

7.5.3 Confirmability and Disconfirmability Assuming a fixed confirmation measure c.H; E/, we will use Cy.H / to denote the confirmability of a particular hypothesis H , amounting to the maximum degree of confirmation that H could possibly receive (given its current probability). It is easy to see that, by the derived condition (FPI-H) above, Cy.H / D c.H; H/ for any incremental measure. That is, for incremental measures the confirmability of a given H

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corresponds to the degree of confirmation provided in the limiting case of H itself having been ascertained. Notably, our basic conditions for incremental confirmation leave the following quite natural question unanswered: does Cy.H1 / D Cy.H2 / generally hold for any two distinct p-normal hypotheses H1 and H2 ? The following statement amounts to an ordinal level structural condition implying a positive answer:

(ECy) Equiconfirmability For any two p-normal hypotheses H1 and H2 ; Cy.H1 / D Cy.H2 /. By a parallel line of argument, let Dy.H / D c.H; :H / be the disconfirmability of H (again given the fixed incremental measure considered), by which the following condition can be stated:

(EDy) Equidisconfirmability For any two p-normal hypotheses H1 and H2 ; Dy.H1 / D Dy.H2 /. Kemeny and Oppenheim (1952, 309) seem to have at least implicitly advocated (ECy) and (EDy). More recently, Fitelson (2006, 502) has approvingly mentioned a condition, named logicality, apparently implying both principles, i.e., “c.H; E/ should be maximal (minimal) when EjD H.EjD :H /”. Kuipers (2000, 54–55), on the other hand, has argued in favour of confirmability being hypothesis specific, i.e., in favour of:

(HCy) Hypothesis Specific Confirmability For any two p-normal hypotheses H1 and H2 , if p.H1 / ¤ p.H2 /, then Cy.H1 / ¤ Cy.H2 /. whose analogue for disconfirmability is of course the following: (HDy) Hypothesis Specific Disconfirmability For any two p-normal hypotheses H1 and H2 , if p.H1 / ¤ p.H2 /, then Dy.H1 / ¤ Dy.H2 /. Quite clearly: Theorem 15. (ECy) and (HCy) are logically inconsistent, as well as (EDy) and (HDy). A less obvious fact to be pointed out is that: Theorem 16. (ECy) and (EDy) are logically independent, as well as (HCy) and (HDy).

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7.5.4 Confirmation and Complementary Hypotheses As a final point, we would like to illustrate how one can shift from a derived to a structural ordinal property, and from the latter to a structural quantitative one by subsequently strengthening a given condition. Consider the following similar but increasingly strong principles connecting the confirmation and disconfirmation of pairs of complementary hypotheses:

(CCO-H) Confirmation Complementarity: Ordinal with Fixed Hypothesis Let .H; E1 / and .H; E2 / be two p-normal pairs such that p.H jE1 / > p.H / and p.H jE2 / > p.H /. Then c.H; E1 / > c.H; E2 / iff c.:H; E1 / < c.:H; E2 /. (CCO) Confirmation Complementarity: Ordinal (General) Let .H1 ; E1 / and .H2 ; E2 / be two p-normal pairs such that p.H1 jE1 / > p.H1 / and p.H2 jE2 / > p.H2 /. Then c.H1 ; E1 / > c.H2 ; E2 / iff c.:H1 ; E1 / < c.:H2 ; E2 /. (CCQ) Confirmation Complementarity: Quantitative For any p-normal pair .H; E/; c.H; E/ D c.:H; E/. First of all, as suggested above, it is quite easy to show that: Theorem 17. (CCQ) implies (CCO), which implies (CCO-H). Moreover, it turns out that: Theorem 18. (CCO-H) follows from the basic condition (FPI). Thus (CCO-H) describes a derived property of incremental measures: the confirmatory impact of evidence on one given hypothesis (be it positive or negative) is a decreasing function of its impact on the negation of that hypothesis. By contrast, (CCO) is a structural condition at the ordinal level – demonstrably violated, for instance, by any measure ordinally equivalent to the probability ratio cr .H; E/ – stating that one hypothesis is better confirmed than another iff the negation of the former is more severely disconfirmed. Finally, as far as or third condition (CCQ) is concerned, consider the following measures:  .H; E/ D cor

o.H jE/  o.H / o.H jE/ C o.H /

 cor .H; E/ D

o.H jE/  o.H / o.H /

cd .H; E/ D p.H jE/  p.H /

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  Measures cor .H; E/ and cor .H; E/ are ordinally equivalent to the odds ratio measure cor .H; E/ but distinct from the third measure listed, i.e., the simple probability difference cd .H; E/. (Also, all three measures listed have 0 as their neutrality value.)  .H; E/ and cd .H; E/ satisfy condition (CCQ), It can be shown, however, that cor  whereas cor .H; E/ does not. This shows that (CCQ) is a properly quantitative structural condition, as it specifies one particular form of the decreasing function connecting c.H; E/ and c.:H; E/, whose fulfilment is orthogonal to the ordinal equivalence relationship among measures. To the best of our knowledge, conditions (CCO-H) and (CCO) have never been explicitly discussed in the literature. By contrast, it is interesting to notice that the strongest condition (CCQ) has a rather long history: it was first clearly stated as an adequacy condition by Kemeny and Oppenheim (1952, 309), then more recently defended by Eells and Fitelson (2002, 134) and by Crupi et al. (2007) in a more general framework.10 Let us conclude this discussion by a final remark. Being presented with the derived condition (CCO-H) above, some reader might have wondered about its “fixed evidence” counterpart, i.e., about the following rather appealing principle:

(CCO-E) Confirmation Complementarity: Ordinal with Fixed Evidence Let .H1 ; E/ and .H2 ; E/ be two p-normal pairs such that p.H1 jE/ > p.H1 / and p.H2 jE/ > p.H2 /. Then c.H1 ; E/ > c.H2 ; E/ iff c.:H1 ; E/ < c.:H2 ; E/. Just as its counterpart (CCO-H), (CCO-E) is also a consequence of the more general condition (CCO), i.e.: Theorem 19. (CCO) implies (CCO-E). However, unlike (CCO-H), condition (CCO-E) specifies a property which is not derived but only structural for incremental confirmation measures. Once again it is demonstrably violated by measures ordinally equivalent to the probability ratio cr .h; e/. This is not by chance, as the probability ratio measure satisfies the law of likelihood (LL), which in turn contradicts (CCO-E), i.e.: Theorem 20. (LL) and (CCO-E) are logically inconsistent. Notice that, by contradicting (CCO-E), (LL) also contradicts both (CCQ) and (CCO), which are logically stronger (by Theorems 17 and 19). This illustrates further how strong a constraint the law of likelihood is as a structural property for incremental confirmation.

10

A major issue in Crupi et al. (2007, 236–242) is a thorough analysis of so-called “symmetries and asymmetries” in Bayesian confirmation theory (see Eells and Fitelson 2002). In our current terms, their convergent symmetries are all ordinal structural conditions, whereas their divergent ones are all quantitative structural conditions.

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7.6 Concluding Remarks: the Call for a Grammar The foregoing analyses were meant as laying the foundations of a set of theoretical tools for the formal analysis of reasoning, i.e., a detailed grammar of Bayesian confirmation. Our present results are preliminary, and still already telling, we submit, as suggested by the graphical summary appearing in Fig. 7.1 below. We would like to conclude with a few remarks indicating why we see the endeavour outlined here as fruitful. To begin with, the distinction between basic/derived and structural properties may serve as a firm guide for differentiating issues concerning Bayesian incremental confirmation as such as compared to relatively more subtle puzzles involving its many variants. In particular, the appeal (or lack thereof) of basic and derived features should be seen as a crucial benchmark for the assessment of the notion of Bayesian incremental confirmation per se, as distinct from its diverse possible formalizations. On the other hand, debated issues such as the so-called irrelevant conjunction problem (see Hawthorne and Fitelson 2004; Crupi and Tentori forthcoming), Matthew effects (Festa forthcoming), so-called “likelihoodist” principles (Fitelson 2007; Steel 2007) and symmetries and asymmetries (Eells and Fitelson 2002; Crupi et al. 2007) can all be seen as examples in which specific and possibly alternative structural conditions (or sets thereof) are formally investigated and arguments are scrutinized concerning their more or less compelling nature. In this

Fig. 7.1 A graphical representation of the currently investigated logical relationships among basic, derived and structural conditions for Bayesian incremental confirmation. Arrows indicate relationships of logical implication. Dotted lines denote relationships of logical independence. Links marked with a bar (/) represent logical inconsistencies. Figures refer to corresponding theorems in the text

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connection, a fully developed grammar of confirmation would contribute in clarifying which options are theoretically viable and which are not, by pointing out, say, that one cannot logically satisfy both the law of likelihood (LL) and the confirmation complementarity condition (CCO), so that such a pair of principles would amount to an inconsistent set of desiderata. To sum up, the investigation of the logical relationships among basic, derived and structural properties as defined above seems to represent an appropriate general framework of inquiry for a number of analyses and discussions surrounding confirmation and Bayesian confirmation in particular.

References Bovens L, Hartmann S (2003) Bayesian epistemology. Oxford University Press, Oxford Carnap R (1950/1962) Logical foundations of probability. University of Chicago Press, Chicago, IL Christensen D (1999) Measuring confirmation. J Philos 96:437–461 Crupi V (2008) Confirmation and relative distance: the oddity of an odds counterpart (unpublished manuscript) Crupi V, Tentori K (forthcoming) Irrelevant conjunction: statement and solution of a new paradox. Philos Sci Crupi V, Tentori K, Gonzalez M (2007) On Bayesian measures of evidential support: theoretical and empirical issues. Philos Sci 74:229–252 Eells E, Fitelson B (2000) Measuring confirmation and evidence. J Philos 97:663–672 Eells E, Fitelson B (2002) Symmetries and asymmetries in evidential support. Philos Stud 107:129–142 Festa R (1999) Bayesian confirmation. In: Galavotti M, Pagnini A (eds) Experience, reality, and scientific explanation. Kluwer, Dordrecht, pp 55–87 Festa R (forthcoming) For unto every one that hath shall be given: Matthew properties for incremental confirmation. Synthese Finch HA (1960) Confirming power of observations metricized for decisions among hypotheses. Philos Sci 27:293–307; 391–404 Fitelson B (1999) The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philos Sci 66:S362–S378 Fitelson B (2001) A Bayesian account of independent evidence with applications. Philos Sci 68:S123–S140 Fitelson B (2006) Logical foundations of evidential support. Philos Sci 73:500–512 Fitelson B (2007) Likelihoodism, Bayesianism, and relational confirmation. Synthese 156: 473–489 Gaifman H (1979) Subjective probability, natural predicates and Hempel’s ravens. Erkenntnis 21:105–147 Good IJ (1950) Probability and the weighing of evidence. Griffin, London Hawthorne J, Fitelson B (2004) Re-solving irrelevant conjunction with probabilistic independence. Philos Sci 71:505–514 Heckerman D (1986) Probabilistic interpretations for MYCIN’s certainty factors. In: Kanal L, Lemmer J (eds) Uncertainty in artificial intelligence. North-Holland, New York, pp 167–196 Horwich P (1982) Probability and evidence. Cambridge University Press, Cambridge Howson C, Urbach P (2006) Scientific reasoning: the Bayesian approach. Open Court, La Salle, IL Joyce J (1999) The foundations of causal decision theory. Cambridge University Press, Cambridge

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Joyce J (2004) Bayes’s theorem. In: Zalta EN (ed) The Stanford encyclopedia of philosophy (Summer 2004 Edition), URL D http://plato.stanford.edu/archives/sum2004/entries/bayes-theorem/ Kemeny J, Oppenheim P (1952) Degrees of factual support. Philos Sci 19:307–324 Keynes J (1921) A treatise on probability. Macmillan, London Kuipers T (2000) From instrumentalism to constructive realism. Reidel, Dordrecht Milne P (1996) LogŒp.h=eb/=p.h=b/ is the one true measure of confirmation. Philos Sci 63: 21–26 Mortimer H (1988) The logic of induction. Prentice Hall, Paramus Mura A (2006) Deductive probability, physical probability and partial entailment. In: Alai M, Tarozzi G (eds) Karl Popper philosopher of science. Rubbettino, Soveria Mannelli, pp 181–202 Mura A (2008) Can logical probability be viewed as a measure of degrees of partial entailment? Logic Philos Sci 6:25–33 Nozick R (1981) Philosophical explanations. Clarendon, Oxford Oaksford M, Chater N (2007) Bayesian rationality: the probabilistic approach to human reasoning. Oxford University Press, Oxford Rescher N (1958) A theory of evidence. Philos Sci 25:83–94 Shortliffe EH, Buchanan BG (1975) A model of inextact reasoning in medicine. Mathematical Biosciences 23:351–379 Sober E (1994) No model, no inference: a Bayesian primer on the grue problem. In: Stalker D (ed) Grue! the new riddle of induction. Open Court, Chicago, IL, pp 225–240 Steel D (2003) A Bayesian way to make stopping rules matter. Erkenntnis 58:213–222 Steel D (2007) Bayesian confirmation theory and the likelihood principle. Synthese 156:55–77 Tentori K, Crupi V, Bonini N, Osherson D (2007) Comparison of confirmation measures. Cognition 103:107–119 Todhunter I (1865) A history of mathematical theory of probability from the time of Pascal to that of Laplace. Macmillan, London (reprinted: 1949, 1965, Chelsea Publishing Company, New York)

Appendix: Proofs of Theorems Theorem 1. The basic conditions (FPI), (IPI) and (EN) are logically independent. Proof. Logical independence amounts to both consistency and non-redundancy. As for consistency, it can be shown that all confirmation measures presented in Section 7.2. (i.e., measures cd ; cr ; crd ; cod , and cor ) jointly satisfy all three conditions (FPI), (IPI) and (EN). As for non-redundancy, consider the following functions of a joint probability distribution p.˙H ^ ˙E/: (i) p.H jE/=p.H /2 (ii) p.H /Œp.H jE/  p.H / (iii) Œ1  p.H jE/Œp.H jE/  p.H / Non-redundancy is proven by the following set of easily demonstrable facts: (i) satisfies both (FPI) and (IPI) but violates (EN); (ii) satisfies both (FPI) and (EN) but violates (IPI); (iii) satisfies both (IPI) and (EN) but violates (FPI). Theorem 2. (QD) follows from the basic conditions (FPI) and (EN). Proof. (EN) immediately implies (QD.2). Then, since by (FPI) c.H; E/ is a strictly increasing function of p.H jE/, both (QD.1) and (QD.3) follow.

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Theorem 3. (IFPD) follows from each of the basic conditions (FPI) and (IPI). Proof. For any p-normal pair .H; E/, a joint probability distribution p.˙H ^ ˙E/ is completely determined in a non-redundant way by p.H /; p.H jE/ and p.E/. As a consequence, if c.H; E/ is a function of p.˙H ^ ˙E/ but not a function of p.H / and p.H jE/ only, that is because it is a (non-constant) function of p.E/ as well. If that’s the case, however, probability models exist showing that c.H; E/ violates (FPI) as well as (IPI). Theorem 4. (QD) and (IFPD) are logically independent. Proof. Consider the following functions of p.˙H ^ ˙E/: (i) p.H jE/  p.H j:E/ (ii) p.H jE/=p.H /2 It is easy to prove that: (i) (originally proposed by Christensen (1999, 449), and Joyce (1999), Ch. 7, as a confirmation measure) satisfies (QD) while violating (IFPD); (ii), on the other hand, violates (QD) while satisfying (IFPD). Theorem 5. (QD) and (FPI-H) are logically independent. Proof. Consider the following functions of p.˙H ^ ˙E/: (i) p.H jE/  p.H j:E/ (ii) p.H jE/ It is easy to prove that: (i) satisfies (QD) while violating (FPI-H); (ii), on the other hand, violates (QD) while (trivially) satisfying (FPI-H). Theorem 6. (FPI-H) follows from basic condition (FPI). Proof. (FPI-H) trivially follows from (FPI) in the special case H1 D H2 . Theorem 7. (FPI-E) follows from basic condition (FPI). Proof. (FPI-H) trivially follows from (FPI) in the special case E1 D E2 . Theorem 8. (QD) and (FPI-E) are logically independent. Proof. Consider the following functions of p.˙H ^ ˙E/: ˘ (i) sin 32  .p.H jE/  p.H // (ii) p.H jE/ It is easy to prove that: (i) satisfies (QD) while violating (FPI-E); (ii), on the other hand, violates (QD) while (trivially) satisfying (FPI-E). Theorem 9. (FPI-H) and (PS) are logically equivalent.

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Proof. For any two p-normal pairs .H; E1 / and .H; E2 /; p.H jE1 / > = D = < p.H jE2 / iffp.H jE1 /=p.H / > = D = < p.H jE2 /=p.H / iff p.E1 jH /=p.E1 / > = D = < p.E2 jH /=p.E2 / iff q.H; E1 / > = D = < q.H; E2 /. Theorem 10. (PS) implies (SB). Proof. Assume (PS). Then notice that, for any two p-normal pairs .H; E1 / and .H; E2 /, if H jD E1 ; E2 , then c.H; E1 / > = D = < c.H; E2 / iff q.H; E1 / > = D = < q.H; E2 / iff p.E1 jH /=p.E1 / > = D = < p.E2 jH /=p.E2 / iff 1=p.E1 / > = D = < 1=p.E2 / iff p.E1 / < = D = > p.E2 /. Theorem 11. (LL) is logically independent from incrementality, i.e., from the set of basic conditions (FPI), (IPI) and (EN). Proof. Consider the following functions of p.˙H ^ ˙E/: (i) p.H jE/=p.H / (ii) p.EjH /  p.E/ (iii) o.H jE/=o.H / D p.EjH /=p.Ej:H / It is easy to prove that: the probability ratio measure (i) satisfies both (LL) and all basic conditions for incrementality; (ii) (originally proposed by Mortimer (1988), Section 11.1, as a confirmation measure) satisfies (LL) while violating the basic conditions for incrementality; the odds ratio measure (iii), on the other hand, violates (LL) while satisfying all basic conditions for incrementality. Theorem 12. (LL) implies the derived condition (FPI-E). Proof. Assume (LL). Then notice that, for any two p-normal pairs .H1 ; E/ and .H2 ; E/, if p.H1 / D p.H2 /, then c.H1 ; E/ > = D = < c.H2 ; E/ iff p.EjH1 / > = D = < p.EjH2 / iff p.EjH1 /p.H1 /=p.E/ > = D = < p.EjH2 /p.H2 /=p.E/ iff p.H1 jE/ > = D = < p.H2 jE/. Theorem 13. (LL) implies (WLL). Proof. Assume (WLL) is false. Then there exist two p-normal pairs .H1 ; E/ and .H2 ; E/ such that p.EjH1 / > p.EjH2 / while c.H1 ; E/  c.H2 ; E/, so that (LL) is violated. Theorem 14. (WLL) is logically independent from incrementality, i.e., from the set of basic conditions (FPI), (IPI) and (EN). Proof. Consider the following functions of p.˙H ^ ˙E/: (i) cor .H; E/ D o.H jE/=o.H / D p.EjH /=p.Ej:H / (ii) p.EjH /  2p.Ej:H / (iii) p.H jE/10  p.H /10

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It is easy to prove that: the odds ratio measure (i) satisfies both (WLL) and all basic conditions for incrementality; (ii) satisfies (WLL) while violating the basic conditions for incrementality; (iii), on the other hand, violates (WLL) while satisfying all basic conditions for incrementality. Theorem 15. (ECy) and (HCy) are logically inconsistent, as well as (EDy) and (HDy). Proof. Recall that c.H; E/ is assumed to be a function of p.˙H ^ ˙E/. Then simply notice that, if (ECy) holds, then Cy.H / is a constant for any p-normal H . If (HCy) holds, on the contrary, Cy.H / must be a non-constant function of p.H /. A strictly analogous line of argument applies to (EDy) and (HDy). Theorem 16. (ECy) and (EDy) are logically independent, as well as (HCy) and (HDy). Proof. Consider the following incremental measures: o.hje/  o.h/ o.hje/ C o.h/ (ii) cd .h; e/ D p.hje/  p.h/ p.:h/  p.:hje/ (iii) cg .h; e/ D p.:h/ C p.:hje/ p.hje/  p.h/ (iv) cr .h; e/ D p.hje/ C p.h/  .h; e/ D (i) cor

Measure (i), proposed by Kemeny and Oppenheim (1952), is ordinally equivalent to the odds ratio measure cor .h; e/ D o.hje/=o.h/ and can be easily shown to jointly satisfy (ECy) and (EDy). This proves that (ECy) and (EDy) are consistent. On the other hand, it is easy to show that the probability difference measure (ii) jointly satisfies (HCy) and (HDy). This proves that (HCy) and (HDy) are consistent. Finally, it is easy to show that: measure (iii) (ordinally equivalent to the one proposed by Gaifman (1979)) jointly satisfies (ECy) and (HDy), thus violating both (HCy) and (EDy); on the other hand, measure (iv) (ordinally equivalent to the probability ratio) jointly satisfies (HCy) and (EDy), thus violating both (ECy) and (HDy). This proves that (ECy) and (EDy) are non-redundant, as well as (HCy) and (HDy). Theorem 17. (CCQ) implies (CCO), which implies (CCO-H). Proof. Assume (CCQ). Then for any two p-normal pairs .H1 ; E1 / and .H2 ; E2 / such that p.H1 jE1 / > p.H1 / and p.H2 jE2 / > p.H2 /; c.H1 ; E1 / > c.H2 ; E2 / iff c.:H1 ; E1 / D c.H1 ; E1 / < c.:H2 ; E2 / D c.H2 ; E2 /. Moreover, simply notice that (CCO-H) trivially follows from (CCO) in the special case H1 D H2 . Theorem 18. (CCO-H) follows from the basic condition (FPI). Proof. Assume (FPI) and recall that (FPI-H) follows (Theorem 6 above). Then for any two p-normal pairs .H; E1 / and .H; E2 / such that p.H jE1 / > p.H / and p.H jE2 / > p.H /; c.H; E1 / > c.H; E2 / iff p.H jE1 / > p.H jE2 / iff p.:H jE1 / < p.:H jE2 / iff c.:H; E1 / < c.:H; E2 /.

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Theorem 19. (CCO) implies (CCO-E). Proof. (CCO-E) trivially follows from (CCO) in the special case E1 D E2 . Theorem 20. (LL) and (CCO-E) are logically inconsistent. Proof. Consider the following probability distribution over p-normal statements H1 ; H2 and E W p.H1 ^ H2 ^ E/ D :16; p.H1 ^ H2 ^ :E/ D 0; p.H1 ^ :H2 ^ E/ D :04; p.H1 ^ :H2 ^ :E/ D 0; p.:H1 ^ H2 ^ E/ D :24; p.:H1 ^ H2 ^ :E/ D :20; p.:H1 ^ :H2 ^ E/ D :06; p.:H1 ^ :H2 ^ :E/ D :30. It can then be computed that p.EjH1 / D 1 > :67 D p.EjH2 / and p.Ej:H1 / D :38 > :25 D p.Ej:H2 /. Thus, by (LL), c.H1 ; E/ > c.H2 ; E/ and c.:H1 ; E/ > c.:H2 ; E/, contrary to (CCO-E).

Chapter 8

Epistemic Accuracy and Subjective Probability Marcello D’Agostino and Corrado Sinigaglia

8.1 Introduction De Finetti’s favourite justification of probabilism – namely the fundamental tenet that rational partial beliefs must conform to the axioms of probability – was in terms of “scoring rules” (de Finetti 1974). These are rules that are often employed in evaluating the accuracy of probabilistic forecasters and measuring their predictive success. De Finetti showed that if a specific scoring rule is adopted, the so-called Brier’s rule, consisting in taking the mean squared error over a series of predictions, then the score of a forecaster whose predictions are in accordance with the probabilistic laws dominates that of any forecaster whose predictions violate them, in the sense that it turns out to be better in any possible situation. A natural question that has been raised and intensely debated in the literature – even among the supporters of probabilism (e.g., Lindley 1982; Rosenkrantz 1981; Joyce 1998) – is: why Brier’s rule? Is there any good reason for adopting such a quadratic loss function, rather than some other scoring rule of a different mathematical form? Ingenious attempts have been made to answer this question by showing that Brier’s rule satisfies some general, more or less compelling, properties that make it appropriate for the kind of scoring game that de Finetti had in mind (e.g., Savage 1971; Lindley 1982). However, most of these attempts are either marred by internal difficulties, or are based on pragmatic arguments that do not seem to be in tune with the epistemic context in which the fundamental question “why should degrees of belief obey the laws of probability” is properly asked (Kennedy and Chihara 1979; Rosenkrantz 1981; Joyce 1998). To put it with James M. Joyce:

M. D’Agostino () Dipartimento di Scienze Umane, Universit`a di Ferrara, Italy e-mail: [email protected] C. Sinigaglia Dipartimento di Filosofia, Universit`a degli Studi di Milano, Italy e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 8, c Springer Science+Business Media B.V. 2010 

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M. D’Agostino and C. Sinigaglia There is a distinction to be drawn between prudential reasons for believing, which have to do with the ways in which holding certain opinions can affect one’s happiness, and epistemic reasons for believing, which concern the accuracy of the opinions as representations of the world’s state.1

In a similar vein, Roger Rosenkrantz has labelled this kind of pragmatic arguments as a “roundabout way of exposing the irrationality of incoherent beliefs” (Rosenkrantz 1981, p. 214). In this paper we endorse the epistemic view put forward by Rosenkrantz and Joyce, to which we refer the reader for a thorough critical discussion of the pragmatistic approach and its shortcomings, but propose a new strategy that leads to sharper results. Instead of attempting a direct epistemic justification of Brier’s rule, we treat it as a special case of a more general function measuring the distance, or disagreement, between two arbitrary series of non-categorical predictions, each of which is represented by a real-valued vector. The special case arises when one of the two series is generated by an ideal “infallible” forecaster who makes categorical predictions that mirror the observed outcomes. Then, taking advantage of a recent characterization result (D’Agostino and Dardanoni 2009), we argue that such a distance function can be justified in terms of general properties that have a straightforward epistemic interpretation. We finally suggest that, in this way, an epistemic justification of probabilism may be accomplished without appealing to the usual, and somewhat misleading, arguments based on pragmatic considerations.

8.2 Scoring Rules and Epistemic Accuracy A major concern of methodological investigations has always been that of providing justified means for evaluating forecasters – in the broad sense, including theories and models used for this purpose – and measuring their predictive success, especially in contexts where predictions are inevitably associated with some degree of uncertainty. In uncertain situations the forecaster’s predictions are rarely categorical. What the forecaster asserts is not the full belief that a given event will certainly occur or will certainly not occur, but only a graded belief that the event will occur or not occur.2 The accuracy of such non-categorical predictions is not as simple to assess as in the case of categorical ones. Indeed, non-categorical predictions are never entirely “right” or “wrong”, and yet one has somehow to compare them with the actual outcomes.

1

Joyce (1998), p. 584. As Murphy and Winkler put it: “Categorical or deterministic forecasts suffer from two serious deficiencies. First, a forecaster or forecasting system is seldom, if ever, certain of which event will occur. Second, categorical forecasts do not provide users of the forecasts with the information that they need to make rational decisions in uncertain situations.”(Murphy and Winkler 1984, p. 489). 2

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The distance between the series of observed outcomes and the prediction series, assessed according to some suitable “distance” function,3 provides a good measure of the forecaster’s accuracy, i.e. what is usually called a “scoring rule” in the statistical literature. These are rules by which the forecaster is given a virtual payoff (a penalty or a reward) depending on his predictions and on the actual outcomes. The more distant the outcomes from the predictions, the greater the loss for the forecaster. The forecaster’s goal, therefore, is that of minimizing the distance from the observed outcomes. Here the score represents a penalty that the forecaster must suffer for his prediction error, rather than a reward.4 Now, a problem that has received a great deal of attention, is: how should we measure such prediction error? How can we choose a suitable scoring rule? In the case of categorical predictions a natural rule consists in counting the number of “hits” and taking their average. How does this natural rule properly generalize to the non-categorical case? Another related problem, which has also been thoroughly investigated in connection with the choice of a suitable scoring rule, is that of “eliciting” personal degrees of belief: how can a subject be persuaded to reveal her true estimates concerning a set of events? How can we make sure that she will not lie about her own judgements, maybe adopting some fraudulent strategy to raise her score? To make this point crystal-clear, let us consider a simple example. Suppose our scoring rule n P consists in taking the mean absolute error: n1 jei  xi j, where xi are the prei D1

dictions made by the given forecaster and ei are the observed outcomes, namely the values of the binary random variables ei representing the aleatory events Ei . This is often called the linear scoring rule and appears to be a natural generalization of the simple “count the hits” rule for categorical predictions. Suppose that a forecaster “true” degree of belief in the occurrence of an event E is 0.7. If the forecaster makes her prediction according to her true estimate, the expected score is 0:7  j1  0:7j C 0:3  j0  0:7j D 0:42. On the other hand, if the forecaster “lies” and makes the prediction that the event in question will certainly occur, so assigning to it the maximum degree of belief (i.e. 1), then her expected score will be 0:7  j1  1j C 0:3  j0  1j D 0:3 which is lower (and therefore better) than the score obtained on the basis of the “honest” prediction. This example is sufficient to show that some scoring rules are inadequate to measure forecasting accuracy because they fail to elicit a forecaster’s true estimate and leave room to strategic behaviour. In particular, the linear scoring rule encourages forecasters to be “opinionated”, that is, to make predictions, which concentrate on the extreme values 0 and 1. Other scoring rules may encourage different, maybe

3 Our use of the expression “distance function”, in this paper, is rather loose and refers to any continuous function of two real-valued vectors (of the same finite size) which can be intuitively regarded as measuring their distance, including functions which do not fully satisfy the standard textbook definition. Such non-standard “distance” functions have often been used to solve measuring problems in several applications areas. 4 Some authors prefer to define scoring rules so as the forecaster’s goal is that of maximizing his score. Trivial algebraic manipulation is sufficient to turn one scenery into the other.

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more subtle, strategies. Adequate scoring rules are those that force any homo economicus to make his predictions in accordance with his true degrees of belief, in order to minimize the expected score (and therefore the expected loss). Such rules are called “proper” and their mathematical form is determined ad hoc for the purpose of addressing the elicitation problem. A typical example of a proper scoring rule is Brier’s rule, a widely used one which was first proposed in the context of weather forecasting (Brier 1950): 1X .ei  xi /2 n n

(8.1)

i D1

where, as before, xi is the forecaster’s prediction concerning the aleatory event Ei and ei is equal to 1 or 0 depending on whether Ei occurs or not. Using the same values of the previous example, the expected score obtained by the forecaster who is “honest” in making his predictions, assigning to the event E the “true” degree of belief 0.7, would be 0:7  .10:7/2 C 0:3  .00:7/2 D 0:7  0:09 C 0:3  0:49 D 0:21, while the expected score for the “opinionated” prediction assigning to the event the value 1 would be 0:7  .1  1/2 C 0:3  .0  1/2 D 0:3, as before. It can be shown that the expected score obtained by means of Brier’s rule is, in general, minimal when the predictions are made in accordance with one’s real degrees of belief. It is one of de Finetti’s merits to have shown how the relevance of the notion of proper scoring rule goes beyond the forecasting and elicitation problems, to provide an argument in favour of probabilism. In particular, he proved that, if Brier’s rule is adopted for evaluating forecasting accuracy over a set of arbitrary events, then the score of a forecaster whose predictions are in accordance with the probabilistic laws dominates that of any forecaster whose predictions violate them, in the sense that it turns out to be better in all possible situations (this is the so-called de Finetti’s Lemma). Consider, for example, the two events E and :E and suppose a forecaster’s degrees of belief in these events do not sum up to 1. For instance, assume they are 0.5 for E and 0.4 for :E. Then, the total scores obtained by Brier’s rule are .10:5/2 C .0  0:4/2 D 0:41 in case E turns out to be true, and .0  0:5/2 C .1  0:4/2 D 0:61 in case E turns out to be false. Let us now change the assignments as follows: 0.55 for E and 0.45 for :E (so that now they sum up to 1). It is easily verified that the total scores obtained by Brier’s rule for these new assignments are .1  0:55/2 C .0  0:45/2 D 0:405 in case E turns out to be true, and .0  0:55/2 C .1  0:45/2 D 0:605 in case E turns out to be false. So, the score obtained is lower in both cases, for the new pair of values. It is not difficult to show that, in general, given any assignment to E and :E of degrees of belief, say x and y, that do not sum up to 1, it is always possible to find x 0 and y 0 such that x 0 C y 0 D 1 and the score obtained by Brier’s rule for these values is lower both in the case in which E is true and in the case in which E is false.5 A similar argument can be devised to justify the other

5

For this purpose, it is sufficient to add .1  .x C y//=2 to both x and y.

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probabilistic laws. In this way, the problem of providing a subjectivistic justification of the probabilistic laws is reduced to the problem of measuring forecasters’ accuracy via a suitable scoring rule. Notice that the general argument does not depend on the notion of expected score, since the score is lower in all possible cases. It only relies on the so-called sure-thing principle: if an assignment x is to be preferred to an assignment y both in the case in which E is true and in the case in which E is false, then it is to be preferred when E is uncertain. If this has to be read as a justification of probabilism, a natural question to ask is: why Brier’s rule? Why couldn’t we measure forecasting accuracy by means of any other natural rule, such as the one that consists in taking the linear scoring rule (i.e. the mean absolute error) or any other function of two vectors that satisfies some minimal requirements for being a measure of the disagreement between a series of predictions and the observed values? De Finetti’s typical answer is that Brier’s rule is a “proper” scoring rule, i.e. one that forces the forecaster to be honest about her true probability estimates, so as to provide also a good solution to the elicitation problem discussed above. However, Brier’s rule is by no means the only proper scoring rules, and so its choice requires some further justification. For this purpose, de Finetti often resorts to aesthetical (“it is the simplest proper scoring rule”) or empirical considerations. Several attempts have been made in the literature to justify Brier’s rule as one satisfying some desirable properties that a scoring rule should enjoy in order to elicit the true estimates of any subject who aims at minimizing the expected loss,6 so bringing in the whole apparatus of expected utility. Generally speaking, however, any argument for probabilism based on the notion of proper scoring rule has the undesirable effect of giving undue prominence to pragmatic considerations that, when not affected by blatant circularity with respect to the main foundational issue, end up leading astray by focusing on non-epistemic aspects.7 In the next section we take a different approach that does not rely on the notion of proper scoring rule, but only requires the basic epistemic assumption that a forecaster, who plays the “game of knowledge”, aims at minimizing the inaccuracy of her predictions, that is the distance between her predictions and the observed outcome.

8.3 Towards a Metric of Beliefs We construe the problem of measuring the distance between a forecaster’s predictions and the observed events as a special case of the general problem of measuring the distance between two series of predictions made by two different forecasters, one of which is a fictitious “infallible” forecaster, i.e. one whose predictions are

6 Or gain, depending on the setting; see footnote 4 above. For such characterizations (see, for example, Selten 1998; Savage 1971; Offerman et al. 2009; Winkler 1969). 7 On this point, see the already cited (Joyce 1998).

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always 1 or 0 and is a 100% accurate. We then present a set of natural properties that a distance function between two forecasters’ prediction series should satisfy and show that these properties uniquely determine (up to a monotonic transformation) a distance function which, in the special case that one of the two is the infallible one, coincides with Brier’s scoring rule. Let Ei , with i  1, be a sequence of events and let xi be a real number in [0, 1] that represents a given forecaster’s degree of belief in the event Ei . Let v.x/ be the proportion of i ’s for which the forecaster’s degree of belief in the occurrence of Ei is x. One can consider how sharp a forecaster is in his predictions by observing how concentrated the function v.x/ is near the values 0 and 1. We say that a forecaster is opinionated if v.x/ > 0 only if x D 0 or x D 1, that is the forecaster’s predictions are always “Ei will certainly occur” or “Ei will certainly not occur”, leaving no room for doubt. We then call infallible an opinionated forecaster whose predictions are always 100% correct. So, comparing the predictions of a real forecaster with the observed outcomes is tantamount to comparing them with the predictions of an ideal “infallible” forecaster. After making this heuristic shift, we address the general problem: “how far” from each other are two series of predictions, made by two different forecasters, concerning the same events? In this setting, both comparison and evaluation of forecasters boil down to measuring the distance between two forecasters’ prediction series. Once we agree on the right notion of distance to be used in comparing such prediction series, i.e. in establishing “how far” they are from each other, measuring the accuracy of each forecaster is tantamount to measuring the distance between her predictions and those made by the (fictitious) “infallible” forecaster. So, the problem of evaluating forecasting accuracy (measuring the distance between a forecaster’s predictions and the observed events) is construed as a special case of the general problem of measuring the distance between two forecasters. Let us, therefore, concentrate on this more general problem. Given a forecaster A and a sequence of events E1 ; : : : ; En , we call belief-vector of A over fEi g, any real-valued vector x such that xi expresses A’s degree of belief in the occurrence of Ei . So, the general problem is: how should we measure the distance between the belief-vectors of two forecasters over the same series of events? We now introduce a set of natural properties that any distance function between belief-vectors should satisfy. The properties presented in this section have been proposed, in a different context, in (D’Agostino and Dardanoni 2009). Here we show that these properties are also well suited to the issue discussed in this paper. Since we are concerned with the distance between real-valued vectors of the same finite size, we shall speak of a “distance measure over Œ0; 1n ” to mean a continuous function dn W Œ0; 1n  Œ0; 1n ! RC . In what follows we shall use the lightface letters a, b, c, d, etc. to denote arbitrary real numbers and the boldface letters x, y, w, etc. to denote arbitrary vectors. The vector whose only element is the real number a will be denoted simply by “a”. We shall write [x, y] for the concatenation of the two vectors x and y. Property 1 (One-dimensional value-sensitivity). For all a; b 2 Œ0; 1, d1 .a; b/ D G .ja  bj/

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for some continuous and strictly increasing function G W Œ0; 1 ! RC such that G.0/ D 0. This property says that, in the simple case in which we are dealing with a single event E, the distance between the degrees of belief assigned to E by two forecasters depend monotonically on their absolute difference (G.0/ D 0 is a harmless normalization requirement) and leaves entirely open the problem of how to measure distance when more than one event is concerned. The second property requires that the distance between two belief-vectors is monotonically consistent with the distance between their sub-vectors: Property 2 (Sub-vector Consistency). For all k; j 2 N and whenever x, y, x0 ; y0 2 Œ0; 1k ; u, v, u0 ; v0 2 Œ0; 1j , dk .x; y/ > dk .x0 ; y0 / and dj .u; v/ D dj .u0 ; v0 / ) ) dkCj .Œx; u; Œy; v/ > dkCj .Œx0 ; u0 ; Œy0 ; v0 /: Property 2 expresses a compositionality principle that seems uncontroversial in this context. This property also arises in many different contexts and implies the fundamental independence assumption, which plays a crucial role in the theory of additive conjoint measurement (Debreu 1960). Tverski and Krantz show how to derive the latter from three more primitive axioms of measurement theory (Tverski and Krantz 1970, Theorem 1). The next property requires that our distance measure is order-sensitive in the following sense. Consider, for example, a pair of events E1 and E2 and the pairs of belief vectors (x, y) and .x, y0 / defined as in the following tables:

E1 E2

x 0.3 0.6

y 0.6 0.9

E1 E2

x 0.3 0.6

y0 0.9 0.6

Observe that, going from y to y0 , the values of y1 and y2 are “swapped”, so as to reverse their order. Notice that if the distance function dn were linear, d2 .x; y/ D d1 .x1 ; y1 / C d1 .x2 ; y2 / D d1 .x1 ; y20 / C d1 .x2 ; y10 / D d2 .x; y0 / and the distance between the two pairs of vectors would turn out to be the same. However, it seems natural to judge that the distance between x and y0 be greater than the distance between x and y: for x and y agree qualitatively on the degree of belief they assign to the events E1 and E2 , since they both express a higher degree of belief in E2 than in E1 , and so any inversion of this qualitative judgement – as in y0 – must be regarded as increasing the distance between the belief-vectors; intuitively, y0 disagrees with x more than y. Moreover, it seems reasonable to assume that the additional distance between y0 and x grows monotonically with the difference between the inverted values (0.3 in this example). This also appears to be

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intuitively sound, since the difference between the inverted values can be regarded as a good quantitative measure of the qualitative disagreement between y and y0 (and therefore of the additional disagreement between x and y0 ). Generalizing the example, we obtain a notion of “order-reversing swap”: consider a pair of belief-vectors x and y; a swap between yi and yj is orderreversing when .xi  xj /.yi  yj / > 0, i.e. the swap turns a positive order association into a negative one.8 Let us denote by ¢ij .y/ the vector obtained from y by “swapping” yi and yj , i.e. the vector y0 such that: (i) yk0 D yk for all k ¤ i; j , (ii) yi0 D yj , and (iii) y 0 j D yi . Property 3 (Monotonic Order-Sensitivity). For all n  4, for all x, y 2 Œ0; 1n and all i; j; k; m 2 f1; : : : ; ng, if  .xi  xj /.yi  yj / > 0  .xk  xm /.yk  ym / > 0  d1 .xi ; xj / D d1 .xk ; xm / and d1 .yi ; yj /  d1 .yk ; ym /,

then dn .x; y/ < dn .x; ij .y//  dn .x; mk .y//: Our Property 3 then requires (i) that the distance between two belief-vectors increases with each “order-reversing” swap, and (ii) that it does so in a way that depends monotonically on the distance between the degrees of beliefs assigned to the two events that are involved in the swap. In other words, the effect of an order-reversing swap in the y’s depends monotonically on the distance between the swapped y’s, provided that the distance between the corresponding x’s is the same. The next two properties are standard invariance properties. Property 4 (Permutation Invariance). For all x, y 2 Œ0; 1n , dn .x; y/ D dn . .x/;  .y// for every permutation  . This property simply says that the distance between the belief-vectors of forecasters A and B is not altered if each of them performs the same permutation in the assigned degrees of belief. Property 5 (Replication Invariance). For all x, y 2 Œ0; 1k , and all k; n 2 N, n

n

‚ …„ ƒ ‚ …„ ƒ dk .x; y/ D dnk .Œx; : : : ; x; Œy; : : : ; y/ n

‚ …„ ƒ where Œu; : : : ; u denotes the result of concatenating the vector u with itself n times. 8 Such order-reversing swaps are discussed in mathematical statistics (Tchen 1980), economics (Epstein and Tanny 1980), and mobility measurement (Atkinson 1983; Dardanoni 1993).

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Property 5 says that the distance between the belief-vectors of forecasters A and B remains unaltered if each of them replies exactly the same predictions over a new (and equally numerous) series of events. D’Agostino and Dardanoni have proved the following theorem (D’Agostino and Dardanoni 2009, Theorem 1): Theorem 1. A distance measure dn satisfies Properties 1–5 if and only if for all n 2 N and all x, y 2 Œ0; 1n , " dn .x; y/ D H

1X .xi  yi /2 n n

#

i D1

for some continuous and strictly increasing function H W RC ! RC with H.0/ D 0. When one of the two vectors is the belief-vector e of the “infallible” forecaster, namely the vector of the observed outcomes, the above theorem implies that " dn .x; e/ D H

1X .ei  xi /2 n n

# (8.2)

i D1

where, for each i; ei is equal to 1 or 0 depending on whether the associated aleatory event occurs or not. When H is chosen as the identity function, the distance defined in Eq. 8.2 above coincides with Brier’s rule. The theorem provides immediate grounds for rejecting other proposed scoring rules for the evaluation of forecasters, such as the linear scoring rule, 1X jei  xi j; n n

S.x, e/ D

i D1

which may appear as a natural generalization of a plausible rule for deterministic forecast of binary random variables (namely the one that prescribes just to count the hits and take their average). Observe that the linear scoring rule – which is nothing but the averaged city-block distance between a belief-vector and the vector of observed outcomes – is rejected here on the ground of Property 3, which incorporates the requirement that the distance measure be “order-sensitive”. Not only does this property rule out the linear scoring rule (as being order insensitive), but it also rules out other proper scoring rules, such as the logarithmic or the ’-power ones (with ˛ ¤ 2),9 by requiring that the order-sensitivity of the distance be monotonically related to the difference between the swapped values. To obtain exactly Brier’s rule (up to a linear transformation) from the class of loss functions defined by Eq. 8.2, 9 Observe that any scoring rule based on the generalized ’-power (with ’ > 1) of the absolute differences between subjective estimates and observed outcomes is proper. On this point see (Selten 1998).

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which are all monotonically related to Brier’s rule, it is sufficient to introduce a mild extra-assumption to the effect that the loss determined by the rule grows linearly by replicating the same predictive error: Error replication: Let A, B and C be three forecasters making, respectively, the predictions [x, 1, 1], [x, 1, z] and [x, z, z], with observed outcomes [e, 1, 1]. Then, the difference between the inaccuracy of C and that of B is equal to the difference between the inaccuracy of B and that of A. This reasonable assumption, requiring that reproducing the same error causes the same additional inaccuracy, is sufficient to force H to be linear and therefore to single out exactly Brier’s rule (up to a linear transformation) from the class of monotonically related functions defined by Eq. 8.2.

8.4 Conclusions The theorem discussed in the previous section allows for a justification of the use of Brier’s scoring rule for evaluating epistemic accuracy, and it does so by means of general epistemic considerations concerning the distance between belief-vectors over a series of uncertain events. This results immediately follows simply by requiring (i) that one of the two vectors represents the observed outcomes, regarded as the “belief-vector” of an ideal “infallible forecaster” and that (ii) every forecaster aims at minimizing the distance between her predictions and the ones of the infallible forecaster. Such distance-based scoring rule, which coincides with Brier’s rule, turns out to be “proper”, despite nowhere its characterization makes explicit reference to expected loss or other ad hoc elicitation devices. To put it differently, charging a subject depending on the objective disagreement between his forecast and that of the infallible forecaster (i.e. the observed outcomes), is a natural way of evaluating forecasting that automatically makes “cheating” impossible. This desirable property is a side-result of a “proper” way of measuring accuracy, rather than the sought-for effect of ad hoc cheater-busting scoring rules. Our analysis can therefore be regarded as an independent argument for adopting Brier’s rule that is not an ad hoc adjustment motivated by the elicitation problem. Finally, our approach suggests that de Finetti’s idea of providing a subjectivistic justification of the probabilistic laws in terms of Brier’s rule can be accomplished via a strong direct argument in favour of this rule which bypasses any pragmatic roundabout. Acknowledgments We wish to thank Wolfgang Spohn for very useful suggestions.

References Atkinson A (1983) The measurement of economic mobility. In: Atkinson A (ed) Social justice and public policy. Wheatsheaf Books Ltd., London Brier G (1950) Verfication of forecasts expressed in terms of probability. Mon Wea Rev 78:1–3

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D’Agostino M, Dardanoni V (2009) What’s so special about Euclidean distance? A characterization with applications to mobility and spatial voting. Soc Choice Welfare 33:211–233 Dardanoni V (1993) Measuring social mobility. J Econ Theory 61:372–394 Debreu G (1960) Topological methods in cardinal utility. In: Arrow SK, Suppes P (eds) Mathematical methods in the social sciences. Stanford University Press, Stanford, CA Epstein L, Tanny S (1980) Increasing generalized correlation: a definition and some economic consequences. Can J Econ 13:16–34 de Finetti B (1974) Theory of probability, vol 1. Wiley, New York Joyce JM (1998) A non-pragmatic vindication of probabilism. Philos Sci 65(4):575–603 Kennedy R, Chihara C (1979) The dutch book argument: its logical flaws, its subjective sources. Philos Stud 36:19–33 Lindley D (1982) Scoring rules and the inevitability of probability. Int Stat Rev 50:1–26 Murphy A, Winkler R (1984) Probability forecasting in meteorology. J Am Stat Assoc 79:489–500 Offerman T, Sonnemans J, Kuilen Gv, Walker P (2009) A truth-serum for non-Bayesians: correcting proper scoring rules for risk attitudes. Resource document. Rev. Econ. Stud., forthcoming Rosenkrantz R (1981) Foundations and applications of inductive probability. Ridgeview, Atascadero, CA Savage L (1971) Elicitation of personal probabilities and expectations. J Am Stat Assoc 66: 783–800 Selten R (1998) Axiomatic characterization of the quadratic scoringrule. Experiment Econ 1:43–62 Tchen A (1980) Inequalities for distributions with given marginals. Ann Probability 8:814–827 Tverski A, Krantz DH (1970) The dimensional representation and the metric structure of similarity data. J Math Psychol 7:572–596 Winkler R (1969) Scoring rules and the evaluation of probability assessors. J Am Stat Assoc 64(327):1073–1078

Chapter 9

Interpretation in the Natural Sciences Jan Faye

The distinction between the natural sciences and the liberal arts is usually regarded as significant. Not only do they deal with ontologically distinct objects, but the ways they come to terms with these objects are very different. In philosophy of science there has been a focus on explanation, in contrast to interpretation, because providing explanation was thought to be a key issue in the natural sciences. Since Carl Hempel’s seminal works on explanation, the world of philosophy has seen a growing body of literature devoted to explanation. The results have been prolific. Elsewhere I have argue in favour of a pragmatic-rhetorical theory of explanation, and it is in light of this theory that I suggest we can understand interpretation in the natural sciences (Faye 1999, 2007). Although philosophers of science refer to both scientists’ understanding and the interpretation of data, measurements, and theories in their accounts of the natural sciences, they make little attempt to develop philosophical theories of understanding and interpretation to grasp this side of the formation of scientific knowledge. This is undoubtedly due to the old, but long standing, positivistic distinction between the context of discovery and the context of justification. The context of discovery, where interpretation is thought to belong, is regarded as part of psychology, whereas the context of justification, including explanation, is seen as an object to which logical and philosophical methods apply. After Thomas S. Kuhn, modern philosophers of science tend to be more sceptical about the possibility of drawing such a sharp distinction. In the present paper it will be argued that the natural sciences involve interpretation as much as the human sciences. I distinguish between two notions of interpretation which are rarely set apart. One is concerned with the question what X represents; the other deals with the question of how to represent Y . In the first sense interpretation can be regarded as a form of explanation by which one explains a representational problem.

J. Faye () University of Copenhagen, Njalsgade 80. DK-2500 Copenhagen S e-mail: [email protected]

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9.1 The Standard Wisdom of Interpretation In recent years there has been a growing philosophical interest in interpretation. Most of the work on interpretation is still done within the narrow perspective of making sense out of meaning. The problem is, however, that interpretation is not only restricted to meaning within humanities. Interpretation is used within the natural sciences as well. It is common wisdom that interpretation is associated with the understanding of meaning. The objects of interpretation are considered to be intentional objects or objects having intentional properties. Therefore, interpretation is seen as a process that leads us to an understanding of persons, actions, or products of these actions, such as linguistic expressions, texts, paintings, sculptures, music, film, dance, plays and social institutions. What we understand is the meaning being expressed by these products and an interpreting activity is what shows the way to this meaning. So an interpretation is a response to a question like “What is the meaning of X ?” An interpretation states or formulates some meaning, significance, character, etc., and often interpretation is characterized in semantic terms. But this view is too narrow and simplistic. In one of his many studies of interpretation, Jerrold Levinson (Levinson 1999:3) characterizes the received wisdom of semantic interpretation in three points: (1) “Interpretation standardly involves the formation and entertaining of hypotheses, the weighing of possibilities of meaning, significance, role, or function in regard to a given phenomenon or thing.” (2) “Interpretation standardly involves conscious, deliberate reflection, explicit reasoning, or the like. Not all perception or understanding or apprehension is properly viewed as interpretative, some such is clearly preinterpretative, and serves as that on which interpretation rests, or that from which it departs.” (3) “Interpretation standardly presupposes the nonobviousness of what is being interpreted; if one simply and securely sees that X is F , if there is no question of choosing or deciding to do so, then remarking that X is F is not a matter of interpreting it.” The received wisdom has been called into question by so-called post-modern philosophers who argue that every belief, idea, or opinion is acquired in virtue of an interpretation. There is, however, very little that supports such an extreme view (Faye 2003). Levinson is no post-modern philosopher. He more or less accepts “these three features as definitive of any activity worth labelling interpretative.” I very much agree. The first feature, mentioned by Levinson, is that interpretation consists of ‘formation and entertaining of hypotheses’. If we include the hypothetical character as a necessary feature of interpretation, we may define interpretation as (I) The connection between X and Y constitutes an interpretation for some person P , if and only if (i) P believes that X represents Y because X is in some manner

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attached to Y , and (ii) P ’s belief as expressed in (i) is presented as the result of a hypothesis. (Cf. Faye 2002:56) How X is attached to Y is determined by the kind of objects being interpreted. If X and Y stand for physical phenomena it may be a case of cause and effect, but if they stand for items relating to human thought and agency, the connection may be intentional or conventional. Thus, there are two kinds of “representing”: causal, as when effects “represent” their causes and therefore act as the evidence for holding certain causes occurred, and non-causal, intentional, or conventional as in what a work of art “represents”. Levinson believes that interpretation is concerned with meaning, significance, purpose, or role which he associates with semantic issues in a broad sense. For instance, he assumes that interpreting whether or not a rock is a meteorite, an unexpected natural event, readings or measurements are all examples of semantic interpreting, admitting that ‘semantic’ should be understood broadly. As far as interpreting aims at finding out which conceptual category covers a particular specimen or a natural event, it is certainly justified to call it “semantic.” I think, however, that there are other forms of interpretation that depend on the kind of object under consideration and the epistemic character of one’s representational problem. Hence, I suggest a distinction between proper semantic interpretation as an activity directed towards linguistic or symbolic meaning from other kinds of interpretation such as causal, structural, functional or intentional interpretation. The third feature of those mentioned above indicates that we make use of an interpreting activity in case we are facing something which we cannot immediately recognize or understand. But, then, how do we differentiate between explanation and interpretation? If both supply the explainee and interpretee with understanding, an obvious answer seems to be that explanation provides understanding in virtue of causation whereas interpretation is occupied with understanding in virtue of meaning. We carry out explanation whenever there is something we don’t understand, and we engage ourselves in interpretation for similar reasons whenever we are facing a representational problem or a representational exigency.

9.2 Interpretations in Science We do talk about interpretation in the natural sciences. Think of interpretation of visual phenomena, experiments, measuring effects, data, formalisms, mathematical models and theories. Interpretation takes place in cases where we want to understand what is going on in astronomy, physics, chemistry, and biology. If this is true, then the objects of interpretation need not be intentional objects. Interpretation is not merely oriented towards objects that carry linguistic or symbolic meaning like languages, actions, and social institutions, but just as well towards the unanimated and meaningless nature. Interpretation should not be characterized as a cognitive activity which involves understanding meaning. Being a cognitive activity it should be characterized with respect to what it does with the interpreter. The functional role

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of interpretation is to make a conventional sign or a natural phenomenon meaningful for the interpreter; that is its role is to provide him or her with a further understanding of the object in question. In science what makes a phenomenon meaningful is our ability to place that phenomenon into a causal story or to subsume it under a general law. Looking for applications of the notion of natural law or the notion of causation seems to be the way we attempt to understand things in science. As in other areas, the state of understanding is reached when a badly understood phenomenon is connected with some other phenomenon according to our background assumptions. So a question like “What does X mean?” may in the right context be equivalent to posing the question “What causes X ?” or “What is X evidence of?” So whereas the objects of interpretation may differ, it also seems to be the case, regardless of the nature of the object under investigation, that the cognitive act of interpreting within science and humanities have something in common. What turns a question into one about interpretation is not the kind of object that is subject of the question but the kind of epistemic context in which this question appears. Such an interpretation-seeking question arises, so it seems, in an epistemic context in which the interpreter faces a representational problem. A person may be presented with an interpretation by another person as an appropriate reply to her interpretation-seeking question. But if nobody (to her knowledge) is able to answer her, she has to respond herself. Whenever a person comes up with a hypothetical answer as a reply to questions like “What does X mean?” etc., she is involved in an act of interpretation. We are engaged in an interpretive process in situations where we try to understand (or improve our understanding of) a particular phenomenon – whether it is verbal meaning, visual signs or unknown or unexpected natural events – and whenever we can get no help from other people who may understand what we actually don’t understand. We interpret by asking interpretation-seeking questions and then go on by answering them in terms of positing a hypothesis. In situations, which produce an underdetermined answer, a more provisional hypothesis is formed. But interpretation need not be more tentative than explanation; it simply depends on the consensus of the interpretive community. Strangely enough, philosophers of science who have been occupied with explanation have paid little interest in characterizing interpretation in spite of the fact that they themselves speak of interpretation.1 This lack of interest is partly due to the fact, I think, that they intuitively assume that these two concepts belong to each side of Reichenbach’s famous distinction between the context of discovery and the context of justification. Thus, interpretation has to do with the context of discovery, whereas explanation belongs to the context of justification. They simply didn’t take the notion of interpretation serious because they considered it to be too psychological with its close ties to meaning and understanding; tacitly, they seem to have accepted the hermeneutic division between explanation and understanding as 1 An exception is van Fraassen and Sigman (1993) in which Bas van Fraassen and Jill Sigman write about interpretation in the natural sciences and the fine arts. But van Fraassen does not attempt to relate their discussion of interpretation to his pragmatic theory of explanation.

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important for a characterization of the difference between the natural sciences and the humanities. In contrast, hermeneutic philosophers have dealt with understanding and interpretation, but paid no attention to explanation. An important consequence is that the rigorousness of the various accounts of explanation is missing with respect to the accounts of interpretation. Explanation was the object of a logical analysis, interpretation involved a psychological specification.

9.3 Two Forms of Interpretation But there is more to interpretation than the fact that the natural sciences also make use of it. There is a general ambiguity in the way we think of interpretation which seems to have gone unnoticed. Sometimes the object of an interpretation is what is considered to represent something such as signs, symbols, and symptoms. The interpretation-seeking question is then questions like “What does X mean?”, “What does X stand for?”, “What is X evidence for?”, “What kind of role does X have?”, or “What causes X ?” We shall call a response to any such questions, for the lack of anything better, a determinative interpretation.2 In science these kinds of questions are posed in connection with data, observation, mathematical models, and theories. The industry around concocting interpretations of quantum mechanics reveals better than anything that determinative interpretation in science takes place on the scale of metaphysics. But the separation of mathematical models and physical reality is also a place for determinative interpretation. This is so because there is no blank inference from a statement that X is mathematically well-defined or X figures in a mathematical structure to a claim that X has physical meaning, or what X stands for is physically real. A mathematical model may have a surplus structure which has no real counterpart. Take, for instance, the existence of advanced solutions to the Maxwell equations or the negative energy solutions of the relativistic four-momentum vector. From these solutions we cannot automatically deduce the existence of backward causation of some sort. Finally, on the level of discovery of new data or measurement results, a great amount of determinative interpretation is present all the time. For instance, the observation of type 1a supernovas by Perlmutter et al. and Smith et al. in the last 7 years has shown that the light is dimmer when comparing light curves with red shifts than would be expected if the Universe were expanding or slowing down at a constant rate. This observation is then interpreted as a sign that the expansion of the Universe is increasing, but also the experimental data, which define the actual light curve and redshift, are constructed based on determinative interpretations.3

2 Levinson isolates two notions of interpretation which he calls the ‘determinative mode of interpretation’ and the ‘exploratory modes of interpretation’. The first is concerned with the question “What does it means”; the second is dealing with “What could it mean?” Even though the first notion is similar to the one suggested here, the second is not. 3 See Saul Perlmutter’s review article (Perlmutter 2003), in which he talks about “Such a supernova CAT-scan is difficult to interpret” p. 53. A supernova CAT-scan is the measurement of the

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Sometimes, however, interpretation cannot be considered a cognitive response to a question like “What does X mean?” or similar questions. In these cases the object of interpretation is a phenomenon Y that lacks a proper conceptual or mathematical representation. Facing this kind of epistemic problem the interpretative questions are like “What is Y ?” or “How can Y be represented?” We shall call a proper response to such a question an investigative interpretation. Clearly, there is a difference here between the two types of interpretation. The distinction is between whether or not it is the representation or the would-be represented that is the object of one’s curiosity and attempts of understanding. A determinative interpretation suggesting whether or not X represents Y is a form of explanations, whereas an investigative interpretation telling us how Y may be represented can be seen as a conceptual or theoretical presentation of Y which may then be used for explanatory purposes. Determinative interpretations act as explanations of meaning in a broad sense. It is not the degree of certainty being associated with the response which determines whether it should be considered as an interpretation or an explanation. In the constellation Norma, 10,000 light years away, astronomers recently discovered a strange object in the centre of a supernova remnant (De Luca 2006). At first sight it looks like a neutron star. It is estimated to be about 20 km across like other neutron stars. But a closer study shows that its X -ray outburst is tens of thousands of times longer than expected from newly created neutron stars. And 1E161348-5055, as the object is called, is still young, approximately 2,000 years. So we have a situation which calls for interpretation: What does this mean? In the actual context this question is identical to “What causes the abnormal behaviour of 1E?” One answer is that the object is a magnetar, i.e. an unusual subclass of neutrons that is highly magnetized. However, these spin several times faster than this object. The suggestion is then that the object is surrounded by a debris disk slowing down the rotation of the star. Nothing like this has ever been observed before. Another answer might be that 1E is a part of a binary system where the other half is a low mass object smaller than our sun. Similar systems are known but in general they are millions of times older. Thus, scientists do not yet know how to explain the unusual behaviour of this, object and until one of these speculations is confirmed, they all count as possible interpretations of data. On the other hand, every proposal of classifying and representing an object or a class of objects, a structure or a class of structures, a relation or a class of relations in a non-obvious and unexpected way is an example of investigative interpretation. Famous examples are Copernicus’ heliocentric model, Newton’s three laws, Bohr’s semi-classical model of the atom, or Einstein’s field equations around the time when these constructions were presented to the scientific world. It was not until later that these conceptual constructions lost their hypothetical and tentative character and gained their emblematic nature. This happened at the very moment the scientific

atmosphere of the exploding type 1a supernova. When the outer layer of atmosphere is thinning it allows us to observe the inner layers and the changing luminosity of the energy spectrum.

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community accepted them, at least for a while, as being empirically successful and therefore correctly representing the observable fact. The above example of 1E161348-5055 is not a case of investigative interpretation. Based on models of star evolutions and the data of observation, astronomers still believe that the object left behind is a neutron star. It is only the X -ray outburst data that does not fit neutron stars seen so far. The astronomers do not even question what these data are evidence of. They agree about their interpretation. They merely want to know what causes them to stand out from similar data from other neutron stars. Investigative interpretations are concerned with classification and categorization. A realist concerning natural kinds might argue that this kind of interpretation is explanatory because classifications by theories are literally true. But a more pragmatic view on natural kinds and theories may take them to be vocabularies or conceptual tools for the construction of models which then can be used to give explanation. Thus, investigative interpretations are necessary presuppositions for generating explanations.

9.4 Interpretation and What-Questions Often explanations are associated with responses to why-questions. So a possible way of trying to separate explanation from interpretation would be to suggest that an explanation-seeking question is a why-question whereas an interpretation-seeking question is a what-question. The idea is that we ask what-questions as long as we have very little or no knowledge of the subject being asked about. But as soon as we acquire more information about the subject we begin to formulate how-questions and finally we pose why-questions to get the ultimate information. A typical example would be one in which we start out with “What is it?” Depending on the context that gives rise to the question, the requested information seems to require either a determinative or an investigative interpretation. Assume you are looking at a bright white spot on a starry sky. You know, as part of your background knowledge, that what you see is not a planet or a comet, but a hitherto unobserved big and bright star. This was also Tycho’s conclusion after he had argued, based on observation of no parallax, that the very bright spot he saw in the constellation Cassiopeia didn’t belong to the spheres of the planets. The question “What is it?” then became equivalent to a question like “What does an unexpectedly appearing star mean?” The interpreting answer might then be “It’s a newborn star.” Tycho, believing that the star he saw shining bright in the sky year 1572 was a new star, was in fact wrong in his interpretation of the phenomenon. But not until last century did astronomers realize that the phenomenon witnessed by Tycho was a star dying of age. It was a supernova. Baade and Zwicky (1934a) were the first to interpret observational data of suddenly very bright objects by separating common novas from supernovas in terms of their brightness. Furthermore, based on the luminosity of observed supernovas and by using Einstein’s mass-energy equation they

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calculated the amount of mass being dispersed into space. Their conclusion was “that the phenomenon of a super-nova represents the transition of an ordinary star into a body of considerably smaller mass.” (p. 258) But they did not account for the nature of this object. In the consecutive paper published in the same issue, Baade and Zwicky (1934b) proposed that the object might be a neutron star. “With all reserve we advance the view that a super-nova represents the transition of an ordinary star into a neutron star, consisting mainly of neutrons.” (p. 263). This suggestion was made just a year after James Chadwick discovered the neutron. Thus, you may say that their supernova hypothesis was an example of a determinative interpretation, whereas the neutron star hypothesis may count as an example of an investigative interpretation. It was mainly due to theoretical reasons that they identified the leftover of a supernova explosion as a neutron star because such a star might “posses a very small radius and an extremely high density.” This, they noticed, is a result of the fact that neutrons can be packed much more closely than electrons and nuclei. The next question might then be something like “How does a supernova develop?” A qualified response to this question would, assuming that light coming from a supernova contains information about this process, require an answer to the following question: “How does the light of a supernova vary over time?” Baade and Zwicky were not able to answer any of these questions in 1934. As they stated: “A more detailed discussion of the super-nova process must be postponed until accurate light-curves and high-dispersion spectra are available. Unfortunately, at the present time only a few underexposed spectra of super-novae are available, and it has not thus far been possible to interpret them.” (p. 259) An answer came in 1941 when Rudolph Minkowski suggested that supernova could be divided into type I and type II according to their different spectra and different light-curves. The same year, an answer to the question “How does a supernova take place?” appeared. The idea was that a star becomes a supernova through an explosion and a mechanics was suggested for how such an explosion was possible. It was only thereafter that astronomers had reached a level of understanding where the stadium of explanation could be introduced. Astronomers could now hope to answer a question like “Why does a supernova explosion happen?” However, it was not until 1960, after the standard theory of stellar nucleosynthesis had come to light (Burbidge et al. 1957), that Fred Hoyle and William Fowler (1960) were able to set up a quantitative theory of supernovas. According to this theory, the explosion of type I supernovas is caused by the “ignition” of heaver nucleons, especially carbon, in the centre of the stars; whereas type II is generated by an implosion of non-degenerated matter to a neutron star in the core of very heavy stars. A reasonable theory of supernovas was available around 1970, although a revised and even better understanding arose around 1990. This was a result of the fact that the astronomers became aware of the explanatory advantage it had to make a finer distinction among supernovas (type Ia, Ib, Ic, IIP and IIL) and to combine nuclear physics with hydrodynamical models (describing chock waves.)

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Unfortunately, the proposed distinction between explanation and interpretation does not work. There are four reasons for this: (1) we can rephrase some whatquestions as why-questions, and vice versa. For instance, “What makes X happen?” is semantically equivalent to “Why does X happen?” The questioner may therefore posses as little or as much information about X when he or she puts forward a whyquestion or a what-question. (2) Likewise, some what-questions can be translated into how-questions, and vice versa. The question “What is the relationship between X and Y ?” has the same semantic content as “How does X relate to Y ?” (3) It is not every what-question that invites an interpretation. Take examples like “What time is it?” and “What is an electron?” Similarly, not all why-questions are requests for explanation. It depends on the actual context whether or not they are. (4) Finally, everyone will probably agree that a response to a question such as “Who is the murder?” “When was the victim killed?” or “Where did the killing take place?” may be classified as an interpretation given the epistemic uncertainty by which the answer is produced. But it also seems to be the case that some questions formulated as why-questions or how-questions may only be addressed tentatively and answered with a great amount of doubt. Any such question addressed in terms of a hypothesis that is not testable, or even not tested, can rightly be called an interpretative inquiry. For instance, nobody knows why the universe began expanding around 14 billion years ago, and any proposal based on theoretical and experimental information has the character of an interpretation.

9.5 Interpretation as a Response to a Representational Question A determinative interpretation is, I suggest, an explanation that intends to solve a cognitive problem concerning understanding a representational issue. It is a result of a cognitive activity by which one explains the representational role of some given phenomenon. Inquiries about the representational role appear in connection with the consideration of natural effects, data, measurements, objects, signs, symbols, texts, or actions where the inquirer does have an epistemic problem of not understanding the representative task of what she is seeing, hearing, reading, observing, etc. A determinative interpretation arises in contexts where a phenomenon is considered to represent something else, say a peak on a graph, but where there are doubts about what the phenomenon is a sign of. Similarly, we can say that an investigative interpretation takes place whenever the inquirer has an epistemic problem of not understanding what she is seeing, hearing, reading, observing, etc. She then attempts to solve her cognitive disability by looking for a possible candidate of an appropriate conceptual classification or theoretical construction. Such a cognitive description may then be used with the purpose of explanation. Thus, we ask for an interpretation whenever we believe that we do not possess the right and/or necessary information to solve a representational problem but

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believe that we, or somebody else, may have the capacity to provide us with a suggestive clue. An appropriate response is generated by the interpreter based upon a certain understanding of the cognitive problem raised by the interpretation-seeking question. As we have seen from the supernova examples, what is considered a relevant response is constrained by our background assumptions. Tycho assumed that a bright object in the sky belonged to the stellar sphere in case it didn’t show any parallax, an assumption that has never been put into doubt. Similarly, Baade and Zwicky presupposed that Einstein’s mass–energy formula is correct and that Chadwick had discovered electrically neutral particles with no electrostatic forces between them and therefore densely packable. The relevant hypothesis in Tycho’s understanding was that the sudden appearance of a star presented a birth whereas in the Baade and Zwicky’s understanding, the same phenomenon pointed to a supernova, i.e. a star dying of age in transition from the stage of an ordinary star to the stage of a neutron star. So if no acceptable explanation of a certain phenomenon is available, we must ask the right interpretation-seeking questions and answer them by proposing a relevant hypothesis that can be used for explanation. Promoting a particular answer is exactly what interpretation is. In situations where we understand things straight away, where we have knowledge of the facts involved and of the representational conventions, no interpretation is needed, and any response to a representational question, which relies on these facts and conventions, does not involve an interpretation. A pragmatic notion of interpretation sees it as a context-dependent response to an interpretation-seeking question, and because the role of interpretation is more or less the same as that of explanation we may apply a pragmatic-rhetorical theory of explanation to interpretation as well. According to this approach, an interpretation is a deliberately produced answer to an interpretation-seeking question. How the interpretation turns out depends in part on the process and therefore, among other things, on the aim and cognitive interest of those who do the interpretive work. My claim is that the type of interpretation is determined partly by the interpreter and partly by the object of the interpretation. Indeed, the object plays an important role in the interpreter’s selection of the relevant type of interpretation. The interpreter constrains her interpretation in accordance with her grasp of the object by choosing the type of interpretation accordingly. A natural phenomenon will give rise to a different kind of interpretation than a text or a painting. But the interpreter’s knowledge of the situation, her goals and interests are also elements in determining the form of interpretation. Thus the person’s background assumptions and his pre-understanding of the object influence the hypothesis she generates. This applies not only to the form of hypothesis, but to the content as well. The content of an interpretation is as much context-dependent as its form. But, again, the object of interpretation imposes some constraints on any possible understanding of the content.

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9.6 Conclusion Interpretation issues an answer to a question about the representation of a phenomenon whose comprehension falls outside the inquirer’s background knowledge. Whenever we interpret something it is because we can’t explain it since we don’t understand it. The answer transforms a phenomenon, now understood in terms of some theory, from being somehow unfamiliar to something less unknown. The phenomena, or rather beliefs about the phenomena, are thereby included among that person’s background assumptions and connected to his or her background knowledge. Phenomena become intelligible and meaningful because by attributing identity to them or providing a representational explanation of them, an interpretation brings them in connection with our theories or belief systems. Thus, the aim of interpretation is to reach a proper understanding of a representational phenomenon regardless of whether the proposed explanatory hypothesis is concerned with traditional meaning, function, intention or causation. In the end an interpretation is a hypothesis which is presented against a background of accepted conventions and ontological assumptions.

References Baade W, Fritz Z (1934a) On super-nova. Proc Nat Acad Sci USA 20:254–259 Baade W, Fritz Z (1934b) Cosmic rays from supernovae. Proc Nat Acad Sci USA 20:259–263 Burbidge EM, Burbidge GR, Fowler WA, Hoyle F (1957) Synthesis of elements in stars. Rev Modern Phys 29:547 De Luca A et al. (2006) A long-period, violently-variable X-ray source in a young SNR. Science Express. 6 July issue Faye J (1999) Explanation explained. Synthese 111:61–75 Faye J (2002) Rethinking science. A philosophical introduction to the unity of science. Ashgate, Aldershort Faye J (2003) Neo-modernism: a new approach to the humanities. In: Julio Jensen H (ed) The object of study of the humanities. Museum Tusculanum, Copenhagen, pp 48–66 Faye J (2007) The pragmatic-rhetorical theory of explanation. In: Persson J, Ylikoski P (eds) Rethinking explanation. Series: Boston studies in the philosophy of science, vol 252. Springer, Dordrecht, pp 43–68 Hoyle F, Fowler W (1960) Nucleosynthesis in supernovae. Astrophys J 132:565–590 Levinson J (1999) Two notions of interpretation. In: Haapala A, Naukkarinen O (eds) Interpretation and its boundaries. Hensinki University Press, Helsinki, pp 2–21 Perlmutter S (2003) Supernova, black energy, and the accelerating universe. Physics Today, the April Issue:53–60 van Fraassen B, Sigman J (1993) Interpretation in science and the arts. In: Levine G (ed) Realism and representation. University of Wisconsin Press, Madison, pp 73–99

Chapter 10

Multiple Realizability and Mind-Body Identity Simone Gozzano

One of the purposes of science is to provide identifications such as “water is H2 O”. The process of setting such identifications goes hand in hand with the answers to many “why” questions: “Why is water boiling at 100 ı C and freezing at 0 ı C?” Such a task is ubiquitous in all empirical sciences. Consider now the sciences of the mind, from cognitive science to psychoanalysis. Can such “theoretical identifications”, to use an expression from David Lewis, be provided in case of psychological properties? If I am right in characterizing this as one of the aim of science, the importance of the question is evident: a negative answer to it would mark a limit for science. Such a boundary would extend to all those mental phenomena that have to do with mental properties, in general, and properties concerning consciousness in particular, because these have proven to resist the individuation strategies adopted for other mental properties, as the intentional ones. Phenomenal consciousness would be beyond the domain of the scientific method, not to mention our cognitive capacities (cf. McGinn 1991). Hence, mental phenomena that would prove intractable within the method of science should be considered as not naturalizable, as frequently the issue is posed, or would mark the incompleteness of science as to the natural world. In order to avoid this serious limit, many forms of non reductive physicalism have emerged, all trying to vindicate the naturalness of mental phenomena while avoiding any theoretical identification, as construed by Lewis. The mental, its properties in particular, have been considered at most token-identical with physical properties, or in some or other relation with them, being this of supervenience (Kim 1998), determination (Yablo 1992), realization (Shoemaker 2007) constitution (Rudder Baker 2000) or emergence (Chalmers 1996). In recent years, however, a number of philosophers (Bickle 1998; Polger 2003; Hill 1991) have reaffirmed the possibility of providing the most radical form of theoretical identification: type-identity. The motivating reason in favour of the type identity theory of mind is that it provides a powerful solution to the problem of the causal efficacy of mental properties vis a vis the acceptance of the principle of causal closure of the physical domain and the rejection of overdetermination. True, one may challenge both these assumptions, S. Gozzano () Universit`a di L’Aquila, L’Aquila, Italy e-mail: [email protected]

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but if one endorses them, as I do, the clearest way of defending the causal efficacy of mental properties is to identify them with physical properties. In the following, leaving aside a defence of the two mentioned assumptions, I will confine my defence of the identity between mental and physical properties just to sensations, thereby excluding intentional properties from the outset (cf. Hill 1997).1 How can such an old and disregarded theory be rescued? Some have argued that we should get at these identities by empirical research (Block and Stalnaker 1999); others invoke the Armstrong-Lewis’ way, that consists in having conceptual analysis and empirical investigation in reciprocal evolution, delivering at the end the desired identities. Jaegwon Kim (1998) develops such a strategy, in what he calls the “functionalization” of mental properties. However, he thinks that this process could bring positive results in case of intentional properties, while being almost hopeless if applied to the phenomenal ones (Kim 2005). So, why is the type-identity theory (henceforth identity theory) so disregarded? Two main arguments have been marshalled against the identity theory. The first is the multiple realizability argument, according to which any type of mental property can be realized by different types of physical properties; the second, let us call it the phenomenological argument, indicates that no description, explanation or understanding of physical properties is sufficient to grasp the qualitative character of mental properties. George Bealer (1997) has argued that at the origin of both arguments there is Kripke’s argument concerning necessary identities statements. A large part of this paper is devoted in blocking this argument. I will argue that a causal approach to sensation will fit the bill. One of the main objections to the identity theory points out that the supposed identity “pain D C-fibers firing” fails because it does not present a unique condition of realization. The multiple realizability argument says that other realizers of pain are possible. However, if terms like “pain” and “C-fibers” designate natural kinds, and Kripke is right, then the criticism is misplaced: the purported identity would simply be empirically false but not for the reason that natural kinds are multiply realizable, because none could be so. At most, this natural kind which is pain could be associated with many other natural kinds, but surely not be realized by any of them. If, on the other hand, the terms involved are not natural kinds, then it is the argument by Kripke against the identity theory that is misplaced, even if in that case we would have to reconsider whether we have a theoretical identification at all. So, if you like exegesis, Putnam and Kripke are not on the same boat, at least as to their critical remarks to the identity theory. A form of dissatisfaction toward Kripke’s argumentation was already present in some papers by Lewis and has been further elaborated by Mark Wilson (1985) who noticed that the failure to consider relative identities is a mistake from the perspective of philosophy of science that cuts philosophy of mind across. On the same score, Hooker (1981), Enc¸ (1983) and Paul Churchland (1984) have pointed out 1 For ease of formulation, in this paper I will use, somewhat interchangeably, “properties” and “states”. I take mental states to be exemplifying mental properties, so that being in a pain state is having the property of being in pain.

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that “heat D molecular motion” is a first approximation statement of identity. In fact, heat is molecular motion in gases and solids (with differences in the mathematical Methods of measurement) blackbody temperature in the vacuum and ions movements in plasma, where molecules have been ripped apart (Bickle 1998). So, you can keep with the idea that identity statements if true are necessarily true, but the identity statements you want to consider have to be identities all the way down from the very beginning. If you have a first approximation statement, such as “heat D molecular motion”, you won’t go that far unless much more specific local identities are considered, such as “plasma heat D ions motion”. This line of reasoning, that was a way to preserve the idea of rigid designator from prima facie objections, has been pursued by Kim as well. He has argued that psychological properties get specific identifications depending on the species or structures in which these are realized: “: : : any system capable of psychological states : : : falls under some structure type T such that systems with structure T share the same psychological base for each mental state-kind that they are capable of instantiating” (Kim 1992, p 517). The specificity issue, though, can be further extended. Let turn our attention just to, for instance, gases, letting aside considerations about quantum-mechanics, as raised by Wilson. If heat is the movement of molecules, it remains to specify which molecules are at stake. Molecules of water and molecules of oxygen, for instance, constitute different natural kinds. Heat is independent from these finegrained considerations, and the same applies to molecular motion, because both could be realized by molecules of H2 O or O2 . If so, then neither “heat” nor “molecular motion” are natural kind terms, indeed not a surprise, nor they seem to be proper names or definite descriptions2 ; but if so, then what kind of identity is “heat D molecular motion?” I take heat and molecular motion to be categorical concepts, whose identity conditions can be given in terms of a similarity relation among various entities. In fact, in order to measure heat is not necessary to have this or that molecule moving, what is essential is the moving of some molecules. However, if the goal is to provide identity statements for this kind of concepts, it is essential to place specific co-referential rigid designators on both sides of the identity sign. For instance, applying the identity between heat and molecular motion to, say, water, should result in something like “water heat D H2 O motion”. This is a necessary identity statement that provides a full theoretical identification, because both “water” and “H2 O” are rigid designators and co-referentially so.3 What I have said so far can be applied to the case of pain, to a certain extent, by reformulating the original identity statement proposed in the 1950s. The analogous of “heat D molecular motion” would not be “Pain D C-fibers activation”, rather “Pain D pain-fibers activation”. The essential element of the statement is that the

2

At least prima facie. As I said, my argument is not restricted to heat. The identity “light D electromagnetic radiation” is schematic as well. Its specific applications have this form: “white light D electromagnetic radiation at n wavelength”. The same applies to “gene D chain of DNA”. The identity then has the form (x) Hx D Mx with both H and M being functional descriptions ranging over variables that could be replaced by names or natural kind terms. 3

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sensation under consideration, pain, is nothing but the activity of specific fibers. When we get to the details we arrive at something like “human pain D C-fibers activation”, an identity statement limited to a particular species. However, human and C-fibers are not co-referential stricto sensu, but one could consider C-fibers as a place-holder for a much more complex structural description of human beings, one that picks painful human beings and them alone. The above argument, I think, blocks the idea that natural kinds, and in general all the referents of rigid designators, can be multiply realizable. The point is that as long as terms such as ‘heat’ are used in a generic way, they can be multiply realizable but cannot be considered as rigid designators. Undoubtedly, there is something that all hot things have in common, the movement of their constituents, but one cannot do much science with this knowledge alone, without mentioning that this knowledge, after all, comes after the discovery that a still object has moving parts, making the immobility of x a non supervening property on the movement of x’s parts. Even accepting the above argument, we still have to face a further challenge: pain is a kind of property that requires sentient beings, while heat is not. In a vivid way of reporting this problem Kripke says: Suppose we imagine God creating the world; what does He need to do to make the identity of heat and molecular motion obtain? Here it would seem that all He needs to do is to create heat, that is, the molecular motion itself : : : but what is substantive task for the Deity is the task of making molecular motion felt as heat. To do this He must create some sentient beings to insure that molecular motion produces the sensation S in them. (Kripke 1980, p 153)

Moreover, and most importantly to Kripke’s eyes, in case of pain and other apparently “intransitive sensations”, as Armstrong (1968) called them, the na¨ıve distinction between appearance and reality collapses. In case of pain we may say what you feel is what you get: pain just is feeling pain, something that is not true in case of heat, or red. If pain is a rigid designator what is its reference? Because in that case appearance and reality coincides, the result is that “Pain is not picked out by one of its accidental properties; rather it is picked out by the property of being pain itself, by its immediate phenomenological quality” (Ibid., p 152). However, such a quality is not, according to Kripke, identical with any accompanying physical state: “It would seem, though, that to make the C-fibers stimulation correspond to pain, or be felt as pain, God has to do something in addition to the mere creation of the C-fibers stimulation; He must let the creature feel the C-fibers stimulation as pain, not as tickle, or as warmth, or as nothing, as apparently would also have been within His powers”. (Ibid., p 154). If we stick with the idea that both “pain” and “C-fibers” designate natural kinds, then when we are in pain we simply have the co-occurrence of these natural kinds. Whenever is true of me that I am in pain, is true of me that I have C-fibers firing, but no further relation between these two properties of me can be established, because it is not necessarily true that a tokening of pain is a tokening of C-fibers firing. So, the referent of pain is the very feeling we may have in the most disparate circumstances. In other cases, the referents are the, often, hidden nature of the entities designated: in case of x’s heat is x’s parts motion, in case of water, or gold, is the

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chemical structure, in case of living beings is their “internal structure”, the one that makes us to suppose that they form a certain species or natural kind. Kripke’s point concerning the sensation of pain applies to any sensation, as the quotation concerning heat shows, so the element of contingency between the physical accompanying state and the phenomenological state holds in all those cases. This contingent relation calls for what can be considered a naturalistic question: how are the sensations fixed? How to we get to have this or that sensation? Let’s imagine God creating H-fibers, that is the very fibers, in our nervous system, that are activated by heat. If God wanted to create some fibers devoted at revealing increasing or decreasing of heat, the best design option would be that of making the activation of these fibers causally entrenched in the very phenomenon these are supposed to reveal, i.e. molecular motion. If “heat” is rigid the only warranty we have for being justified in affirming that we feel heat4 is that H-fibers are necessarily activated by heat. In this sense, H-fibers are natural thermometers necessarily activated by differential changes of temperature (heat).5 H-fibers activation, then, could reasonably be taken as the result of a necessary relation – the holding of a law of nature – due to the sensitivity of these fibers to the property “heat” picks out, namely, molecular motion. Surely these fibers, as any other thermometer, may fail to work properly, but their failure is not due to the violation of a law of nature, rather to some disturbing condition or to their relation with heat obtaining caeteris paribus. Granting that the fibers for heat are necessarily activated by heat, how about the relation between the activation of these fibers and the sensation of heat? According to Kripke, this is a duty for the Deity: S/He has to make the activation of these fibers to be felt as heat and not as, say, tickle. But is this a real option? Consider Susan, a person like you and me: she touches a warm stove, has her H-fibers activated and, here the only difference, feels a tickle. By ‘feeling a tickle’ here we must mean that Susan feels the tickle as a tickle; had God set the feelings in a different way, she could have felt heat, or nothing. The view that Kripke is licensing, then, is that the qualitative character of mental states and properties is intrinsic and independent of their activation conditions, something more radical than qualitative inversion. In fact, what Kripke is assuming is that Susan can feel heat even if no conditions of the kind responsible for the activation of the H-fibers has ever be present in her. That is to say, God (or chance, or Kripke) may associate the feeling of heat with the activation of some non warm condition. Now, if all Susan’s reactions and interactions with the warm stove were identical, let’s say similar enough, to our own, how

4 I think we should take the nomological and causal relation to obtain also in the case of cones in the retina regarding colours perception. We would not be justified in asserting that we perceive colors unless we admit that cones activation is the causal effect of a necessary causal relation between light being reflect at such and such wavelength and these structures reacting so-and-so to such a reflection. This point has many consequences on arguments regarding qualia such as the absent qualia and the inverted spectrum ones. For reason of space and of argumentation I will not consider these issues here. 5 Here is pretty evident the sloppiness in Kripke’s use of the term “heat” instead of “temperature”.

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can we make sense of the idea that she has a tickle sensation when we have a warmth sensation? If we touch a warm stove, our H-fibers get activated and we have a heat sensation; if Susan does, her H-fibers get activated but she has a tickling sensation. Because, as I have argued, the relation between the property of the stove and the activation of the H-fibers is covered by a causal law, then this must hold for us and Susan. So why the similarity breaks after that point? Here the kripkian should affirm that H-fibers firing does not causally necessitate feeling hot, otherwise Susan would feel hot, nor they necessitate not feeling hot, otherwise we would not feel hot. Two options are available at this point: either sensations are only contingently caused by corresponding physical conditions, or the link between sensations and physical conditions is not even causal, rather the result of a pure association. If the first option is taken, it all depends on how the contingency is interpreted. If we mean that in this nomological world these physical conditions necessarily cause this kind of sensation, but there can be other nomologically possible worlds in which the relation is different, I would have my point because I think that in the case under consideration nomological necessity is the highest degree of necessity (and Kripke himself admits such possibility). Other nomologically possible worlds are simply not relevant for the present issue. The more radical construal of causal contingency, according to which in this nomological worlds in touching something hot sometimes we feel hot and sometimes we feel a tickle seems just inappropriate and empirically false in most of the cases. Endorsing the second option mentioned entails that the relation between sensations and activating conditions, being a pure association, is arbitrary and conventional, depending on God’s action. So, back to the case of Susan, qualitative state would be causally idle because the pure association hypothesis is compatible with the idea of two people manifesting the same overall causal roles – and not just the same behaviouristic roles – while having different qualitative states. Hence, the qualitative component of our mental life would play no role in our behavioural and physical life. In such a case not only sensations would be causally impotent, but we would also face a conceptual mystery: I could feel disgust in touching a hot stove, and feeling hot while hearing a C-major chord. Disgust, then, would not concern tasting and hot would not necessarily concerns temperature notwithstanding that their qualitative features would remain constant. I have insisted on the idea that sensations participate in the causal structure of the properties they give us feelings about. It is time for me to frame this idea in a wider perspective. I take sensations to be information bearing states: they provide information on the conditions of the receptors. Having a sensation of hot is having the information that the temperature receptors are thus and so activated. Receptors are activated in virtue of their participating in the causal structure of the properties they are tuned at. So, heat receptors are causally embedded in molecular movements, light receptors react to electromagnetic radiation, gustatory receptors are activated by bonding with molecules of quite proximal stimuli, and so forth. Hence, sensations provide the information that a certain causal relation has been established. A second feature of sensations is the following: the information provided, concerning receptors, has to be distinctive if it has to play any role for the system’s life.

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That is to say, the information concerning temperature receptors has to be distinctive, qualitatively speaking: it is only that kind of receptor that provides that qualitative state. One and the same receptor cannot sometimes give a sensation of hot and sometimes a sensation of disgust, because the system would find no advantage (or perhaps some damages) in having such mixed up information. Distinctiveness, or qualitative stability, is an essential feature of sensations. We rely on it in considering what information our receptors are giving us on what is happening in the world around us. Now, if a Deity creates a receptor that detects a specific property in the world and brings about a distinctive sensation, what such sensation is like is basically irrelevant. Sensations are information bearing and qualitatively distinctive states; if these are their essential properties then what it is like to have one quale or the other is inessential provided that the quale in question is featured just in a given physical condition by that kind of receptor. What is essential is that that feeling accompanies that information, in a unequivocal way. If these are the operating conditions of the Deity, then the supposed freedom of association imagined by Kripke is illusory. What God can do is to establish causal connections giving distinctive information, this is enough for heat, pain and so on. However, two aspects oppose to the view I am espousing: qualia seem intrinsic and are subject to modulation. The intrisicness of qualia seems manifest: how can one discuss what it is like to have pain, or pleasure? The qualitative component of our internal states seem self-evident, a sort of inner Given. It seems preposterous to say that a pain quale in different conditions could have been a pleasure quale. I need to qualify my point: I think that the qualitative component is a consequence – perhaps of evolutionary nature – of the overall role that a given sensation plays in the system. Consider this sensation of mine. It comes along with many other sensations. But the specific one I want to tell you about, informs me that some damage is occurring on my body. It is quite distinctive: every time I suffer damages to the body I have this sensation. When this information is brought to my attention I have to react promptly and quickly if I want to preserve my body at its best. In order to get the highest saliency, a qualitative character as the one I feel when I feel pain is just appropriate. It overcomes all the other sensations I am having in this very moment: sounds, odours, the movements around me and so forth. So, the qualitative character of sensations, far from being independent of its activating conditions, must be a consequence of their overall role for the system. Perhaps its qualitative saliency has been established both philogenetically and ontogenetically, by natural selection, and this would explain the possibility of people with particular pathologies (hyperalgesic, analgesic, asymbolic). The essential point is that far from being independent from the conditions in which they occur, sensations have the qualitative features they have because the receptors have the role they have. Moreover, imagining that the specific qualitative features of sensations are the result of a natural process would allow to find a causal role for them, avoiding any charge of epiphenomenalism. A second problematic aspect of my proposal concerns the reliability of the information. The neuronal story of pain begins with local receptors, whose signal are sent to distinct layers or laminae of the spinal cord up to subcortical centres such as the

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thalamus, amygdale and the brainstem. These centres project the signal to various cortical areas, in particular primary and secondary somatosensory cortex, the anterior cingulated, the insula, and prefrontal areas (Polger and Sufka 2005). During these stages, the signal can be modulated, even deeply so. The injured soldier that does not feel pain during the battle is a typical case in point, as is the hyperalgesic, who feels pain when something gently touch her. If, as I have argued, sensations have to reliably inform us about the state of the receptors, something seems wrong. Indeed, it is natural to think that reliability comes down to the idea that increasing or decreasing in the stimulus have to correspond to increasing or decreasing in the sensation; that identity of stimulus intensity must be reflected in identity in the sensation, and so forth. I have two observations on this. First of all, I mentioned as a crucial feature of sensations their distinctiveness: no two type distinct sensations can have the same qualitative character.6 This is the essential reliability of sensations. So, in a way, the objection misfires. Nevertheless, there is a part of truth in expecting sensations being reliable in the way described. In baseline or normal conditions, they have to work in that way. But in case a modulation occurs, one should keep in mind that modulation still is a causal process. As such it must be subsumed by one or many causal laws, even if there could be cognitive aspects, subject to those causal laws anyway. From a neuronal point of view, such modulation, as far as I know, occurs in the spinal cord and in its ganglia, so not in cortical areas, even if the modulatory signals comes after the subcortical areas have been activated. Neuroscientific theories of pain, from the gate-control to the neuromatrix, give the details of such a complex sensation. But the essential point I want to make is that such modulation is part of the causal working of the fibers. It may happen that, thanks to some form of self-training, one modulates its own pain, but this is due to the activation of downward sensory modulation, not to upward modified signals. So far I have not explicitly said what the receptors for pain detects. I dare to say the obvious: they detect potential or actual body damages. The activation of pain receptors inform us about their condition, so about a local condition. Such information is, qualitatively, unequivocally brought to our attention in a very vivid way. In giving us information on the state of receptors, feeling states indicate the condition of some specific location of the body. So, pain is the activity of these receptors reporting body damages, “C-fibers firing”; the sensation of pain is our conscious attention on the distinctive information coming from these. Heat is molecular motion, the sensation of heat is our conscious attention on the distinctive information coming from heat receptors. The difference between pain and heat is solely the difference between a biological and a physical phenomenon: the latter does not need biological organisms to occur, the former does. Such a difference, however, is not metaphysically deeper. It is time to sum up: on the metaphysical side sensations are information bearing states on the conditions of receptors and have a distinctive phenomenology. The content of sensations, what sensations are about, is the condition of receptors. 6 After all this is Chalmers’ definition of quale: “those properties of mental states that type those states by what it is like to have them” 1996, p 359, n.2.

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The phenomenology, and this is the empirical side, is the way it is in virtue of the causal, i.e. evolutionary, role it plays for the organism or system. If will turn out that the receptors of pain are the famous C-fibers, then pain after all is C-fibers firing. Feeling pain is having a sensation as any other one, a sensation that could be true or false, as any other piece of our epistemic life.

References Armstrong D (1968) A materialist theory of the mind. Routledge, London Baker Rudder L (2000) Persons and bodies: a constitution view. Cambridge University Press, Cambridge Bealer G (1997) Self-consciousness. Philos Rev 106:69–117 Bickle J (1998) Psychoneural reduction. The new wave. MIT Press, Cambridge, MA Block N, Stalnaker R (1999) Conceptual analysis, dualism, and the explanatory gap. Philos Rev 18:1–46 Chalmers D (1996) The conscious mind: in search for a fundamental theory. Oxford University Press, Oxford Churchland P (1984) Matter and consciousness. MIT Press, Cambridge, MA Enc¸ B (1983) In defence of identity-theory. J Philos 80:279–298 Hill C (1991) Sensations: a defence of type materialism. Cambridge University Press, Cambridge Hill C (1997) Imaginability, conceivability, possibility, and the mind-body problem. Philos Stud 87:61–85 Hooker C (1981) Toward a general theory of reduction, part iii: cross-categorical reductions. Dialogue 20:496–529 Kim J (1992) Multiple realization and the metaphysics of reduction. Philos Phenomenol Res 52:309–335; now in Kim J, Sosa E (eds) (1999) Metaphysics. Blackwell, Oxford, pp 515–530 Kim J (1998) Mind in a physical world. MIT Press, Cambridge, MA Kim J (2005) Physicalism, or something near enough. Princeton University Press, Princeton, NJ Kripke S (1980) Naming and necessity. Blackwell, Oxford McGinn C (1991) The problem of consciousness. Basil Blackwell, Oxford Polger T (2003) Natural minds. MIT Press, Cambridge, MA Polger T, Sufka K (2005) Closing the gap on pain. In: Aydede M (ed) Pain. MIT Press, Cambridge, MA, pp 325–350 Shoemaker S (2007) Physical realization. Oxford University Press, Oxford Wilson M (1985) What is this thing called ‘pain? – the philosophy of science behind the contemporary debate. Pacific Philos Q 66:227–267 Yablo S (1992) Mental causation. Philos Rev 101:245–280

Chapter 11

Why Should Philosophers of Science Pay Attention to the Commercialization of Academic Science? Gurol ¨ Irzik

11.1 Introduction There is considerable evidence that since 1980 a new regime of science organization became dominant in the US, replacing the old one which was operative since 1945 (Etzkowitz and Webster 1995; Jasanoff 2005; Mirowski and Sent 2008). The old regime was formulated vividly in Vannevar Bush’s famous 1945 report, Science – The Endless Frontier, according to which a simple division of labor between the state and the scientists was envisioned: while the former would set the research prerogatives and provide the funds, the latter would produce scientific discoveries which would then be developed into useful products by the industry for the benefit of the nation. In this mode of scientific knowledge production, universities would be the major actors in producing “basic” science and enjoy a high degree of internal autonomy and academic freedom. Under the pressure of a number of forces, this old regime broke down. The new regime was established on the basis of an ever-expanding intellectual property rights, the privatization of publicly funded research, and new forms of collaboration between the university, the state and the industry (Bok 2003; Boyle 1997; Greenberg 2001; Krimsky 2004; Magnus et al. 2002; McSherry 2001; Mirowski and Sent 2008). It can be seen as responding to the demands of what is often called “post-industrial capitalism” or “knowledge economy”, to use a less politically charged phrase. The common assumption is that expert knowledge, which is above all scientific knowledge, has become a factor of production more important than labor, land and money and a key to economic competitiveness. As a result, scientific knowledge became commodified and certain segments of academic science, notably biomedicine and genetics, have become rapidly commercialized in unprecedented ways primarily in the US and to a lesser degree elsewhere.

G. Irzik () Sabanci University, Istanbul, Turkey e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 11, c Springer Science+Business Media B.V. 2010 

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Although, in the last decade or so there has been an explosion of publications, drawing attention to and discussing various aspects of commercialization of academic science and commodification of scientific knowledge more specifically, not withstanding a few exceptions, philosophers of science have been largely impervious to this phenomenon. My main thesis is that this phenomenon has direct bearing on some of the central problems in the philosophy of science and that as philosophers of science we should be well advised to take its impact on science seriously. The plan of my article is as follows. In Section 11.2 I outline briefly the political, economic, legal and scientific developments that led to this phenomenon in the U.S. Based on the existing literature on the topic, I argue in Section 11.3 that while commodification of scientific knowledge does make economies more competitive and productive, it also has a number of negative effects on certain aspects of science, such as the choice of scientific problems and the direction of scientific research, the social norms and the function of science. Commercialization also affects the distinctions between discovery and invention, between fact and artifact and between nature and culture, more broadly speaking. I discuss these in Section 11.4. I conclude with some general remarks.

11.2 Science for Sale: The Road to Commercialization We are faced with a conceptual issue right at the beginning: how is this new regime of science organization to be understood and described? Several terms are used in the existing literature – “commodification of academic research”, “commercialization of (academic) science”, “globalized privatization regime” (see, for example, Radder forthcoming; Mirowski and Sent 2008). However we call it, it is an extremely complex and heterogeneous phenomenon that defies a simple definition, but the basic idea is that academic science begins to be commercialized when scientific research is done, scientific knowledge is produced, and scientific expertise is mobilized in the universities and other academic institutions primarily for the purpose of profit. When scientific knowledge is produced primarily for making money, we may speak of its commodification. Commodification of knowledge is made possible via intellectual property rights, in terms of patents, copyrights and licensing. During most of the twentieth century, the prevalent attitude was that academic science and property did not go together. The latter was considered to be a notion antithetical to the scientific enterprise in the universities, and accordingly most university scientists were reluctant to patent the results of their inventions, especially when they concerned public health. As a result, many inventions were not patented. Two of the most important of these were magnetic resonance imaging and the polio vaccine. In line with this, most universities did not have any patent policies until after World War II and approached the issue of patents in health sciences unfavorably (Irzik 2007). Things began to change dramatically in the last three decades, however. While I cannot do justice the history of this complex change, I can summarize the factors behind it schematically as follows:

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Economico-political: Since the 1970s the economies of the most developed countries entered a new phase and became “knowledge economies”, where expert knowledge became the major factor of production. At the same time, a global world market became a reality more than ever, and economic competition between countries at the global scale reached new heights. With Reaganism in the U.S. and Thatcherism in England, neoliberal economic policies swept the world. National barriers against the free mobility of capital were removed, privatization was seen as the magical solution to all economic problems from unemployment to inefficiency. To facilitate cooperation between universities and the industry, with the hope that such cooperation would boost the United State’s competitiveness in the knowledge economy especially against the rising “Asian Tigers” such as China and South Korea, the U.S. government passed a number of laws (see Krimsky 2004, pp 30–31). The most important of these was the Bayh-Dole Act of 1980. This act gave small firms and universities the right to patent the results of publicly funded research. In 1987 the act was extended to cover big firms as well. The rational behind these legal arrangements were purely commercial; they encouraged collaboration between universities and industry, more specifically, a technology transfer from the former to the latter. Ideological: An ideology of neoliberalism accompanied these and similar arrangements. It was argued that a free, unregulated market economy was the most efficient mechanism for the allocation of resources. Accordingly, universities began to be seen as firm-like entities that needed to be guided by economic values such as efficiency, productiveness and profit. Universities were pushed to become entrepreneurial, and when coupled with the fear that their budgets would be cut due to economic concerns, they received the ideology positively. Legal: A crucial Supreme Court decision in 1980 opened the gate for patenting both genetically modified living creatures and the genetic material itself. In the famous Diamond v. Chakrabarty case, the Supreme Court ruled with a 5–4 vote that artificially created organisms can be patented under the U.S. Patent Act. Thus, a patent was granted for a genetically engineered bacterium capable of breaking down crude oil. The majority opinion held that the bacteria was a useful “manufacture” not found anywhere in nature. The rest, as they say, is history. Soon after the Supreme Court decision, patents for DNA, RNA, proteins, cell lines, genes, genetic tests, gene therapy techniques, recombinant RNA techniques, genetically modified plants and even living animals were allowed by the U.S. Patent and Trademark Office (USPTO). By the year 2000, the USPTO issued about six thousand patents on genes, and about one sixth of them were human genes (Krimsky 2004, p 66; for more about the role of the courts, see Irzik 2007). Scientific: In the last several decades, we have also witnessed the revolutionary emergence of what might be called “technosciences”: computer science and technology, communication and information technologies, genetic engineering and biomedicine. Two features of technosciences strike the eye immediately: first, they blend science and technology in such a way that it is virtually impossible to make

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a distinction between “pure” or “basic” science and “applied” science in these domains (hence the name “technoscience”); and, second, they hold the potential to respond to the demands of a globalized market by producing innovations that can bring generous profits. The technosciences became rapidly commercialized under the political, economic, legal and ideological conditions summarized above.

11.3 Benefits and Costs of Commercialization On the surface everybody seems to benefit from the commercialization of academic science. Let us begin with the impact of the Bayh-Dole act. Prior to it, the U.S. federal government held approximately 30,000 patents, but only a very small part of it (roughly, 5%) led to any new products. The federal government simply did not have enough resources to convert the inventions into any commercial use. Through the act, it was hoped that universities, in collaboration with industry, would do what the federal government could not. Indeed, universities responded well; within less than two decades after the law was enacted, university-held patents increased tenfold, as contrasted with only a twofold increase in overall number of patents during the same period (Jasanoff 2005, p 235; see also Krimsky 2004, p 32 for further statistics on this issue). This brought financial (admittedly, modest) gains to the universities through royalties out of patents they hold or share. For example, in the year 2000 universities’ earnings from patent licensing totaled more than one billion dollars (Bok 2003, p 101). Individual scientists, too, benefited from this situation as they enjoyed new opportunities to fund their researches and make money at the same time. While still holding their university positions and often being encouraged by the university administrators, many scientists became consultants, CEO’s or partners in these firms, others have started up their owns companies, making literally millions of dollars (Kenny 1986; Krimsky 2004; Slaughter and Leslie 1997). Business firms were happy because they capitalized on the new inventions and increased their profits. Moreover, in return for the funds they offered to the universities, they enjoyed not only expert labor power, lab and equipment, but also prior or privileged access to the results of scientific research and shared or sole ownership of patents. Finally, it could be argued that the public also won because they benefited from new drugs and therapies that would otherwise not have occurred. In short, a miracle seems to have occurred. There is, however, increasing evidence that this miracle has occurred at a considerable cost. The negative impact of commercialization on academic science can be seen both at the institutional and cognitive-epistemic level. Let us begin with the latter. Consider first the research problems and agendas. Generally speaking, these are shaped and given priority through a very intricate system that bears the marks of intrinsic theoretical interest and intellectual challenge, past scientific achievements, and the public benefit. The policies and developments outlined in the previous section resulted in a university-industry collaboration that skewed research toward what

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is patentable and commercially profitable, especially in biomedicine, genetics and pharmacology. Research interests are increasingly shaped by commercial and corporate interests rather than by scientific value or social utility (Brown 2008). For example, there is little new research towards curing tropical diseases although millions of people, almost all of whom live in developing countries, suffer from them. “According to the World Health Organization, 95% of health related R&D was devoted to issues of concern primarily to the industrial countries, and only 5% to the health concerns of the far more populous developing world.” (World Development Report 1998, p 132) The reason for apathy seems to be that such research is just not sufficiently profitable. In addition to the choice of research problems, commercialization seems also to affect the very content of scientific research in medicine. Several studies found a significant association between the source of funding and the outcome of scientific research. More precisely, they indicated that “private funding can bias the outcome of studies toward the interests of the sponsor” (Krimsky 2004, p 146). For example, an article published in the Journal of General Internal Medicine examined 107 controlled clinical trials which were classified along two dimensions: one, according to whether they favored a new or a traditional therapy, and, two, according to whether they were supported by a pharmaceutical manufacturer or by a nonprofit institution. The study found that 71% of the trials favored new therapies, and 43% of these were supported by a pharmaceutical firm. By contrast, of the 29% of the trials that favored the traditional therapies, only 13% were supported by pharmaceutical companies. Thus, there was a statistically significant association between the source of the support and the outcome of the research (Davidson 1986). Perhaps more tellingly, in none of the 107 cases examined a drug manufactured by the sponsoring company was found to be less effective than a rival drug manufactured by another firm! (For this and other examples, see Krimsky 2004, ch. 9 and Brown 2008). One cause of such and other biases seems to be conflicts of interest, which can be defined as follows: “A researcher has a conflict of interest if and only if he or she has personal, financial, professional, or political interests that have significant chance of compromising the judgment of the average scientists in the conduct of research.” (Resnik 2007, p 111) Given that corporate-sponsored researches in the universities are increasing since the 1980s, we should expect to find an increase in the number of conflicts due to the financial interests of the scientists. Indeed, social researchers point out that financial conflicts of interests among scientists are relatively recent, and they have found a number of such cases (Krimsky 2004, ch. 8, Resnik 2007, pp 23–28). A typical case goes like this, as suggested by the preceding paragraph. Scientist A conducts a research that “shows” that drug D manufactured by company C is more effective than a rival drug R produced by another company. Later, it turns out that A has been sponsored by the manufacturer of D. An independent research by another scientist refutes the finding of the first research. Or, similarly, scientist A conducts a research that “shows” that drug D is effective in treating condition C. Later, it turns out that A has been sponsored by the manufacturer of D. Again, an independent research by another scientist refutes the finding of the first research.

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Such cases are certainly interesting from a methodological viewpoint. Even if it is true that the biased outcome is indeed caused by the financial interest in question, as we all know, the existence of a correlation by itself is no “proof” of this. Are there then alternative explanations? For instance, could it be that journals are not much interested in publishing negative results, or might it be the case that drug companies support only those studies for which they have preliminary data favorable to them, as Koertge asks? (Koertge 2008; see also Krimsky 2004, p 147) Which explanation is the best and simplest? These are exactly the kind of questions philosophers of science are well equipped to answer. The examples of bias discussed above should be of interest to philosophers of science for another reason. Whether interests affect the content of science is a hotly debated issue in the philosophy of science. As is well known, the claim that it does and therefore the claim that the very content of science can be explained sociologically constitutes the cornerstone of the Strong Program in the Sociology of Scientific Knowledge. If it is true that financial interests are causing bias in scientific research in medicine, that would provide strong support for the Strong Program. Perhaps, then, its defenders should pay more attention to case studies in medicine than elsewhere. Let me now turn to the impact of commercialization on the institutional aspects of science. Commercialization is threatening the social norms of science, what the famous sociologist Robert Merton has dubbed “the ethos of modern science”. By the term “scientific ethos”, Merton means the institutional values and norms that bind the community of scientists in their scientific research and activity. Merton lists four such norms: universalism, communalism, disinterestedness, and organized skepticism (Merton 1973, pp 268–270). For lack of space, I will discuss only the first of these. Communalism refers to the common ownership of scientific discovery or knowledge. Merton expresses it as follows: “The substantive findings of science are a product of social collaboration and are assigned to the community : : : Property rights in science are whittled down to a bare minimum by the rationale of scientific ethic. The scientist’s claim to ‘his’ intellectual ‘property’ is limited to that of recognition and esteem which, if the institution functions with a modicum of efficiency, is roughly commensurate with the significance of the increments brought to the common fund of knowledge.” (ibid., p 273) The rationale Merton has in mind is that new scientific knowledge always builds upon old knowledge and that scientific discoveries owe much to open and free discussion and exchange of ideas, information, techniques and even material (such as proteins). To be sure, there is competition, but it is mostly friendly and excludes collaboration seldom, if at all. As we have seen in Section 11.2, as a result of the Supreme Court decision in Diamond v. Chakrabarty, genes, DNA, cell lines, and even living organisms like mice, whose genetic structure is sufficiently modified, became objects of intellectual property. It is no longer the case that “property rights in science are whittled down to a bare minimum by the rationale of scientific ethic”. This may very well be the reason why secrecy, which is the opposite of communalism, is spreading in an alarming way. When universities receive industrial support for their researches, they

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sign protocols that often contain non-disclosure clauses that ban university scientists from publishing their findings without the written consent of the supporting company. In 1995 a study conducted by New England Journal of Medicine revealed that among the scientists in the top 50 universities receiving money from the US National Institute of Health, one out of four was involved in industry relationships and that they were twice as likely to engage in trade secrecy or to withhold information from their colleagues in comparison to those who were not involved in relationships with industry (Greenberg 2001, p 357). A recent study by Harvard Medical School reached similar conclusions. Forty-seven percent of geneticists reported that they were denied information, data, or materials related to published research results at least once in 3 years; 28% of them said that because of this they could not confirm the accuracy of published results (Krimsky 2004, p 83). The relationship between the commercialization of academic science and the social norms of science have attracted the attention of many scholars (Brown 2008; Krimsky 2004; Resnik 2007; and especially Radder (ed.) forthcoming). Indeed, it would not be an exaggeration to say that Mertonian norms are going through a Renaissance after they were dismissed by some practitioners of social studies of science especially in the seventies (see, for example, Mulkay 1976 and Mitroff 1974). These critics argued that in practice scientists seldom acted in accordance with Mertonian norms, which in reality functioned as an ideology serving the interests of scientists, and that they even respected counter-norms. As Sergio Sismondi put it, “if there are both norms and counter-norms, then the analytical framework of norms does no work” (Sismondo 2004, p 26). In a penetrating article, Hans Radder has responded to these criticisms. In particular, he has pointed out that the really interesting question is an ethical-normative one which goes beyond the narrow, descriptive concerns of the Strong Program: it is the question of “whether Merton’s ethos of science is a valuable perspective in an age of pervasive commodification of academic research” (Radder forthcoming, p 7). The answer, I think, is obvious. Indeed, there has been a growing interest in the ethics of science, not just in Mertonian norms. Although the ethics of science owes much to Merton’s pioneering ideas, it contains other values such as scientific integrity, trust and openness not discussed by Merton. Moreover, the ethics of science goes beyond a general characterization of the ethos of science to cover specific codes of behavior. The topic of the ethics of science is receiving a great deal of attention not only by philosophers but also by scientists and scientific institutions. Many universities and institutions like National Institute of Health and scientific academies have established ethical codes of conduct for research. In 2007 the first World Congress on scientific integrity was held in Lisbon, organized by the European Science Foundation (ESF) and the U.S. Office of Research Integrity and presented its report (see the web page of ESF at http://esf.org/index.php?idD4479). In the report commercialization is especially mentioned as encroaching on academic science. Similarly, a 2003 Royal Society report with the sobering title “Keeping Science Open: The Effects of Intellectual Property Policy on the Conduct of Science” warned that there is evidence that “patenting can encourage a climate of secrecy that does limit

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the free flow of ideas and information that are vital for successful science (see http://royalsociety.org/document.asp?tipD0&idD1374). Thus, as Radder rightly points out, the present situation of commercialized academic research is very different from the one in which Merton wrote about the social norms of science in 1942 and also from the one in which the advocates of the Strong Program criticized him in the seventies (Radder forthcoming, p 9). Today, ethical codes of conduct have been pretty much institutionalized, and this very fact can be seen as a reflection of a sensitivity to the unease caused by commercialization. Indeed, the framework of values and norms such as communalism, scientific integrity and openness can and does function as at least a partial shield against its negative effects, doing its “work”.

11.4 Discovery Versus Invention, Fact Versus Artifact Customarily, we think of the distinctions between discovery and invention and between fact and artifact as follows: while facts are discovered, artifacts are invented; whereas facts belong to the domain of nature, artifacts belong to the domain of culture. Thus, the concept of discovery applies to entities like planets and electrons, phenomena such as blackbody radiation and the Compton effect, facts like E D mc2 ; by contrast, things like microscopes, air pumps, radios and atomic bombs are invented, they are artifacts. Through discovery secrets of nature are disclosed, through invention new objects that did not exist in nature before are created by human ingenuity and skill. All of this suggests that the distinctions in question are ontologically grounded. However, the situation is a lot more complicated than this. To see this, look at some “hard” cases (Resnik 2002). Genes are clearly part of our biological make-up, but they do not occur in nature in a pure and isolated form; they must be removed from their chromosomes, an activity which naturally requires much ingenuity and skill. Are genes then discovered or invented items? Or consider the Harvard “oncomouse”, a genetically modified animal that is made susceptible to cancer. While mice are certainly natural creatures some of which may develop a predisposition to cancer due to natural mutations, the Harvard oncomouse is “created” by Harvard scientists by genetic engineering. Again, is the Harvard oncomouse an invention or not? All of it or only a part of it? As David Resnik points out, “I think people most people would agree that a person who carves out a flute out of a stick of wood invents part of the item but not the whole item. One part of it – its design – is a human invention, but another part – its material – is not. If the whole flute is not an invention, then does it make sense to say that the whole mouse is an invention?.” (Resnik 2002, p 144). David Resnik has also argued that in such borderline cases whether something is an invention or not is a pragmatic matter that depends more on human purposes and values than on ontology or metaphysics. These values may be scientific, technological, religious, moral, economic or legal, which may sometimes conflict with one

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another. Here is then an interesting set of questions for philosophers of science: is there a way of reducing the hard cases to matters of ontology? If not, which values should decide the issue and when they conflict, how should they be weighed? How do scientists themselves conceptualize their findings in borderline cases: as discoveries or as inventions? Is there a change in their outlook in the last several decades? How we draw the discovery-invention distinction has a direct bearing on patenting practices: whereas inventions can be patented according to the patent laws in the U.S. and in many other countries, discoveries cannot. If the discovery-invention distinction is a matter of ontology, then it follows that whether something can be patented or not is also a matter of ontology and therefore objectively decidable. But if the distinction is a pragmatic (“socially constructed”, as social constructivists might say) one at least so far as some cases are concerned, then the discussion shifts to the domain of values and purposes. As it turns out, the U.S. patent office did grant a patent for the whole of Harvard oncomouse in 1988, and as we saw earlier genes and many similar items are also being routinely patented since the 1980 Supreme Court decision. This has another striking consequence that should be of interest to philosophers of science. Whatever commercial benefits it may provide, patenting of such life forms diminishes the space of intellectual commons. As Sheldon Krimsky put it, “the upshot of this decision [of the United States Patent and Trademark Office to patent genes] has made every gene sequencer an ‘inventor’ or ‘discoverer of patentable knowledge,’ which has inadvertently thrust normal genetic science into entrepreneurship and basic biological knowledge into a realm of intellectual property.” (Krimsky 2004, pp 69–70) Thus, what used to belong to the realm of public knowledge becomes private property for a period of time (often 20 years), excluding others from using it or requiring them to pay for it when they want to use it. No doubt, patents can stimulate scientific/technological innovations, but they can also hinder the development and progress of science since new knowledge always builds upon the old one.

11.5 Concluding Remarks I have argued that commercialization of academic science and commodification of scientific knowledge more specifically has a number of effects on science, some good and others plainly undesirable. These effects range from the choice of scientific problems to the content of science, from the discovery-invention distinction to the ethos of science, all of which should be of interest to philosophers of science in one capacity or another. I would like to conclude by drawing attention to a final global worry I have. Commercialization of academic science has the potential of subverting science’s cognitive and social functions. Science is held in high esteem by the public precisely because it has delivered what it is expected of it. People generally have confidence in the findings of science, trust the scientists’ judgments especially in matters of health and environment, and count on their independent critical voice. The image

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of a scientist who is secretive, partial, and interested more in money than in truth or social utility is destructive of the social status of science. Such an image may erode public confidence in the results of science and undermine science’s social legitimacy. Anyone who cares for science cannot and should not remain indifferent to such a disastrous possibility. Acknowledgements I acknowledge the support of the Turkish Academy of Sciences.

References Bok D (2003) Universities in the market place. Princeton University Press, Princeton, NJ Boyle J (1997) Shamans, software, and spleens. Harvard University Press, Cambridge Brown JR (2008) Community of science (R). In: Carrier M, Howard D, Kourany J (eds) The challenge of the social and the pressure of practice: science and values revisited. University of Pittsburgh Press, Pittsburgh, pp 189–216 Davidson RA (1986) Source of funding and outcome of clinical trials. J Gen Int Med 1:155–158 Etzkowitz H, Webster A (1995) Science as intellectual property. In: Jasanoff S, Markle GE, Petersen JC, Pinch T (eds) Handbook of science and technology studies. Sage, Thousand Oaks, CA, pp 480–505 Greenberg DS (2001) Science, money, and politics. The University of Chicago Press, Chicago, IL Irzik G (2007) Commercialization of science in a neoliberal world. In: Bu˘gra A, A˘gartan K (eds) Reading Polanyi for the twenty-first century. Palgrave MacMillan, New York, pp 135–154 Jasanoff S (2005) Designs on nature. Princeton University Press, Princeton, NJ Kenny M (1986) Biotechnology: the university-industrial complex. Yale University Press, New Haven, CT Koertge N (2008) Expanding philosophy of science into the moral domain: response to Brown and Kourany. Philos Sci 75:779–785 Krimsky S (2004) Science in the private interest. Rowman & Littlefield, Lanham, MD Magnus D, Kaplan A, McGee G (eds) (2002) Who owns life? Prometheus Books, Amherst McSherry C (2001) Who owns academic work? Harvard University Press, Cambridge Merton R (1973) The sociology of science. The University of Chicago Press, Chicago, IL Mirowski P, Sent E-M (2008) The commercialization of science and the response of STS. In: Edward JH, Amsterdamska O, Lynch M, Wajcman J (eds) The handbook of science and technology studies, 3rd edition. MIT, Cambridge, pp 635–689 Mitroff I (1974) Norms and counter-norms in a select group of the Apollo moon scientists: a case study of the ambivalence of scientists. Am Sociol Rev 39:579–595 Mulkay M (1976) Norms and ideology in science. Social Sci Inform 15:637–656 Radder H (ed) (forthcoming) The commodification of academic research: analyses, assessments, alternatives. University of Pittsburgh Press, Pittsburgh Radder H (forthcoming) Mertonian values, scientific norms, and the commodification of academic research. In: Radder H (ed) The commodification of academic research: analyses, assessments, alternatives. University of Pittsburgh Press, Pittsburgh Resnik D (2002) Discoveries, inventions, and gene patents. In: Magnus D, Caplan A, McGee G (eds) Who owns life? Prometheus Books, Amherst Resnik D (2007) The price of truth. Oxford University Press, Oxford Sismondo S (2004) An introduction to science and technology studies. Blackwell, Malden Slaughter S, Leslie L (1997) Academic capitalism. The John Hopkins University Press, Baltimore, MD World development report (1998) World Bank. Oxford University Press, New York

Chapter 12

Some Consequences of the Pragmatist Approach to Representation Decoupling the Model-Target Dyad and Indirect Reasoning Tarja Knuuttila

12.1 Introduction In an interesting recent effort to specify the distinct nature of modeling Michael Weisberg (2007) and Peter Godfrey-Smith (2006) argued that what distinguishes modeling from other types of theory construction is the strategy of indirect representation and analysis it makes use of. By this they mean that instead of directly striving to represent some aspects of real target systems, modelers seek to understand the real world through the procedure of constructing and analyzing hypothetical systems, in other words models. Thus they posit that modeling constitutes a specific theoretical practice, something that has escaped the notice of many philosophical accounts concerning the interrelationships between theories and models. Whereas Weisberg focuses on explicating in detail what modeling as indirect representation and analysis consists of, Godfrey-Smith approaches it also from a wider perspective, “as an approach with both strengths and weaknesses, with effects on the sociology of science and perhaps with a distinctive historical signature” (2006, 726). I find both proposals feasible and intuitively very much to the point as regards modeling practice. However, even though the notion of indirect representation constitutes the core of modeling as a distinct theoretical practice, neither Weisberg nor Godfrey-Smith really attempts to relate his views on indirect representation to the recent discussion on scientific representation.1 This is understandable given that they are both first and foremost interested in the nature of modeling per se. Yet, as the bourgeoning discussion on scientific representation has taken place exactly in the context of models, I think it would be worthwhile to study how the notion of indirect representation relates to it. T. Knuuttila () P.O. Box 24 (Unioninkatu 40 A), SF – 00014 University of Helsinki, Finland e-mail: [email protected] 1

Although Godfrey-Smith (2006) discusses Giere’s (1988, 1999) views on models and representation, and Weisberg in turn goes quickly through several recent positions taken in the debate on scientific representation, settling for the observation that no consensus has emerged in that discussion.

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 12, c Springer Science+Business Media B.V. 2010 

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In the following I will show how Weisberg and Godfrey-Smith effectively decouple through their thesis of indirect representation the model-target dyad, which has been the constitutive unit of analysis2 in the discussion on models and scientific representation. What is more, I will show how a similar conclusion has been drawn in the discussion on scientific representation, although on different grounds. Taken together, these positions challenge us to think anew the ways in which models give us knowledge and enable us to learn from them about real-world systems. To this effect, I will suggest that modeling as results-driven activity gives us knowledge through indirect reasoning, with which I refer to the way modelers proceed via the output and results of their models to consider the underlying mechanisms that might have produced the phenomena of interest.

12.2 The Thesis of Indirect Representation In his article “Who is a Modeler” Weisberg (2007) redirects the focus from models to the activity of modeling, suggesting that modeling proceeds in three stages. Firstly, a model is constructed, after which and secondly, the modeler proceeds to refining, analyzing and articulating its properties and dynamics. It is not until the third stage that the relationship between the model and any target system is assessed, “if such an assessment is necessary” (2007, 209). Godfrey-Smith, in turn, offers two stages or “moves”. The first is that of “specification and the investigation of the hypothetical system”, i.e. the model. Like Weisberg he claims that in modelbased science the “resemblance relations” between the model and the real systems are typically first considered in the second stage – although this stage is often left implicit as the modelers may go on studying the model systems created without too much explicit attention to their relationship with the world. The claim that model construction happens before the possible real target systems are considered runs counter to the conventional philosophical understanding of models as representations of some target systems, an idea that has motivated recent discussion on scientific representation, as I will argue further below. More often than not, target systems are understood in terms of real world systems. This being the case, the burden of proof lies on the shoulders of Weisberg and Godfrey-Smith. If models are not representations of some real target systems at the outset, what is represented in them and how that is supposed to happen? What, then, is indirect representation all about? Interestingly, neither Weisberg, nor Godfrey-Smith tries to define indirect representation. In trying to specify the characteristics of indirect representation both authors rather revert to scientific examples and their observations concerning them.

2 I am indebted to Paul Humphreys (2004) the idea of the unit of analysis: in an insightful way he has applied this notion, which plays an important role in the methodology of the social sciences, to the analysis of the computational science.

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Weisberg contrasts Vito Volterra’s style of theorizing, which he takes as an example of modeling, to “abstract direct representation” as exhibited by Dimitri Mendeleev’s Periodic Table. According to Weisberg, Volterra studied the special characteristics of post-World-War-I fish populations in the Adriatic Sea by “imagining a simple biological system composed of one population of predators and one population of prey” to which he attributed only a few properties, writing down a couple of differential equations to describe their mutual dynamics. The word “imagining” used by Weisberg here is important since it captures the difference between the procedures of direct and indirect representation. He stresses the fact that Volterra did not arrive at these model populations by abstracting away properties of real fish, but rather constructed them by stipulating certain of their properties (210). Unlike Volterra, he claims, Mendeleev did not build his Periodic Table via the procedure of constructing a model and then analyzing it. In developing his classification system he was rather working with abstractions from data in an attempt to identify the key factors accounting for chemical behavior. Thus, in contrast to modelers such as Volterra, he was trying to “represent trends in real chemical reactivity, and not trends in a model system” (215, footnote 4). Godfrey-Smith (2006) studies more recent examples, focusing on two influential books on evolutionary theory: Leo Buss’s The Evolution of Individuality (1987) and Smith and Szathm´ary’s The Major Transitions in Evolution (1995). For him they represent an ideal example being written about at the same time and on partly overlapping topics. In his study on the evolution of multicellular individuals from the lower-level competition on the level of cell lineage, Buss examined the “actual relations between cellular reproduction and whole-organism reproduction in known organisms” (2006, 731). As opposed to Buss’s approach, Smith and Szathm´ary describe “idealized, schematic causal mechanisms”. Rather than studying actual systems they engage in modeling, that is in examining “tightly constrained” possible – or fictional – systems. Thus their explanations “would work just as well in a range of nearby possible worlds that happen to be inhabited by different organisms”, which endows them with what Godfrey-Smith aptly calls “modal ‘reach”’ (2006, 732). The crucial difference between abstract direct representation and indirect representation does not concern whether one abstracts or approximates, selects or even idealizes. Scientific representation involves all these, but in engaging in such activities modelers do not even pretend to be primarily in the business of representing any specific real system. For them the models come first. The distinguishing feature of the “strategy of model-based science” is that the modelers do not try to identify and describe the actual systems, but proceed by describing another more simple hypothetical system (Godfrey-Smith 2006). Thus model-based science could be characterized by the “deliberate detour through merely hypothetical systems” of which it makes use (2006, 734). Consequently, it follows from the thesis of indirect representation that models should be considered independent objects in the sense of being independent from

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any real target system.3 As such, I argue, it means a departure from the representational paradigm, which has taken the model-target dyad as a basic unit of analysis concerning models and their epistemic value. Even though this is not the specific goal Weisberg and Godfrey-Smith set themselves, it is a clear consequence of their approach. Interestingly, but for quite different reasons, the recent discussion on models and representation has also led to the same conclusion. A look at this discussion will shed light on the reasons why.

12.3 Models and Scientific Representation The rather striking feature of the discussion on scientific representation is that it has been, so far, conducted almost exclusively in the context of modeling. This may seem curious given that scientific endeavor employs manifold representations that are not readily called models. Such representations include visual and graphic displays on paper and on screen, such as pictures, photographs, audiographic and 3D images, as well as chart recordings, numerical representations, tables, textual accounts, and symbolic renderings of diverse entities such as chemical formulas. One rationale for this discussion, apart from the specific historical reasons for it – a topic I will not touch upon here – is that models have traditionally been taken to be representations. This conviction is of far more distant origin than the semantic approach to models in its various guises, which until the recent decade has been the dominant approach to models. What has been characteristic of the recent discussion on models and representation is the double move of treating models as representations and ascribing their epistemic value to representation. Accordingly, what several philosophers have taken as their task is to give an account of scientific representation, given that it is generally agreed that models give us knowledge because they are able to represent some real target systems (e.g., French 2003; Giere 2004; Su´arez 2004; Contessa 2007; M¨aki forthcoming; Frigg forthcoming). The basic unit of these accounts has been the model-target dyad, and the question has concerned the kind of relationship between a model and its real target system by virtue of which the model can give us scientific knowledge. The most straightforward answer to the question of representation has been given by the semantic or structuralist accounts. These accounts have focused on the properties or features that models supposedly share with their target systems, thus concentrating solely on the model-target dyad. According to the semantic or structuralist notion of representation, models specify structures that are posited

3 Other authors have also recently suggested that models could be conceived of as independent objects, although by this they mean different things. Morrison and Morgan (1999) conceive of models as partly independent of theory and data. Knuuttila (2005) treats them as independent entities in the sense of loosening them from any predetermined representational relationships to real target systems. This comes close to what Weisberg and Godfrey-Smith mean by independence.

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as possible representations of either the observable phenomena or, even more ambitiously, the underlying structures of the real target systems. This relation of representation between a model and its target system has been formulated in terms of isomorphism, partial isomorphism, or – less frequently – similarity (e.g., van Fraassen 1980; French and Ladyman 1999; da Costa and French 2003; Giere 1988). Thus, according to the semantic view, the structure specified by a model represents its target system if it is either structurally isomorphic or somehow similar to it. Pragmatist critics of the semantic conception have argued, among other things, that isomorphism – being a symmetric, reflexive and transitive relation – does not satisfy the formal and other criteria we might want to affirm of representation (see e.g., Su´arez 2003 and Frigg 2003, of whom Su´arez has extended this critique also to similarity). For instance, both isomorphism and similarity denote a symmetric relation, whereas representation does not: we want a model to represent its target system but not vice versa. Moreover, the isomorphism account does not accept false representations as representations. The idea that representation is either an accurate depiction of its object – which is interpreted in terms of isomorphism within the structuralist conception – or it is not representation at all does not fit our actual representational practices. These problems appear to be solved once the pragmatic aspects of representation are taken into account. The users’ intentions create the directionality needed to establish a representative relationship: something is being used and/or interpreted as a model of something else, which makes the representative relation triadic, involving human agency. This also introduces indeterminateness into the representative relationship: human beings as representers are fallible. In stressing the importance of human agency for what representation is all about, the pragmatic approaches criticize the assumption of the semantic conception that representation is a dyadic relation of correspondence between the representational vehicle (a model) and its target (Su´arez 2004; Giere 2004). The dyadic conceptions attempt, as Su´arez has put it, “to reduce the essentially intentional judgments of representation-users to facts about the source and target objects or systems and their properties” (2004, 768). Thus Su´arez spells out that what is actually at stake is whether or not the possibility of representation can based on some privileged parts or properties that the actual representative vehicles are supposed share with their target objects. Even though the basic problem of representation that the pragmatist approaches have set out to solve has been cast out in terms of the model-target dyad, their analyses in fact decouple that dyad in introducing representation users and their intentions and purposes. Thus, the outcome of this discussion fits in well with the idea of indirect representation, according to which models, being independent objects, “do not have a single, automatically determinable relationship to the world” (Weisberg 2007, 218). It is also worth noting that the question of fiction and the ontology of models has started to interest pragmatists of representation in particular (e.g., Frigg forthcoming; Su´arez 2008), which resonates well with both Weisberg’s and Godfrey-Smith’s views.

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However, the weight given by both Weisberg and Godfrey-Smith to similarity (or resemblance) concerning how models give us knowledge and understanding seems questionable in the light of the pragmatist view on representation. The problem is not only about the vagueness of the notion of similarity – which point is habitually noted in this context – but also that it does not accomplish much from the philosophical point of view. Namely, by invoking the notion of similarity Weisberg and Godfrey-Smith are implicitly taking a stand on the issue of representation, and whereas the way they loosen the model-target dyad is something that pragmatists of representation would agree on, here the roads divide. For instance Weisberg puts it bluntly that in order for us to learn about the real world “the model must be similar to a real-world phenomenon in certain appropriate respects” (2007, 218). Currently, it seems that those engaged in the discussion on scientific representation are not willing to endorse the similarity account without also reverting to users. A good example is provided by Ronald Giere, the most well known proponent of the similarity account, who instead of arguing for similarity prefers to account for representation in terms of an “intentional account of representation” (Giere forthcoming). It seems to me that the reason why evoking mere similarity in an effort to establish a representational relationship between the model and a real-world target system is problematic, apart from the arguments already referred to, lies in its observerdependent nature. If it is a case that many if not most things can be taken to be similar to most other things, then it is we who pick the “appropriate similarities” – and in this sense Giere’s turn from the similarity account of representation to an intentional account seems an entirely appropriate step to take. Indeed, this observation was already present in Giere’s classic 1988 account, in which he did not appear too worried about the vagueness of the notion of similarity, claiming that cognitive sciences are accumulating evidence that “human cognition and perception operate on the basis of some sort of similarity metric“(1988, 81). Thus similarity has its proper place in our cognitive endeavor, but not the place to which it is habitually relegated in the discussion on representation. The point is that it tells more about our cognitive functioning than specifically about the epistemic value of modeling. We may tend to recognize similarities between different things, but that does not yet make the similarities in question epistemically interesting. Consequently, even though similarity considerations undoubtedly play a part in our cognitive judgments, they do not take us very far in understanding how we learn from models. Apart from decoupling the model-target dyad, the pragmatist accounts of representation have also some other consequences worth of mentioning. Namely, once we introduce users into the relationship of representation, its explanatory power starts to fall apart. The gesture of relating representation to the intentional activity of model users solves many problems of the semantic notion, but this comes at a price: if representation is grounded primarily in the specific goals and the representing activity of humans as opposed to the properties of the representative vehicle and its target, nothing very substantial can be said about it in general. This has been explicitly admitted by proponents of the pragmatic approach (cf. Giere 2004), of whom Su´arez (2004) has gone farthest in arguing for a “deflationary”, or minimalist, account of representation that seeks not to rely on any specific features that

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might relate the representational vehicle to its target. The minimalist approach has rather radical consequences in terms of how the epistemic value of models should be conceived of. Namely, if we attribute the epistemic value of a model to its being a representation of some target system and accept the minimalist pragmatic notion of representation, not much is established about how we can learn from models. This naturally raises the question of whether there is any other way to approach models that could give us some more insight into their epistemic functioning. Before I go into this question allow me to make still one more point concerning the relationship of the thesis of indirect representation to the general discussion on scientific representation. As far as the relationship of representation is concerned, the thesis of indirect representation divides it into two parts: to the construction of models and to the use of them. I find this distinction an important contribution to the discussion on scientific representation. Since the model-target dyad has been taken as the starting point of the analysis, no such distinction has been made so far in this discussion. One reason for this is the frequently tacit assumption that models are inherently models of some pre-established target systems. They are taken to depict some real-world target systems at the outset and thus the question of representation concerns the conditions under which a model succeeds in representing the target (given that it is also assumed that representation is a condition for our learning from models). One common idea behind this line of reasoning is that models typically isolate some causal factors or tendencies of a system of interest and abstract away from other disturbing factors by means of suitable idealizations (e.g., Cartwright 1998; M¨aki 2005). However, according to the thesis of indirect representation, the model need not be bound in this way to a real-world system. Even though the model construction makes use of available theoretical and empirical knowledge, this knowledge is mediated by the construction of a simpler imagined system. In the following I will suggest that the same characteristic detour also applies to our learning from models. In this case too, the links forged with real-world systems are looser and more complicated than the mere appeal to similarity suggests. Thus, from the perspective of scientific practice, the knowledge and understanding gained via modeling are achieved through various kinds of inferences derived from models combined with various kinds of background knowledge and other evidence.

12.4 Results-Drivenness in Modeling and Indirect Reasoning Given both the thesis of indirect representation and the minimalist pragmatist account of representation the crucial question is how models as independent hypothetical objects enable us to understand and learn about the world. In order to answer this question let me to consider once again the assumed similarity of models to real-world target systems, this time not as a general answer to the question of representation but rather from the perspective of the practice of modeling. In this respect, two relevant observations arise as regards the further features of modeling

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as a specific theoretical activity. Firstly, in considering models as imaginary entities both Weisberg and Godfrey-Smith note how they frequently concern non-existing systems such as three-sex biology. In these cases the modelers are clearly trading with fiction, in other words dealing with the possible and the non-actual. Indeed, scientific models typically provide exemplifications of the functioning of ideal, schematized mechanisms, as well as how-possibly and what-if-things-weredifferent types of explanations. It seems to me far from clear what kind of similarity comparisons between these modeled imaginary and non-existent systems and the real-world ones we are supposed – or even able – to make. This, in turn, is bound to lead one to ask, secondly, what sort of similarity appraisals are inherent in modeling. I suggest that modeling is fundamentally a results-driven theoretical activity in which surrogate hypothetical systems, or models, are constructed keeping in mind the effects they are supposed to produce4. As models are typically valued for their performance and their results or output, the relevant similarities that modelers are primarily after are those between the model output and some stylized features of the phenomena of interest. The way interesting models are also expected to produce a priori unexpected results or to account for different empirical findings that, according to earlier theoretical knowledge, have been considered to be contradictory also point to the results-driven nature of modeling. Furthermore, it is backed up by the systemic holistic character of models, which distinguishes them from many other scientific representations that often fragment and analyze an object or specimen to its further details. From this perspective, I suggest, that modelers engage in indirect reasoning by making use in their knowledge acquisition the results derived from purposefully designed hypothetical systems. Thus indirect reasoning makes a natural companion for indirect representation. Instead of directly trying to represent some selected aspects of a given real target system – as has conventionally been assumed – modelers proceed in a roundabout way, seeking to build hypothetical systems in the light of their anticipated results or of certain general features of phenomena they are supposed to exhibit. If a model succeeds in producing the expected results, i.e. some features of the phenomena of interest, it provides an interesting starting point for further theoretical conjectures and inferences, concerning the underlying real mechanisms, for instance. This results-orientation also accounts for why modelers frequently use the same cross-disciplinary computational templates (Humphreys 2004), such as well-known general equation types, statistical distributions and computational methods. The overall usability of computational templates is based on their generality and the observed similarities between different phenomena. Thus there is an element of opportunism in modeling: the template that has proven successful in producing certain features of some phenomenon will be applied to other phenomena, often studied within a totally different discipline. This is certainly true of Lotka-Volterra equations, the example cited by Weisberg, which have been used in disciplines as 4 In his work on robustness Weisberg has targeted the epistemic importance of model results and the ways of guaranteeing their generality (e.g., Weisberg 2006).

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different as biology, ecology, chemistry, physics and economics. In these areas they are typically applied to phenomena that usually exhibit complex fluctuations. It is also telling that the Lotka-Volterra model had a renaissance in the 1970s in the context of chaos and complex systems theory, when researchers became interested in exploring the nonlinear dynamics of the model. Last but not least, the aim of getting the model to bring forth results also explains why tractability considerations frequently override the search for realistic representation. Looking at models from the perspective of their results-orientedness, I suggest, explains the very interest modelers have in their properties and dynamics, but it also accounts for their important instrumental uses in prediction, for instance, which also relies on the results they produce. Moreover, this perspective avails itself of different cognitive strategies: it is not limited to simplified mathematical models, but also takes in simulations in which output representations are crucial in terms of creating pragmatic understanding oriented towards control, design rules and predictions. In fact, simulations have been considered problematic in terms of the representational understanding of models because “instead of creating a comprehensive, though highly idealised, model world, [they] squeeze out the consequences in an often unintelligible and opaque way” (Lenhard 2006, 612). The epistemological justification of indirect representation and indirect reasoning lies, as I see it, in contesting the traditional representational view that assumes that we already knew the relevant systems or causal mechanisms to be represented, and had the suitable representational means at hand for doing it. As far as scientific practice is concerned, this is hardly the case, which also accounts for the characteristic modal nature of modeling: the very interest of modelers in also studying different non-actualized and inexistent systems in an effort to chart various possibilities and thus to gain further understanding of the phenomena in question. This, in turn, has consequences for how models as entities should be understood. I take it that the path to the imaginary goes through the concrete and the manipulable, in other words through the model description, which allows modelers to experiment with various possibilities. Thus the material, concrete dimension of models embodied in some representational medium is crucial to their epistemic functioning.

12.5 Conclusion Both the thesis of indirect representation and the pragmatic notion of representation point out that the ties between models and real-world systems are looser than is customarily assumed. The specific contribution of the former lies in its distinguishing of two aspects in the relationship of representation, the construction of models on the one hand and their use on the other. This shifts the focus from the model-target dyad to the very activity of modeling. As far as the discussion on scientific representation is concerned, however, the appeal of both Weisberg and Godfrey-Smith to similarity (or resemblance) with regard to our learning from models seems somewhat too hasty and would need more fine-grained analysis. Towards this end I have suggested that

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not just model construction but also inferring from models (i.e. their use) is indirect, proceeding through the results they give to consider the possible underlying mechanisms. Studying the model results under various assumptions – and in relation to other models and evidence, allows further inferences concerning the actual and the possible, which is why I have called this specific kind of model-enabled reasoning indirect reasoning.

References Cartwright N (1998) Capacities. In: Davis JB, Wade Hands D, M¨aki U (eds) The Handbook of economic methodology. Edgar Elgar, Cheltenham, pp 45–48 Contessa G (2007) Representation, interpretation, and surrogative reasoning. Philos Sci 71:48–68 da Costa NCA, French S (2003) Science and partial truth. Oxford University Press, New York French S (2003) A model-theoretic account of representation (or, I don’t know much about art : : : but I know it involves isomorphism). Philos Sci 70(Proceedings):1472–1483 French S, Ladyman J (1999) Reinflating the semantic approach. Int Stud Philos Sci 13:103–121 Frigg R (2003) Representing scientific representation. Ph.D. dissertation, London School of Economics, London Frigg R (forthcoming) Models and fiction. Synthese (forthcoming 2009) DOI: 10.1007/s11229009-9505-0 Giere RN (1988) Explaining science: a cognitive approach. The University of Chicago Press, Chicago, IL/London Giere RN (2004) How models are used to represent reality. Philos Sci 71(Symposia):742–752 Giere RN (forthcoming) An agent-based conception of models and scientific representation. Synthese (forthcoming 2009) DOI: 10.1007/s11229-009-9506-z Godfrey-Smith P (2006) The strategy of model-based science. Biol Philos 21:725–740 Humphreys P (2004) Extending ourselves. Computational science, empiricism and scientific method. Oxford University Press, Oxford Knuuttila T (2005) Models, representation, and mediation. Philos Sci 72(Proceedings):1260–1271 Lenhard J (2006) Surprised by a nanowire: simulation, control, and understanding. Philos Sci 73(Symposia):605–616 M¨aki U (2005) Models are experiments, experiments are models. J Econ Method 12:303–315 M¨aki U (forthcoming) Models and the locus of their truth. Synthese (forthcoming 2009) DOI: 10.1007/s11229-009-9566-0 Morrison M, Morgan MS (1999) Models as mediating instruments. In: Morgan MS, Morrison M (eds) Models as mediators. Perspectives on natural and social science. Cambridge University Press, Cambridge, pp 10–37 Su´arez M (2003) Scientific representation: against similarity and isomorphism. Int Stud Philos Sci 17:225–244 Su´arez M (2004) An inferential conception of scientific representation. Philos Sci (Symposia) 71:767–779 Su´arez M (2008) Scientific fictions as heuristic rules of inference. In: Su´arez M (ed) Fictions in science: philosophical essays on modeling and idealization. Routledge, London, pp 158–178 van Fraassen B (1980) The scientific image. Oxford University Press, Oxford Weisberg M (2006) Robustness analysis. Philos Sci 73(Symposia):730–742 Weisberg M (2007) Who is a modeler. Br J Philos Sci 58:207–233

Chapter 13

The Gray Area for Incorruptible Scientific Research An Exploration Guided by Merton’s Norms Conceived as ‘Default-Norms’Ž Theo A.F. Kuipers In Memory Of Annie Kuipers (1938–2003)

13.1 Introduction Science and ethics have a complex relation. They cannot easily be separated. Although pleas for completely autonomous science as well as for extreme ethical

T.A.F. Kuipers () Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, 9712 GL Groningen, The Netherlands e-mail: [email protected] 

A Dutch version of this paper appeared already in 1999 (Kuipers 1999). Next it was first translated, revised and extended as my contribution to a planned Liber Amicorum for Annie Kuipers, to be published on the occasion of her retirement. Very dreadfully, she died of cancer in 2003 soon after the plan was set up and the volume never appeared. Annie Kuipers (unfortunately, no family) was for about 25 years the leading person in the field of philosophy at the publishing house Reidel, later Kluwer Academic Publishers (and now part of Springer). It is difficult to overestimate the role she played in the recruitment of authors and the running of book series and journals and setting up new ones. For example, in cooperation with Jaakko Hintikka and Robert Cohen she ‘managed’ for years the Synthese Library book series and the Boston Studies in the Philosophy of Science, respectively. She played a great role in the well functioning of the journals Erkenntnis and Synthese. Several other books, book series and journals in the area of philosophy, logic and linguistics profited enormously from her efforts. Despite her attempts to the contrary, the prices of such publications became at most, if at all, payable for libraries. This will also apply to the present Springer volume. However this may be, it is worth noting at the start of the European Philosophy of Science Association (EPSA) that Annie Kuipers was a main figure in paving the way for the interaction between philosophers of science of Europe and America, and stimulated in this way the re-vitalization of philosophy of science in Europe where it had made a flourishing start in the Interbellum. 

A revised version of the draft for the Liber Amicorum turned out to be very useful as the last chapter (13) of my Structures in Science (2001), in which it is entitled “‘Default-Norms’ in Research Ethics”. That version is here included with the originally intended title, some marginal revisions, and updating notes. I like to thank David Atkinson, Martin van Hees, Erik Krabbe, Anne Ruth Mackor and Jeanne Peijnenburg for their comments on the draft of the chapter. Finally I like to thank the Netherlands Institute of Advanced Study (NIAS, Wassenaar) where I could update it for the present volume. M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 13, c Springer Science+Business Media B.V. 2010 

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dirigisme still occur, an interaction model for science and ethics is more and more widely propagated. This model is not only presented as characteristic of the factual relation, but also as desirable, that is, in the interest of science and society, of course, under rationally defensible conditions. It concerns in particular moral dilemmas with respect to: – Incorruptible professional behavior in scientific research – The present and future well-being of humans and (laboratory, domestic, and wild) animals and the state of their environment – The communication between science and society In the last 30 years all kinds of initiatives have been taken in order to shape the interaction between science and ethics on three levels. On the individual level, universities organize courses for students and post-graduates in an effort to activate their moral sensibility. On the institutional level codes of the professional behavior of scientists and codes governing the behavior of the scientific and non-scientific staff in private firms have been designed, suggesting or prescribing rules of behavior. On the societal level, public debates are organized between laity and experts about possible and desirable scientific and social developments. In this paper I like to contribute to the discussion about the integrity of scientists as researchers, that is, about the possibility and limitations of incorruptible professional behavior in scientific research. For this purpose I take the famous of Robert K. Merton as a point of departure, not in order to note that scientists do not always conform to them,1 but to raise questions about which deviations may be defensible and which ones are not.2 Accidentally, this inquiry will also illustrate the fact that a choice between so-called deontological and utilitarian ethics is not plausible: a reasonable compromise between principles-whatever-the-consequences and deviations based on possible consequences seems also in this case the only serious option. After presenting the four norms I will briefly consider three of them as ‘defaultnorms’. Then I will discuss the disinterestedness norm in some more detail. I will conclude with a brief discussion of the possibility and usefulness of subsuming all these concerns in a general professional code for scientific researchers.

13.2 Merton’s Norms Conceived as ‘Default-Norms’ As is well-known, Robert K. Merton (1942) formulated in the forties four norms which scientists, ideally speaking, should live up to and which have become known as the CUDOS-norms, after the initials of their names: Communism, Universalism,

1 See e.g. Mulkay (1977) and Ziman (1994). Ziman not only shows that present-day research cannot be characterized by Merton’s CUDOS norms, but even argues that its conditions can better be characterized by PLACE: Proprietary, Local, Authoritarian, Commissional, Expert work. 2 Such considerations evidently play a role in the degree in which scientists support these norms, as was recently demonstrated by Macfarlane and Cheng (2008).

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Disinterestedness, and Organized Skepticism. I will start by briefly characterizing them: Communism: scientific knowledge is the product of common effort, for which reason newly acquired knowledge should be made public and should be considered as a collective good, with explicit recognition, of course, of the discoverer or inventor. Universalism: one should judge the work of others irrespective of persons (‘blind refereeing’) and in the selection among applicants for a position sex, race, nationality and the like should not play a role. Disinterestedness: personal and group interests should be subordinated to the interests of research, which excludes evident kinds of fraud, such as plagiarism, forgery, and feigning. Organized skepticism: new research results and methods should be presented to colleagues, with an open mind for criticism.

It will be clear that these norms need not be exhaustive and that they will overlap now and then. Moreover, although Merton was of the opinion that the norms were in the interest of science, he was also well aware that they did not have rigorous descriptive validity. I will argue that they even cannot have rigorous prescriptive validity, because there are, besides evidently non-defensible deviations, various kinds of conceivably well-argued deviations. Moreover, and at least as important, there appears to be a large ‘gray area’ where every researcher has to find his own way in every particular case. Precisely due to the existence of this gray area it is difficult to conceive of a detailed prescriptive professional code. Merton’s norms are clearly principles with a deontological flavor in the sense of deontological ethics: whatever the consequences in specific cases, they prescribe what to do or not to do. Defensible deviations are, of course, based on utilitarian considerations pertaining to the consequences of a dogmatic application of the norms in concrete cases. In other words, these norms are ‘default-norms’. Depending on whether or not the deviations are supposed to be catchable in subrules, defaultnorms have, besides their deontological reminiscence, also the flavor of so-called rule-utilitarianism or act-utilitarianism. In the subsequent subsections I will try, for each norm, to explore the possibilities for defensible and non-defensible deviations, though without presenting them in each case explicitly in terms of their consequences and without investigating whether or not defensible deviations can be caught in subrules. For ‘disinterestedness’ I start a new section.

13.2.1 Communism Scientific knowledge is the product of common effort, for which reason newly acquired knowledge should be made public and should be considered as a collective good, with explicit recognition, of course, of the discoverer or inventor. Merton intended with his ‘communism’ norm primarily that new scientific knowledge, as soon as it is sufficiently trustworthy, should be made public, not only for colleague researchers, but also for society.

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13.2.1.1 Secrecy and Publicity This claim raises, first of all, the question of whether there can be good reasons for secrecy. Kaiser (1996) distinguishes three kinds of interest that might be considered as justifying secrecy: military, commercial, and public interest. Reservedness about new findings that might be used on a large scale for military purposes can at least count on good arguments of a utilitarian nature. The case for secrecy is less convincing when only commercial interests are involved, and commercial and contract research is a rapidly growing area of concern in this respect. Temporary secrecy, for example, waiting for the approval of a patent request, may be defensible. Permanent secrecy of a scientifically interesting finding, however, does not seem to be ever justifiable. We may hope that recipes which are cautiously kept secret, such as the one for Coca-Cola, are not scientifically interesting. That public interest does not easily justify secrecy may be illustrated by what happened in the early 1970s in the Norwegian industry of salmon fish farming, an example extensively discussed by Kaiser and here restricted to the crucial facts. A team of scientific researchers advising the salmon farming industry kept one of their discoveries as a secret of the team at a great risk to public health. They had discovered that a generally used food supplement for the salmon was carcinogenic for the human consumers of the salmon, despite initial good reasons to assume that this could not be the case. The team faced the dilemma between a general health interest and a general employment interest; the latter was especially important since so many people were directly or indirectly involved in the salmon industry. The team leader decided to let the employment interest overrule the health interest. More precisely, he decided that first a functionally equivalent replacement should be found or developed for the food supplement before use of the health endangering one would be discontinued. As Kaiser (1996, 220) reports, the leader’s message to his team was: “I urge you to keep this strictly secret, until we have developed for substance X a replacement that is more desirable. Just imagine how this finding would stir up the public if it becomes known.” This consideration was apparently convincing to the other members of the team; that is, at least no ‘whistle blowers’ appeared. The new supplement was found and the old one replaced without public uproar. Despite our possible inclination to want to believe that such things could not happen anymore in the twenty-first century, the example suggests that more or less comparable cases could still occur.

13.2.1.2 Timely Publication It is clear that in most cases there are no good reasons for secrecy. Nevertheless, publication of new findings at the proper time and in the proper way is a matter of great concern. Regarding the proper manner of publication, Solomon (1996) stresses that, in case of experimental results, enough should be specified in order to enable the repetition of the experiment by others and that, in relevant cases, data, samples and, I add, computer programs should be made available upon request.

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Regarding timely publication, it is important to distinguish between the informal communication network of friendly colleagues, locally and otherwise, the official scientific publication circuit and, finally, the media for the general public. The problematic cases of untimely publication concern primarily the general media. Notorious examples in the twentieth century history of science are N-rays (around 1900), polywater (late 1960s) and, in the late 1980s, cold nuclear fusion (Ponns and Fleischmann), memory molecules (Benveniste) and, quite a row at least in The Netherlands, an AIDS-inhibiting substance (Buck and Goudsmit). It is important to note that untimely publication does not cause debates when it happens to become a success story. The first messages about superconductivity at high temperature, for example, came also in the newspapers, with speculations about possible applications, before the phenomenon was considered to be well-established by the community of physicists. Untimely publication is stimulated, among other factors, by interest in being the first, and to be recognized as such, by the aim of obtaining as soon as possible new sources of money or other means for further research, by the sincere belief that the discovery renders society a good turn, by vanity even to the extent of having Nobel prize expectations and, last but not least, by dubious science journalism. The most important factor preventing untimely publication is likely to be the potential loss of face among colleagues when things go wrong. For the rest, standard checkpoints like the referee system, repetition of experiments and proof checks by oneself and others, prevent new results from being officially published in a too early stage. For the general media, adequate science journalism is a prerequisite. Good science news reporting prevents, first of all, the expectations of many vulnerable groups from being unjustifiedly raised. Not only Buck and Goudsmit gave false hope to AIDS-patients but the Dutch public television news was also responsible for that. Moreover, in general, it would be a good thing if not only scientists but also science reporters and the media that publish their stories were to lose credibility whenever a lame-duck discovery is reported with great fanfare.

13.2.2 Universalism One should judge the work of others irrespective of persons (‘blind refereeing’) and in the selection among applicants for a position sex, race, nationality and the like should not play a role. The use of authority arguments is strictly speaking a deviation from the universalism norm because somebody’s prestige is brought into play. But in everyday and scientific practice we cannot live without such arguments. Consider, for example, the mutual trust one needs to have for doing efficient interdisciplinary research. However, we are inclined to make a difference between defensible and non-defensible authority arguments, for example, depending on whether or not the scientist in question makes a statement within the domain of his recognized competence. Well-known examples of problematic transgressions concern genuine and

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near Nobel price winners making or supporting claims in a field in which they have no special expertise, and, frequently, cannot be contradicted by real experts, as there are none in the area concerned. In the latter kinds of areas, e.g. regarding certain long term future developments about which everyone is of course free to speculate, utterances by laureates are taken more seriously than those made by other, equally incompetent, people. Another type of problematic deviation from the universalism norm concerns all kinds of (supposed) discrimination, in particular, of women and ethnic minorities. The policies of ‘positive discrimination’ or ‘positive action’ are considered by its proponents as defensible in the face of the consequences of the normal ‘laissez faire’ policy. One may compare it with forbidding political parties that are against democracy, in order to protect democracy against attacks from inside. In the US, however, positive action in favor of minorities is in several states again being retracted. The same development seems to be taking place in The Netherlands regarding extreme forms of positive discrimination in favor of women, such as appointing a sufficiently qualified female candidate on an academic position in the presence of (much) better qualified male candidates. Nevertheless, it has to be noted that, at least in The Netherlands, it turns out to be very difficult to get a reasonable number of women on higher academic positions without positive action. Besides the admission of hidden differences in treatment of female candidates and male-biased limitations to parttime work, flexible-time work and telework, the notion that respective differences in ambition also play a role seems to be gaining ground. For women with appropriate ambitions, however, besides fighting against all kinds of unequal treatment and male-biased limitations, new kinds of networks and mentorship may need to be found.3

13.2.3 Organized Skepticism New research results and methods should be presented to colleagues, with an open mind for criticism. Probably the best known relativization of the idea of (organized) rigorous skepticism comes from the historical findings of Kuhn and Lakatos, who concluded that some dogmatism has been rather productive in the history of science. However different their elaborations, they showed that persistent tenacity in supporting a paradigm or research program should not always be considered as dubious dogmatic behavior, but may also be considered as evidence for fruitful perseverance, seemingly against better knowledge. “The function of dogma in science” is the telling title of an article by Kuhn. Of course, not all dogmatic research becomes respectable in this way. Within the boundaries, that is, the dogmas, of a research program, one 3 I would like to mention that in 2002 a very successful stimulation program started at my home University of Groningen, called Rosalind Franklin fellowships. (http://www.rug.nl/corporate/ vacatures/rff/index).

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may or may not systematically aim at empirical progress and even truth approximation. The presence of this striving is a characteristic difference between examples of fruitful ‘dogmatic science’ and static pseudoscience. For example, the attempts and debates aiming at improving the specifications of the evolutionary theory have no serious analogue in ‘creation science’ (see e.g. Sober 2000). For a general elaboration of the claimed contrast, see (Kuipers 2000, Section 6.3, or 2001, Section 8.3). This point is associated with a latent, very productive, division of labor among scientists. Besides the manifest division of labor between theoreticians and experimenters, without, of course, neglecting the double talented exceptions, there seems to be another division operative that is less well known. In particular, among theoreticians there are not only many constructive researchers, who build on their own research program or, more frequently, on the work of others, but also researchers whose strength it is to play a critical role. One may even question whether the current ideal type of a researcher, who is alternately constructive and destructive, is the proper ideal type for modern science. Precisely because science is a co-production of many people, it is more plausible that a functional division of labor is more fruitful than a homogeneous group of researchers, alternately playing the roles that have to be fulfilled. Instead of a deviation of Merton’s fourth norm, we come here across a possibility for realizing it, of which Merton himself did not seem to think.

13.3 Disinterestedness, and Its Challenges Personal and group interests should be subordinated to the interests of research, which excludes evident kinds of fraud, such as plagiarism, forgery, and feigning. Regarding offenses of the disinterestedness norm, one thinks in the first place of evident cases of fraud, such as plagiarism, forging of data, feigning of experiments and their results. One frequently reads that, happily enough, such cases of fraud are rather exceptional. The classic The betrayers of truth (Broad and Wade 1982) and the Dutch variant Valse vooruitgang (False Progress, Van Kolfschoten 1993) confirm this belief. Nevertheless, it is worthwhile to pay attention to the possibility of such occurrences in academic education, because sooner or later one may be confronted, directly or indirectly, with such a case, and one will be forced to have an opinion about it. Moreover, there are all kinds of semi-fraud, in particular semiplagiarism. Van Kolfschoten distinguishes three categories: conscious plagiarists, unconscious plagiarists, and synthesizers who give poor acknowledgements. Unconscious or inadvertent, and hence in good faith, plagiarism not only occurs, but perhaps even more frequently than one is inclined to think.4 One way to minimize

4 Once I discovered by myself a case of inadvertent plagiarism, also called cryptomnesia, of an idea of someone else, many years after its publication, which was a strange experience. In a paper in the Dutch journal of philosophy ANTW (Kuipers 1972) I have at least suggested that it was my own idea to write Carnapian inductive probabilities as the weighted sum of a logical and an empirical factor. This was rather embarrassing in view of the fact that I had read no more than two years

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the risk is by answering the question to oneself, after finishing a manuscript, whether some of the ideas in it may have been taken from others, learnt by reading or conference visiting, in particular in the period before actually working on the manuscript. Finally, when conceiving and writing a synthetic work, it is extremely difficult to indicate all the sources that may have played a role, let alone, to specify that role. Apologizing in advance for this possibility, and thus relativizing ones own apparent originality, may give some comfort. In assessing manuscripts, e.g., when writing referee reports, in editorial work, in advising or working for a publisher, all kinds of variants of fraud and semi-fraud occur (see Lafollette 1992). Referees may be tempted to lie in a referee report or, at least, to manipulate information, they may postpone the completion of a report unnecessarily long in view of some personal interest, and they can even steal ideas or even fragments from the manuscript. Members of editorial boards and publishers may feign or forge referee reports and they can lie about the referee process. All this occurs, probably not on a large scale, but there are variants, which are worthy of some further attention to. I will restrict myself to the gray area of strategic behavior aiming at the allocation of personnel and material means: about influencing the number of publications and citations, about writing research proposals and their assessment and, finally, about the formation and extension of networks. In contrast to evident cases of fraud, one frequently encounters behavior that is difficult to classify as objectionable or not. In these cases everybody will use his own standards, with the risk of being judged in a specific case by others, using other standards. In popular empirical science research (Latour 1987; Woolgar 1988; and others) it is not only suggested, rightly, that strategic behavior plays a large role in circles of scientific research, but it is frequently presented in a way which unconditionally sanctions and stimulates it, although at ones own risk. Such convictions even grant scientists a license to luxuriate in their own power. To be sure, scientists not only aim at cognitive goals like empirical success or even the truth of their theories, but they also have social aims like recognition and power, and hence means to reach such aims. And although these goals frequently strengthen each other, such convergence by no means implies that the conscious pursuit of these social goals is good for science. With regard to this question, I will consider five examples of strategic deviations from the norm of disinterestedness.

before in Carnap’s famous The continuum of inductive methods (Carnap 1952) that and how he introduced such probabilities precisely in this way. In my master’s thesis I had chosen for Kemeny’s alternative presentation, which is probably the reason why I had apparently forgotten Carnap’s own way of introduction. Happily enough, nobody else noticed it before; it was discovered later by my then Ph.D.-student Sjoerd Zwart. However, then I could immediately concede and explain. Since this discovery, I know how to minimize the risk, see the main text.

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13.3.1 Number of Publications The average number of published articles and books is an important measure for assessing individual scientists and groups of scientists. “Publish or perish” became a well-known saying. Originally, only the pure number of publications was counted, but gradually one started to differentiate between scientific or scholarly publications and ‘professional publications’, that is, publications for non-experts. Whereas, at least in The Netherlands, professional publications are almost neglected, a practice which is certainly debatable in some areas of the social sciences and the humanities, scientific publications are divided into categories with different weights. Usually, but not always in these disciplines,5 a book is higher rated than one article, a local, e.g., Dutch, publication lower than an international one. Moreover, one distinguishes between a conference abstract, a paper in conference proceedings, a chapter in an edited book and an article in a blindly refereed international journal. However this may be, it is frequently easy to increase the number of publications, a practice which need not be solely for the purpose of padding one’s curriculum vitae. Of course, this is almost excluded in top journals. However, in other contexts it is plausible to modify, combine and extend earlier work. For example, invitations are frequently extended to established scientists to deliver specific contributions based on earlier work.6 In addition, translations frequently originate in this way. Another possibility for increasing the number of publications, in particular in the natural and medical sciences, is by being a co-author, where one and the same article is frequently counted as one publication for each co-author. Most of the suggested types of publications are as such unproblematic and even useful for spreading ones ideas and findings. The only problem is that others can interpret them as attempts to multiply the number of publications, leading to a feeling of guilt. However, nobody accuses scientists for giving two different versions of essentially the same talk for totally different audiences. The same should be the case for versions of the same publication in different media. One way to diminish the feeling of guilt of multiplication behavior in the latter case is by supplementing the usual, at least in The Netherlands, minimum norm of about two scientific publications as the principal author per year with a kind of maximum of, say, three. That is, above three scientific publications, all the other kinds of publications should also be taken into account. Such a practice would leave the primary publication task of scientists untouched, but provide substantial room for other kinds of publications. Incidentally, one may doubt whether such norms should be used as requirements for individual scientists. In the first place, it is not so clear that one should prefer three scientific publications per year above one very influential publication in 3 years. This uncertainty makes the norm of at least two scientific publications on average 5 Note that this is also quite different from the natural sciences and medicine, where writing books became something for leisure time. This seems very unfortunate, for overviews of a field by an advanced researcher are frequently very helpful for colleagues in related fields and stimulate interdisciplinary research. 6 The present paper is a variant, see notes 1 and 2, stimulated by the editors.

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per year and per group member much more appropriate than requiring such production from each researcher separately. Regarding other publications, a functional division of labor within a group may be very useful, depending on everybody’s strong and weak points. Recall that we have already met other kinds of functional divisions of labor in the context of organized skepticism.

13.3.2 Number of Citations Citations may of course be problematic, in the first place because they can be misleading or even outright fraudulent, but this is not my topic here. The increased importance of citations is frequently summarized by a variant of the “publish or perish” slogan: “Be cited or perish”. Many publications are seldom read, let alone quoted. Publications frequently have another function. In the first place one may want to reach primarily the group of kindred colleagues by way of the publication itself or by its reprints, in order to get comments that may be useful for a version intended for a renowned journal. This is of course also possible with manuscripts, preprints and nowadays mostly in an electronic way. However, in the case of published materials the effective potential readership for a publication is usually somewhat larger, in particular due to a greater possibility of unintended readers. A publication, in effect, is placed into one of many reading circuits, which can be classified to the extent that they are centered on authoritative journals, authoritative and popular authors, journals paying in particular attention to certain new developments and, finally, a frequent consequence of this, research program bound journals. Strategic citation behavior is partly related to this variety of circuits. More important for my present purposes is it to note that it is more effective to quote an authoritative author or journal than a further unknown researcher who published the idea earlier in a rather unknown journal. The fact of the matter is that the average reader is, consciously or unconsciously, sensitive to authority arguments. The result is the Matthew-effect: who is frequently cited, will be cited still more. Such citation popularity may of course be legitimate or illegitimate, that is, authors may become popular for good and for bad reasons. One is also inclined, when one has a choice, to quote from a more recent publication than from an older one; otherwise it may appear that one does not read recent publications. For both strategies, there may be some justification, but two other strategies are not justifiable: “one good turn deserves another”, and “don’t quote countrymen or (other) scientific opponents”. The strong focus on American authors and journals, not only by many American researchers, but also by many European ones, is in general already a problem, but particularly insofar as citation behavior is concerned. It is clear that much of the indicated citation behavior forces one to relativize the use of numbers of citations as a measure of quality or impact, the more so because there are considerable differences in the degree of strategic citation behavior among scientists. Only self-citations and ‘in-group’ citations are easily removed, all other problematic citations are difficult to exclude by some clear criterion. A better alter-

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native for measuring impact seems to me to be the following: let researchers present from time to time a verifiable survey of the substantial use of their own publications by others. To be sure, citation indexes remain very important for this purpose, and should preferably be as complete as possible.

13.3.3 Writing Research Proposals The writing of research proposals has become an important part of the work of scientific researchers. It may concern the application for special university funds, for special national funds, and for contract research paid by governments, profit and non-profit organizations. Henk Withaar (1979) argued that, besides the so-called Context of Discovery and Context of Justification, there should be distinguished a Context of Persuasion in which research plans are set up and defended. However this may be, an accepted research proposal is seldom realized precisely in the way in which it was proposed. Three factors are important in this respect: the difficulty to plan research, exaggerated optimism of researchers, and misleading formulations in the proposal. It is generally acknowledged that it is difficult to plan research and that it is wise to change plans when other routes seem better. Moreover, researchers usually are rather optimistic about what they can achieve in a given amount of time. This shortage of realism is not problematic by definition. On the contrary, if researchers would know in the advance the actual amount of time that it will take to complete some project, they would frequently lose their motivation. Finally, misleading presentation is the third and here most important reason why research plans are not realized in detail. In research proposals one can frequently read about the likely social relevance and the relevance for other disciplines. Moreover, frequently a strong relation is claimed with an area that is announced as a focus for the relevant research fund or with some recent development that received much media attention. Also claimed connections with the work of likely reviewers of the proposal are sometimes impressive. Experienced reviewers of research proposals are usually alert for such kinds of inflationary statements. However, since they are mostly but not completely nonsensical, it is difficult to evaluate such expositions. Moreover, the future results of the research may well be worthwhile, despite the fact that many of the suggested expectations are not fulfilled. As far as misrepresentation is really problematic, it usually has, in contrast to fraud, no further negative consequences for science. Nevertheless, claims to social relevance, may only be pertinent when they are one of the main motives for the research. Misleading claims that come close to being fraudulent seem to occur most frequently in requests for continued support of research. In the sensational book written by K¨obben and Tromp (1999), some revealing Dutch examples of this nature are presented. The temptations are considerable for the research manager of an independent research institute who is also an entrepreneur and who is trying to serve the continuity of the institute. Moreover, the employees of such an institute use to have much to lose and not much to gain by whistle

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blowing. However, at least in The Netherlands, the conditions for whistle blowers have recently been improved to some extent, but they are still far from optimal. There is a totally different way in which research proposals are sometimes not executed after their acceptance; simply because the research has already been done before, and with success. The background of such behavior is the following. Research funds frequently ask for clear research plans with clear methods and phases and expected results. Scientists, however, may want to focus on new topics for which it is impossible to provide the required clarity. Hence, one way to beat the system in such a case, is to propose to do research that has already been successfully performed, but not yet published. The proposal can then be written with hindsight on the way it could in fact be realized and, if it satisfies the relevant referees and committees, the research grant is in fact used for the really new, but vague research plans, with the safe perspective that the promised results can be reported. Of course, I leave it to the reader to judge to what extent this type of behavior is defensible.

13.3.4 Assessment of Research Proposals The assessment of research proposals varies strongly with the type of funding. In the case of university and governmental funds (e.g., NWO in The Netherlands, DFG in Germany, NSF in the USA) usually first a few referees are appointed to write a report of varying length. Then a committee or board prepares and/or takes the main decisions: whether the proposal is subsidizable and, if so, which degree of priority it is assigned.7 Partly on the basis of my own experience with NWO, it is my impression that the Matthew-effect also occurs here, perhaps to a more limited extent: who has great means will get still more, who has only little means will get less. To be sure, this effect is to some extent justified, but there is also likely a point where it becomes problematic. Implicitly or explicitly a number of factors play a role here, apart from the merits of the proposal itself. The reputation, according to the assessors and the committee, of the researcher or research leader or research team definitely plays a role. When a proposal is, as such, not of the highest quality, reputation may increase the appreciation. Moreover, the value assigned to the number of publications and citations, the so-called ‘past performance’, tells something, but not very much about the value of future research. Last but not least, sometimes one gets the impression that administratively active researchers, despite systematic exclusion from discussion about their own proposals, are somewhat more successful

7 Surprisingly enough, NWO has introduced in the twenty-first century the rule that committee and board members do not come to know the names of the referees, let alone, that they might choose them. If one compares this with editors of a journal when they would be in the same position it becomes clear that anonymity is here brought to the absurd.

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with their proposals than researchers who do not play an active role in the assessment circuits. Be it, because they are supposed not to be able to perform such a role, or because they feel themselves above spending time on such things.

13.3.5 Networks Participation in administrative and assessment circuits is one of the ways in which one can build a network that is functional for one’s striving at truth, recognition and power. However, building other types of networks, with researchers in the country and abroad and with people potentially interested in applications of research findings, is of course at least as effective. In all cases, the personal and didactic qualities play a role that is at least as important as the purely scientific qualities. For instance, the early twentieth-century philosopher Bolland from the University of Leiden could present, in a very charming way, views which are now not only considered to be nonsensical, but nobody can understand how they could be taken seriously by so many scholars and laymen at the time. The fact that he was taken seriously suggests that, in philosophy and other disciplines, there may always be new Bollands around, which have not yet been identified as producers of humbug. The problem is, of course, that there are also several exemplary researchers who are able to present their views in an excellent and charming way and so build a useful network. Hence, it is only important to always be alert to the fact that somebody may sell ideas which are not as yet recognized as humbug, and build further on a network to promote these ideas.

13.4 Concluding Remarks It will be clear that Merton’s norms are not principles from which one should deviate under no circumstances. However, they may well function as ‘default-norms’. That is, norms of which deviations have to be specifically motivated in terms of the expected differences between the consequences when they are followed and when they are violated. Deviations, which are difficult to motivate in this way, may be considered as problematic. My claim is not to have given a complete and thorough survey of defensible and indefensible deviations. However, in particular, I aimed to show the existence of gray areas. Despite these areas, it makes sense to address the question of how Merton’s norms may optimally function as default-norms. Sensibility for gray areas needs, of course, to be stimulated, and an informed judgment should be made in such cases. The desirability of this type of norm consolidation will be the subject of the final paragraphs.

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In general, consolidation of norms is primarily a matter of socialization in the relevant community, supplemented with explicit attention to the awakening of the individual’s awareness of these norms. However, rules for behavior will only function properly if the relevant reward system does not itself promote problematic deviations. As far as the assessment system of researchers can be characterized truthfully by slogans like “publish or perish” and “be cited or perish”, the relevant scientific bureaucracy is to my opinion co-responsible for the increase in dubious publication and citation behavior. When discussing above deviations from the subnorm of timely publication, a number of factors preventing untimely publication were mentioned: the threat of loss of face, the need of repeating experiments and checking proofs, the referee system and responsible science journalism. These and similar factors function of course also to maintain the other norms. The ideal way to internalize the norms, however, requires that the aims of the knowledge be legitimate. The more legitimate the research goals, the easier is the self-imposing of the norms, at least as far as one subscribes to that legitimization and believes that the norms are functional for these goals. In terms of knowledge goals, one may think in the first place of the search for truth, or at least for empirically successful approaches. From Part II of (Kuipers 2000) and Part IV of (Kuipers 2001) it becomes immediately clear that, for example, fabrications and fraud will retard genuine confirmation and empirical progress. Moreover, from Part III of (Kuipers 2000) it then follows that truth approximation is retarded as well. I also like to quote Ilkka Niiniluoto (1999, 300) on this subject: But it is important to realize that many norms in science, in both ethics (e.g. rules against fabrication of data and fraud) and methodology (e.g. rules for testing statistical hypotheses), are truth-centred: they are designed to guarantee the reliability and self-corrective nature of scientific inquiry. In other words, these social norms are epistemologically, not only sociologically, highly relevant and interesting.

However, scientific, technological and societal relevance may also function as self-chosen supplementary signposts, including sensitivity to societal problems originating from the application of scientific findings, e.g., several environmental problems. As already stated, the more one subscribes to such goals in the interest of science and society and the more one believes that the norms are functional for these goals, the more easily will one conform to these norms. The question remains whether this ‘ideal approach’ is sufficient. Let us have no illusions about the possibility of totally excluding evident kinds of fraud. Like in any other social sector, there will always be a number of more or less pathological individuals who insist on going wrong. A more serious problem is the demarcation of the gray areas between clearly defensible and indefensible deviations. In particular, it may be worthwhile to consider a general code of conduct for incorruptible scientific research, with a clear statement of its status, and covering such ‘gray-area’ practices. To be sure, the subject of incorruptible research is usually discussed in the various codes of conduct for specific groups of researchers, such as chemists and psychologists. However, as far as I know, there are no initiatives for

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formulating a general scientific code.8 Such a general code should be distinguished from general brochures that try to make scientists sensitive to ethical issues. The first example of this nature probably was On Being a Scientist: Responsible Conduct in Research of the National Academy of Sciences in the USA, published in 1989 (NAS 1989). Other countries followed sooner or later. For instance, the Royal Dutch Academy of Sciences (KNAW) published in 2000 the booklet (KNAW 2000) Wetenschappelijk onderzoek: dilemma’s en verleidingen (Scientific research: dilemmas and temptations). In contrast to such valuable brochures, the still incomplete draft resulting from the unsuccessful attempts of the ICSU (the International Committee of Scientific Unions) to install a ‘Hippocratic oath for scientists’, suggests the kind of general code indicated above, but it focuses on social consequences of science and almost entirely neglects the matter of incorruptible research.9;10 According to the most recent Web-information (also in October 2008), the same applies to the debate within the AAAS (American Association for the Advancement of Science, www.aaas.org) about a possible oath. However, I hope to have made it clear that it makes much sense to consider the possibility of a general code of incorruptible conduct in research and to include it perhaps in an encompassing oath. In particular, the existence of gray areas asks for general recognition. They do not seem to differ very much among various disciplines, but the attitude to them differs very much among scientists. Hence, these gray areas will have to be addressed with much prudence, which almost excludes a strictly prescriptive code. It is telling that the “Office of Scientific Integrity”, founded in the USA in 1989, was transformed already in 1992 into the “Office of Research Integrity”, with weakened terms: investigations of accusations of undesired behavior were no longer to be followed by ethical judgments (KNAW 2000, 14). Certainly without disposing of a general code, taking gray areas into account, this was a highly plausible development. However, even though such a code would remain very useful for such offices, it may have too much and too strong undesirable effects on scientists. In this respect it is interesting to compare it with ‘ethical review’ procedures for research proposals. Pettit (1992) argues that such procedures endanger valuable research on human beings. Without precautionary measures, “it is likely to carry us along a degenerating trajectory”, avoiding all kinds of important research which might lead to ethical blockades. Hence, the question is whether a general code is possible that is not the start of a degenerating trajectory but a useful new point of reference in the interest of science and society.11

8

In the meantime the KNAW has published in 2004 such a general code (KNAW 2004), entitled The Netherlands Code of Conduct for Scientific Practice (www.knaw.nl/pdf), which happens to be mildly prescriptive. It concludes with a section on dilemmas explicitly dealing with ‘grey areas’. This is very relevant for the rest of this section. 9 From a personal communication in 2000 with Matthias Kaiser, chair of the ICSU Standing Committee of Ethics and Responsibility in Science. 10 According to a meeting report of March 2007 (www.icsu.org), this project has never been completed. 11 For interesting critical comments on this paper and further discussion, see Zandvoort (2005), and my reply immediately after that paper.

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References Broad W, Wade N (1982) Betrayers of the truth. Simon en Schuster, New York Carnap R (1952) The continuum of inductive methods. The University of Chicago Press, Chicago, IL Kaiser M (1996) Towards more secrecy in science? – Comments on some structural changes in science and their implications for an ethics of science. Persp Sci 4.2:207–230 KNAW (2000) Wetenschappelijk onderzoek: dilemma’s en verleidingen. Koninklijke Nederlandse Akademie voor Wetenschappen, Amsterdam KNAW (2004) The Netherlands code of conduct for scientific practice. Koninklijke Nederlandse Akademie voor Wetenschappen, Amsterdam K¨obben A, en Tromp H (1999) De onwelkome boodschap. Mets, Amsterdam Kolfschoten F. van (1993) Valse Vooruitgang. Veen, Amsterdam Kuipers T (1972) Inductieve waarschijnlijkheid, de basis van inductieve logica. Algemeen Nederlands Tijdschrift voor Wijsbegeerte (ANTW) 64.4:291–296 Kuipers T (1999) De integriteit van de wetenschapper. In: red Kimman E, Schilder A, en Jacobs F (eds) Drieluijk: godsdienst, samenleving, bedrijfsethiek. Liber Amicorum voor Henk van Luijk. Thela-Thesis, Amsterdam, pp 99–109 Kuipers T (2000) From instrumentalism to constructive realism. Synthese Library, Kluwer, Dordrecht Kuipers T (2001) Structures in science. Synthese Library, Kluwer, Dordrecht Lafollette M (1992) Stealing into print. Fraud, plagiarism, and misconduct in scientific publishing, University of California Press, Berkeley, CA Latour B (1987) Science in action. Open University Press, Milton Keynes Macfarlane B, Cheng M (2008) Communism, universalism and disinterestedness: re-examining contemporary support among academics for Merton’s scientific norms. J Acad Ethics 6:67–78 Merton RK (1942) Science and technology in a democratic order. J Legal Polit Sociol 1:115–126. Reprinted under several titles, e.g. The normative structure of science. In: Merton RK The sociology of science. The University of Chicago Press, 1973, pp 267–278 Mulkay M (1977) Some connections between the quantitative history of science, the social history of science, and the sociology of science. In: L¨opp¨onen P (ed) Proceedings of the International Seminar on Science Studies, Publication of the Academy of Science, Helsinki, 4:54–76 NAS (1989) On being a scientist: responsible conduct in research. National Academy of Sciences, Washington, DC Niiniluoto I (1999) Critical scientific realism. Oxford University Press, Oxford Pettit Ph (1992) Instituting a research ethics. Chilling and cautionary tales. Bioethics 6.2:89–112 Sober E (2000) Philosophy of biology, 2nd edition. Westview, Boulder/Oxford Solomon M (1996) Information and the ethics of information control in science. Persp Sci 4.2: 195–206 Withaar H (1979) De Context of Persuasian – een voorstel tot ruilverkaveling. Kennis en Methode 3.1:41–50 Woolgar S (1988) Science: the very idea. Tavistock, London Zandvoort H (2005) Knowledge, risk, and liability. Analysis of a discussion continuing within science and technology. In: Festa R, Aliseda A, Peijnenburg J (eds) Rodopi cognitive structures in scientific inquiry. Essays in debate with Theo Kuipers, vol 2. Amsterdam, pp 469–498. Reply T. Kuipers, pp 499–502 Ziman J (1994) Prometheus bound: science in a dynamic steady state. Cambridge University Press, Cambridge

Chapter 14

Epistemic Replacement Relativism Defended Martin Kusch

14.1 Introduction In this paper I shall offer a response to Paul Boghossian’s recent criticism of “replacement relativism”. Replacement relativism is the main semantic strategy for making sense of philosophical forms of relativism. Replacement relativism was first formulated by Gilbert Harman (1996a, b). It models philosophical relativism on relativization in the natural sciences.

14.2 Replacement Relativism Galileo proposed a relativistic thesis in physics. He discovered that motion is relative to a variable frame of reference. Put differently, Galileo recognized that facts about motion are relative facts. The semantics of assertions about motion before Galileo’s discovery can be reconstructed as follows. Sentences like “the ship moves” express the proposition the ship moves, and the latter is true, if and only if the ship at issue has the monadic property expressed by “moves”. Galileo showed that there is no such monadic property; thus utterances of the form “x moves” are untrue – they are either false or incomplete. Moreover, Galileo also pointed out that the closest truths in the vicinity of these untruths are relational truths of the form x moves relative to frame of reference F. This makes it natural to suggest that Galileo was asking us to change the way we speak: replace the non-relativized sentences with relativized ones, and assert only the relational propositions. Finally, Galileo also offered an analysis of what kinds of frames are possible.

M. Kusch () Institut fuer Philosophie, Fakultaet fuer Philosophie und Bildungswissenschaft, Universitaet Wien, Universitaetsstrasse 7, A-1010 WIEN e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 14, c Springer Science+Business Media B.V. 2010 

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Galileo’s relativism is the paradigm instance of the template of “replacement relativism”. Boghossian formulates the template as follows: Relativism about a monadic property P is the view that: (A) “x is P” expresses the proposition x is P which is true if and only if x has the monadic property expressed by “P”. (B) Because nothing has (or can have) the property P, all such utterances are condemned to untruth. (C) The closest truths in the vicinity are the related relational truths of the form: x is P relative to F where “F” names some appropriate parameter. (D) If our P-utterances are to have any prospect of being true, we should not make judgements of the form: x is P but only those of the form: x is P relative to F. There are the following constraints on the value that F may assume: : : : (2006b: 20–21).

In what follows I shall focus on epistemic forms of replacement relativism. The epistemic replacement relativist takes himself to have discovered that a sentence like (1) (1) Otto’s belief in ghosts is unjustified. that expresses the proposition (2): (2) Otto’s beliefs in ghosts is unjustified is untrue since there is no monadic property for “unjustified” to express. The closest truth in the vicinity of (2) is the relational proposition (3): (3) According to epistemic system ES1 , Otto’s belief in ghosts is unjustified. The epistemic replacement relativist recommends that we honour his insight in the way we speak (4): (4) According to epistemic system ES1 , Otto’s belief in ghosts is unjustified. Replacement relativism can be developed further in alternative ways. One important choice concerns the character of the relativizing frameworks. Boghossian considers two main options: the components of the frameworks can be taken to be either general propositions or imperatives. Boghossian dubs the first alternative “fictionalist”, and we might call the second “non-fictionalist”. Fictionalist replacement relativism needs to specify whether the original, non-relativized sentence (1) is false or incomplete. I shall dub the first option “error-theoretical”, and the second “incompleteness-theoretical”. On the latter proposal, Boghossian suggests, (1) is interpreted as expressing an “incomplete proposition, in much the way that Tom is taller than : : : is clearly incomplete” (Boghossian 2006a: 88; cf. 2006b: 25).

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14.3 Boghossian’s Criticism of Incomplete-Theoretical Replacement Relativism Boghossian argues that no philosophical version of replacement relativism is acceptable. In what I follow I shall show that at least incompleteness-theoretical replacement relativism can survive his criticism. I shall identify possible responses to the main problems that Boghossian counts as decisive evidence against incompletenesstheoretical fictionalism. First on the list is the Normativity Problem. Whereas the original sentence (1) is normative, sentence (4) is not; the latter merely reports what is epistemically unjustified according to an epistemic system (2006b: 25). The Endorsement Problem starts from the observation that for the fictionalist replacement relativist, epistemic systems consists of general propositions, like (5) Beliefs formed on the basis of wishful thinking are unjustified. Moreover, fictionalist replacement relativists are best taken to assume that general epistemic propositions or principles entail particular epistemic judgements. Unfortunately, these assumptions land the fictionist in trouble: if all particular sentences of kind (1) are incomplete, then so must be the general principles like (5). After all, the principles are merely more general versions of the particular sentences. Both contain the predicate “unjustified”; both express incomplete propositions. But if both particular judgements and general principles are incomplete, then how can the relativist ever accept them, how can a relativist ever endorse them? How can a rational person endorse an incomplete proposition like Tom is taller than : : :? (2006a: 85–86; 2006b: 27). The Infinite Regress Problem is closely related to the Endorsement Problem. In order to express a complete proposition, the advocate of incompleteness-theoretical fictionalism tells us, we need to complement particular sentences like (1) with a phrase specifying an epistemic system. Specifying an epistemic system involves identifying a set of general principles. Alas, as we have just seen, general principles too are incomplete. Hence we need to complement them with a phrase specifying a set of general principles. But these are again incomplete : : : and so on (2006b: 29). The fourth difficulty is the Entailment Problem. Incompleteness-theoretical replacement relativism holds that general principles entail particular judgements. But it is difficult to understand how incomplete general principles can entail incomplete particular propositions (2006a: 89; 2006b: 26).

14.4 Replacement Relativism in Physics Versus Philosophy If Boghossian is right, then replacement relativism does not work for philosophical contexts. This raises the question how philosophical contexts differ from physicalscientific contexts – in the latter replacement relativism obviously does succeed.

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Boghossian offers the following answer. The physical and the epistemic cases are similar in that both the physical and epistemic relativist regard the unrelativized sentences as untrue. But the “underlying logical forms” of the two replacements (6) x moves relative to framework F and (7) according to epistemic system ES1 , x is epistemically unjustified are very different. Philosophical replacement relativism preserves the original untrue sentence (here capitalized) within the relativistic statement. In moving from (1) to (4), we move “from a judgement of the form: x is P to a judgement of the form: (x is P) bears [relation] R to S.” (2006b: 30) The physical case is not of this kind (2006b: 31). Here the logical form of the replacing proposition is: x R y. The replacing proposition is not constructed around the original x is P. The claim is not: According to some frame of reference, x moves. It is: x moves-relative-to(-frame-of-reference)-F1 . That is, physical replacement relativism replaces the original predicate “moves” (expressing a monadic property) with the new relational predicate “moves-relativeto-F1 ” (expressing a dyadic property). Boghossian recognizes that his interpretation of physical replacement relativism might be accused of failing to separate relativism from eliminativism. Why should we say that Galileo relativises rather than eliminates the unrelativized “motion”? Why is the relation between “moves” and “moves-relative-to-F1 ” not like the relationship between “phlogiston” and “oxygen”? In response Boghossian suggests that there is “a more general concept, MOTION, itself neither absolutist nor relativist, such that both the absolutist and the relativistic notions could be seen as subspecies of it”. More generally, replacing non-relativized concepts with relativized ones is relativism rather than eliminativism if, and only if, the old and new concepts are “sufficiently intimately related to each other” (2006b: 32).

14.5 The Relativist’s Discovery and the Incompleteness of Propositions I now turn to my defence of epistemic incompleteness-theoretical replacement relativism. My main move is to insist that the relativist and absolutist disagree over a second-order or meta-epistemic issue, and that one can become a relativist without ever having been an absolutist first.

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It is important to distinguish between three viewpoints: the position of the nonphilosophical “ordinary person”, the standpoint of the absolutist, and the stance of the relativist. By “ordinary person” I mean a man or woman who is a competent user of epistemic language, who participates routinely in epistemic discourse, and whose actions and beliefs are judged in various epistemic dimensions by others. The crucial point for my argument is that the “ordinary person” is not a philosopher. That is to say, he has no philosophical commitments to meta-epistemic views and thus no commitments to either epistemic absolutism or relativism. Moreover, ordinary person, relativist and absolutist can belong to one and the same epistemic community: they can share the same (first-order) epistemic system. Boghossian himself allows for this possibility in a different context (2006a: 83). Consider the dialectical situation in which the relativist makes his “discovery” concerning the correctness of relativism. Start once more with (1): (1) Otto’s belief in ghosts is unjustified. Sentences like (1) are routinely used by ordinary persons to pass epistemic judgement. According to Boghossian’s rendering of incompleteness-theoretical replacement relativism, the advocate of this view has to dismiss (1) as incomplete on the grounds that there is no monadic property for the predicate “unjustified” to express. I beg to differ. I see no reason why the replacement relativist could not be more charitable. Imagine we ask ordinary persons in our own society what conception of knowledge they have in mind when uttering (1). It seems obvious that most would answer: (8) Our conception, of course. This suggests to my replacement relativist that the ordinary person would not object to the suggestion that (1) is – roughly – synonymous with (9): (9) According to our epistemic system, Otto’s belief in ghosts is unjustified. In order to do justice to this readily available gloss, and in order to be charitable to the ordinary person, my replacement relativist takes (1) to expresses the proposition (10): (10) According to our epistemic system, Otto’s belief in ghosts is unjustified. My replacement relativist agrees with Boghossian’s that there is no monadic property for “unjustified” to express. But my replacement relativist regards the question ‘monadic or dyadic properties’ as orthogonal to the real issue. As he sees it, the ordinary person as well as some versions of absolutism can readily accept that “unjustified” in (1) expresses a dyadic property. The “real issue” is whether the predicate (11): (11) : : : unjustified according to our epistemic system : : : expresses a real dyadic property. For my relativist this depends on how we understand “our epistemic system” in (11). If we take (11) to mean (12): (12) : : : unjustified according to the one and only epistemic system : : :

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then my relativist denies that (11) expresses a real property. In other words, to accept the rendering of (11) as (12) is as unacceptable to my relativist as is assuming the reality of monadic properties of epistemic justification. Once more, the issue is not, or not only, whether the relevant properties here are monadic or dyadic; the issue is whether there is only one valid epistemic system or whether there are many. My relativist interprets (11) as expressing a real property only if it is taken to mean (13): (13) : : : unjustified according to our epistemic system which is one of many equally valid epistemic systems : : : To be an epistemic absolutist is to reject the thought that (13) expresses a real property. But absolutists can either accept or reject dyadic properties of epistemic justification. Some absolutists maintain that (1) is complete as it is; others prefer the following rendering: (14) According to the one and only valid morality, it is wrong of Otto to hit Mary. It is central to my overall argument that the ordinary person is neither a relativist nor an absolutist. Within the confines of this paper, I cannot make a conclusive case for this view of the ordinary person. To do so would be to conduct, and present the results of, an extensive empirical investigation. In this paper I shall be satisfied to make only the following hypothetical argument: if the ordinary person is neither an epistemic relativist nor an epistemic absolutist, then we can better understand both the context of the relativist’s discovery, and see why a certain version of incompleteness-theoretical replacement relativism can survive Boghossian’s criticism. Although I shall not defend the antecedent of my argument in any detail, I should at least briefly explain my intuition that it must be roughly on the right track. Philosophers often count the frequency with which the ordinary person makes non-relativized statements like (1) as conclusive evidence for his commitment to absolutism. I am not convinced. I have already mentioned the readiness of the ordinary person to gloss (1) as (10), and thereby to express himself in ways that suggest a dyadic-property view. More importantly, note that in at least some contexts philosophers judge people without proper philosophical training to be an easy prey for relativistic views. Remember for instance the familiar philosophers’ lament about the allegedly flat-footed relativism of their undergraduates. Moreover, according to my own experience of epistemic discussions with untrained students, when pressed on their stance vis-`a-vis the relativism-absolutism opposition, they find it hard to come up with a straightforward answer. This does not of course suggest that philosophically untrained people are epistemic relativists; what it does indicate instead is that being introduced to, and becoming competent in, the practice of epistemic discourse does not involve deciding between epistemic absolutism and relativism. Most of our epistemic discourse functions in ways that do not bring this meta-epistemic alternative into view. And hence ordinary persons tend not to be committed either way. My main interest here is with philosophical forms of relativism. It seems at least possible however that the same proposal might also work for the physical cases. Recall that Boghossian himself suggests that there is “a more general concept,

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MOTION, itself neither absolutist nor relativist, such that both the absolutist and the relativistic notions could be seen as subspecies of it” (Boghossian 2006b: 32). Boghossian does not elaborate on this proposal and thus it is difficult to know how he wants it is to be taken. One way of interpreting it is to say that before Galileo made the distinction between absolute and relative motion clear and concise, people simply were not aware that there was a choice to be made. Their concept of motion was not one of absolute motion, and it was not a concept of relative motion. It was a concept of MOTION. It is because the epistemic judgements of the ordinary person carry neither absolutist nor relativistic commitments that the relativist takes these judgements to be incomplete rather than false. Statements like (1) can – as far as the ordinary person is concerned – be interpreted along both absolutist and relativistic lines. This is my relativist’s discovery. And of course he defends the relativistic rendering. Up to this point I followed Boghossian in formulating the relativistic interpretation of (1) as (9) or (10). The final step of my reworking of incompletenesstheoretical replacement relativism introduces a correction to this idea. My relativist takes a leaf out of the physicist’s book and reconstruct (1) as expressing the proposition: (15) Otto’s belief in ghosts is unjustified-according-to-epistemic-system-ES1 which-is-one-of-many-equally-valid-epistemic-systems. Interestingly enough, Boghossian himself mentions the possibility that the philosophical replacement relativist might make this move. He promises to look at this proposal later in his paper, but does so only for the case of non-fictionalist replacement relativism (2006b: 31–32). Of course, following the physicist comes at a price: I need to explain why my version of epistemic incompleteness-theoretical replacement relativism does not collapse into eliminativism. I shall treat this as a fifth problem, the Eliminativism Problem, for the position I have outlined.

14.6 Solving Boghossian’s Problems I can now turn to showing that the new and improved version of replacement relativism mooted above is able to solve Boghossian’s problems. I begin with the Endorsement Problem, according to which “it is hard to see how anyone could believe [and hence endorse] a set of propositions they knew to be incomplete” (2006b: 29). My proposal is not affected by this worry. True, the particular epistemic judgements and general epistemic principles of the ordinary person are – in the eyes of my relativist – incomplete insofar as they do not express the thought that ours is just one of many equally valid epistemic systems. This incompleteness is not like Tom is taller than : : :. In our case what is needed to effect the completion is the addition of a specific meta-epistemic philosophical gloss. However, the absence of this specific complement does not leave behind a meaningless torso of words or concepts: it leaves behind the very principle to which the relativist – insofar

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as he too has been an ordinary person all along – has been, and continues to be committed. Put another way, I am proposing that we distinguish between a first-order incompleteness and a second-order incompleteness regarding epistemic systems. First-order incompleteness has the effect that no epistemic system has been singled out. Second-order incompleteness means that no meta-epistemic stance (of relativism or absolutism) vis-`a-vis one and the same epistemic system has been determined. Boghossian collapses the two forms of incompleteness into one; this allows him to say that the replacement relativist is unable to pick out and endorse any particular system. Distinguishing the two forms of incompleteness avoids this problem. Our first-order epistemic commitments based on our epistemic system remain unaffected by our adopting the relativistic position. My response to the Infinite Regress Problem is closely related to my suggested solution to the Endorsement Problem. Again it is important to remember that the relevant incompleteness is not of the form Tom is taller than : : : According to my proposal the incomplete propositions that the relativist starts from may well constitute a very specific conception of being epistemically justified or unjustified, a conception that we ordinary men and women of a specific community have had all along. The relativist does not need to go through all levels of meta-epistemic complementing before his epistemic system has a content. At this point a further worry might seem pressing. For my relativist, general epistemic principles and particular epistemic judgements involve predicates like “epistemically-unjustified-according-to-ES1 -(which is one of many equally valid epistemic systems)”. How are we going to determine what this predicate means? It seems that in order to answer this question, we need to identify the content of ES1 . And to identify this content we have to study the general principles that constitute ES1 . Alas, the general principles again contain the predicate “epistemically-unjustified-according-to-ES1 -(which is one of many equally valid epistemic systems)” : : : and so on. This problem too is solved by remembering that “epistemically-unjustifiedaccording-to-ES1 -(which is one of many equally valid epistemic systems)” is a close successor to the concept of “unjustified as a claim to knowledge” in the language of ordinary persons. We do not need to work out laboriously what it is for something to be “epistemically-unjustified-according-to-ES1 -(which is one of many equally valid epistemic systems)”; we pretty much know it already. The extension of this predicate is pretty much what we learnt as the extension of the predicate “unjustified as a claim to knowledge” in ordinary, pre-philosophical life. We only need to add the qualification that our understanding of knowledge and epistemic justification is just one of many equally valid ones. The Entailment Problem was the difficulty of having to explain how incomplete propositions can entail one another. As Boghossian puts it: : : : how are we to understand the phrase ‘relative to [epistemic system ES1 ]’? Since we have said both that the propositions which constitute an [epistemic system] as well as the target propositions are incomplete, that relation cannot be the relation of logical entailment. (2006b: 29)

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Boghossian’s thinks that since incomplete propositions lack truth value they cannot entail or be entailed by other (incomplete) propositions. Boghossian takes this to be too obvious to deserve further argument. This is surprising. Boghossian’s primary source for replacement relativism is Harman (1996a,b); and Harman tries to convince his readers that there can be entailments between propositions that lack truth value: : : : many philosophical logicians suppose that claims that lack truth value because they involve false presuppositions can be entailed by other claims. For example, many philosophical logicians hold that ‘The present King of France is bald’ has no truth value because both it and its seeming denial, ‘The present King of France is not bald’, presuppose falsely that there is a present King of France. They might also hold that ‘The present King of France is bald’ is entailed by ‘Either the present King of France is bald or the present Queen of England is bald’ and ‘The present Queen of England is not bald.’ One version of an ‘error thesis’ takes moral claims to involve a false presupposition, e.g. of Moral Absolutism. In this version, moral claims are neither true nor false, even though entailments can hold among them. (1996a: 173).

Be this as it may, my replacement relativist has a ready response to the Entailment Problem that is independent of Harman’s argument. The point is simply that in adopting the relativist or absolutist meta-epistemic position we retain the inferential relations between general principles and particular judgements. The entailments are not affected by our removing the second-order incompleteness. The preservation of first-order entailments also helps in avoiding the Eliminativism Problem. “Unjustified-according-to-ES1 ” does not eliminate “(epistemically) unjustified”. Boghossian insists that the pair absolute motion and relative motion differs from the pair phlogiston and oxygen. Only in the case of the first pair are the old and the new concepts “sufficiently intimately related to each other”. This intimate relation is due to the existence of a “more general concept, MOTION, itself neither absolutist nor relativist, such that both the absolutist and the relativistic notions could be seen as subspecies of it” (2006b: 32). Can we make a related case for philosophical forms of relativism? We can. The relativist’s relativized concepts are intimately related to the concepts of the ordinary person. This intimate relation is due to the fact that the relativist’s successor-concepts preserve the original inferential relations between the ordinary person’s concepts. The Normativity Problem is not specific to incompleteness-theoretical replacement relativism; it affects all forms of replacement relativism. (1) seems clearly normative, and yet (3) or (4) seem to be descriptions of what is unjustified according to some epistemic system. The problem is real. But Boghossian fails to mention that relativists have not only been aware of it, they have even addressed it at some length. One intriguing proposal is to combine relativism with a form of emotivism or “quasi-absolutism” (Wong 1984, 2006; Harman 1996a,b). The proposal was developed for the case of moral relativism but it can easily be adapted to the epistemic case. The basic idea is that we sometimes, though not always, use epistemic terminology to express – not talk about – our approval of certain epistemic systems

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or principles. I shall mark such uses of epistemic terminology by capitalising the relevant words. Consider (16): (16) Otto’s belief in ghosts is UNJUSTIFIED. Uttered by me, this sentence expresses my approval of an epistemic system according to which Otto’s belief in ghosts is unjustified. Assume you approve of a different epistemic system according to which Otto’s belief in ghosts is justified. You might express yourself by means of (17): (17) Otto’s belief in ghosts is JUSTIFIED. We disagree with one another on what Otto should do. You approve of an epistemic system according to which Otto’s belief is justified, I do not. Moreover, (16) is not synonymous with (1), but if I accept (16) I must also accept (1). Are (16) and (17) normative? It is hard to see how one could give a negative reply. A sentence is normative if it expresses a norm. And being a norm is related to the phenomena of praise and criticism, approval and disapproval. To pick a definition almost at random: “any respect in which performances of an act can deserve praise or criticism is a norm for that act” (Williamson 2000: 238). When I utter (16) I criticise Otto’s belief in ghosts; when you utter (17) you refuse to criticise him (perhaps indicating criticism of those who would criticise him). Of course, the respects in which we assess Otto’s action are not identical: I assess his belief relative to one epistemic system, you assess his belief relative to another epistemic system. But this relativity does not cancel out the criticism. My criticism of Otto’s belief involves my disapproval of epistemic systems that permit (and require) him to believe in ghosts. Your regarding his belief as justified commits you to approving epistemic systems that assess his belief positively. Having an attitude of approval towards ES1 amounts to having the disposition to disapprove of beliefs that run counter to ES1 , the disposition to try hard to follow ES1 , the disposition to attempt to convince others of ES1 , and the disposition to apportion praise or criticism on the basis of whether beliefs are conforming to ES1 or not. It is a special virtue of Wong’s and Harman’s suggestion that it also helps with a sixth problem (not mentioned by Boghossian), the Disagreement Problem. Assume two epistemic relativists – you and I – differ in their response to Otto’s belief. You insist: (18) Otto’s belief in ghosts is unjustified-according-to-my-system-ES1 . I claim: (19) Otto’s belief in ghosts is unjustified-according-to-my-system-ES2 . The problem here is that we do not disagree at all. Once “unjustified” is appropriately indexed to our respective systems, we can both be right. And this undermines relativism; after all relativism in all its varieties is committed to the idea of faultless disagreement. Here is how quasi-absolutism helps. The relativist using the concept unjustified-according-to-my-system-ES2 , and the relativist using the concept

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unjustified-according-to-my-system-ES2 can disagree over the question whether a given action is (epistemically) UNJUSTIFIED: their disagreement resides in their approving or endorsing different epistemic systems.1

14.7 Conclusion In this paper I have tried to show that incompleteness-theoretical replacement relativism can be defended against Boghossian’s intriguing arguments. Key to my defence was the suggestion that we are not “born absolutists” and that relativism and absolutism insist on interpreting and complementing our first-order epistemic judgements and principles. These moves might well prove to be useful resources also for other debates about different forms of relativism.

References Boghossian P (2006a) Fear of knowledge: against relativism and constructivism. Oxford University Press, Oxford Boghossian P (2006b) What is relativism? In: Greenough P, Lynch MP (eds) Truth and realism. Oxford University Press, Oxford, pp 13–37 Harman G (1975) Moral relativism defended. Philos Rev 84:3–22 Harman G (1996a) Harman’s response to Thomson’s Part II. Moral relativism and moral objectivity. Blackwell, Oxford, pp 157–187 Harman G (1996b) Moral relativism. Moral relativism and moral objectivity. Blackwell, Oxford, pp 1–64 Harman G, Thomson JJ (1996) Moral relativism and moral objectivity. Blackwell, Oxford Williamson T (2000) Knowledge and its limits. Oxford University Press, Oxford Wong DB (1984) Moral relativity. University of California Press, Berkeley, CA Wong DB (2006) Natural moralities: a defense of pluralistic relativism. Oxford University Press, Oxford

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This paper grew out of my contribution to a symposium on Fear of Knowledge organised by the Institute of Philosophy in London, in November 2006. Boghossian acted as commentator. Despite the fact that we found little common ground, I have learnt much from his reply. – I have also benefited from discussing Boghossian’s work with Arif Ahmed, David Bloor, Adrian Haddock, Jeff Kochan, Richard Raatzsch, Simon Schaffer, and Barry Smith. For comments on previous drafts, I am grateful to Stephen Grimm, Jeff Kochan, Markus Lammenranta, Peter Lipton, Ram Neta, Richard Raatzsch, Mark Sprevak and David B. Wong. I have presented this paper to philosophical audiences in Cambridge, Edmonton, Madrid and Tilburg, and have learnt much from questions asked on these occasions.

Chapter 15

Models and Truth The Functional Decomposition Approach Uskali M¨aki

15.1 Introduction Science is often said to aim at truth. And much of science is heavily dependent on the construction and use of theoretical models. But the notion of model has an uneasy relationship with that of truth. Not so long ago, many philosophers held the view that theoretical models are different from theories in that they are not accompanied by any ontological commitments or presumptions of truth, whereas theories are (e.g. Achinstein 1964). More recently, some have thought that models are not truth-valued at all, but truth-valued claims can be made about similarity relations between models and real systems (e.g. Giere 1988). Others suggest that models are instruments that can be used for attaining truths, for example that models are false means for true theories (e.g. Wimsatt 2007). At the same time, philosophers and others keep talking about models being ‘correct’ and ‘incorrect’, ‘accurate’ and ‘inaccurate’ or getting facts ‘right’ or ‘wrong’. Among practicing scientists, one can find both the notion of a ‘true model’ and the idea that ‘it is in the nature of models that they are false’. There seems to be enough variety of views and confusion around them to invite a little bit of further investigation (see also M¨aki 1992, 1994, 2004, 2009a,b,c). Different conceptions of the model-truth relationship involve different ideas of what models are and what truth is, as well as how the two are related. Views of how they are related range broadly, including the following. Models are not truth valued, but they are useful vehicles for generating true claims about the world. Models are

U. M¨aki () Academy of Finland e-mail: [email protected]  Many of the ideas in this paper have been presented at Models and Simulations 2 Conference in Tilburg (October 2007), the European Philosophy Association Conference in Madrid (November 2007), Cambridge University (March 2008), 35th Annual Philosophy of Science Conference (Dubrovnik, April 2008), Paris I Sorbonne-Pantheon (May 2008), University of Buenos Aires (October 2008). I thank the audiences of these events for reactions. Special thanks go to Emrah Aydinonat for extensive written comments.

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 15, c Springer Science+Business Media B.V. 2010 

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not truth valued, but truth-valued claims can be made about how they relate to the world. Models are truth valued, but always inescapably false about the immensely rich and complex real world. Models are truth valued, and possibly true. Some of this variety of views may appear in one writer. Consider William Wimsatt’s case for “False Models as Means to Truer Theories” (Wimsatt 2007, 94–132). Wimsatt implies that models are truth valued: they are false. He also seems to imply that the difference between model and theory is a matter of their relative truth content: less (or none) in model, more in theory. He says models can be false in many ways, by being “oversimplified, approximate, incomplete, and in other ways false” such as getting the interactions of variables wrong, the variables not denoting real entities, being phenomenological, and failing to predict the data. And he characterizes these ways as “errors” in models (100–102). By contrast, I don’t take all those various ways as ways of models being false. And I think that in the practice of modelling, some important falsehoods in models are often not errors at all, but rather deliberately adopted strategic falsehoods. Wimsatt next lists (104–105) 12 ways in which false models may be useful (but now no more useful in helping get to “truer theories” but rather just truer or otherwise more realistic models or measurements). Some of these ways involve moving from thin, simple, and incomplete models to thicker, more complex and more complete models – that is, from false to more truthful in his vocabulary. This is a rather popular idea that appears in the notion of getting closer to truth by “concretization” by authors such as Nowak (1980) and Cartwright (1989). This is another manifestation of the “Perfect Model Model” (Teller 2001) according to which a perfect and possibly true model is a precise photographic replica of its target. By contrast, I have disputed this by suggesting that the simplest and thinnest model versions employing strategic false idealizations may be true. In what follows, I will give examples of the sorts of step that can be taken towards spelling out the intuition that, after all, good models might be true. Along the way, I provide an outline of my account of models as ontologically and pragmatically constrained representations. And I emphasize the importance of examining models as functionally composed systems in which different components play different roles and only some components serve as relevant truth bearers. This disputes the standard approach that proceeds by simply counting true and false elements in models in their entirety and concludes that models are false since they contain so many false elements. I call my alternative the functional decomposition approach.

15.2 Models as Representations Like many others, I take models to be representations. I have found it useful to dissect the idea of representation a little further by thinking of it as having two aspects: the representative aspect and the resemblance aspect. Models as representatives stand for some target systems. They represent their targets by serving as surrogate systems that are of direct interest in scientific inquiries. A representative may or

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may not resemble its target. Resemblance is an additional relationship between the surrogate system and the target system. In order for the model as a representative to do its job as a surrogate system that provides an epistemic gateway to the target, the two systems must resemble one another. If they do, one may hope to (indirectly) acquire information about the target system by (directly) examining the properties and behaviour of the surrogate system. Provided resemblance is ensured, models can be examined in place of their targets without sacrificing the quest for knowledge about real systems. But as I’ll explain in a moment, actually achieved resemblance is not required for representation to be in place. Nor does resemblance need to be detailed and comprehensive. Dividing representation into these two aspects enables having a rather rich and synthetic account of models. For example, it helps incorporate both pragmatic and realist ingredients in the account. The representative aspect brings out the intentionality, creativity and contextuality of models. Models are created by modellers to serve their interests in certain situations. The modellers’ goals and contexts provide the pragmatic constraints on models. So my account has a strong pragmatic dimension. But it also has a strong realist dimension. The resemblance aspect highlights the involuntary character of representation: models are, or at least many of them should be, constrained by the characteristics of their targets. This imposes an ontological constraint on modelling. But even requirements of resemblance are pragmatically constrained, as we will see. There are more nuances in the account. A formulation goes like this: [A] Agent A uses object M (the model) as a representative of target system R for purpose P ; addressing audience E; at least potentially prompting genuine issues of resemblance between M and R to arise; describing M and drawing inferences about M and R in terms of one or more model descriptions D; and applies commentary C to identify the above elements and to align them with one another.

Three distinctive characteristics of this account deserve attention. I join those, such as Giere, who have emphasized the importance of purposes and intentionality in the notion of model as representation. The relationship so conceived has the form: A uses M to represent R for purpose P (Giere 2006, 60). So for an object to represent at all, an agent’s intentionality is required. Furthermore, one and the same model object can be used for a number of different purposes, and this makes a difference for how well it functions as a representation. One way in which my account extends this idea is to incorporate the notion of audience as part of the pragmatics of representation. Models are built and examined so as to meet and shape audience expectations. The audience-dependence of modelling is one manifestation of the collective nature of scientific work. Models are constructed and used so that they enable communication, convey information, promote agreement, and help persuade others to revise their belief intensities. Just as other purposes, meeting and shaping audience expectations make a difference for how a model fairs in representing. The second novelty in [A] is that it is put in terms of at least potentially prompting genuine issues of resemblance to arise – while other accounts may make no separate reference to resemblance or may require actually achieved successful resemblance. That there be an issue of resemblance that is being raised or that can

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be raised – and perhaps even settled – makes room for a variety of models at different stages of their epistemic trajectories, from highly conjectural and speculative to highly secure and warranted. The range of ‘representational models’ becomes thereby extended. By requiring that the issue be ‘genuine’ I mean to put forth two ideas. First, genuine issues are about non-utopian resemblances: M or its modifications should have the capacity to resemble R so that successful resemblance does not appear as an unattainable utopian goal, but should instead lie within the horizon of our cognitive possibilities. Second, genuine issues are not about just any of the numerous arbitrary ways in which M and R do (or do not) and might (or might not) resemble one another, but rather about specific respects and degrees of resemblance that meet the pragmatic constraints. This will play an important role when dealing with the issue of truth. The third novelty in [A] is the incorporation of what I call commentary. A model commentary C has a crucial role to play in turning a model object M into a representation. Model objects are mute and passive, they are unable to do the representing by themselves. For this, an active agent is required to use a model object for representing some facets of the target so as to serve some purposes and to communicate all this to some relevant audiences. Use must involve talk. The agent must speak on behalf of the mute model object. This must be done in a way that aligns the model object with the other components of representation. Model commentary is an activity of the modelling agent that seeks to identify the relevant components of representation and to coordinate model objects with the model descriptions, purposes, audiences and issues of resemblance involved in representation. Model commentary also plays a crucial role in dealing with the issue of truth. Model commentary C is needed for the task of coordination since model description D is not sufficient for this – while D is necessary for C , since one must describe what one comments. Here I consider a class of models that can be conceived as imagined objects or systems. Model descriptions are necessary for such models, for them to come about and to play their roles in scientific inquiry. What is merely imagined must be described by concrete means, such as material objects, mathematical equations, diagrams, visual images, graphs, verbal accounts, and so on. One and the same model can be described variously, using different concrete devices. These devices are used in constructing models, characterizing their properties, and reasoning about them. Reasoning or inference takes place among model descriptions D. Some inferences lead to conclusions about the imagined model world M : about what properties the model has, about what happens in the model. Other inferences lead to conclusions about the real target system R. These latter conclusions are hypothetical if genuine issues of resemblance can be raised, and they become increasingly warranted the more reliably those issues get settled in favour of actual resemblance. It makes no sense to make such inferences in case no genuine issues of resemblance can be broached. So on this account, a model permits inferences about the target if it is representational in the sense of [A]. By contrast, Suarez (2004) suggests that a model is representational provided it enables inferences about the target. My account reverses this relationship: inferential capacity depends on representational

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capacity. From an epistemic point of view, however, the two interact: to determine whether a model has representational capacity, one needs to exercise a lot of inference. There is no inference-independent way to find out about whether a model succeeds in representing. A model description does just what the term suggests: it describes a model. But it does not say what in model M is relevant for what purpose and audience, and what facts about target R it is supposed to highlight in a given context of model use. This is where the idea of functional decomposition becomes acute. And this is where model commentary C is called for its services.

15.3 Models and Truth Account [A] of models as ontologically and pragmatically constrained representations offers numerous opportunities for linking models with truth. These various possible lines are based on isolating different components of [A] and exploiting them in truth ascription. Model commentary plays a crucial role in pointing out the relevant components and their roles in determining the truth-value of a model. One possibility is to focus on the pragmatic components of model representation, namely purpose P and audience E. The strategy is to adopt a suitable pragmatic concept of truth and to ascribe the respective pragmatic property to models. Account [A] makes two such pragmatic properties available, namely usefulness in relation to a purpose, and persuasiveness in relation to an audience. The respective concepts of truth then are truth as usefulness in serving a purpose, and truth as persuasiveness in conforming to and shaping the beliefs of an audience. Truth ascription is a matter of ascribing such pragmatic properties to models. A model is true if it succeeds in serving a purpose such as contributing to the attainment of a policy goal; or if the audience addressed finds the model persuasive enough to accept it. In each case, further requirements should be imposed on usefulness or persuasiveness for these to qualify as definitive of truth (such as sustained long-run usefulness and persuasiveness as an outcome of a rhetorical conversation observing some ethical principles). Even though I take models to be pragmatically constrained representations, I prefer not to adopt a pragmatic concept of truth, thus the above is not my way of getting truth into models. There are a couple of intuitions that I am not prepared to sacrifice. An agent A can successfully use a false model M to impress an audience E. And A can successfully use a false model M to serve some other purpose P , such as prediction within some range of reliability. I take these intuitions to suggest that truth is independent of persuasiveness and usefulness (while these can be included among the fallible criteria of truth). Both of these options – truth as usefulness and as persuasiveness – are based on picking out distinct components – P and E – in the composite act of representation as relevant to the model’s truth. Note, however, that both tend to treat models in an indiscriminate manner, thus model object M itself is not decomposed. Truth

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is ascribed to models as wholes, not to some limited parts of them. The view I am pursuing here, on the other hand, takes a decompositional approach to M as well, not only to the composite act of representation. So I take two steps away from the pragmatic view of the truth of models. First, we should not begin with focusing on the M-P or the M-E relations as key to models possibly being true. We should rather start first with isolating the M-R relation from the pragmatic components in representation. It is the resemblance aspect of representation that is akin to truth in some intuitively obvious manner. Nevertheless, the pragmatic components of a representation do play an important role in truth ascription as we will see. Second, because it is in the nature of models that they in no way resemble their targets accurately and in their entirety, resemblance has a chance only if models themselves are functionally decomposed. Indeed, the key principle that informs this approach is that a model is a structure with component parts that have different and varying functional roles, among them the role of the primary truth bearer. Models are not candidates for truth as wholes, rather their privileged parts can be considered for truth. Other model parts may be idle or they may actively facilitate the pursuit of truth without themselves claiming any such status. To enable truth ascription, the modeller must be able to identify the relevant model parts and the relevant respects and degrees of resemblance – instead of complete and precise resemblance. The model itself is unable to discriminate between its various parts .m1 ; m2 ; m3 ; : : :/ as playing different functional roles. It is here that the pragmatic components become active. The pragmatic constraints shape the limited respects and degrees of resemblance between model M and target R. The recognition of the relevant purposes P and audiences E informs the assignment of different functions to different model parts in a particular context. The required respects and degrees of resemblance are a function of where M consists of m1 ; m2 ; m3 ; : : : They are not constant across contexts. In different pragmatic situations, different bits of truthful information are being sought. I said above that M-P and M-E relations do not constitute truth. But as soon as we settle on M-R relations as key to truth, we must bring P and E back to the stage because they make indispensable contributions to truth acquisition. They help isolate relevant truth bearers within models. They determine the respects and degrees of resemblance that matter. Of all possible bits and pieces of truthful information that a model can capture – and that are true or false in virtue of the properties of the target system R – the pragmatic components of representation select the ones that are pursued in any given context. In this way, truth acquisition is a joint product of a pursuit that meets the pragmatic and ontological constraints of modelling simultaneously. These various components are not self-identified, nor is their coordination automatic and transparent. It is necessary to identify the components, to assign them with functional roles, and to align them with one another in such a way that the ontological and pragmatic constraints have a chance of being met in a given context. This is where model commentary C becomes indispensable. It provides connections between the components and makes clear what aspects and degrees of

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resemblance are being sought, and how various model parts play their roles in the endeavour. Only a model commentary can answer questions such as: what in M is supposed to resemble what in R?

15.4 Idealization, Isolation, and Truth Consider the structure and composition of models from the point of view of the use of idealizing assumptions in describing models. It is generally recognized that such idealizing assumptions are put in terms of extreme or limit values (zero, infinity, one), and as such they may often appear to be brutally false about any real world situation. If one were to have an idea of models on which such idealizing assumptions are among a model’s elements, an unavoidable conclusion would be to admit that there is a lot of falsehood in models, or even that models are inescapably false. So there would be no chance for a model to be true. But let us look at such idealizations from the functional decomposition point of view. If we consider models to be imagined objects or systems that are to be distinguished from their descriptions, we can think of idealizing assumptions as belonging to model descriptions D. Their function is to describe the imagined system by telling what is not in it and what is included in it. Other assumptions identify items – for example, important causal factors – to be included more directly. Models are often imagined systems in which a simple streamlined mechanism is in operation isolated from any other complexities and interferences. Those potential interferences are neutralized by means of idealizing assumptions. Such assumptions are among the vehicles that have the function of isolating mechanisms from disturbances. Making and manipulating idealizations is analogous to experimental controls in material laboratory experimentation – it is the experimental moment in theoretical modelling. In both cases, one controls for other things in order to isolate one thing so as to let it act on its own. In material experiments, the controls are based on causal manipulation, while in theoretical models they are implemented by making idealizing assumptions. (M¨aki 1992, 1994, 2005, 2009a, b) Now thinking of idealizing assumptions as truth bearers with truth-values, the crucial first decision to make is about what their appropriate truth makers might be. If they are interpreted as claims about actual real world systems, they typically emerge as false claims. But if they are interpreted as claims about models viewed as imagined systems, they are straightforwardly true for the simple reason that as part of model descriptions idealizing assumptions not only are about models, but also determine what those models are. They not only describe a pre-existing imagined system, but also articulate the details of the product of the imagining. Or, as it has also been put (Giere 1988, etc), they define the model, and what defines a model is trivially true about it. So conceived, the falsehood of idealizations with respect to real world systems may seem apparent or irrelevant. Again, the story is more nuanced, but cannot be told here (see Musgrave 1981; M¨aki 2000; Hindriks 2006).

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15.5 The Locus and Stuff of Truth There are two interrelated issues about truth in regard to models. The locus issue is about where in, or around, models is truth possibly located. The stuff issue is about the ontology of truth-bearers, about the stuff they are made of. A stance on one constrains the range of possible stances on the other. On Giere’s account, truth-bearers must be linguistic. This stance on the stuff issue has implications for the locus issue. For Giere models are non-linguistic “abstract objects” that are linguistically described or defined by assumptions that are trivially true of the models they describe. Since models are not linguistic, they are devoid of truth-value. This does not mean that models are unconnected to their targets – they are, but not by truth. The connection is that of similarity. Model systems may be similar to their target systems in varying respects and degrees. Statements about these relationships are “theoretical hypotheses” that are truth-valued claims about (respects and degrees of) similarity between the model and the real system (Giere 1988, 2006). So two kinds of true claims can be made about models. Models themselves cannot be true or false. Since I am looking for ways of avoiding this last conclusion, I begin with questioning Giere’s view of the stuff issue. I don’t require truth bearers to be linguistic. A simple step to take is to permit thoughts among possible truth bearers. Thoughts can be expressed linguistically, diagrammatically, and otherwise. If thoughts can be true, such expressions can also be – perhaps derivatively – true. A thought that things are thus and so is true if things are thus and so. Models viewed as imagined systems might be made of the kind of stuff that is fit for this line (but the details depend on whether models are viewed as thoughts or as what is thought; see M¨aki 2009c). A modeller thinks of a simple system governed by a streamlined mechanism undisturbed by any interferences. The system is described in terms of assumptions many of which are idealizations that appear false if taken as claims about real world systems. By exercising inferences and manipulations among model descriptions, the modeller refines her thought about the structure and functioning of the modelled mechanism. Model commentary may point to this thought as the primary truth bearer within the model. This thought is true of those real world systems in which the mechanism is in operation (or is possibly in operation if this is the thought). The above presupposes that the model is being used for representing a target, with the components identified by [A] in place. A model as an imagined system may serve as a representative of a target and may resemble the target in certain selected respects. Many characteristics of such a model system fail to resemble features in real systems, but this does not have to be taken to imply that the model is false since those characteristics have not been included among the relevant truth bearers. The model and its target relevantly resemble one another in case the mechanism in the model and a mechanism in a target resemble one another. In such a case, one may choose to go as far as saying that the model is true. A more moderate line would be to say that a part of the model is true. (For qualifications, see M¨aki 2009c.)

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15.6 A Brief Illustration The ideas outlined in the foregoing are well illustrated by the simple model of agricultural land use distribution provided in Johann Heinrich von Th¨unen’s famous book on the Isolated State (1826/1842). Here land use allocation takes place in a highly idealized simple model world. The book begins with the following passage: Imagine a very large town, at the centre of a fertile plain which is crossed by no navigable river or canal. Throughout the plain the soil is capable of cultivation and of the same fertility. Far from the town, the plain turns into an uncultivated wilderness which cuts off all communication between this State and the outside world. There are no other towns on the plain. (von Th¨unen 1966, 7)

This is part of von Th¨unen’s model description. Here he lists some of the idealizations that characterize the Isolated State, his simple model world. Later literature has amended the list with many other idealizing assumptions (such as the town being a point and agents being perfectly informed). If taken as truth-valued claims about real-world land use, they are false, many of them utterly so. It is notable that von Th¨unen implies that the Isolated State is an imagined system. Note also that the book is directed to an audience from the start: it invites the reader to join the author in “imagining” a model system. The author’s model commentary is informative. Much of it is directed to the audience of readers. Here is von Th¨unen on the function of idealizing assumptions: I hope the reader who is willing to spend some time and attention on my work will not take exception to the imaginary assumptions I make at the beginning because they do not correspond to conditions in reality, and that he will not reject these assumptions as arbitrary or pointless. They are a necessary part of my argument, allowing me to establish the operation of a certain factor, a factor whose operation we see but dimly in reality, where it is in incessant conflict with others of its kind. (von Th¨unen 1966, 3–4; italics added)

Indeed, idealizing assumptions are vehicles employed in the method of isolation that captures the operation of a causal mechanism undisturbed by others such as those that transmit the influence of rivers, roads, mountains, uneven fertility, foreign trade etc. – ones that actually contribute to the shaping of land use in real world systems. But in the imagined world of the Isolated State, land use allocation is governed by a simple mechanism of transportation costs and land rents that depend on distance. Land rents are higher closer to the city and transportation costs are higher further away from the city. Land users compete in the land market trying to maximize their net revenues, and are pulled by the two cost factors, finally settling on a location that balances them. The equilibrium outcome is a neat pattern of concentric rings around the town, each zone accommodating just one kind of specific activity. The geometric image of concentric rings is another description of an aspect of von Th¨unen’s model. Considered as representations about real world systems, the assumptions and the outcome of the model do not get the real world facts right. But they are true about the model. Could the model in turn be true of real systems? Yes it can – at least this is von Th¨unen’s view as his model commentary suggests:

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The principle that gave the isolated state its shape is also present in reality, but the phenomena which here bring it out manifest themselves in changed forms, since they are also influenced at the same time by several other relations and conditions: : :. we may divest an acting force [eine wirkende Kraft] of all incidental conditions and everything accidental, and only in this way can we recognize [erkennen] its role in producing the phenomena before us. (von Th¨unen 1910, 274; my translation, italics added)

I read this passage to suggest that the principle or mechanism isolated in the imagined model world – the thought of the mechanism – is the relevant truth bearer, and the respective mechanism in real systems is the respective truth maker. Whatever else the model contains, and whatever else modifies the manifestation of the mechanism in real systems do not directly participate in the truth making of the model. The model and the real world may resemble one another in limited but important respects, thus the model may be a true representation. (For a more extended discussion, see M¨aki 2009c.)

15.7 Conclusion I have outlined what I’ve called a functional decomposition approach to the issue of whether models might be true. The approach insists on decomposing both the activity of representing and the model that is being used for representing a target. Allowing models and truth bearers to be made of the same stuff – thoughts or what is thought – truth can be located inside models. While one should agree with Wimsatt that models can serve as means for other true (and in many cases, truer) models, the account submitted here suggests that the initial models may be true as well. The key to seeing this is to ask: what in a model might be true about what in a target? There are many different truths to be pursued about a target, not just different models in pursuit of one truth. The Perfect Model Model is indeed false.

References Achinstein P (1964) Models, analogies and theories. Philos Sci 31:328–350 Cartwright N (1989) Nature’s capacities and their measurement. Clarendon, Oxford Giere R (1988) Explaining science. University of Chicago Press, Chicago, IL Giere R (2006) Scientific perspectivism. University of Chicago press, Chicago, IL Hindriks F (2006) Tractability assumptions and the Musgrave-M¨aki typology. J Econ Methodol 13:401–423 M¨aki U (1992) On the method of isolation in economics. Poznan Stud Philos Sci Humanit 26: 319–354 M¨aki U (1994) Isolation, idealization and truth in economics. Poznan Stud Philos Sci Humanit 38:147–168 M¨aki U (2000) Kinds of assumptions and their truth: shaking an untwisted F-twist. Kyklos 53: 303–322

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M¨aki U (2004) Some truths about truth for economists, their critics and clients. In: Mooslechner P, Schuberth H, Schurtz M (eds) Economic policy-making under uncertainty: the role of truth and accountability in policy advice. Edward Elgar, Cheltenham, pp 9–39 M¨aki U (2005) Models are experiments, experiments are models. J Econ Methodol 12:303–315 M¨aki U (2009a) Realistic realism about unrealistic models. In Kincaid H, Ross D (eds) Oxford Handbook of the philosophy of economics. Oxford University Press, Oxford, pp 68–98 M¨aki U (2009b) MISSing the world: models as isolations and credible surrogate systems. Erkenntnis 70:29–43 M¨aki U (2009c) Models and the locus of their truth. Forthcoming in Synthese Musgrave A (1981) ‘Unreal assumptions’ in economic theory: the F-twist untwisted. Kyklos 34:377–387 Nowak L (1980) The structure of idealization. Reidel, Dordrecht Suarez M (2004) An inferential conception of scientific representation. Philos Sci 71(5):767–779 Teller P (2001) Twilight of the perfect model model. Erkenntnis 55:393–415 von Th¨unen JH (1910) Der isolierte Staat in Beziehung auf Landwirtschaft und National¨okonomie. Verlag von Gustav Fischer, Jena von Th¨unen JH (1966) Von Th¨unen’s isolated state (trans: Wartenberg CM) Peter H (ed). Pergamon, Oxford Wimsatt W (2007) Re-engineering philosophy for limited beings. Harvard University Press, Cambridge

Chapter 16

Theory Change, Truthlikeness, and Belief Revision Ilkka Niiniluoto

As EPSA07 is the first congress of the European Philosophy of Science Association, it seems appropriate to give a survey of some of the main currents in the philosophy of science in Europe. In my paper, I consider three important research programmes in the philosophy of science: structuralism, truthlikeness, and belief revision. They all emerged some 30 years ago as formal or logical accounts of the dynamics of science. They have ever since been developed largely independently of each other, but there are important systematic differences and similarities between these approaches. Comparison of the three programmes allows me also to introduce some open problems and work in progress.

16.1 Scientific Change After 30 Years During the first half of the twentieth century, philosophers of science started to apply logical tools in the analysis of the language of science, the structure of scientific theories, the nature of deterministic and probabilistic laws, scientific explanation, inductive confirmation, truth, and simplicity. The leading figures of this trend of logical empiricism include Rudolf Carnap, Hans Reichenbach, Carl G. Hempel, Alfred Tarski, and Ernest Nagel. The main focus of their work was in non-temporal structural relations between various kinds of scientific statements. However, revolutionary developments in physics – such as the theory of relativity and quantum theory – had already challenged traditional naive assumptions about the cumulative growth of scientific knowledge. In the 1950s and 1960s, scientific change became a central topic through the writings of Karl Popper, Thomas Kuhn, N. R. Hanson, Paul Feyerabend, Imre Lakatos, and Stephen Toulmin (see Lakatos and Musgrave 1970). With inspiration from the history of science, it became

I. Niiniluoto () Department of Philosophy, 00014 University of Helsinki, Finland e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 16, c Springer Science+Business Media B.V. 2010 

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fashionable to consider examples and patterns of theory change, where one theory T is replaced by another rival theory T0 . In Lakatos’s terms, sequences of such successive theories constitute “scientific research programmes”. One of the hot issues concerned the notion of truth in connection with scientific theories. Philosophers of science – among them Herbert Feigl, Wilfrid Sellars, and Hilary Putnam – had just learned to defend the realist interpretation of scientific theories against instrumentalism, but now Kuhn’s and Feyerabend’s ideas about scientific revolutions with conceptual meaning variance and incommensurability seemed to refute scientific realism. Popper, who rejected Kuhn’s ideas about normal science, advocated permanent revolutions in science. But still, applying Tarski’s semantic theory of truth, Popper proposed a new comparative notion of truthlikeness, and thereby attempted to save the realist view of scientific theories and scientific progress (see Popper 1963). Some other philosophers with broadly pragmatist leanings, like Larry Laudan (1977), accepted the Kuhnian idea that science is a problem-solving rather than a truth-seeking activity. Another hot topic was the possibility of a logical theory of inductive inference. Popper argued against Carnap that inductive logic is inconsistent. However, in the mid 1960s Jaakko Hintikka showed how inductive generalization can be treated in a system of inductive logic with two extra-logical parameters (see Lakatos 1968). Hintikka called such an approach “logical pragmatics”. Isaac Levi (1967) and Hintikka started to apply measures of probability and information in cognitive decision theory. Richard Jeffrey (1965) coined the term “probability kinematics” for the study of dynamic changes of probabilities on the basis of Bayesian conditionalization. In this situation, some philosophers of science wished to show that logical tools are useful also in the diachronic study of scientific change. This perspective was strongly emphasized in the conference on “Formal Methods in the Methodology of the Empirical Sciences”, organized by Polish logicians and philosophers in Warsaw in 1974 (see Przelecki et al. 1976). On December 12–14, 1977, a colloquium on “The Logic and Epistemology of Scientific Change” was organized in Helsinki by the Philosophical Society of Finland (see Niiniluoto and Tuomela 1979). It brought together several new trends in the formal, epistemological and historical study of the structure of scientific theories, theory change, and scientific inference. Today, after 30 years, this colloquium (LESC, in short) gives us a perspective on the paths that the European philosophy of science was going to follow. Some of the participants of LESC were inspired by Kuhn’s work. Among them, Richard Rorty was soon to become famous as a leading critic of realism in epistemology and philosophy of language (see Rorty 1980). H˚akan T¨ornebohm proposed a semi-formal treatment of the notion of paradigm. (Feyerabend and Laudan were invited to Helsinki, but were not able to attend.) The structuralist programme, which followed Patrick Suppes’s advice in applying set theory and model theory to the study of scientific theories and intertheory relations, was represented in LESC by Wolfgang Stegm¨uller, Joseph Sneed, Wolfgang Balzer, Walter Hoering, J. H. Harris, and Erhard Scheibe. With Sneed’s modified

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Ramsey sentence treatment of theoretical terms, and Stegm¨uller’s advocacy of a “non-statement view” of theories (see also Stegm¨uller 1979), this approach had a leaning towards instrumentalism. The followers of Popper and Lakatos, associated with the London School of Economics, were represented by John Watkins, Alan Musgrave, John Worrall, and Graham Oddie. Worrall criticized Feyerabend’s account of empirical content, and Musgrave the claims about meaning variance and incommensurability. Oddie was preparing a doctoral dissertation on truthlikeness at the L.S.E. Detailed studies of intertheory relations were presented by Balzer (on reduction within the structuralist framework), Marian Przelecki (on commensurable referents within the model-theoretical framework), and Veikko Rantala (correspondence relation analysed by means of non-standard analysis). Besides Oddie, the problem of verisimilitude was discussed by the Finnish philosophers Raimo Tuomela and Ilkka Niiniluoto. Tuomela studied distances between theories, and my own paper gave an account of progressive theory-change in terms of their degrees of truthlikeness. Finally, Isaac Levi, William Harper, and Peter G¨ardenfors studied changes of probabilistic belief systems. Levi related his account of inductive acceptance to Charles S. Peirce’s notion of abduction. Harper and G¨ardenfors were lead to study minimal revisions of beliefs by Frank Ramsey’s test of counterfactuals: the conditional “If A then B” is acceptable in a belief system K, if the minimal change of K needed to accept A also requires accepting B. G¨ardenfors proposed his epistemic semantics as an alternative to the possible world approach of David Lewis (1973).

16.2 Three Programmes Apart from “soft” approaches, appealing mainly to qualitative and historical aspects of science, the LESC colloquium allows us to distinguish three main programmes of philosophy of science which attempt to study scientific change by means of formals methods from logical proof theory, model theory, set theory, and probability theory. These three programmes are structuralism (STR), truthlikeness (TL), and belief revision (BR). It is interesting to observe that, after the 1977 meeting in Helsinki, for each of these programmes it took about a decade to produce mature formulations of their main results. For STR, the classical exposition is An Architectonic for Science (1987) by Balzer, Moulines, and Sneed. The structuralist programme has been primarily a movement within European philosophy of science – prominent especially in Germany and Spain. Its American counterpart, with less technicalities, is the semantic view of theories, developed by Bas van Fraassen, Fred Suppe, and Ron Giere. On both continents (and in the United Kingdom), the main line of research has later moved from theories to the study of scientific models and their representational capacities.

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For TL, the first full-blown expositions are Oddie’s Likeness to Truth (1986) and Niiniluoto’s Truthlikeness (1987) (cf. Niiniluoto 1998). Other active scholars in this programme include Theo Kuipers (2000) in the Netherlands and Roberto Festa (1993) in Italy. The study of belief systems and Bayesian probability kinematics has been continued by Levi in several books (see Levi 1991). The theory of belief revision studies expansions, contractions, and revisions of belief systems in the light of new input information. A classical exposition of the so called AMG-theory is given by G¨ardenfors in Knowledge in Flux (1988). Besides G¨ardenfors, this programme of BR has been developed by logicians in Sweden (see Hansson 1999) and Germany (see Rott 2001). Besides philosophy of science, BR has found applications in law, computer science, and artificial intelligence. Unfortunately, the three programmes discuss with each other only accidentally. This is the case in spite of their common domain of interest: theory change in science. The most dramatic difference between these approaches is related to truth: while STR and BR attempt to do epistemology and philosophy of science without the concepts of truth and falsity, TL employs the realist notion of truth. Indeed, TL defends critical scientific realism with the thesis that the notions of truth and truthlikeness are needed for an adequate understanding of the nature of science (see Niiniluoto 1984, 1999a). On the other hand, all of the three programmes allow an important role for the concept of similarity. When this concept is introduced, it turns out that STR and TL can be reconciled at least to some extent, but the difference or even the opposition between TL and BR is highlighted. This is the main argument that I will develop in the next sections.

16.3 Scientific Theories The classical “statement view” treats a scientific theory T as a deductively closed set of statements in a formal language L. Thus, T is the consequence class Cn(A) of a set of axioms A in L. The claim of theory T is that the axioms A (and, hence, all theorems in T) are true in the actual world W . The semantic version of the statement view employs the model-theoretical notion of truth: the claim of theory T is that the actual world W is a model of T, i.e., W belongs to the class Mod(T). For a scientific realist, theories are attempts to describe both the observable and theoretical entities in the world W . With some simplifications, the structuralist view treats a theory as a net of theory-elements , where M is a class of structures and I is a set of intended applications. Here I includes those situations where the supporters of the theory think the core laws M to be applicable. The empirical claim of the theory is that I is a subclass of M. As no language is mentioned, the notion of truth is avoided in this analysis. Or at least it seems to be so: the notion of truth is not even mentioned in the Subject Index of Balzer et al. (1987).

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However, in typical cases, the structures in M are L-structures for some sufficiently rich language L and the class M itself is axiomatized by some set of statements T in L (see Niiniluoto 1984, Ch. 6). Thus, M D Mod.T/. Then the claim that I M asserts that theory T is true in all intended models I, i.e., I Mod.T/. So after all the notion of truth is not the crucial difference between the statement view and the structuralist view: the idea that a theory has more than one intended application can be understood by dividing the actual world W into several fragments or situations W in I and by considering the truth of the axioms (and their specializations) in each application in I separately. Similar remarks can be made about intertheory relations between theories: the structuralists have given useful analyses of reduction as a relation between theoryelements, but typically such relations between L-structures have their counterparts in relations between statements in L (see Pearce 1987). The main difference of STR and scientific realism arises from the empiricist treatment of theoretical entities: for STR, intended applications in I are assumed be structures without T-theoretical functions (see Niiniluoto 1984, p 124), and the Ramsey sentence formulation of the empirical claim does not demand or guarantee that the full theory gives true descriptions of real entities in the world (see Niiniluoto 1999a, p 119).

16.4 Truthlikeness The basic ideas of the “similarity” or “likeness” approach to truthlikeness were developed since 1974, immediately after the refutation of Popper’s attempted definition by David Miller and Pavel Tich´y. In the Warsaw congress in 1974, Risto Hilpinen treated theories as sets of possible worlds. Following Lewis (1973), he assumed as an undefined primitive notion the similarity of possible worlds: all possible worlds are located in nested spheres of similarity around a given world. If the actual world is placed in the center, then the relative distances of theories depend on their location in this system of spheres (see Hilpinen 1976). In 1975, using techniques employed in Hintikka’s inductive logic, I modified Hilpinen’s treatment by replacing possible worlds with constituents, i.e., maximally informative descriptions of such worlds in a given first-order language L, so that a theory in L is represented by a disjunction of constituents. Then the distance  between constituents can be defined explicitly (see Niiniluoto 1977). In the context of propositional logic, this idea was proposed by Tich´y (1974). In the richer framework of monadic first-order languages L, all individuals belong to “cells” described by Q-predicates, and a monadic constituent Ci tells that certain kinds of individuals exist and others do not exist; the Clifford distance between monadic constituents is the relative number of their diverging claims about the Q-predicates. The same idea can be generalized to full first-order logic (for details, see Niiniluoto 1987). Distance  may also be directly definable by a natural metric underlying the structure of a cognitive problem. For example, if the rival theories are point estimates

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of an unknown real-valued parameter, their distance can be given simply by the geometrical or Euclidean metric on R (or RK ). If the elements of B are quantitative laws, then their distance is given by the Minkowski metrics between functions. The next technical step is to extend the distance function  so that it measures the closeness of a theory T in L from a given constituent Ci , as a function of the distances of the disjuncts in the normal form of T from Ci . Tich´y and Oddie favour the average distance, while my “min-sum” proposal is the weighed combination of the minimum distance and the sum of all distances. As constituents of L are mutually exclusive and jointly exhaustive, there is one and only one constituent C which is true in the actual world (or in the fragment of the actual world described or conceptualized by L). This unknown C is the target of the logical problem of truthlikeness. Theory T is approximately true, if it includes disjuncts that are close to C . Theory T is truthlike, if it includes disjuncts close to the truth C but also effectively excludes serious falsities. The quantitative degree of truthlikeness Tr.T; C / of T relative to target C can be defined as a simple function of the distance .T; C /. If the distance function  is trivial, so that all false constituents are equally far from the truth C , then the min-sum-measure reduces to a special case of Levi’s (1967) definition of epistemic utility. As the target C is unknown, the absolute or real value of Tr.T; C / cannot be directly calculated. However, there is a method of making rational comparative judgments about verisimilitude, if we have – instead of certain knowledge about the truth – rational degrees of belief about the location of truth. Thus, to estimate the degree Tr.T; C /, where C is unknown, assume that there is an epistemic or inductive probability measure P defined on the class of constituents, so that P.Ci =e/ is the rational degree of belief in the truth of Ci given evidence e. The expected degree of verisimilitude of T given evidence e is then defined by (1) ver.T=e/ D † P.Ci =e/Tr.T; Ci /. i2I See Niiniluoto 1977. One of the interesting properties of (1) is that ver(T/e) may be high, even when P.T=e/ D 0. Measures Tr and ver give us comparative notions of truthlikeness and estimated verisimilitude: theory T0 is more truthlike than theory T if Tr.T; C / < Tr.T0 ; C /, and T0 seems more truthlike than T on evidence e if ver.T=e/ < ver.T0 =e/. These comparisons can be used in the characterization of scientific progress (see Niiniluoto 1984).

16.5 STR Versus TL The structuralist explication of Kuhnian and Lakatosian normal science by “progressive theory-evolution” requires that the later theory has more “firm” or confirmed applications than the former (Balzer et al. 1987, p 222; Moulines 2000). This idea is covered by the explication of progress in terms of expected verisimilitude.

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C. Ulises Moulines (1976) has shown how the concept of approximate application can be defined within the structuralist framework. He uses the topological notion of uniformity (see Balzer et al. 1987, p 332; Niiniluoto 1987, pp 19–22). As a nested system of sets, a uniformity resembles the Lewisian spheres of similarity. This notion allows one to say that two structures W and W0 are “close” to each other or “approximate” each other up to a bound or degree. Then, for example, the class of intended applications I can be replaced by the “blurred” class -I- which includes all structures sufficiently close to some element of I. The blurred claim of the theory is then -I- M, i.e., all applications in -I- belong to M. In this case, the law M applies approximately to I. Alternatively, the class M may be blurred, and the blurred claim of theory is I --M --. These structuralist notions are directly comparable to truth approximation (cf. Niiniluoto 1987, p 398). Theory T is approximately true if it is close to a theory T0 which is true in the real world; alternatively T is approximately true if it is true in a system or model which is close to the real system (cf. Niiniluoto 1999a, p 141). Here T may be an idealized theory and T0 its concretization in the sense of Leszek Nowak, and T is approximately reducible to T0 (cf. Kuipers 2000; Rantala 2002; Niiniluoto 2007). Also for comparative purposes, STR and TL give similar results. For STR, a law M0 applies more closely to structures I than another law M if the sets of the relevant uniformities or bounds of accuracy of M0 are sharper than those of M (see Balzer et al. 1987, p 360). In practice, uniformities are typically defined by relying on a quantitative metric , so that comparisons of accuracy in STR agree with the explication of progress by TL (see Niiniluoto 1987, p 399). If the rival theories have several intended applications in I, so that now the target includes more than one constituent C , the overall performance of theories should be evaluated with respect to all elements of I. In this case a strong sufficient condition of progress is dominance: theory T0 is more truthlike (or seems to be more truthlike) than T for all structures W in I. A more flexible approach is to define the cognitive value of theory T as the weighted sum of its degrees of truthlikeness Tr(T,W) relative to targets W in I, and to estimate this quantity by the ver-function (see Niiniluoto 1987, p 370; cf. Zamora Bonilla 1996). This notion can be suggested as a realist counterpart to Laudan’s (1977) problem-solving capacity of a theory.

16.6 Belief Revision and TL In the theory of belief revision, belief states are represented by consistent and deductive closed sets of sentences within a given language L. Thus, a belief set K in language L corresponds to a theory in the statement view. It can be understood as consisting of all the statements in language L which an epistemic agent X is committed to believe (cf. Levi 1991). Let A be an input sentence that agent X receives or learns from some source. Assume that A is consistent with the initial belief set K. Then A can be incorporated into K by adding it to K together with all logical

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consequences of K and A. This procedure is called the expansion K C A of K by A. If the input A contradicts K, i.e., K already contains :A, but we wish to include A in the new belief set, psome elements of K have to be revised to maintain consistency. The contraction K A of K with respect to A is obtained by retracting from K the sentence A and all sentences which logically entail A. The revision K A of K by A leads to a new belief set which contains A. According to the Levipidentity, revision can be defined in terms of contraction and expansion: K A D .K :A/ C A. The notions of contraction and revision are guided by the principle of “conservation” or “informational economy”: when changing beliefs in response to new evidence, one should continue to believe as many old beliefs as possible (G¨ardenfors 2005, p 51). But this minimality principle does not uniquely determine the process of contraction. Suppose you learn that :(A & B), and both A and B belong to your belief set K. Then you should give up at least one of the sentences A and B, but there is no principle of logic which decides your choice. G¨ardenfors proposes that sentences in K are ordered by their degree of epistemic entrenchment which tells how important they are in “planning future actions, conducting scientific investigations, or reasoning in general” (ibid., p. 57). The idea is that sentences with lower degrees of epistemic entrenchment are given up easier that those with higher degrees. If A  B means that A is at most as epistemically entrenched as B, and A & B is not logically valid, we should have p (2) B  A iff B … K .A&B/. This approach leads to the AMG-postulates for a “transitively relational partial meet contraction” (see Hansson 1999, p 100). Another method of ordering the elements of K, proposed by Adam Grove (1988) (see also G¨ardenfors 1988, Ch. 4.5; Hansson 1999, pp 294–304), is to employ the spheres of similarity of Lewis (1973). Grove construes such spheres so that they are centred on a given belief set K. Let A be a proposition, and SA the smallest sphere around K that intersects A. Let CK .A/ D A \ SA be the “closest” elements of A to K. Then Grove defines revision K A of K by A as the theory generated by CK .A/, i.e., K A is the intersection of all possible worlds (maximally consistent sets of sentences) in CK .A/. This is equivalent to the condition B 2 K A iff SA&B

SA&:B , i.e., Bpbelong to revision K A iff A & B is “closer” to K than A&:B. Contraction K A can be defined as the theory generated by K [ CK .:A/. G¨ardenfors argues that the AMG theory of belief revision supports the thesis that “many epistemological problems can be attacked without using the notions of truth and falsity” (G¨ardenfors 1988, p 20). Therefore, it is interesting to see what happens if the model of belief revision is translated into the framework used in the theory of truthlikeness. The first attempt in this direction was given in Niiniluoto (1999b) (see also Cevolani 2006). Assume that a theory T is represented as a disjunction of constituents in language L, and let  be the distance between constituents. If min .Ci ; T/ is the minimum of the distances .Ci ; Cj / for constituents Cj in the normal form of T, then the class CT .A/ can be defined by (3) CT .A/ D fCi in A j min .Ci ; T/  min .Cj ; T/ for all Cj in Ag.

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Then we have simple definitions for the expansion, revision, and contraction of T by A: .4/ T C A D T & A T A D _CT .A/ p T A D T _ T :A: This approach has some good news for the programme of BR. It is surprising that the logical framework of BR has so far been restricted to propositional logic. Since the late 1980s, some attempts have been made in artificial intelligence to study BR with quantitative distance functions (without any references to earlier work in TL), but they have also been restricted to propositional constituents (cf. Peppas et al. 2000). As we have seen, the programme of TR has already in 1975 provided an explicitly defined distance function  that can be used in the study of belief revision in predicate logic. It is clear that this kind of tool is needed, if BR hopes to give realistic account of theory change in science. Applying my min-sum-measure, what can we say about the behaviour of belief revision with respect to truthlikeness? The answers are not simple. For example, as two mutually incompatible statements can both be truthlike, the following principle is not valid: (5) If T is truthlike and A is truthlike, then T C A is truthlike. Unlike Oddie’s (1986) average measure, my definition satisfies the Popperian condition: (6) If T and A are true, then T C A is at least as truthlike as T. Usually expansion of a true theory by a false input A lead us farther from the truth, but not always: some informative falsities may be more truthlike than logically weak truths. Further, the expansion of a false theory by true input need not increase truthlikeness: (7) If T is false and A is true, then T C A may be less truthlike than T. For example, if T states that the number of planets is 9 or 20, and A that this number is 8 or 20, then TCA is the bad theory that there are 20 planets. For revision we have (8) If T is false and A is true, T A may be more or less truthlike than T. Contraction of a false theory by false input may, but need not always, lead to a more truthlike theory. Practical rules of belief revision cannot be directly based upon absolute Tr-values of truthlikeness, since in typical situations the location of the true constituent C with respect to old beliefs T and new input A is unknown. The possibility of using probabilistic methods suggests that the rule of maximizing expected verisimilitude ver could be applied here. Comparisons to Hintikka’s recent work on the interrogative model of inquiry (see Hintikka 1999) and Levi’s model of acceptance (see Levi 1991) may seem promising, but there is also a systematic problem. Levi and BR assume the accepted information model and deductive closure: if T is accepted as

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true, then all deductive consequences of T are accepted as true. This principle is not valid for truthlikeness: if T is truthlike, and T entails A, then A need not be truthlike. It is an open question what is the best way of approaching this question. Perhaps one could separate the level of beliefs B that are accepted as true; if this set B is revised to B A by new input A, we can evaluate the expected ver-truthlikeness of rival theories by conditionalizing probabilities on B A. As an alternative to conditionalization, probabilities could also be directly revised by the method of “imaging” (see G¨ardenfors 1988). Traditional models of BR rely on the idea of revising beliefs systems so that consistency is maintained. At the same time, in the process of updating, new input information is trusted and accepted (cf. van Ditmarsch et al. 2007). The results (7) and (8) show vividly that such updating need not always improve our beliefs. Recently the programme of BR has been complemented by the study of non-prioritized belief revision (see Hansson 1997, 1999), where the new information A is received and weighed against the old beliefs in T. This is an important move, but it is still an open question what kinds of properties the new models of non-prioritized BR may have. These observations serve to illustrate how the comparison of the programmes of BR and TR leads to interesting new problems for further research.

References Balzer W, Moulines CU, Sneed JD (1987) An architectonic for science: the structuralist program. D. Reidel, Dordrecht Cevolani G (2006). Belief change, nonmonotonic reasoning and scientific method. Bononia University Press, Bologna Festa R (1993) Optimum inductive methods: a study of inductive probabilities, Bayesian statistics, and verisimilitude. Kluwer, Dordrecht G¨ardenfors P (1988) Knowledge in flux: modeling the dynamics of epistemic states. MIT Press, Cambridge, MA G¨ardenfors P (2005) The dynamics of thought. Springer, Dordrecht Grove A (1988) Two modellings for theory change. J Philos Logic 17:157–170 Hansson SO (1997) What’s new isn’t always best. Theoria 63:1–13 Hansson SO (1999) A textbook of belief dynamics: theory change and database updating. Kluwer, Dordrecht Hilpinen R (1976) Approximate truth and truthlikeness. In Formal methods in the methodology of the empirical sciences. D. Reidel, Dordrecht, pp 19–42 Hintikka J (1999) Inquiry as inquiry: toward a logic of scientific discovery, selected papers V. Kluwer, Dordrecht Jeffrey R (1965) The logic of decision. McGraw-Hill, New York Kuipers T (2000) From instrumentalism to constructive realism: on some relations between confirmation, empirical progress, and truth approximation. Kluwer, Dordrecht Lakatos I (ed) (1968) The problem of inductive logic. North-Holland, Amsterdam Lakatos I, Musgrave A (1970) Criticism and the growth of knowledge. Cambridge University Press, Cambridge Laudan L (1977) Progress and its problems: towards a theory of scientific growth. Routledge & Kegan Paul, London

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Levi I (1967) Gambling with truth: an essay on induction and the aims of science. Alfred A. Knopf, New York Levi I (1991) The fixation of belief and its undoing: changing beliefs through inquiry. Cambridge University Press, Cambridge Lewis D (1973) Counterfactuals. Blackwell, London Moulines CU (1976) Approximative application of empirical theories: a general explication. Erkenntnis 10:210–227 Moulines CU (2000) Is there genuinely scientific progress? In: Jonkisz A, Koj L (eds) On comparing and evaluating theories. Rodopi, Amsterdam, pp 172–197 Niiniluoto I (1977) On the truthlikenss of generalizations. In: Butts RE, Hintikka KJ (eds) Basic problems in methodology and linguistics. D. Reidel, Dordrecht, pp 121–147 Niiniluoto I (1984) Is science progressive? D. Reidel, Dordrecht Niiniluoto I (1987) Truthlikeness. D. Reidel, Dordrecht Niiniluoto I (1998) Verisimilitude: the third period. Br J Philos Sci 49:1–29 Niiniluoto I (1999a) Critical scientific realism. Oxford University Press, Oxford Niiniluoto I (1999b) Belief revision and truthlikeness. In: Hansson B et al. (eds) Internet Festschrift for Peter G¨ardenfors. Lund. http://www.lucs.lu.se/spinning/ Niiniluoto I (2007) Idealization, counterfactuals, and truthlikeness. In: Brzezinski J et al. (eds) The courage of doing philosophy: essays dedicated to Leszek Nowak. Amsterdam, Rodopi, pp 103–122 Niiniluoto I, Tuomela R (eds) (1979) The logic and epistemology of scientific change. Acta Philosophica Fennica 30:2–4. North-Holland, Amsterdam Oddie G (1986) Likeness to truth. D. Reidel, Dordrecht Pearce D (1987) Roads to commensurability. D. Reidel, Dordrecht Peppas P, Foo N, Nayak A (2000) Measuring similarity in belief revision. J Logic Comput 10: 603–619 Popper KR (1963) Conjectures and refutations: the growth of scientific knowledge. Routledge & Kegan Paul, London Przelecki M, Szaniawski K, Wojcicki R (eds) (1976) Formal methods in the methodology of the empirical sciences. D. Reidel, Dordrecht Rantala V (2002) Explanatory translation: beyond the Kuhnian model of conceptual change. Kluwer, Dordrecht Rorty R (1980) Philosophy and the mirror of nature. Princeton University Press, Princeton, NJ Rott H (2001) Change, choice, and inference: a study of belief revision and nonmonotonic reasoning. Oxford University Press, Oxford Stegm¨uller W (1979) The structuralist view of theories. Springer, Berlin Tich´y P (1974) On Popper’s definition of verisimilitude. Br J Philos Sci 25:155–160 van Ditmarsch H, van der Hoek W, Kooi B (2007) Dynamic epistemic logic. Springer, Dordrecht Zamora BJP (1996) Verisimilitude, structuralism and scientific progress. Erkenntnis 44:25–47

Chapter 17

Mechanisms: Are Activities up to the Job? Johannes Persson

17.1 MDC and External Validity Together with his colleagues Lindley Darden and Carl Craver, Peter Machamer has designed an influential framework for understanding mechanisms. In the following discussion, I shall examine some of the key ideas in this framework, although it is not my intention to replicate it exactly. The building blocks of the MachamerDarden-Craver account (or MDC, as I will call it) are entities and activities. These are, furthermore, organized in such a way that they produce regular changes in the mechanism’s condition between onset and termination. As Machamer et al. put it in a key passage: Mechanisms are entities and activities organized such that they are productive of regular changes from start or set-up to finish or termination conditions. (Machamer et al. 2000, 3)

The decision to put activities to contemporary philosophical use is interesting in many ways, and activities will be the primary focus of this article. Before we enter that discussion, however, we need to know what problem MDC is supposed to shed light on. Is MDC a hypothesis about what mechanisms are? Is it a metaphysical or ontological account of mechanisms? This is the most straightforward interpretation. The above quotation supposedly tells us what mechanisms are – in an ontological sense. How else could we understand the passage? One reason why MDC, construed in this way, may be problematic is that its external validity appears to be weak. Machamer and colleagues base their view almost exclusively on data concerning productive mechanisms of certain complex kinds. The mechanistic situations they consider are normally examples from scientific research in molecular biology and neurobiology where a lot happens.1

J. Persson () Department of Philosophy, Lund University, Lund, Sweden e-mail: [email protected] 1 However, it is clear both from the original work and from Machamer’s further elaboration of the metaphysics of activities that the intended application is wider. The vast majority of activities

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However, in some mechanistic situations no “regular changes from start or setup to finish or termination conditions” occur. In these, nothing goes on inside the mechanism; it is static. Moreover, some mechanisms never, or only occasionally, bring about changes, and some mechanisms never, or only occasionally, bring about regular changes (cf. Persson 1999). Idle mechanisms, static or not, are not uncommon. But static mechanisms cannot be characterized in terms of the activities they are composed of; nor can idle mechanisms be characterized in terms of the activities they produce. The fact that a number of mechanisms seem less dependent on their activities than MDC implies raises doubts about MDC as a general account of mechanisms. What has been identified here is a form of sampling bias. Such bias does not entail the falsity of MDC as a general metaphysical or ontological account of mechanisms: MDC might be on the right track in spite of it. The original account might, for instance, be finessed in a modified version including the ontological elements needed to make room for temporarily, or even permanently, static or idle mechanisms. Again, it might be possible to account for static and idle mechanisms as ‘quasi-mechanisms’,2 leaving the basic MDC account of mechanisms intact. However, developing the account in any of these ways will increase the risk that some of the original MDC-components prove redundant. To examine this issue a little more closely, I suggest we temporarily interpret MDC strictly as a characterization of ‘genuinely’ explanatory mechanisms. At the core of MDC is a hypothesis about what constitutes the explanandum and the explanans in a mechanistic explanation. If MDC succeeds as a constitutive theory of this sort, there is a reasonable chance that it will, after suitable modification, handle static and idle mechanisms as well. If it does not, a more sceptical attitude to the entire metaphysical project of which it is a part will become attractive.

17.2 Activities and Actualization One aspect that makes MDC particularly interesting, in my opinion, is that, in the relationship between activities and entities, activities are supposed to play the more important causal role: Activities are the producers of change. Entities are the things that engage in activities. (Machamer et al. 2000, 3)

To examine whether or not activities are up to the job assigned to them by MDC we need to identify some of their testable consequences. Below, I will describe one such consequence. It should be noted, however, that Machamer and his colleagues

referred to in Machamer (2004) are not limited to scientific settings at all. Examples of these activities include: running, bonding, flowing, the glass shattering and flying into a thousand pieces, breaking, boozing, covering up, and hiding. 2 To paraphrase Dowe’s (2000) analysis of ‘causal’ omission and prevention.

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have not found it easy to provide a useful characterization of activities. They offer plenty of examples; and Machamer (2004, 29) gives quite a number of synonyms, or near-synonyms, of ‘activities’ as well: producings, happenings, ways of acting, processes and behaviours. But nothing resembling a general account of activities has been provided. It should be clear that a central element in the concept of activity is actualization.3 If a wheel (entity) engages in spinning (activity), it spins. It is not enough that it has, say, the capacity to spin. If a heart (entity) engages in pumping blood (activity), it pumps blood; it does not merely have the potential to do so. This relationship between an activity and the actualization of something relates activities to all of the near-synonyms listed above – to producing, happenings, ways of acting, processes, and behaviours; and it should be perfectly obvious. Arguably, anyone who wants to use activities in the causal role attributed to them by Machamer and his colleagues is committed to this relation between activities and actualization. Indeed this characteristic of activities seems to be highly relevant to the MDC research programme. In this programme activities are supposed to provide a productive continuity between cause and effect, and this idea seems very close to the idea of actualization: Productive continuities are what make the connection between stages intelligible. If a mechanism is represented schematically by A ! B ! C, then the continuity lies in the arrows and their explication is in terms of the activities that the arrows represent. A missing arrow, namely, the inability to specify an activity, leaves an explanatory gap in the productive continuity of the mechanism. (Machamer et al. 2000, 3)

There is certainly much more to say about the entailments of activity claims. The claim that they entail actualizations gives us at least one testable consequence of the MDC framework.

17.3 Polygenic Effects and the Organization of Activities MDC speaks about the organization of activities as well. It is a small step from such talk to the idea of polygenic effects, i.e. effects that have more than one cause. That the step is small becomes evident when we remind ourselves that Machamer frequently claims that activities are causes: [: : :] discovering activities, the ‘doing’ or productive parts of mechanisms, is the finding of causes. (Machamer 2004, 28)

Polygenic effects testify to the fact that several causal contributors are sometimes simultaneously involved in causation (cf. Molnar 2003, 194). Hence not every organization of activities results in a polygenic effect. The organization of activities 3 This was more evident in earlier writings on activities. In discussing Aristotle, for example, Ross (1930, 82) said: “In each moment of activity, potentiality is completely cancelled and transformed into actuality.”

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sometimes yields serially related causes and effects only; and those are not instances of polygeny. What is needed to obtain polygeny are activities organized in a parallel fashion. As a simple case of an allegedly polygenic effect, consider a setting in which a motorboat is heading east to B. It is suddenly affected by strong winds from the south. The effect is that it ends up northeast of its present position at C. Prima facie this situation involves several polygenic effects. It is natural to picture this example, as John Stuart Mill (1893, Bk III, ch. VI) did, in terms of forces: “a body is propelled in two directions by two forces, one tending to drive it to the north and the other to the east [: : :].” It is, moreover, tempting to follow Mill (ibid.) in claiming that, in this case, both forces have their full effect. The boat is “left precisely where it would have arrived if it had been acted upon first by one of the two forces, and afterwards by the other.” The motorboat example is interesting, also, because a similar setup has recently been used by the psychologist Phillip Wolff (2007) to study causal perception. In a series of experiments Wolff shows that we judge processes of this kind to be typically causal. That is, we use the word ‘cause’ (and its cousins ‘force’, ‘get’, ‘stimulate’, and so on) to report situations where several causal contributors are simultaneously involved in the polygenic pattern exemplified by the motorboat.4 As far as these psychological findings go, perceived effects are polygenic. Effects are typically thought to be the result of many contributing forces working together in a certain way.

17.4 Two Kinds of Polygeny There is a common and in many ways unproblematic kind of polygeny: polygeny with respect to different properties of the effect or affected object. In many cases polygenic effects emerge precisely because the effect, or the affected object, has many properties which the various causal contributors act upon. An apple, for instance, becomes ripe and red at the same time, but ripening, we may assume, is a response to temperature, and reddening is a response to UV-exposure. Or, to recycle Hempel’s (1970, 421–423) example: the lava stream from the eruption of Vesuvius took a certain path; it had certain physical and chemical properties; and it occurred at a certain time that day in the year 79 CE. Each of these properties may have been affected by different combinations of causal contributors. If the effect is the

4 In fact, we tend to vary the causal expressions we use in accordance with the organization of forces. For instance, depending on whether or not the forces are directed at the actualized endpoint, we use the expression ‘cause’ rather than other types of causal verb such as ‘enable’ (‘help’, ‘leave’, ‘allow’, ‘let’) or ‘prevent’ (‘keep’, ‘block’, ‘hinder’) to describe our causal experiences. Something is reported as a cause, rather than as an enabler or preventer, Wolff claims, when there is a patient (the boat) an affector (the wind) acts upon, and where the tendency of the patient (B) is different from both the affector (the wind) and the actual endstate (C).

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event, i.e. the eruption of Vesuvius, then this event is polygenic in virtue of the contributions to various properties of it. Therefore, polygeny is an especially common feature of theories positing events or other complex “thick” particulars (Armstrong 1978, 114) as causal relata. The motorboat example, however, may be of a different polygenic kind. There the causal contributors act simultaneously, not only on different properties, but also on the same property, of the affected object. The forces exerted by the wind and the boat’s engine may both contribute to literally the same effects – some of which are represented by the boat’s actual track from its starting position to C. So, if we take the causal relata to be events or “thick” particulars with several properties or aspects, polygeny is a phenomenon that emerges in two ways. The first, polygeny 1, emerges when different properties of the particular are affected by different causal contributors. The second, polygeny 2, emerges when there is a joint contribution to one of its properties. Polygeny may also occur where the causal relata are facts or aspects of particulars, but then only as polygeny 2.

17.5 Consequences of Polygeny 2 The importance of polygenic causation was noticed early on by Mill (1893). It has since been shown to be a problem for causal-law approaches to causation (cf. Cartwright 1983, 59) and accounts of causation cast in terms of capacities (Dupr´e 1993 and Glennan 1997). However, polygenic causation needs to be examined more thoroughly in the emerging literature on causal mechanisms, perhaps especially in connection with activities. I will assume that it is primarily the handling of polygeny 2 that threatens to be problematic within the MDC framework. The reason polygeny 1 poses no immediate threat is simply that we can conceive of different properties of an event or a particular as separate from each other. Individual explanations, invoking activities and actualizations, can then be provided for each property. It seems that polygeny 2 cannot be approached in the same way, and this is why it may potentially challenge the MDC framework. Let me explain. MDC makes a lot of sense. Accounts of mechanisms cast in terms of what their many parts do, and what results from this, are useful in a number of ways. However, these accounts have limitations. One limitation becomes visible when we look into two contrasting kinds of polygeny 2 situation. In the first, as a result of balancing causal contributors nothing relevant happens, i.e. there is no relevant activity to explain. I take the problems this poses to be the following: in spite of this absence of an explanandum activity, there is need for explanation, and a mechanistic explanation can be offered. Moreover, since nothing happens, activities cannot be exploited as explanans either. Thus, this should qualify as a ‘genuine’ mechanistic case that does not fit the MDC account. In the second kind of situation, as a result of polygeny there is a different activity to explain than there would have been if the component activities were in fact the explanans to be cited in the mechanistic explanation. Again,

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this should qualify as a ‘genuine’ mechanistic case that does not fit MDC. If this is right, MDC has limitations when construed as a hypothesis about what constitutes the explanandum and the explanans in a mechanistic explanation as well. I discuss the first problem in Section 17.6 and the second problem in Section 17.7.

17.6 The Argument from Perfectly Balancing Causal Contributors Let us start with the first problem and have a look at our motorboat again. Now the wind has turned. It comes directly from the east. Moreover, it perfectly balances the causal contribution made by the engine. Neither the boat nor the engine takes part in any forward-moving activity at all. At the explanandum level nothing happens. No activity is produced. Hence there is no relevant activity to explain. From the MDC perspective, this is an example of an idle mechanism, to be accounted for either as a quasi-mechanism or by adding ontological elements to the account. This must be an unfortunate conclusion. The mechanistic changes have been so small. The boat, the engine, the lake, the intentions of the driver – almost everything is the same. But, according to MDC, rather than the typical mechanism and mechanistic explanation we had before, we do not even have a genuine mechanism any longer. The requirement of an explanandum activity element is to blame. This is the first problem. The second problem emerges from the fact that there is indeed something to explain in this situation – namely, why nothing happens. What we have here is an extreme form of polygeny, one without change at the level of the mechanism we wish to explain. Hence, an explanation can be had in terms of the complete masking of the two capacities involved, or in terms of the perfect balancing of the two forces or causal contributors. This situation may be genuinely mechanistic and be given a mechanistic explanation. The masking or balancing, like the outcome in typical cases of causation, is the result of many contributing forces – only in a different kind of configuration. The situation would also be categorized as causal on many dependency approaches to causation. It is therefore tempting to suggest that MDC should be modified to allow for MDC-explanations why nothing happens. Unlike many other polygenic effects, however, this extreme form of polygeny 2 can occur only where two causal contributors act on the same property of the affected object. It is because the wind and the engine both contribute to the same properties that the one capacity masks the other and the one force, or causal contributor, balances the other. The problematic upshot is that neither of these causal contributors can be activities. To say this is not to deny that there are activities in this situation. There are activities inside the engine, and as a result its propeller takes part in one. But, as we should immediately concede, this is not something located at the mechanistic level of polygeny 2 we are considering. It is not something occurring at a mechanistic

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level relevant to an account of the phenomenon of interest. That is why MDC cannot be adapted in a way that makes it capable of explaining why, as a result of polygeny 2, nothing happens. We have identified at least one kind of situation where the MDC approach breaks down despite the fact that this situation is clearly mechanistic, causal, and apt to be explained. It should be easy to mimic this extreme kind of situation in connection with any other activities lying at the heart of mechanistic interest: pushing/pulling, opening/closing, heating/cooling, attracting/repelling and binding/releasing. I can certainly try to push when someone else is pulling, but the pushing and its effect has to occur for it to be an actualization, i.e. for the entity to engage in the activity. Similarly with extreme polygenic effects that can result from trying to open and close at the same time – to simultaneously heat and cool, attract and repel, bind and release, and so on.

17.7 The Argument from Different Actualizations It is time to turn to the other, possibly much more widespread, kind of situation where advocates of activities are threatened by polygeny. In these cases, the actualization (ˆ-ing) which occurs is substantially different from the actualization (‰-ing) that would have occurred if the entity had engaged in a certain activity ‰. In order to strengthen the argument for this I will offer two versions of it: one where ˆ-ing and ‰-ing are conceptualized strictly in terms of what they actualize (i.e. as effects of the activity), and one where they are characterized by their intrinsic qualities (i.e. as kinds of process). My opinion is that the first of these characterizations is the more important one. Indeed, I do not think that an account of actualizations cast principally in terms of the latter would be viable. But since an element of it may be present in our understanding of actualization, it is of value to learn that it faces a problem similar to the one the main conception does. Let us start with different actualizations understood in terms of their effects. Even our first motorboat example, in all its simplicity, might be a perfect example of how a polygenic 2 effect cannot be accounted for in terms of more than one activity. What is the alternative to understanding what actually goes on as one activity? On the present understanding of actualizations, the only alternative is that the end-effect is a combination of two activities both of which occur. The situation reminds us of Nancy Cartwright’s take on vector-addition of forces: We add forces (or the numbers that represent forces) when we do calculations. Nature does not ‘add’ forces. For the ‘component’ forces are not there, in any but a metaphorical sense, to be added; and the laws that say they are must also be given a metaphorical reading. (Cartwright 1983, 59)

The plausibility of Cartwright’s view depends on the way we conceive forces (cf. Persson 1997, 27). If we understand them as activities defined in terms of the effects they produce, Cartwright’s position seems exactly right. It is simply not the case that an activity, ‰1 , productive of the motorboat ending up in A and another activity, ‰2 ,

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productive of it ending up in B occur. There is but one track describing how the boat moves from its starting-point to position C, and it does not pass through A or B. There is no real sense in which the effect, ˆ-ing, is the combination of the effects of ‰1 -ing and ‰2 -ing. Activities cannot account for the polygeny 2 of the effect. And in many cases the allegedly polygenic effect differs more dramatically from the aggregate effect of ‰1 -ing and ‰2 -ing. The effects of combined medication are well-known cases in point. Let us continue with the parallel problem that emerges from a characterization of activities in terms of the intrinsic qualities of the processes of actualization. Suppose there is an intrinsic difference between being guided by the wind (‰1 -ing) and being guided by the engine (‰2 -ing). Then the actual process, ˆ-ing, resulting in the track from starting point to C, will be neither of these kinds of process. If for no other reason than that the actual process inherits elements from both ‰1 -ing and ‰2 -ing, ˆ-ing will be intrinsically different from both ‰1 -ing and ‰2 -ing. Compare two, more dramatically different, activities for a more radical transformation: we cannot subtract very many of the intrinsic qualities of a closing process without changing the relevant ˆ-ing, and therefore the relevant activity, into something else. For instance, some combinations of simultaneous attempts to increase the amount of water that flows through a pipe (upstream) with closing-attempts (downstream) cannot be represented in terms of their characteristic activities, since they counteract one another and result in other kinds of activity. On an even more mundane level, trying to think and listen at the same time often have the result, at least for me, that there is neither an activity of thinking nor of listening, since another process takes place. It would be fanciful to claim that both activities nevertheless occur. This cannot be because the corresponding ‰1 -ing and ‰2 -ing are absent. But then, if they do not occur, then, of course, they cannot be the two interacting causal contributors to the polygenic 2 effect under investigation. Activities and polygeny 2 do not match. In truth it does not matter whether we focus on effects or intrinsic qualities when we characterize the ˆ-ing in ‘if entity E engages in activity ˆ, then E is ˆ-ing.’ For, potentially, there are plenty of polygenic cases where only one ˆ-ing occurs – a ˆ-ing, moreover, that does not correspond to any of the causal contributors involved. Accordingly, efforts to highlight effects or intrinsic qualities cannot prevent much of the explanatory power of the MDC framework from being lost. Full explanatory power is limited to environments where the mechanism is set up in the right way, i.e. so as to be free of the threat of polygeny 2.Thus the MDC approach breaks down in these circumstances, too. Acknowledgements This article is a short version (with new introductory sections) of a publication, Activity-based accounts of mechanism and the threat of polygenic effects, forthcoming in Erkenntnis. As a visiting fellow at the Center for Philosophy of Science, University of Pittsburgh, in spring 2007, I received invaluable suggestions that improved my thinking about mechanisms – in particular from the other fellows, and from Peter Machamer, Nicholas Rescher, and John D. Norton. Forerunners to this manuscript have been presented at seminars in Lund, Helsinki, Ume˚a, and at EPSA 2007. I am very grateful for the comments I received on these occasions. Finally, I want to thank The Swedish Research Council for funding a research project, the ontology and epistemology of mechanisms, which has made the writing of this article possible.

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References Armstrong DM (1978) Nominalism and realism: universals and scientific realism, vol 1. Cambridge University Press, Cambridge Cartwright N (1983) How the laws of physics lie. Clarendon, Oxford Dowe P (2000) Physical causation. Cambridge University Press, Cambridge Dupr´e J (1993) The disorder of things. Harvard University Press, Cambridge MA Glennan S (1997) Capacities, universality, and singularity. Philos Sci 64(4):605–626 Hempel CG (1970) Aspects of scientific explanation. Glencoe, Oxford Machamer P (2004) Activities and causation: the metaphysics and epistemology of mechanisms. Int Stud Philos Sci 18(1):27–39 Machamer P, Darden L, Craver C (2000) Thinking about mechanisms. Philos Sci 67(1):1–25 Mill JS (1893) A system of logic. Longmans, Green, & Co, London Molnar G (2003) Powers: a study in metaphysics. Oxford University Press, Oxford Persson J (1997) Causal facts. In Library of Theoria, vol 22. Thales, Stockholm Persson J (1999) The determinables of explanatory mechanisms. Synthese 120(1):77–87 Ross WD (1930) Aristotle. Methuen & Co Ltd, London Wolff P (2007) Representing causation. J Exp Psychol 136(1):82–111

Chapter 18

Why the Model-Theoretic View of Theories Does Not Adequately Depict the Methodology of Theory Application Demetris Portides

18.1 Introduction Philosophers of science have long debated issues pertaining to the nature of scientific theories, to their reference, and to how they are applied to phenomena. The logical positivist tradition claimed that scientific theories are formal axiomatic calculi, which when supplemented with the proper sets of correspondence rules entail observational sentences, the latter referring to the observable world. The process by which the deductive consequences of the calculus are stretched all the way to observational sentences is the process by which the theory gets applied to phenomena. The logical positivist conception of scientific theories has long been abandoned based on arguments that rebut several of its consequences which are by-products of its focus on syntax (see Suppe 1974). Namely, that it requires a theoretical/observational distinction and an analytic/synthetic distinction in the terms and sentences of a theory’s language both of which seem to be untenable. Furthermore, that it relies on the obscure notion of correspondence rules for giving a partial physical interpretation to the formal calculus. Finally, this view was criticized because it withholds from models their representational role by attributing to them only the meta-mathematical role of interpreting the syntax. The conception that prevailed and managed to establish its own tradition after the demise of the logical positivist view is the Model-theoretic or Semantic view. In this tradition theories are considered to be classes of structures defined by a set-theoretical predicate. They are applied to phenomena by formal mappings (e.g. isomorphism) between one of their models (i.e. structures) and a data-model constructed from empirical information about the target physical system. The question of what theories refer to, in this view, is replaced with the surrogate question of what models represent. Since a theory understood in this manner is not a linguistic entity ‘representation’ seems to be a more appropriate relation than reference. On the nature of theoretical representation there is no consensus among the advocates

D. Portides () University of Cyprus, Cyprus, Finland e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 18, c Springer Science+Business Media B.V. 2010 

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of the model-theoretic view, as they differ as to how they interpret the mapping relation. Some interpret the relation as an isomorphism (van Frassen 1980) or a partial-isomorphism (da Costa and French 2003) and understand models of theories to be mapped onto appropriate data structures that represent –at least the observable aspects of – target systems. Others hold that the models of a theory represent ‘idealized and abstract systems’, that is, that the models represent only some of the aspects of the target physical systems and they do so counterfactually, i.e. they would represent the physical system if the idealized conditions that underlie the model construction were to obtain in the system (Suppe 1989). The logical positivist and model-theoretic views are not the only attempts to address the three issues mentioned above, but one could claim that they are the only ones explicitly formulated to address all three issues within one formal framework (i.e. either first-order logic or set theory). Attempts by other philosophers are fragmented in the sense that they focus on a particular issue or on aspects of the three issues and do so by exploring how actual scientific modeling and theory application takes place and not by attempting a rational reconstruction through the use of a formal framework. To name some examples, Morrison (1999) and also Cartwright (1999) address how models represent their targets, Morrison (2007) addresses the relation (and distinction) of models to theory, Frigg (2006) and Suarez (2003) address the problem that to adequately explain the notion of scientific representation one needs a conceptual apparatus that goes beyond the idea of formal mappings of structures. The fragmentation of the treatment of the relevant issues is not a weakness of the arguments presented, but rather an indication of the complexity involved especially in the absence of a unifying formal framework. Furthermore, these attempts question whether a formal framework used to unify the treatment of these questions could in fact adequately address them since the existence of such a unifying formal framework is itself a philosophical hypothesis that must be grounded on evidence from actual science. In this paper, I show that the Model-theoretic apparatus of understanding scientific theories and their relation to experimental data is incompatible with how in actual science theories are related to experiment, by exploring the way a scientific theory is applied to phenomena. I base my argument on the assumption that scientific theories do not refer to clearly specified domains. In other words, I hold that scientific theories refer to actual physical systems found in real worldly situations and also to ideal systems. I explore the methodology employed in applying the theoretical claims to actual physical systems in order to show that the application is indirect. The models initially constructed in this process are characterized by features that distinguish them from the theory because they have a highly specified domain, dictated by the underlying idealizations. In the process, however these idealized models are brought to bear the features of actual physical systems. Hence, I conclude that, contrary to the Model-theoretic view, theories are applied to the world indirectly through their models. Furthermore, I argue that the characteristics of our representational models (i.e. those models that represent target physical systems) are such that it is incoherent to identify them as models of a theory in the Model-theoretic view. My argument to this effect is twofold. First I argue that

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the Model-theoretic view misconstrues the methodological characteristics of model concretization (this line of argument is pursued in Section 18.2). And second I argue that the Model-theoretic view cannot adequately explain the notion of representation when ‘decomposition by abstraction’ is employed in scientific modeling (this line of argument is pursued in Section 18.3). The Model-theoretic view identifies a theory with its class of models. Suppe (1989) claims, although in a rather different terminology than the one used in this paper, that a scientific theory makes claims about a class of model-systems that in turn are abstract and idealized replicas of their target physical systems. So, for instance, Newton’s second law of motion, according to Suppe, is a way to define a mathematical structure (i.e. a phase-space) that can be used to construct a particular model, which in turn is subsumed in the phase-space structure and which represents an abstract and idealized replica for e.g. the pendulum in the lab. The law, according to this view, does not refer to the actual world. That is to say, it is not a claim about the world and hence it cannot be true of the world, rather it is a claim about the models hence it is only true in the models which it defines. My starting assumption is that the law could refer to the actual world since its domain is not specified in such a restrictive manner as the advocates of the Model-theoretic view urge. On the contrary, its domain is left unspecified. Newton’s second law says that the sum of forces acting on a body (it is left unspecified as to whether the body is actual or ideal) is proportional to its acceleration. It says nothing about the possibility that we discover the totality of forces acting on the body. Similarly, Schrodinger’s equation says that the total Hamiltonian operator on the wavefunction is proportional to the time-derivative of the wavefunction. It also says nothing about the possibility that we discover the total Hamiltonian operator. Moreover, neither of the laws says anything about the possibility that, once we discover all parts of the function or operator we will be able to express them accurately in the mathematical language of the subject matter of the theory. Nor do they say that if we were able to express them in the language of the respective theories we would be able to solve the resulting equations and be led to any physical insights. As far as scientific practice is concerned, when scientists attempt to apply the laws directly to actual physical systems in the world either they are unable to discover, say, all the forces acting on a body, or they are unable to solve the resulting mathematical equations, think, for instance, of the classical many-body problem. In other words, the laws do not offer recipes that facilitate the ways by which they can be successfully applied. For this reason scientists resort to the construction of models. Contrary to theories the domains of models are specified by the assumptions that underlie their construction. A model of a theory differs from a theory because its purpose is to provide a description of a simplified version of the target physical system. In simplifying the description inadvertently we shift the domain of our discourse from the actual systems of the world to the world of ideal systems. However, this is not the purpose of the simplification. Its purpose is to indirectly apply the law to actual systems occurring in actual physical situations without ending up with intractable mathematical equations. Simplification in the description of the system requires the use

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of idealizing assumptions, and it is on the basis of the methods employed in the use of these assumptions that we can make sense of what I call ‘indirect application’ of the law and consequently of the theory.

18.2 How the Model-Theoretic View Misconstrues Methodological Considerations In the first part of the argument, let me confine myself to Newtonian Mechanics so that I can clarify what I mean when I claim that a theory is applied indirectly by the use of models. When physicists apply Newton’s second law to a particular target physical system they are faced with the problem of discovering all the forces acting on the bodies of the physical system and also of discovering the most appropriate and accurate ways by which these forces can be expressed in the theory’s calculus. But, it is obvious that if they were to express these forces directly into Newton’s second law equation the resulting equation would be intractable. Hence, in the majority of cases scientists proceed indirectly by constructing models of the system. By this, they mean a simplified version of the physical case at hand that when described in terms of the theory’s calculus the resulting equation is tractable. One such popular example is the physical system of the pendulum. The application of the second law to this system is well known. It begins with a highly idealized description of the physical system. By assuming a mass–point bob supported by a massless inextensible cord of length l performing infinitesimal oscillations about an equilibrium point, the equation of motion of the simple harmonic oscillator can be used as the starting point for modeling a real pendulum: R C .g= l/ D 0. The above assumptions are the product of abstracting many of the features displayed by the target physical system. This way a model is constructed which represents a system that displays – in a distorting manner – only some of the features of the actual pendulum apparatus.1 Because many, if not the majority of, theory applications follow this path one may be led to presume that the use of the law is precisely to define such models. In other words, one may be led to identify the theory with the class of idealized and abstract models that its laws define; in doing so, the model-theoretic view overlooks the fact that the laws of the theory had an unspecified domain to begin with. By identifying the theory with a class of models we immediately assume the contrary, we identify the domain of the theory precisely with the class of systems the models represent, namely a class of idealized

1 In the construction of such models some authors have identified two distinct processes at work, ‘abstraction’ and ‘idealization’ (e.g. Suppe 1989; Cartwright 1989). For a long time, I have also thought of scientific modeling processes in this manner (Portides 2005). It is my view now that abstraction is the process at work and idealization is its conceptual result, although I shall not offer any argument for this in this paper.

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and abstract systems. If theory application in actual science consisted solely in the construction of such models then this view would suffice. However, actual science testifies to the contrary. In reference to the pendulum example, a most significant aspect of the physicist’s job is to bring back into the description all the features of the physical system that were initially ignored. This amounts to meeting the demands of Newton’s second law by including in the description all the forces that contribute to the motion of the system. The simple harmonic oscillator is a good starting point for doing this because when all the factors that contribute to the motion of the pendulum are introduced into the above equation the result is a system of tractable linearly independent differential equations the solution of each of which yields the contribution of each factor to the motion of the pendulum. In other words, the problems that lead to the indirect application of the law are tackled by reintroducing the initially abstracted features of the physical system into the simple harmonic oscillator equation. I will refer to this reintroduction of the relevant features as the process of concretization of the model, which I take to be the exact opposite process of that of abstraction.2 By concretizing the model the immediate intention is to bring the model description as close to the actual pendulum apparatus as possible, but the ultimate intention is to indirectly apply the law to that part of its domain to which problems of mathematical tractability in the first place prohibited its application, namely to the actual physical system. The law does not have a clearly specified domain; it could apply to actual as well as ideal systems, hence it is permissible, due to the frequent directives of methodological problems, to apply the law to actual systems by first applying it to ideal systems that display aspects of the features of the former, and then gradually reintroduce the missing features. The process of abstraction is at work when constructing a model that represents an ideal system, and its opposite the process of concretization is at work when attempting to shape such models in order to represent actual systems. Concretized models are not merely the products of our attempts to fit experimental data reports to idealized models, as – at least, some versions of – the Model-theoretic view seem to imply, but they are the products of indirect application of the law to actual systems. This characteristic of science in general and of scientific modeling in particular is obscured by the Model-theoretic view, which focuses on the structural attributes of theories. It thus construes theories as gestating models requiring the midwife to pull one out in order to represent a particular system, as Cartwright (1999) has put it.

2 Others have referred to these processes as the process of idealization and the process of deidealization (see Morgan and Morrison 1999). I prefer to use the terminology of abstraction and concretization, despite tradition in Philosophy of Science, because I wish to clearly distinguish between the processes and their resulting concepts. I think of abstraction as a mental process that results in an idealized concept, e.g. it is by mentally removing features of the actual pendulum system that we construct the idealized concept of the simple harmonic oscillator. Similarly I think of concretization as a mental process that results in a de-idealized concept, e.g. it is by reintroducing the factors of influence into the model equations that results in the de-idealized concept of the final representational equation (that, of course, in the case of the pendulum can be expressed as a system of linearly independent equations). I believe that the choice of my terminology meets its purpose.

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This view, however misses the whole purpose of constructing the idealized model and using it as the starting point upon which to create a more concretized version that would allow an inference to be drawn on whether the theoretical tenets hold in the physical world or not. Although this argument has its own consequences to realist/instrumentalist issues of science, it is not meant to tackle such issues, or in fact any epistemological issues, herein; it is an argument against the methodological character that the Model-theoretic view of theories attributes to science and scientific modeling. In particular, it is an argument against one of the consequences of the Model-theoretic view, that an immiscibly methodological aspect of the application of theories to phenomena is (mistakenly) perceived as part of the innate character of scientific theories.

18.3 The Inadequacy of the Model-Theoretic View to Account for All the Facets of Abstraction Let me for the sake of the argument assume that the Model-theoretic view (contrary to the argument presented in Section 18.2, and contrary to Morrison’s (1999) argument) can deal with the above objection. There is still another side to the processes of abstraction and concretization that causes problems to the thesis that theories are classes of models. So far in the literature only two characteristics of the process of abstraction are clearly discerned. The first is the employment of abstraction to construct an idealized concept; I will label this ‘idealization by abstraction’.3 The second is the employment of abstraction to construct a description of a system that has very specific features that are never observed to occur in isolation (e.g. the pendulum oscillations in vacuum) in the real world; I will tag this ‘isolation by abstraction’.4 There is, however, a third characteristic of the process of abstraction that, to my knowledge, has escaped detection. It is the employment of abstraction to construct a description of a system that, in fact, is an amalgamation of – often qualitatively – different parts. In other words, the description is decomposed into distinct parts, which is another way of saying that within the description some aspects are set apart from each other. I will label this, ‘decomposition by abstraction’. This kind of abstraction is particularly evident in Quantum Mechanics but it is also discernible in the Hamiltonian and Lagrangian formulations of Classical Mechanics. I shall briefly demonstrate by means of an example from an application of Quantum Mechanics to

3 Some authors refer to this as simply ‘idealization’, e.g. some of the contributors to Morgan and Morrison (1999). 4 Some authors call this ‘abstraction’, e.g. Cartwright (1989), others call it ‘idealization’, e.g. Nowak (1980) and Morrison (1999), others call it ‘construct idealization’, e.g. McMullin (1985), and finally others call it ‘isolation’, e.g. Maki (1994).

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the domain of nuclear physics how the third of the three kinds of abstraction process is used in order to model the structure of the nucleus.5 The problem of directly applying Quantum Mechanics to the nuclear domain is the nuclear many-body problem. The problem could be understood as follows. Consider the internal energy E of a nucleus of A nucleons, given as an eigenvalue of the Schr¨odinger equation. If we were to directly apply the Schr¨odinger equation to compute the eigenvalues for E, we would express the Hamiltonian as the sum of the kinetic energy operator for nucleonic motion and the potential energy operator for interaction between the nucleons. The potential energy operator corresponds to the interaction potential between all the pairs of nucleons. It is evident that expressing the potential energy as a sum of pair-wise terms is itself an idealization, since influences on the pair-wise interactions are exerted by the presence of other nucleons, but this fact would merely add redundant complexities to the explication of the problem. The nucleus can exist in different bound states, characterized by different wavefunctions and different values of E, as well as of other observable quantities. The different eigensolutions to the Schr¨odinger equation would correspond to the different states of the nucleus. Thus, if we could solve the Schr¨odinger equation, the eigenvalues E would give us the energy of the different states and from the corresponding eigensolutions we would be able to extract all possible information concerning all other conceivable properties of these states. All this is what quantum theory instructs us; yet solving the Schr¨odinger equation for the nucleus poses enormous problems. Firstly, the nature of the pair-wise nucleon-nucleon interaction is not completely known, nor is the influence on it from the presence of other nucleons. Secondly, and more importantly, even if this interaction is discovered and specified in the calculus of Quantum theory, we would encounter insurmountable computational difficulties for the cases of more than two nucleons that would force us to resort to variational techniques for solving the nuclear many-body problem at the expense of acquiring any significant insight into the nuclear structure and the nuclear properties. It is therefore not surprising that the nuclear structure research program progressed by the construction of models that attempt an indirect application of Quantum Mechanics into the nuclear domain. One of the most successful models for the representation of the nuclear structure was the unified model of the nucleus. It was constructed in order to accommodate two hypotheses previously thought to be incompatible. The first was that the nucleus is a collection of strongly coupled particles whose properties can be explained by accounting only for collective modes of motion, and the second that the properties of the nucleus can be explained by accounting only for the independent motion of the nucleons. These two hypotheses lead to two distinct Hamiltonian operators that are used in the model description of the nucleus. Furthermore, the first hypothesis, in its elaborate form, states that there are four distinct collective modes of motion

5 I analyze and explicate in detail all three kinds of uses of the process of abstraction, and how its opposite process of concretization compensates for the three kinds, in work in progress to be submitted for publication early in 2010, the tentative title of the paper is “The process of Abstraction in Scientific Modeling: How Theories are Applied to Phenomena”.

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namely, rotation, vibration, rotation-vibration, and giant resonance. Each of these modes of motion is expressed in the total Hamiltonian operator as if it functions independently of the others. But, of course, even if the nucleus as a collection of particles is understood in terms of classical intuitions, what one could observe is one motion of some complex form, although in the model description that motion is decomposed into four distinct parts. The second hypothesis in its elaborate form states that there are two distinct modes of independent particle motion. The first, the shell structure motion, is a kind similar to the atomic case, most of the nucleons form pairs that result in a stable collection and – in its simpler form – a loose nucleon moves under the influence of the collection of pairs. The second is the spinorbit coupling, i.e. a motion that is based on the interaction between the orbital and spin angular momenta of the unpaired nucleon. Both of these modes of motion are expressed in the total Hamiltonian as if they function independently of each other. The total Hamiltonian that represents the nucleus is decomposed into the six parts mentioned with a seventh part added to adjust for aggregate interactions between the six different modes of motion. It must also be clarified that the first four Hamiltonian parts are constructed by purely classical considerations and often physicists would refer to them as semi-classical constructions, whereas the shell structure motion is an idealized quantum mechanical model, and finally the spin-orbit coupling motion is the result of quantum mechanical phenomenological considerations. In short, the methods employed to construct the different parts of the Hamiltonian vary and the final results differ in significant characteristics.6 To sum up, decomposition by abstraction divides the total Hamiltonian operator into six distinct kinds of motion (and an interaction part) not all of which are arrived at by the same theoretical considerations or by the same methodological considerations. The unified model which is the result of this highly complex activity of theoretical and methodological considerations is an amalgamation of decomposed parts, each of which is assumed to be independent of the others and of equal importance as the others. Their independence is demonstrated by the process of concretization. Each term of the Hamiltonian operator is concretized as if it is meant to be brought closer to an actual mode of motion that is exhibited by the nucleus. Thinking classically, for the sake of the argument, the nucleus is represented as if it exhibits a rotation and a vibration mode of motion each independent of the other and as if impediments to each of these motions exist and must be reintroduced to construct a representational model. But the actual nucleus demonstrates one motion with existing impediments to that motion alone, which is only conceptualized as if it consists of two independent motions each with its own impediments. In fact the six terms of the total Hamiltonian do not represent different actual motions but the Hamiltonian as a whole represents the exhibited nuclear motion and structure. The reintroduction of corrections to each of the Hamiltonian terms individually has only one purpose, to improve the representational capacity of the model as a whole.

6 I give an elaborate analysis of the construction of the unified model and the reasoning behind its construction in Portides (2006).

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The relevance of this piece of information cannot be appreciated if the model is understood solely as a mathematical structure. This point presents two challenges to the Model-theoretic view. Firstly, if we understand the unified model of the nucleus as a model of (Quantum) theory and fail to see that it is meant as an indirect application of the theory then we overlook all the relevant information which is the product of decomposition by abstraction as outlined above. Secondly, and more importantly, if we understand the notion of representation as merely a mapping between mathematical structures then we will fail to see that mapping the unified model onto a corresponding data model would be mapping a structure stemming from a description that assumes (as part of the process of modeling, i.e. decomposition by abstraction) six different modes of motion to a structure that results from a physical system that displays one integral motion. Moreover, thinking of the model/experiment relation in this manner obscures the fact that the model’s structure is the product of a variety of different conceptual ingredients, some of which are borrowed from classical mechanics, and each of which is independent of the others. More generally my claim is that even if we assume that the Model-theoretic view can accommodate idealization by abstraction and to first approximation isolation by abstraction, it cannot accommodate decomposition by abstraction. Decomposition by abstraction means constructing models that seem to represent systems that are thought to consist of decomposed parts although we know that they don’t. Decomposition leads to the amalgamation of different conceptual ingredients within the model and thus the structure that the model in principle satisfies does not illuminate anything about the model’s target physical system. In the case of the unified model, relying on a structural mapping to make the case for its representational capacity is not enough. Representation by decomposition dictates that we know how each of the model’s parts represents the target and what aspects (or properties) of the target it represents, and these are not questions that can be adequately addressed by using the conceptual apparatus of the Model-theoretic view.

18.4 Conclusion I have argued that The Model-theoretic view misperceives important methodological aspects of scientific modeling and construes them as innate features of the nature of scientific theories. I have also argued that understanding scientific representation as a mapping relation between mathematical structures, as dictated by the Modeltheoretic view, cannot capture important characteristics of models that stem from ‘decomposition by abstraction’, and that this is due to an incompatibility between “decomposition by abstraction’ and the Model-theoretic apparatus of understanding the theory/experiment relation. Both problems teach us that in order to understand what scientific theories and what scientific models are we must distinguish between their innate and their methodological features.

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References Cartwright ND (1989) Nature’s capacities and their measurement. Clarendon, Oxford Cartwright ND (1999) The Dappled world: a study of the boundaries of science. Cambridge University Press, Cambridge Da Costa NCA, French S (2003) Science and partial truth. Oxford University Press, Oxford Frigg R (2006) Scientific representation and the semantic view of theories. Theoria 55:49–65 Maki U (1994) Isolation, idealization and truth in economics. In: Hamminga B, De Marchi NB (eds) Idealization VI: idealization in economics. Poznan studies in the philosophy of the sciences and the humanities. Rodopi, Amsterdam, pp 147–168 McMullin E (1985) Galilean idealization. Stud Hist Philos Sci 16:247–273 Morgan MS, Morrison M (eds) (1999) Models as mediators: perspectives on natural and social science. Cambridge University Press, Cambridge Morrison M (1999) Models as autonomous agents. In: Morgan M, Morrison MC (eds) Models as mediators: perspectives on natural and social science. Cambridge University Press, Cambridge, pp 38–65 Morrison M (2007) Where have all the theories gone? Philos Sci 74:195–228 Nowak L (1980) The structure of idealization. Reidel, Dordrecht Portides D (2005) A theory of scientific model construction: the conceptual process of abstraction and concretization. Foundation Sci 10:67–88 Portides D (2006) The evolutionary history of models as representational agents. In: Magnani L (ed) Model-based reasoning in science and engineering, texts in logic, vol 2. College Publications, London, pp 87–106 Suarez M (2003) Scientific representation: against similarity and isomorphism. Int Stud Philos Sci 17:225–244 Suppe F (1974) The search for philosophic understanding of scientific theories. In: Suppe F (ed) (1977) The structure of scientific theories. University of Illinois Press, Urbana, pp 3–241 Suppe F (1989) The semantic conception of theories and scientific realism. University of Illinois Press, Urbana Van Frassen BC (1980) The scientific image. Clarendon, Oxford

Chapter 19

A Deflationary, Neo-Mertonian Critique of Academic Patenting Hans Radder

19.1 Introduction Since the 1980s, the commercialization of academic science has strongly increased. To be sure, science at large has always included research primarily carried out for its economic benefit, especially since the second half of the nineteenth century. Yet, the large-scale commercialization of academic science is a more recent phenomenon. In the course of the past decade, this phenomenon has been explored and a variety of studies have become available. Assessments of the rise of entrepreneurial academia differ sharply. On the one hand, it is welcomed and sometimes even seen as a necessary step in the history of academic institutions (see Gibbons et al. 1994; Etzkowitz 2004). On the other hand, the problematic consequences of commercialized academic science are also widely discussed and increasingly acknowledged (Shulman 1999; Bok 2003; Krimsky 2003; Radder 2003; Healy 2006; Resnik 2007).1 In response to these problems, universities, research institutes and science policy organizations have adopted a variety of normative codes of good scientific conduct (see Kourany 2008). Almost invariably, these codes are based on, or derived from, the social ethos of science formulated by Robert K. Merton in 1942. The aim of this paper is to find out to what extent a Mertonian ethos can still be useful in the present context of a strongly commercialized science. The discussion will be focused on the strongly increased practices of the patenting of the results of publicly funded research institutions. The structure of the paper is as follows. First, I briefly review Merton’s account of the ethos of science. The next section deals with some criticisms of this account and it proposes a reinterpretation in terms of general Mertonian values and more specific

H. Radder () VU University of Amsterdam, Amsterdam, Netherland e-mail: [email protected] 

This paper draws on some of the material from Radder (forthcoming).

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Barring some exceptions, such as Irzik (2007) and Brown (2008), philosophers of science have completely neglected the study of this issue, which is remarkable in view of the potential implications of commercialization for the epistemic quality of science.

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 19, c Springer Science+Business Media B.V. 2010 

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scientific norms. I then discuss the important issue of the patenting of the results of academic science and I demonstrate the significance of Mertonian values and scientific norms for this issue. The concluding section addresses some further questions regarding the scope and implications of this neo-Mertonian critique of commercialized science.

19.2 Merton’s Ethos of Science In 1942 Robert K. Merton published his well-known article on the normative structure of science. At the time science was, or was perceived to be, threatened by anti-intellectualist criticisms, nationalist ideologies and racist politics. For Merton, this context defined the broader goal of his article: ‘An institution under attack must reexamine its foundations, restate its objectives, seek out its rationale. Crisis invites self-appraisal’ (Merton 1973[1942], 267). In this spirit, he then proposes his four famous norms of science (also called ‘institutional imperatives’) as the backbone of the ethos of science: universalism, communism, disinterestedness and organized skepticism. The claim is that the existence and operation of this ethos, even if it has not been explicitly formulated and codified, can be inferred from the practices, behaviors and verbal expressions of the scientists. Merton explains his four norms as follows. ‘Universalism’ means that the acceptance or rejection of scientific claims should be based on impersonal criteria. Put negatively, nationality, ethnicity, religion, sex, and any other personal qualities of a scientist should be irrelevant to the evaluation of scientific truth-claims. Quoting historical studies of national scientific styles, Merton admits that discoveries may depend on the particularities of the socio-cultural situation. Yet, (what is now called) the context of justification is characterized by universalism and hence ‘sooner or later, competing claims to validity are settled by universalistic criteria’ (Merton 1973[1942], 271, note 6). In a broader sense, the notion of universalism includes the norm that science should be open to anyone who is sufficiently talented. Thus, access to science should be universal and not be blocked on the basis of nationality, ethnicity, sex, religion, and the like. The second element of the scientific ethos is ‘communism’ or the common ownership of goods. For science this means that its fruits should not be privately owned, because they result from an essentially collective effort. ‘The substantive findings of science are a product of social collaboration and are assigned to the community’ (Merton 1973[1942], 273). Priority claims by scientists regarding specific discoveries are compatible with the norm of communism, because they do not lead to ownership of the discovery but rather to general recognition and esteem as a result of having made the discovery. ‘Disinterestedness’ constitutes the third norm of good scientific practice. Merton emphasizes that this should not be mistaken for a lack of individual motivation. Individual scientists may have a variety of motivations for doing science in the way they do, ranging from a craving for fame and wealth to a concern with the well-being of

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humanity. The point of the norm of disinterestedness, however, lies at the institutional level or, in philosophical jargon, in the context of justification. Through the presence of institutional controls – such as peer review, publication and replication of research results – the potential distortion by individual motivations is being filtered out. Conversely, if the accountability of scientists to their peers is diminished or eroded by ideological or economic forces, a real and damaging loss of scientific integrity and objectivity will result. The fourth and last element of Merton’s scientific ethos is ‘organized skepticism’. It requires the ‘temporary suspension of judgment and the detached scrutiny of beliefs in terms of empirical and logical criteria’ (Merton 1973[1942], 277). The reference to empirical and logical criteria implies that this norm is not purely institutional but has a methodological aspect as well. The qualification ‘organized’ means that the locus of this norm is again institutional: individual scientists may be committed to their cherished theories, models or methods, but it is the task of the scientific community as a whole to practice a temporary suspension of judgment.

19.3 Mertonian Values and Scientific Norms Merton’s account of the ethos of science has been both influential and controversial.2 Here I will present some additional points of comment that are important in the context of this paper. For a start, Merton’s terminology and his explanations are not always clear and convincing. One may, for example, question the accuracy of the term ‘universalism’ if this is meant to refer to the impersonal nature of evaluation criteria of scientific claims. In this case, a more appropriate alternative would seem to be ‘(epistemic) objectivity’.3 Merton’s usage of ‘universalism’ may easily lead to confusion, as is for instance the case in those authors who connect it closely to the idea of a universal scope of scientific claims. Another issue is the independence of the four norms. In this respect, one might ask whether disinterestedness is not already implied in universalism. When all scientific claims are being assessed on the basis of impersonal criteria, any impact of particular interests of individual scientists on the processes through which scientific claims are justified has been prevented. Finally, one may question the completeness of the set of four norms. Do they cover the entire normative structure of science, as Merton claims? Or do we need additional values, such as ‘scrupulousness’ or ‘reliability’, which can be found in some of the more recent ethical codes of conduct? Because of these questionable features of Merton’s terminology and explanations, I suggest to make a terminological shift from Merton’s ethos to a Mertonian ethos. By making this shift I assume that the above problems can in principle be

2 For some criticisms, see Barnes and Dolby (1970), Mulkay (1976) and Sismondo (2004, 20–32). For an extensive reply to these criticisms, see Radder (forthcoming). 3 In fact, the term ‘objectivity’ is occasionally used by Merton in this context (e.g., 1973[1942], 270).

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solved by providing a sharper terminology and a better analysis, so that ‘something like’ Merton’s ethos makes sense.4 However, this is not the place to carry out such an analysis. Instead, I will argue that a Mertonian ethos should preferably be phrased in terms of values, while it should be complemented by an account of more specific scientific norms. Although Merton himself uses the terms ‘norms’, ‘imperatives’, ‘mores’ and ‘values’ more or less indiscriminately, in scholarly practice the phrase ‘Merton’s norms’ has become the established usage. However, if we define a norm, as I suggest, as ‘a socially embedded directive about what people should, or should not, do or say’, purely terminologically universalism, communism, disinterestedness and organized skepticism are not norms. Of course, it is trivially possible to derive norms that correspond to given values. Thus, given a value v one may construct the trivially corresponding norm ‘one should strive to realize value v’. However, as compared to the value this norm does not give us any further information about what (not) to do or say. Hence, it is preferable to see an element of a Mertonian ethos as primarily a value, that is, a quality of things, states of affair, events, activities, and the like, that renders them useful or estimable. The idea, then, is that the general Mertonian values should be specified through adding more concrete norms about how to realize these values. Often, values denote rather general or even vague qualities of things. There is a positive and a negative side to this. Positively, because of their generality and vagueness values can be relatively easily shared, and these shared values can serve to promote a sense of community. Who would not endorse the value of scientific integrity, for instance? Negatively, merely endorsing general and vague values ‘as such’ may be vacuous. Hence, in order to know what is meant by a value further interpretation is needed. A first step in this interpretation is to craft more specific norms which may enable or facilitate the realization of the value. A second step involves the clarification of what it means to apply these norms in concrete situations. Making these two steps, however, may lead to disagreement among people who do share the same value. Thus, some scientists may think that any contract research will jeopardize their scientific integrity, while others may hold that not all forms of contract research are excluded by the value of scientific integrity. Similarly, some scientists may interpret a project funded by a national research council as a form of contract research, while others may see this project as a case of independent inquiry. Hence, while general values connect people, the more specific norms and their applications may divide them again. Yet, the specification of values into norms does, of course, not necessarily lead to disagreement. In specific situations it may well be possible to reach agreement on the interpretation and application of particular norms. In the next section, I will argue for the adoption of certain norms in the context of the commercialization of academic research, and advocate their application to the issue of the patenting of the results of this research. 4 For instance, Helen Longino’s four social norms for social knowledge (‘venues’, ‘uptake’ and ‘public standards’ of critical debate, and ‘tempered equality’ of intellectual authority) can be seen as constituting such a Mertonian ethos (Longino 2002, 128–135).

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Finally, it is important to see that neither values nor norms fully determine each and every aspect of the behavior of scientists. Yet, they do guide scientists in certain directions. The norm that scientific articles should be open to critical discussion, which can be derived from the value of organized skepticism, patterns scientific publications in ways that distinguish the typical scientific article from the typical work of literature. Moreover, in a given situation, the norm of writing argumentative discourse directs the way scientists report on their research. In the science studies literature (e.g., Mulkay 1976, 643–645; Sismondo 2004, 29–30) one often finds the weaker claim that norms constitute flexible resources from which scientists pick and choose whatever they see fit with respect to their locally situated construction work. However, even if it is right to assume that norms do not determine practices, this constructivist claim is much too voluntaristic and as such it fails to appreciate the fact that norms also constrain practices.5

19.4 Mertonian Values, Scientific Norms, and the Patenting of Academic Research The commercialization of academic research is a multi-faceted phenomenon. In this paper, I focus on one of its aspects, to wit the practice of patenting the results of academic research and the concomitant pressure on university scientists to engage in patenting applications. In view of this practice and pressure, the question of whether the patenting of academic research conforms to Mertonian values and norms is pertinent. In this section, I will demonstrate that this is not the case. For this purpose, I first review some basic features of the patenting system (see, e.g., Sterckx 2000; Bostyn 2001, chaps. I and II). A patent is an intellectual property right to exploit a particular technological invention. More precisely, it is the right of the patent holder(s) to exclude all other people or institutions from reaping the economic fruits of this invention. The three main criteria for patentability (in the United States’ phrasing) are that the invention should be ‘novel’, ‘useful’ and ‘non-obvious to someone skilled in the art’. Furthermore, the invention should be reproducible by competent peers of the inventor. In return for the granting of the patent, the invention needs to be disclosed, that is, made publicly available through submitting a description of it to the relevant patent office. Over the last twenty-five years, the number of patent applications and grants has increased strongly, in particular in the areas of biotechnology, information and communication technology, and pharmaceuticals. By way of general justification, patent law and regulation is often

5 See for instance Radder (1996, chap. 2) for the case of the norm that scientific experiments should be reproducible. See also Tuunainen and Knuuttila, who conclude from their empirical study that ‘the entrepreneurial researchers in our study were not able to recreate the norms and rules at will’ (2008, 152; emphasis added).

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claimed to constitute a legitimate social arrangement because it rewards the inventor for making available socially beneficial, new technology.6 Of course, patenting takes place primarily in industry and, more generally, in commercial business. However, since the rise of the ‘entrepreneurial university’ during the last quarter of the twentieth century, patenting is also increasingly practiced within academic science, first in the United States and somewhat later also in Europe (Etzkowitz 2004). In a situation of decreasing public funding, university administrators promote patenting as one of the novel ways of financing academic research. As a consequence, granted patents tend to be assessed as equally important and valuable results of academic research as journal publications or books. But can this practice be justified? Can the criteria and practice of patenting conform to the same Mertonian values and norms as the criteria and practice of ‘ordinary’ academic research? Or better (since this is not an all-or-nothing question), phrased as a matter of degree: does the introduction of patenting contribute to, or does it detract from, the realization of Mertonian values? To answer these questions I will consider Merton’s four values in the context of the patenting of the results of academic research. My approach is to analyze and assess the consequences of the introduction of academic patenting as compared to the same situation without this patenting. Of course, this analysis and assessment is not about purely logical consequences but about consequences that can be plausibly inferred in view of the actual situation and context of present-day academic institutions. Let us start with the value of universalism. As we have seen, for Merton universalism means that scientific knowledge claims should be assessed on the basis of impersonal criteria and that access to science should be open to anyone, independently of his or her personal identity or private situation. In line with my analysis in the preceding section, we may interpret these two claims as two different normative specifications of the value of universalism. As far as I can see, the introduction of patenting does not make an immediate difference regarding the impersonal assessment of scientific knowledge claims. However, on the basis of the connection between universalism and disinterestedness (see the preceding section) one could argue that patenting makes an indirect difference: since patenting decreases the measure of disinterestedness (see below), it also goes against the norm of impersonal judgment. The impact of patenting on open access is more straightforward. After all, patents – for instance on research tools or software – introduce an additional barrier to the financially weaker researchers or institutions who aspire to enter a certain field of research. In this sense, patents decrease the accessibility of academic science. To be sure, potentially the ‘experimental use’ of a patented subject matter (such as the clinical testing of patented drugs for non-commercial purposes) may be exempted from protection. In the present situation, however, this exemption is by no means sufficient to warrant the accessibility of academic research. First, the exemption holds in Europe but not in the United States; second, the exemption does 6 However, whether patenting really benefits society, is contested (see Bostyn 2001, chap. II; Danish Board of Technology 2005, chap. 3).

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not apply to patented research tools used in experimentation, and the interpretation of the experimental use clause tends to become ever more restrictive; third, when universities define themselves as entrepreneurial organizations, it will be very difficult to vindicate claims that university experimentation is ‘non-commercial’. Merton’s second value, communism or the common ownership of scientific goods, acknowledges that the fruits of science are the result of an essentially collective effort. Since we are dealing with publicly funded research institutions, we should add that this effort has been financed through public tax money. A natural normative specification of this value is that the results of academic research at wholly or largely publicly funded universities should not be privately appropriated through the acquisition of patents, neither by the university as an institution nor by individual researchers or research groups. Hence, the practice of patenting the results of academic research detracts from the realization of this part of the Mertonian ethos of science. To appreciate the weight of this point it is important to see that patent protection is not limited to the original process through which the invention has been actually produced, but can be extended by adding further claims ‘on the basis of’ this invention. It is these claims that define the scope of the monopoly. In the case of broad patents, the protection granted includes claims that transcend the original invention by far. During the past decades the significance of broad patents has strongly increased, in particular because of developments in the area of biotechnology and genomics (Sterckx 2000; Bostyn 2001). A well-known example is the US oncomouse patent, which is not limited to the actually modified mice but claims the exploitation of the invention for all transgenic, nonhuman, mammalian oncoanimals. Product patents constitute an even stronger form of broad patent. In the case of product patents protection is granted for any use of any process that might be realized to produce this product. Thus, granted product patents imply a particularly strong type of intellectual property, and something similar applies to the wider category of broad patents.7 One might reply to the argument that patenting goes against the value of communism by claiming that, if patents are acquired by public universities or university researchers, we do not have a case of private appropriation, since the profits will be returned to a public institution. This reply will not do, however. First, to allocate the fruits of science to one particular university, research group or researcher is a far cry from assigning it to the collective of scientists on whose prior achievements the inventor built. Furthermore, a patent confers to its owner an exclusive right, a monopoly. That is to say, the appropriation includes the right of patent holders to exclude potential users (for instance, their scientific rivals) from exploiting the patented invention.8 Hence, the impact of patenting by far exceeds its direct financial consequences through licensing. Privatizing the results of academic

7

The justifiability of granting these strong monopolies is a different matter. See Radder (2004) and (2006) for a detailed criticism of the concept and practice of broad and product patenting. 8 For this reason, patents differ substantially from other forms of intellectual property rights, in particular copy rights.

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research through patenting also prevents other scientists from freely developing these results through their own research. Next, consider the value of disinterestedness. Here the following normative specification suggests itself: scientists should not have a direct financial interest in a specific outcome of their research. This norm applies to the case of patenting in a quite straightforward way. A patentable technology should work in the way explained in its public description and be reproducible by contemporary peers. However, in scientific and technological practice, whether a certain invention really works, or really works well, is often contested (just think of the many controversial pharmaceuticals). In case of financial stakes, however, inventors will tend to be biased and inclined to overstate the merits of their invention (see the many shocking illustrations of this tendency in Shulman 1999). After all, if they can get away with their claims, they will be immediately rewarded through acquiring the patent. Thus, the practice of academic patenting will tend to hamper the realization of a disinterested science. Again, one might object to this argument by pointing to the fact that the prospect of gaining scientific credit may just as well incline scientists to publish immature results or overestimate their significance. In fact, however, the two cases are not as similar as suggested by this objection. Generally speaking, in science the relation between scientific achievement and professional reward is far less direct than in business, including the patenting business. First, a mere publication record does not yet amount to professional recognition. The latter is essentially dependent on the fact that other people take up and acknowledge the publications as scientifically worthwhile or significant. Second, obtaining professional recognition often requires a variety of different achievements in different contexts, which also decreases the chances of unjustly awarded credit. Both mechanisms work to discourage the making of immature or overstated claims for one’s work. Merton’s last value is organized skepticism, the attitude of open and critical reflection and debate for the purpose of improving the quality of the scientific claims in question. This value may be specified by the norm that scientific claims should be critically scrutinized from different perspectives. In this respect, the practice of patenting the results of academic research is problematic, since it structurally favors patentable over non-patentable approaches. For instance, under these circumstances medical research into the social causes of illness will be disadvantaged as compared to the study of the physical causes of diseases. Hence, in cases like this scientific debate will be one-sided, and the space for organized skepticism will be limited. Furthermore, the primary criteria for patenting (reproducibility, novelty, usefulness and non-obviousness) do not entail explicit standards of epistemic, methodological, experimental or technological quality.9 Hence, one cannot appeal to such standards in a critical debate aimed at improving the quality of the claims in question. In addition to these structural problems, there are some practical issues concerning the opportunities for practicing organized skepticism. One is that applying for a 9 For example, the holder of a product patent has the legal right to block the realization of higherquality (e.g., more efficient, more sustainable or safer) processes to produce the same product.

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patent will normally delay the publication of the results. Another issue is that, under the present circumstances, patent offices are hardly up to the task of critically examining the justifiability of the claims made by applicants. Indeed, these institutions are often shown to be understaffed and poorly functioning (Shulman 1999; Danish Board of Technology 2005, 41). To be sure, the peer review system is certainly not functioning perfectly. In spite of this, it is vastly superior to the present system of reviewing patent applications. Although these practical issues may also undermine the extent and quality of critical academic debate, from the perspective of this paper I should like to emphasize the more principled, structural problems. The conclusion of this section must be that patenting the results of academic research does not conform to the specific norms derived from the more general Mertonian values. Put differently, the introduction of academic patenting directs science away from, rather than bringing it closer to, the realization of these values. Since these Mertonian values are at the basis of many of the recently adopted codes of good scientific conduct, they can be expected to find quite general support. The same applies to the more specific scientific norms employed in the above argumentation. Hence, the recent patenting practices of public research institutions stand unjustified.

19.5 Concluding Observations In this paper, I have developed an account of Mertonian values and scientific norms and applied it to the patenting of the results of academic research. The conclusion is that academic patenting is normatively undesirable. The same account could also be applied to other aspects of the commercialization of science, such as the rise of contract research, the increasing entanglement of universities and small or large businesses, and so on. This extension will be a matter of further research, though. I conclude this paper with some observations on the scope and implications of my approach. To circumvent the criticism that Merton’s, or Mertonian, norms are too vague and too abstract to be of any help in practical matters, I have reinterpreted these norms as general values that need to be complemented by more specific norms that can be expected to have a substantial plausibility. In the context of the patenting of academic research, I have formulated the following four norms: first, access to science should be open to any sufficiently talented person and should not be hampered by financial barriers; second, the results of academic research at publicly funded universities should not be privately appropriated through the acquisition of patents; third, scientists should not have a direct financial interest in a specific outcome of their research; and fourth, scientific claims should be critically scrutinized from different perspectives. But can any further reasons be given for adopting an ethos consisting of these norms or is its adoption as arbitrary as the entrepreneurial ethos it opposes? Although much more could be said in response to this question, I here offer

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the following, short answer: open access implies that a society and its science fully exploit the available talents; public money should be used to increase the common good; because of its corruptive potential, mixing public responsibilities with private interests should be as undesirable among scientists as it is among judges, politicians and journalists; finally, it is an amply supported experiential fact that people may learn from critical feedback on what they say or do. As can be seen from the phrasing and explanation of these four norms, my analysis does not presuppose strong (and hence potentially controversial) philosophical interpretations of the results of science, for instance in the sense of a correspondence theory of scientific truth, or a universal notion of objectivity, or a watertight demarcation between science and non-science. Similarly, the analysis does not depend on specific sociological notions, such as the idea that scientific knowledge is a public, that is, a ‘non-excludable’ and ‘non-rival’ good. Finally, my analysis does not require a full endorsement of all of Merton’s views, such as its problematic sociological functionalism, in which there is neither place for the interpretations of individual actors nor for a critical attitude towards a taken for granted, ‘wellfunctioning’ social system. Hence, I suggest a further terminological shift, from a Mertonian to a neo-Mertonian approach. For these reasons, my ‘deflationary’, neo-Mertonian analysis of academic patenting may be expected to be acceptable to scientists, philosophers, and policy-makers with a variety of epistemological and sociological background views.

References Barnes SB, Dolby RGA (1970) The scientific ethos: a deviant viewpoint. Archives Europ´eeennes de Sociologie 11:3–25 Bok D (2003) Universities in the marketplace. Princeton University Press, Princeton, NJ Bostyn SJR (2001) Enabling biotechnological inventions in Europe and the United States. European Patent Office, M¨unchen R . In: Carrier M, Howard D, Kourany J (eds) The Brown JR (2008) The community of science challenge of the social and the pressure of practice. University of Pittsburgh Press, Pittsburgh, pp 189–216 Danish Board of Technology (2005) Recommendations for a patent system of the future. The Danish Board of Technology, Copenhagen (also electronically available at: http://www.tekno. dk/subpage.php3?articleD1132&languageDuk&categoryD11&toppicDkategori11) Etzkowitz H (2004) The triple helix and the rise of the entrepreneurial university. In: Grandin K, Wormbs N, Widmalm S (eds) The science-industry nexus: history, policy, implications. Science History Publications, Sagamora Beach, MA, pp 69–91 Gibbons M et al. (1994) The new production of knowledge. Sage, London Healy D (2006) Let them eat prozac. The unhealthy relationship between the pharmaceutical industry and depression. New York University Press, New York Irzik G (2007) Commercialization of science in a neoliberal world. In: Bu˘gra A, A˘gartan K (eds) Reading Karl Polanyi for the twenty-first century: market economy as a political project. Palgrave MacMillan, New York, pp 135–153 Kourany J (2008) Philosophy of science: a subject with a great future. Philos Sci 75(5):767–778 Krimsky S (2003) Science in the private interest. Rowman and Littlefield, Lanham, MD Longino HE (2002) The fate of knowledge. Princeton University Press, Princeton, NJ

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Merton RK (1973[1942]) The normative structure of science. In: Merton RK, Storer NW (ed) The sociology of science. University of Chicago Press, Chicago, IL, pp 267–278 Mulkay M (1976) Norms and ideology in science. Soc Sci Inform 15:637–656 Radder H (1996) In and about the world. State University of New York Press, Albany, NY Radder H (2003) Wetenschap als koopwaar? Een filosofische kritiek. VU Boekhandel/Uitgeverij, Amsterdam Radder H (2004) Exploiting abstract possibilities: a critique of the concept and practice of product patenting. J Agric Environ Ethics 17:275–291 Radder H (2006) The world observed/The world conceived. University of Pittsburgh Press, Pittsburgh Radder H (forthcoming) Mertonian values, scientific norms, and the commodification of academic research. In: Radder H (ed) The commodification of academic research: analyses, assessments, alternatives. University of Pittsburgh Press, Pittsburgh Resnik DB (2007) The price of truth. How money affects the norms of science. Oxford University Press, New York Sismondo S (2004) An introduction to science and technology studies. Blackwell, Malden Shulman S (1999) Owning the future. Houghton Mifflin, Boston, MA Sterckx S (2000) European patent law and biotechnological inventions. In: Sterckx S (ed) Biotechnology, patents and morality, 2nd edn. Ashgate, Aldershot, pp 1–112 Tuunainen J, Knuuttila T (2008) Determining the norms of science: from epistemological criteria to local struggle on organizational rules? In: V¨alimaa J, Ylijoki O-H (eds) Cultural perspectives on higher education. Springer, Berlin, pp 138–153

Chapter 20

‘I Want to Look Like a Lady, Not Like a Factory Worker’ Rose Rand, a Woman Philosopher of the Vienna Circle Maria Rentetzi

“I know her strangeness” Otto Neurath wrote to Esther Simpson, secretary of the Society for the Protection of Science and Learning, on December 6, 1941. He was referring to Rose Rand, of whom he also said “I know how difficult it is to help her without providing for her a minimum in privacy.” Neurath concludes his letter with a distressing ascertainment: “What a sad world.”1 This letter is part of a significant correspondence archive at Oxford University’s Bodleian Library that covers segments of Rose Rand’s life as an e´ migr´e in England. Known as the Jewish woman who transcribed the meetings of the Vienna Circle, Rand was forced to emigrate from Nazi-occupied Austria in 1938. Struggling to continue her philosophical work, she was instead advised to take up a monotonous manual job in a metal factory. It was then she proclaimed, “I want to look like a lady, not like a factory worker” (Simpson to Wittgenstein, 5 November 1943, BL 180).

M. Rentetzi () Assistant Professor, National Technical University of Athens, Department of Humanities, Social Sciences and Law; Faculty of Applied Mathematics and Physical Sciences, Zografou Campus, 15780 Zografou, Athens, Greece e-mail: [email protected] 1 Otto Neurath to Esther Simpson, 18 December 1941, Bodleian Library, Special Collections and Western Manuscripts, Archive of the Society for the Protection of Science and Learning, 232, hereafter BL.

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 20, c Springer Science+Business Media B.V. 2010 

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Figure 1 Rose Rand in England on 8 February 1949, (photo RR 1–25–26, courtesy of Archives of Scientific Philosophy, Rose Rand Collection, Hillman Library, University of Pittsburgh)

A second remarkable collection of Rand’s papers is to be found at the Archives of Scientific Philosophy at the University of Pittsburgh. Covering a considerable span of time from Rand’s early years in Vienna to her second emigration to the United States in 1954, this collection comprises her personal and professional records, working papers, and a significant amount of correspondence (Figure 1). Despite the richness of these archival sources, Rand has received only a modest amount of attention by historians of philosophy, let alone by philosophers themselves. A fullyfledged biography is still not available (Hamacher-Hermes 2003). Recent works, such as Mathias Iven’s on Rand’s relation to Ludwig Wittgenstein and another by Adelheid Hamacher-Hermes that focuses on Rand’s work on logic, set the stage for further research. Moreover, they bring to the foreground Rand’s remarkable and complex persona along with her philosophical writings, questioning established accounts of the history of philosophy (Iven 2004; Hamacher-Hermes 2003). But what is Rand known for? Is it merely for her role as the ‘secretary’ of the Vienna Circle or is there some merit in her philosophical writings? Despite the testimony of philosophers such as Rudolf Carnap, Felix Kaufmann, and Otto Neurath, to the effect that Rand was indeed a promising philosopher, she was unable to ascend the academic ladder. Rand’s case, nonetheless, is not unique in the male dominated terrain of philosophy. Women’s contributions to philosophical thought have frequently been disparaged, their works have rarely been reprinted, and their significance has been belittled. Often, when women philosophers are remembered at all, they are remembered for the wrong reasons. As the philosopher Jane Duran notes, “in many instances their [women writing on philosophical issues] work has been believed to be an attack on the work of some noteworthy male, or perhaps a failure to understand his work completely. This, combined with female authorship, has no doubt led to work’s being ‘lost’ or ‘misplaced”’ (Durane 2006, 3). In her attempt to answer the question of why there have been so few women philosophers, historian Gerda Lerner highlights issues of systematic educational disadvantage, material constraints, and social restrictions (Lerner 2000, 8). Historically, the few who persisted against all

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odds appear in the pages of standard reference books such as Mary Ellen Waithe’s A History of Women’s Philosophers (Waithe, 1991) or Linda McAlister’s Hypatia’s Daughters (McAlister, 1996). Rand’s name, however, does not appear on the pages of even such standard biographical dictionaries. Caught in a transition period of forced migration from Nazi Austria, Rand’s career as a philosopher was deeply affected to the point of preventing her from gaining professional status. Within a male dominated discipline, the lack of an academic position proved to be an insuperable obstacle to Rand’s recognition. Even in “Red” Vienna, where several intellectual circles were known for their egalitarian values, philosophers tended to be more conservative in this respect than others in different disciplines. In a recent biography on Karl Popper, Malachi Haim Hacohen draws attention to the fact that the presence of women in Viennese philosophical circles was insignificant in comparison with the liberal circles of the psychologists Karl and Charlotte B¨uhler (Hacohen 2000). Moving from Vienna to Oxford and then to the United States, Rand came up against diverse cultural challenges and equally diverse gendered cultures. This paper explores Rand’s years in Vienna both as a student of Rudolf Carnap and Moritz Schlick and as a member of their circle, contrasting it with another intellectual circle, that of the psychologists.

20.1 Rand’s Early Years in Vienna Rozalia Rand was born on June 14, 1903 to Jewish parents in Lemberg, the capital of Galicia. At the time, Galicia was the Austrian Empire’s northernmost and most populous province. It also occupied an important place on the Jewish Diaspora map. In 1900, Galician Jews made up 66.9% of all Jews in the Hapsburg Monarchy, excluding Hungary. Economic difficulties and the limited possibilities available to Jews for improving their social status drove many away from their homeland to other Hapsburg lands (Wrobel 1994). In the meantime, the dissolution of the Dual Monarchy at the end of the First World War resulted in the loss of Galicia, which now belonged to the newly created state of Poland. This forced many Galician Jews who had already left the region to a somewhat stateless position, while those who remained suffered a devastating pogrom in 1918. According to New York Times ‘riot and robber developed into the most awful pogrom ever heard of.’ (NYT 2/12/1918, “Charges Officials Aided in Pogroms). Most probably Rand’s parents left about that time and moved to Vienna. In 1920 we find Rand registered at W¨ahringer M¨adchen-Mittelschulen. Two years later she moved to the public Reform-Realgymnasium at the second district of Vienna, from which she graduated in July 1924 (RR 2–3–15, 1).2 In the midst of important political changes in Vienna, Rand enrolled at the Faculty of Philosophy at the city’s university in October 1924, as one of 671 women. That year the university’s female students accounted for almost 35% of 2 Rose Rand Collection, Archives of Scientific Philosophy, Hillman Library of the University of Pittsburgh, Special Collections Department, hereafter RR.

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the total number of students (Tuma 1990, 81). During the 1920s there was indeed a substantial increase in the percentage of enrolled women, the result of a program set up by the Social Democratic Party (Probst 1987, 468). Over the next eight semesters, her Meldunsgbuch lists several philosophy courses taught mostly by Robert Reininger and Moritz Schlick, but also by Hans Hahn, Heinrich Gomperz, and Rudolf Carnap (Figure 2). The logic course was taught by Karl B¨uhler, whose psychology course Rand attended for two semesters. Rand chose physics as her minor and took courses taught by the physicists Stefan Meyer, Gustav J¨ager, and Egon von Schweidler (RR 2–3–15, 2; RR 2–1–5).

Figure 2 The first two pages of Rose Rand’s Meldungsbuch at the Philosophical Faculty of the University of Vienna (photo RR 2–3–15, courtesy of Archives of Scientific Philosophy, Rose Rand Collection, Hillman Library, University of Pittsburgh)

What was otherwise a fairly typical curriculum proved to be unusual in one respect. Rand’s professors in philosophy, psychology, and physics all belonged to a wider intellectual circle of liberals and socialists whose political profiles posed a major challenge to the fairly conservative university (Stadler 1995). Figures such as Schlick, Reininger, and B¨uhler, nonetheless, changed the city’s intellectual map by creating alternative centers of power on the margins of the academy. All held posts at the Faculty of Philosophy around the same time, despite opposition by conservative circles. The Vienna Circle and the Institute of Psychology, the institutions that they created and which flourished within the political context known as “Red” Vienna, were directly or indirectly supported by the Social Democrats.

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20.2 The Intellectual Circles of Red Vienna: The Vienna Circle Versus the Institute for Psychology Immediately after the First World War Social Democrats emerged as the strongest party in Austria and one that dominated mostly in the capital and the industrial regions. Weakened by unstable coalition governments with the Christian Socialists, the Austrian Democrats eventually lost their influence on major policy decisions as the last coalition dissolved in June 1920. Their only option now was to focus their energies on the municipal level. Indeed, on May 4th, 1919 Social Democrats won Vienna’s municipal elections mostly by extending the franchise to women and young adults. From 1919 to 1934 they carried out extensive social reforms that drastically transformed the city (Rabinbach 1983). This Red Vienna period has been historically considered as the ‘model of cultural experimentation in the socialist movement’ (Gruber 1991, vii). Under the leadership of Austromarxists such as Otto Bauer, Karl Seitz, Otto Gl¨ockel, and Julius Tandler, the Social Democrats sought to reform public education, to improve housing and transform architecture, to launch workers’ health and welfare programs, and to form a distinct socialist party culture. Vienna’s intellectual life during the interwar years was also marked by the emergence of several intellectual circles that flourished on the margins of the academy and were supported by the socialists. These included the Vienna Circle, the philosophical movement which, given its anti-metaphysical and empiricist stance and, most importantly, efforts by its members to forge ties with political institutions and movements in Austria and in Europe in general, came up against the harsh politics of the German nationalists and National Socialists by the end of the 1920s (Stadler 1995, 44). The core members of the group included Moritz Schlick Ordinarius Professor (1922–1933), Rudolf Carnap Privatdozent and Titularprofessor (1926– 1931), Viktor Kraft also Privatdozent and Titularprofessor (1914–1938), Hans Hahn Ordinarius in Mathematics since 1921, all at the Philosophical Faculty of the University of Vienna. Also Felix Kaufman, a lecturer in the philosophy of jurisprudence, the German mathematician Kurt Reidemeister, Philip Frank, professor of physics at the University of Prague, and the economist Otto Neurath. The Vienna Circle was known as an empiricist, anti-metaphysical, and languageoriented philosophical circle whose members participated in progressive organizations and saw a social mission for their scientific philosophy (Hacohen 2000; Feigle 1968; Stadler 1995; Reisch 2005). As Thomas Uebel has convincingly argued, the Vienna Circle was not a monolithic movement of philosophers who tried to rehash traditional foundationalist epistemology but rather a forum whose members questioned the very nature of philosophy (Uebel 1996). But this meant that the Circle posed a threat to the Christian world-view and the German idealism that underpinned the philosophical life of the University of Vienna. The group was established in 1922 when the mathematician Moritz Schlick was appointed to Ernst Mach’s former chair at the University of Vienna. From 1924 onwards, through Schlick’s initiative, the members of the Vienna Circle began a series of regular meetings to discuss their philosophical interests. Though this was not

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widely known, the Vienna Circle also included a few women. Rand was actually the only one whose name was in the protocol-list of the Circle’s meetings (Korotin 1997, 301–303; Rose Rand’s curriculum vitae, RR 2–5–21). Yet, one of the first to participate in Thursday’s meetings was Olga Hahn. Even though blind, Hahn studied mathematics at the University of Vienna with the help of Otto Neurath and his first wife, Anna Schapire. In 1912, after Anna’s death, Neurath married Olga. Her brother Hans introduced both Neurath and Olga to the Circle’s meetings (Cartwright et al. 1996, 12–13). Another woman, the Viennese mathematician Olga Taussky-Todd was introduced to the Circle by Hahn’s assistant, the mathematician Walter Mayer, and attended the meetings occasionally: “I was probably the youngest in age there and I did not associate myself with it for the purpose of working in it, but in the expectation of using their ideas to further my mathematical work” (Tausky-Todd 1985, 319). But her greater dedication to mathematics, as opposed to philosophy, made Tausky-Todd leave the Circle soon after. The psychologist Else Frenkel also joined the group (Hacohen 2000, 187). Frenkel came from the same town as Rand and their life stories crossed several times, though they eventually took completely different turns. Frenkel’s Jewish parents left Lemberg in 1914 to escape the pogrom that year and moved to Vienna where her father established his own bank. In contrast to Rand who received public education, Frenkel graduated from Eugenie Schwarzwald’s girls’ gymnasium in 1926, a prestigious private institution at Vienna’s first district 2 years after Rand (Anderson 1992). She immediately enrolled at the University of Vienna to study psychology. Already in 1922 Otto Gl¨ockel, president of the Vienna School Council and a leading figure of the socialist movement of educational reform, had offered one of the philosophy chairs at the University of Vienna to the eminent German psychologist Karl B¨uhler. He was eager that the university appoint a philosophy professor who specialized in experimental psychology, and B¨uhler matched his expectations. Furthermore, B¨uhler would be accompanied by his wife, Charlotte B¨uhler (n´ee Malachowski), a Berliner Jew, who was a child psychologist. In Gl¨ockel’s mind, the two could turn Vienna into the center for psychology research. He was right. The University of Vienna lacked a specialized psychology department and thus negotiations with B¨uhler were threatened with failure. On behalf of the city of Vienna, Gl¨ockel guaranteed the establishment of a municipal institution dedicated to advancing teacher training and for use as a university institute on psychology. The agreement led to the establishment of the Institute of Psychology under the auspices of the city of Vienna in 1923 (Benetka 1995, 128). B¨uhler was under the obligation to teach at the University while the city agreed to provide him with accommodation and funds for one assistant and one mechanic at the Vienna School Supervisory Council. In the following years, the institute’s prominence made it the only European institution to receive funds from the Rockefeller Foundation for the purpose of constructing a biologically grounded theory of development. The very structure of the institute reflected the political tensions between the Social Democratic Party and the Ministry of Education, which was controlled by the

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Christian Socialists. Its double status was reflected in the fact that it was known both as “The Institute of Psychology of the City of Vienna” and “The Institute of Psychology of the University of Vienna”. But for Charlotte B¨uhler this was advantageous: the city appointed her as ordentlichen Assistentin at the institute and she was also de facto a university assistant. Only in 1929 did the university faculty appoint her as associate professor. Furthermore, B¨uhler directed the Reception Center for Children (Kinder¨ubernahmestelle), a modern center that monitored and took care of abused or neglected children from problematic families. For Charlotte B¨uhler, the center provided an institutional setting to advance her practical studies on child psychology (Benetka 1995, 128). Every Wednesday night the B¨uhlers held a psychology colloquium at the institute, which provided collaborators and doctoral students with a context to present their work and test their theories. In addition, students were not merely allowed but actually encouraged to follow the B¨uhlers to international congresses to present their own work. This brought most of the students – men and women alike – into close contact with the international community of psychologists and worked as a springboard for their own careers (Benetka 1995, 130). Indeed, besides sponsoring innovative projects, Charlotte B¨uhler opened doors for women. Many young and committed educationalists entered the institute, among them prominent women psychologists such as Frenkel-Brunswik, Marie Jahoda, Edith Weisskopf, Else K¨ohler, and Editha Sterba (Gardner and Stevens 1992). Lote Danziger was Charlotte’s assistant and K¨athe Wolf offered courses in child psychology. The boldness of Jahoda’s words is indicative of women’s new self-confidence during Red Vienna. “At the time I was completely convinced that I would once become socialist minister of education in Austria. There was no question about it!” (Benetka 1995, 128). Frenkel worked closely with Karl B¨uhler as she completed her dissertation on the principles of associationism in psychology. In 1930 she became Charlotte B¨uhler’s assistant, a position that was supported by a grant from the Rockefeller Foundation (Paier 1996). There she met Egon Brunswik, her husband to be, who was also B¨uhler’s assistant and member of the Vienna Circle (Smith 1990, 89). Earlier in 1922 he was a candidate for the position to which Schlick was eventually appointed and was probably he who introduced Frenkel to the Circle’s meetings. Brunswik left Vienna in 1935 to become a visiting fellow at the University of California Berkeley, where Frenkel joined him after the Anschluss. The two in fact got married on the ship that brought her to New York City harbor (Paier 1996). Her marital status turned out to be an advantage vis-`a-vis her appointment to a position at the Institute of Child Welfare at Berkeley. It was also instrumental in her appointment as lecturer at the department of psychology (Smith 1990, 89). She never got tenure, though it should be borne in mind that during the 1940s and 1950s women were scarcely considered for tenure track positions, and were instead hired on annual contracts (Rossiter 1995). Frenkel’s later career as a research psychologist at the Institute of Child Welfare was greatly influenced by two Viennese intellectual movements. One was psychoanalysis, which she resumed in 1937 with Egon Kris – though it is interesting that

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she kept this a secret from the B¨uhlers (Smith 1990; Ash 1995, 239). The second was the Vienna Circle. During her studies at the University she attended courses taught by Schlick and Carnap, but only later did she occasionally attend their meetings (Paier 1996). Both intellectual groups left a major mark on her subsequent work. While she was in American exile in 1954, Frenkel published The Integration of Psychoanalysis into the Unity of Science. It was there that she argued for the scientific status of Freud’s theory and defended the idea that psychoanalysis was a legitimate part of the unity of science (Borcher 2003).

20.3 Rand’s Participation in the Vienna Circle Although Rand’s career is not in any way comparable to Frenkel’s relatively successful integration within the American academic system, both shared an interest in philosophy and psychology. Rand completed her undergraduate studies in philosophy in 1928 and immediately began work on her dissertation. She focused on the philosophy of Tadeusz Kotarbinski’s, a Polish logician and a major philosopher of the Lvov-Warsaw School. As Ilkka Niiniluoto has recently argued, Kotarbinski’s philosophy of science has not received as much attention as his contributions to semantics and ontology (Niiniluoto 2002). Still, Rand had already recognized the importance of his work by the end of the 1930s. On July 6, 1937 Robert Reininger approved her thesis, which had as its second referee Richard Meister, professor of Physics at the University of Vienna (RR 2–3–28). At the time Reininger actually questioned the value of her aim to collect and analyze approximately 18 of Kotarbinski works. But he also said the following: Despite the high appraisal of her philosopher, the author shows to be free at all of dogmatic prejudices in respect to logistics and neopositivism. These [Rand’s] critical comments reveal a trained reasoning and a good orientation in philosophical problems. They represent the ultimate high accomplishment of the author and prove the sufficient level of scientific maturity (Iven 2004, 19).

Meanwhile, Rand tried to carve out a niche for herself within the male dominated network of Vienna’s philosophers. During the fall semester of 1933–1934, she held a series of seminars on the philosophy of the Vienna Circle at the Ottakring Volkhochschule, following an invitation by Edgar Zilsel, a Circle member (RR 2–5–1). In 1936 she took part in the Krakow Philosophical Congress, where she presented the paper “The Logic of Various Kinds of Sentences” (Hamacher-Hermes 2003, 367). Her paper was published in the Polish journal Przeglad filozoficzny (Philosophical Review) in same year (Rand 1936). In 1937, even before she passed her final Ph.D. exam (July 21, 1938), Rand published a second paper drawn from her doctoral work in Erkenntnis (Rand 1938). A year later, a further paper was published in Internationale Zeitschrift f¨ur Theorie des Rechts (Rand 1939). In a letter of recommendation in 1938, Felix Kaufmann wrote: “I have known Miss Rose Rand as a specially gifted philosopher with high promises.” Recognizing

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this ability, Schlick had admitted her to his “private discussion circle” in the late 1920s, long before she was awarded her Ph.D. In Kaufmann’s words “this admission was a special distinction also because of the fact that the circle constituted almost exclusively of male members” (RR 2–5–2). Indeed, the core group of the Vienna Circle remained quite exclusive and a personal invitation from Schlick was the only admission ticket. Despite the fact that Rand was among the few – if not the only – permanent female participant at Schlick’s meetings, she was an opinionated and outspoken member of the group. For instance, though she considered Wittgenstein to be a genius, she believed that the style of his Tractatus was a “manifestation of helplessness rather than of a deliberate choice.” For Rand, Wittgenstein had failed to express his views adequately. Naess, who ranked her as one of the two most prominent young members of the seminar, writes: “Later she gave lectures on Wittgenstein at Cambridge, but her consistently hyper-critical comments contributed to the closure of her teaching” (Naess 1993, 15). Wittgenstein’s response to Rand’s kind request for advice and a letter of recommendation on October 5, 1946 confirms Naess’ hypothesis. I am unable to recommend you for an academic job myself, and I can’t advice you to try for such a job as I do not think that you have a chance. The only advice I can give you is to do work in which you can make use of your manual skill and not to think that it is shameful to do decent work with your hands. As this is all that I can say, please stop asking me for my opinion and advice. May a ray of real intelligence enlighten you! (RR 3–13A-22). During the time she lived in Vienna, and despite a main focus on philosophy and especially logic, Rand reached beyond the philosophers’ network to the psychologists. From 1930 to 1937 she conducted research at the University of Vienna’s Psychiatric Clinic under the directorship of Otto P¨otzl. There, she worked with patients suffering from mental and nervous disorders, but also on numerous cases at the clinic’s Women’s Ward. P¨otzl later wrote “I am convinced that Dr Rose Rand is uncommonly gifted for the right treatment of insane patients and for their advantageous influence. Her deep psychological knowledge is a great help for her work” (4 June 1938, RR 2–5–7). But soon the political upheavals in Vienna forced Rand to exile. With the help of Otto Neurath and Susan Stebbing, an English logician, Rand arrived in England in 1939. Despite her persistent efforts to attain an academic position, Rand was only able to work as a nurse and, later on, in a metal factory, striving all along to adjust and survive. Always short of money, she taught evening classes in German and psychology, translated several philosophical papers, and in vein tried to keep up with her own philosophical work (Curriculum Vitae, RR 2–1–5). Yet, she was constantly reminded that “philosophy : : : is rather an art, that does not payunfortunately” (Neurath to Rand, 2 May 1945, RR 3–11–81) or that “there is no demand for philosophers right now” (Simpson to Neurath, 13 December 1941, BL 230). Moreover, her persistence to continue her philosophical work was perceived as a problem. In a telling report to Simpson, May Hermes, secretary of the International Federation of University Women, wrote that “The difficulty up till now has

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been that Miss Rand would insist on the necessity for carrying on her philosophical work” (12 February 1942, BL 360). Indeed, Rand was unable to get an academic position either in England or in the United States where she immigrated in 1954. The reason was obvious. “Since there was no possibility for women to teach and in particular not in philosophy I resigned from my post in Notre Dame University and returned to the East of the States and tried to get a fellowship from the National Science Foundation” (Curriculum Vitae, RR 2–1–5). By that time Rand was already 51-years-old, too late to adjust to American academic life. Until her death on July 28, 1980 at the age of 77 in Princeton, Rand had held only temporary teaching positions and lived on soft money. Her correspondence with her Viennese friend Herta Leng reveals a predominantly miserable and unhappy life (from RR 3–3–45 to RR 3–3–72).

20.4 Why So Few Women in the Vienna Circle? An obvious question emerges from the study of Rand’s life and work in Vienna: why was the participation of women insignificant in the Vienna Circle, an otherwise ground-breaking intellectual forum? I believe that there are two ways to answer this question. One is to argue, as Malachi Hacochen does, that during the interwar years philosophy was not an expanding profession likely to attract women (Hacochen 2000, 187). Undoubtedly, the percentage of women who studied philosophy dropped dramatically: whereas before the war women studying philosophy accounted for approximately 80% of the total number of students enrolled at the Faculty of Philosophy, between 1928 and 1929 this fell to 29% – still a considerable number (Tuma 1990, 87–88). During the 1920s and early 1930s, women could primarily look forward to careers as teachers, a highly competitive profession that even required a Ph.D. for employment at the top high schools. This may explain the comparatively high percentage of women who chose philosophy as their major. But women philosophers, who – like Rand – sought academic positions, stood no chance: as women in a conservative university and as Jews in a hostile city they were doubly disadvantaged. But there is a second way to explain the male dominated milieu of the Vienna Circle, especially if we compare it to the Institute of Psychology. There was no analogy between Schlick and Charlotte B¨uhler in relation to the women attending his seminars. He was not the welcoming figure who would create a friendly atmosphere for newcomers, regardless of their gender. Arne Naess, a Norwegian philosopher who attended Schlick’s seminars had “little to say” about him. Few of us had any access to his private life. We felt him as somewhat ‘distant’ and we called him an aristocrat. He did not talk very much. When a discussion led us into an impasse he might ask ‘What would Wittgenstein say here?’ When someone offered a quotation of Wittgenstein’s writing or from his appearance to seminars or private conversations, it was clear that only very, very clever interpretations could be accepted (Naess 1993, 14).

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Indeed, Schlick seems to have been formal and strict with Rand as well. In a letter to her in which he discusses formal issues on the use of the seminar room, he underlines that if she wished to speak with him, she could do so “only during my official office hours” (28 October 1935, RR 3–5–29). Devotion to research involves enthusiasm, a significant part of which usually stems from supportive and encouraging individuals within one’s field. If we also take into account the fact philosophy offered few professional opportunities to women, we can see how the lack of support and mentoring resulted in their slim participation within the Vienna Circle. Yet although the presence of women was insignificant, Rand’s prominence in the Vienna Circle was acknowledged by her peers and colleagues. When she moved to England, however, she was faced with an emerging gender hierarchy both within academic philosophy and applied psychology. This mentality clashed with her own, a blend of the egalitarianism and socialism of Vienna’s philosophical circles but also of the attitudes of clinical psychology, a profession surprisingly open to women. In addition to her difficult personality, all the above pushed Rand to obscurity and let history of philosophy oblivious of her philosophical talents. Acknowledgments I would like to thank Adelheid Hamacher-Hermes for suggesting sources in relation to Rose Rand. Also my thanks go to archivist Brigitta Arden from the Archives of Scientific Philosophy, Rose Rand Collection and the archivist Colin Harris from the Bodleian Library for providing archival materials and further sources. To Spiros Petrounakos I owe my acknowledgments for editing an earlier version of this paper.

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Hacohen MH (2000) Karl Popper: the formative years, 1902–1945. Cambridge University Press, Cambridge Hamacher-Hermes A (2003) Rose Rand: a woman in logic. In: Friedrich S (ed) The Vienna Circle and logical empiricism: re-evaluation and future perspectives. Kluwer, Boston, MA, pp 365–378 Iven M (2004) Rand und Wittgenstein: Versuch einer Ann¨aherung. Peter Lang: Europ¨aische Verlag der Wissenschaften. Wittgensetin Studien, 9 Korotin I (1997) Auf eisigen Firnen, Zur intellectuellen Tradition von Frauen. In: Stadler F (ed) ¨ Wissenschafts als Kultur, Osterreichs Beitrag zur Moderne. Ver¨offentlichungen des Wiener Kreises, Wien, pp 291–306, Bd 6 Lerner G (2000) Why have there been so few women philosophers? In: Tongas C, Ebenreck S (eds) Presenting women philosophers. Temple University Press, Philadelphia, PA, pp 5–14 McAlister L (1996) Hypatia’s daughters: eighteen hundred years of women philosophers. Indiana University Press, Bloomington, IN Naess A (1993) Logical empiricism and the uniqueness of the Schlick seminar: a personal experience with consequences. In: Stadler F (ed) Scientific philosophy: origins and developments. Kluwer, Boston, MA, pp 11–25 Niiniluoto I (2002) Kotarbinski as a scientific realist. Erkenntnis 56:63–82 Paier D (1996) Else Frenkel-Brunswik (1908–1958). Archiv f¨ur die Geschichte der Soziologie in ¨ Osterreich, Newsletter 13:11–12 Probst E (1987) Emigration und Exil o¨ sterreichischer Wissenschafterinnen. In: Stadler F (ed) Vertriebene Vernunft I, Emigration und Exil o¨ sterreichischer Wissenschafter 1930–1940. Jugend und Volk, M¨unchen, pp 444–470 Rabinbach A (1983) The crisis of Austrian socialism: from Red Vienna to civil war 1927–1934. The University of Chicago Press, Chicago, IL Rand R (1936) Die Logic der verschiedenen Arten von S¨atzen. Przeglad filozoficzny 39:438 Rand R (1937) Kotarbinskis Philosophie auf Grund seines Hauptwerkes: Elemente der Erkenntnistheorie, der Logic und Methodologie der Wissenschaften. Erkenntnis 7:92–120 Rand R (1939) Die Logic der Forderungss¨atze. Internationale Zeitschrift f¨ur Theorie des Rechts, Neue Folge 1:308–322 Reisch G (2005) How the cold war transformed philosophy of science: the icy slopes of logic. Cambridge University Press, Cambridge Rossiter M (1995) Women scientists in America: before affirmative action 1940–1972. The John Hopkins University Press, Baltimore, MD Smith B (1990) Else Frenkel-Brunwik (1908–1958). In: O’Connell A, Felipe Russo N (eds) Women in psychology: a bio-bibliographic sourcebook. Greenwood, New York, pp 88–95 Stadler F (1995) The Vienna Circle and the University of Vienna. In: Stadler F, Weibel P (eds) The cultural exodus from Austria. Springer, Wien, New York, pp 14–26 Tausky-Todd O (1985) Olga Tausky-Todd: an autobiographical essay. In: Albers D, Alexaderson G (eds) Mathematical people: profiles and interviews. Birkh¨auser, Boston, MA, pp 309–336 Tuma R (1990) Die o¨ sterreichischen Studentinnen der Universit¨at Wien (ab 1897) In: Waltraud H, Tichy M (eds) Durch Erkenntnis zu Freiheit und Gl¨uck. Frauen an der Universit¨at Wien. Universit¨at Wien, Schriftenreihe des Universit¨atsarchivs, Band 5, Wien, pp 79–107 Uebel T (1996) Anti-foundationalism and the Vienna Circle’s revolution in philosophy. Br J Philos Sci 47(3):415–440 Waithe ME (1991) A history of women philosophers. Modern women philosophers, vol III. Kluwer Academic, Boston, MA Wrobel P (1994) The Jews of Galicia under Austrian-Polish rule, 1867–1918. Austrian Hist Yearbook XXV:97–138

Chapter 21

Natural Kind Theory as a Tool for Philosophers of Science Thomas A.C. Reydon

21.1 Introduction Opinions are divided on the question whether the notion of ‘natural kind’ plays any important role in philosophy of science – that is, on whether having a satisfactory theory of natural kinds is a prerequisite for the success of the philosophical project of trying to understand what science is and how it works. Some authors have entertained a negative view of the importance of the notion of ‘natural kind’ in philosophy of science, arguing that the idea of natural kinds features only in the early stages of the development of scientific fields of work and ceases to play a role once a field becomes established. Others have defended a similar view with the argument that natural kinds are found only on the most fundamental levels of organization, so that most scientific fields of work do not study natural kinds and, consequently, most fields of science can be studied without making use of the idea of natural kinds. But the actual situation in many domains of philosophy of science gives rise to a different picture: the notion of ‘natural kind’ can be seen to play a role in many domains of philosophy that focus on a particular special science of cluster of sciences. In fields like the philosophy of chemistry, the philosophy of biology, the philosophy of psychology and cognitive science and the philosophy of economics an “enthusiasm for natural kinds” – as Boyd (1991) has called it – can be seen. Recent discussions in these fields have addressed the question whether chemical kinds, biological species, kinds of genes, the category of emotion and the various kinds of emotions, consciousness, the categories of concept and knowledge, economic kinds, etc. could be conceived of as natural kinds and, if not, what this would mean for the field of science under consideration.1

T.A.C. Reydon () Center for Philosophy and Ethics of Science (ZEWW), Leibniz University of Hannover, Im Moore 21, D-30167 Hannover, Germany e-mail: [email protected] 1

For reasons of space, I do not provide references. Examples are easy to find in the literature.

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What are we to make of this difference of opinion? In the present paper I shall argue that the dim view of the importance of the notion of ‘natural kinds’ for philosophy of science is not justified: while it roots in a particular tradition of thinking about the problem of natural kinds, there is an alternative way of thinking about natural kinds that does not give rise to such a dim view. I shall begin in Section 21.2 by discussing the main reasons for thinking that the idea of natural kinds is not all that important in science and hence not in philosophy of science. Section 21.3 then traces two different ways in which philosophers have conceived of the problem of natural kinds, while in Section 21.4. I shall examine in which respects the two main approaches to the problem of natural kinds are deficient. I shall conclude in Section 21.5 by returning the central issue of this paper, i.e., the importance of natural kind theory for philosophy of science.

21.2 The Alleged Uselessness of Natural Kind Theories The classic argument that science has no need for the doctrine of natural kinds – and the implication connected with it, that philosophy of science has no use for a theory of natural kinds – is due to Bertrand Russell (1948) and W.V. Quine (1969). On their view, the assumption that there are kinds in nature and that an important part of scientific activity consists in grouping things under study in such a way that the obtained groupings represented these natural kinds constituted only a temporary phase in the development of scientific fields of work. Any natural kinds that featured in a field of science, Russell and Quine held, would ultimately be reduced away as the field became more established. (The presumption was that kinds could ultimately be reduced to and explained by deeper-lying laws of nature.) Thus according to Russell, “[t]he doctrine of natural kinds, though useful in establishing Œ: : : prescientific inductions Œ: : :, is only an approximate and transitional assumption on the road to more fundamental laws of a different kind” (1948: 462; emphasis added). And for Quine, the fact that a field of work no longer needed an irreducible notion of ‘natural kind’ even constituted an indication that it had finally reached maturity (1969: 22). More recent authors, such as Paul Churchland (1985) and Brian Ellis (2001, 2002), have provided different reasons for thinking that the notion of ‘natural kinds’ is not particularly central in philosophy of science. On their view, if natural kinds play a key role in science they do so only in those domains that study the most fundamental levels of organization in nature. Churchland based this claim on the widespread assumption that natural kinds and laws of nature are inseparably coupled: natural kinds are often thought to be just those kinds that are referred to in statements of laws of nature and, conversely, laws of nature are thought of as precisely those generalizations that reach over natural kinds. And as “proper” laws of nature (in the traditional strict sense of generalizations that hold at any time and any location in the universe without allowing for any exceptions) are only found in the physical and perhaps some of the chemical sciences, it is only there that we find

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“proper” natural kinds. Therefore, Churchland concluded, natural kinds constitute an “aristocratic elite” among the kinds that feature in the various domains of science: while most fields of science study mere “practical kinds”, only a select few are concerned with natural kinds. (Indeed, Churchland acknowledged the possibility that the elite is so exclusive that there are no natural kinds at all.). As an advocate of a form of traditional essentialism, for Ellis the crucial coupling is between natural kinds and kind essences, rather than between natural kinds and laws of nature.2 Ellis endorses a traditional view of natural kinds, according to which any natural kind is characterized by a kind essence, that is, a property or set of properties that all and only the members of the kind possess and that constitutes the (separately) necessary and (jointly) sufficient condition for being a member of the kind in question. On this view, natural kinds exist only in those regions of nature where things by themselves neatly fall into disjoint groups for which such kind essences exist – in Ellis’s words, in regions where there are clear lines between different kinds, that are drawn by nature and not by us (2001: 19–20). As this supposedly is the case only on the most fundamental levels of organization (the levels of elementary particles, atoms and simple molecules – for macromolecules the borders between different kinds already become vague), the idea of natural kinds only plays a role in those domains of science that study these most fundamental levels. Sciences that are pitched at higher levels of organization – most prominently the life sciences, the cognitive sciences and the social sciences – thus do not study natural kinds.3 Both Churchland’s and Ellis’s views would imply that the notion of ‘natural kind’ is relevant in philosophy of science only when the focus is on one of the physical or chemical sciences that actually study natural kinds – most of philosophy of science, thus, would be able to get by just fine without having a theory of natural kinds. There are, then, two basic arguments to the extent that natural kinds play at most a very minor role in science itself and thus in philosophy of science: natural kinds feature in scientific fields only at early stages of their development, or they feature only in those few fields that study the most fundamental levels of organization.4

2

But an important part of Ellis’s philosophical project in Scientific Essentialism (2001) is to ground the laws of nature in the natural kinds that lie at the focus of the fundamental fields of science. 3 This view is strengthened by recent developments in philosophy of biology and of social science. Hacking (1995), for example, argued that the kinds used in the human sciences cannot be conceived of as natural kinds, because human beings can themselves influence the way in which they are classified. And in the last 30–40 years biologists and philosophers of biology became convinced that biological species – one of the long-standing paradigms of natural kinds – probably should not be conceived of as kinds but as concrete individuals. However, despite several decades of debate on the ontology of biological species, this issue still remains undecided and in recent years several philosophers have argued for a return to a view of species as natural kinds (for a very recent example, see Elder (2008)). 4 Hacking (2007) recently presented a third argument for the uselessness of natural kind theories, namely that the history of the philosophical discussion on the topic shows that there are no philosophical questions that arise specifically with respect to natural kinds. That is, all interesting questions about natural kinds arise in a more general context and framing them using the notion of

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If one or both of these are correct, the notion of ‘natural kind’ and the theory of natural kinds do not constitute core parts of the philosopher of science’s toolbox. But are they correct? More clarity on this can be achieved by realizing that the assumptions that lie at the root of these arguments are metaphysical: they are assumptions about what nature is like and how the kinds that exist in nature are related to the laws of nature and the essences of things.5 As such, they are part of a longstanding line of thinking about natural kinds and stand or fall with this line of work. In what follows, I shall argue that two fundamentally different philosophical lines of work on the idea of natural kinds can be identified when taking a closer look at the history of philosophy. Next to the aforementioned line that leads to a rather dim view of the role that the notion of ‘natural kind’ plays in science, there is another line of work that gives rise to a much more optimistic view. However, this latter line of work runs into problems of its own.

21.3 Two Views of the Problem of Natural Kinds A good location to begin an examination of the philosophical history of the topic of natural kinds is a discussion between Ian Hacking and Richard Boyd.6 According to Hacking (1991a, b), the origins of the philosophical discussion on natural kinds are located in nineteenth-century British empiricism. Hacking pointed out that ‘natural kind’ was first introduced into philosophy as a technical term by the logician John Venn in his 1866 treatise on probability, The Logic of Chance. Venn apparently took the notion of ‘kind’ from the works of William Whewell (The Philosophy of the Inductive Sciences, 1840) and John Stuart Mill (who criticized Whewell in A System of Logic of 1843). These works, Hacking claimed, and primarily Mill’s A System of Logic constituted the starting point of a continuous line of thinking about natural kinds that reaches from the mid-nineteenth century to the present day. As Hacking wrote, “Mill introduced, and the tradition continued to use, a new word, “kind”, for a new discussion” (1991b: 151; emphasis added). Responding to Hacking, Boyd (1991) argued that the point of origin of the tradition of thinking about natural kinds lies earlier than the mid-nineteenth century, namely in John Locke’s Essay Concerning Human Understanding, as the focal question for Whewell, Mill and Venn was also one of Locke’s topics. What was

‘natural kinds’ adds nothing (except, perhaps, confusion) to the discussion. For reasons of space, I shall not consider Hacking’s position further. 5 Russell, for instance, equated the doctrine of natural kinds (which he rejects) with the postulate that variation in the universe is limited (1948: 456–462). 6 Besides Hacking and (to a lesser extent) Boyd, so far no one has studied the history of philosophical work on the topic in sufficient depth. As the present paper is not a work in history of philosophy and my aim is not to trace the precise historical lines of work on the topic of natural kinds, here I take Hacking’s and Boyd’s stories at face value. My aim in this section is to make plausible that in present-day philosophy two distinct lines of thinking about natural kinds exist, whatever exactly their historical origins and interconnections might be.

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at stake for Whewell, Mill and Venn was the question what enables us to make inductive statements over groups of things or phenomena. The new discussion that revolved round the new technical term of ‘natural kind’, thus, was epistemological in nature: the problem of natural kinds was the problem which groupings of things were best suited as the bases for making valid inferences and generalizations. But this is a problem that already played a central part in Locke’s Essay, Boyd pointed out (1991: 130–132). In the Essay Locke made the famous distinction between “real essences” and “nominal essences” and argued that the kinds that feature in human reasoning are based on nominal rather than real essences.7 Locke pointed out that, while the similarities between things are due to nature, the sorting of things into groups is our work.8 Although we might have the aim of grouping things according to their objective similarities (i.e., their real essences), Locke argued, we are unable to observe the real essences of things, so that we cannot be certain that the kinds that we construct indeed group things according to the real state of affairs “out there” in nature. Thus, the kinds about which we reason, obtain knowledge and make generalized statements are fundamentally of our own making: kinds, in Locke’s words, are the “workmanship of men”. Notwithstanding their difference of opinion the exact historical origin of the philosophical discussion on natural kinds, Hacking and Boyd agree that the philosophical tradition of natural kinds stands in the line of British empiricism and that its central problem is epistemological. An interesting aspect of Hacking’s and Boyd’s historical accounts is that they exclude some of the authors that are typically mentioned in discussions of the topic of natural kinds – Plato and Aristotle are the most obvious examples – from the philosophical tradition of work on this topic. The problem of natural kinds is often introduced by referring to Plato’s (in)famous slogan that we should attempt to “carve nature at the joints” when classifying the things about we speak, in the same way as good butchers and priests carve the bodies of animals or sacrificial victims.9 Also, in discussions of natural kinds mention is typically made to Aristotle’s theory of substance and form as being about natural kinds (Dupr´e 2000; Haddock and Dupr´e 2006) and many contemporary defenders of essentialist views of natural kinds explicitly position their work in the tradition of the Aristotelian variant of essentialism (e.g., Ellis 2001: 19; 2002: 12–14; Oderberg 2007: x). To be sure, neither Plato nor Aristotle used the term ‘natural kind’ (as the technical term was introduced only much later). Moreover, their principal worries when they discussed kinds and categories were quite different from those of the British empiricists: their interest was metaphysical rather than epistemological. Still, it seems overly purist to exclude these philosophers from the tradition of thinking

7

Essay, Book III, Chap. VI, 6–11. Essay, Book III, Chap. VI, 36–37. 9 Phaedrus, sections 265d–266a; Statesman, section 287c. 8

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about natural kinds. For one, the fact that at some later point in the history of philosophy a particular technical term is introduced does not imply that the questions that from that point onward are discussed under the cover of the new term hadn’t already been in focus in the works of earlier philosophers. In addition, as I shall argue in the following section, the two kinds of worries are intimately connected, so that they are best understood as different manifestations of the same problem. I want to suggest, then, that in the history of philosophy two distinct lines of thinking about the problem of natural kinds can be identified. Both lines of work pertain to the same philosophical problem, they may have not been clearly distinct throughout much of the history of philosophy and several important authors might be counted as being part of both lines of work – but they are best seen as distinct traditions nonetheless. On the one hand there is the tradition that traces back for more than two millennia to Plato and Aristotle and in which natural kinds are understood as real kinds that exist in nature independently of human observation and human reasoning.10 The basic assumption here is that things by their natures or essences come in various kinds, so that every particular thing has a unique kind identity as a particular kind of thing. As Ellis recently put it, “membership of a natural kind is decided by nature, not by us” (2001: 19). There is, then, a unique classification of things into kinds that represents this state of affairs in nature. The problem of natural kinds in this line of work is a metaphysical problem: its central questions are what it means to say that kinds exist in the world (after all, we do not just stumble over kinds in the same way that we regularly bump into particular entities), how the ideas of natural kindhood and real essence are to be conceived of, which sorts of real essences lie at the bases of the various natural kinds that exist, and related metaphysical issues. On the other hand there is the more recent tradition that originated in British empiricism (either in the mid-nineteenth or already in the late seventeenth century) and in which natural kinds are seen as groupings of things that feature in human reasoning and are made by us with the purpose of being useful in this context. Here the problem of natural kinds is an epistemological problem: the central questions are, among others, what roles reference to natural kinds plays in human reasoning and what it is that makes certain groupings of things more suitable for featuring successfully in such types of reasoning as generalization, explanation and prediction. Boyd expressed this view thus: “[i]t is a truism that the philosophical theory of natural kinds is about how classificatory schemes come to contribute to the epistemic reliability of inductive and explanatory practices” (Boyd 1999, 146; 2000: 55–56; original emphasis) and “the theory of natural kinds just is (nothing but) the theory of how accommodation is (sometimes) achieved between our linguistic, classificatory and inferential practices and the causal structure of the world” (Boyd 2000: 66; original emphasis).

10 This view is still alive and well today; compare: “natural kinds are categories that are actually there in nature, as opposed to being impositions on nature for our own convenience” (Garvey, 2007: 127; emphasis added).

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21.4 Why Are the Main Approaches to the Problem Deficient? From the historical sketch given above, it might appear that there are two separate lines of thinking about two distinct problems. If this were indeed the case, Hacking and Boyd would be right to single out one line of work as the tradition of natural kinds and to think of the other line of work as being about a different problem. But this would, I contend, be a misunderstanding of the actual situation, as the two lines of thinking constitute different ways of approaching the same problem. Hacking and Boyd, thus, would be right if their claim is that a new approach to the problem of natural kinds appeared in British empiricism, but not if their claim is that this approach can legitimately monopolize the notion of ‘natural kind’ and be thought of as defining the problem of natural kinds. What makes the two lines of work approaches to the same problem is an inseparable connection between their respective central questions. Recall that the central questions of the epistemological line of work are what roles reference to natural kinds plays in human reasoning, what makes certain groupings of things better suited for these roles, and related questions. If the basic assumption of the metaphysical line of work – that things naturally come in kinds and that kinds exist in some sense in the world – were correct, any sufficiently elaborated metaphysical account of natural kinds would also immediately answer these epistemological questions: those kinds that can successfully feature in human reasoning are precisely those that exist in nature. Conversely, any acceptable theory that answers these epistemological questions must explicate in which respects the kinds that feature in human reasoning represent features of the world. A reasonable assumption, after all, is that a grouping of things can only successfully feature in human epistemic practices if it is (at least in a minimal sense) grounded in the state of affairs in the world “out there”. The principal difference between the two lines of work, then, is which type of questions is given priority, metaphysical or epistemological ones. A problem for the metaphysical approach is that its central questions – in what way can kinds be said to exist in the world, how are the ideas of natural kindhood and real essence to be conceived of, which sorts of real essences characterize existing natural kinds, etc. – are such that they cannot be answered without first having achieved a sufficient overview of which natural kinds there actually are. In order to be able to investigate the natures of the kinds that exist in the world, it seems that one first needs to have a good idea of the actual diversity of kinds. But we do not have any direct access to the world that would allow us to compile the required inventory of the kinds that supposedly make up the world’s furniture. Our best bet at obtaining such an inventory is to consult the various fields of science and to look at the ontologies that these currently adopt. But scientists entertain particular ontologies because these make sense in the context of particular explanatory theories and background ideas – more specifically, they do so because the kinds included in these ontologies can serve as the bases of valid generalizations, explanations, predictions, etc. against the background of the particular theories and views that are adopted. And this brings

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us to the question of the epistemological line of work on natural kinds, i.e., which groupings of things help us to make inferences and to explain phenomena and how they manage to play this epistemic role. For the success of carrying out its project the metaphysical line of work on natural kinds thus depends on the outcome of the investigations of the epistemological line of work.11 The metaphysical approach typically tries to circumvent its dependence on the outcome of epistemological investigations by taking recourse to a priori assumptions about the nature of natural kinds, most importantly the assumption that all natural kinds are characterized by kind essences. This leads the metaphysical approach to a comparatively strict view of what natural kinds are – a view that I think is too limitative. As most kinds that feature in the special sciences are not associated with kind essences, these fall outside the domain of natural kinds that are recognized under the metaphysical approach. Because the metaphysical approach on a priori grounds limits the domain of natural kinds in such a way that many kinds that actually are used in science and everyday contexts fall outside it, it does not seem to be a very promising approach to the problem of natural kinds. Although the epistemological approach thus seems to be in a better position, it runs the risk of adopting a too liberal view of what natural kinds are. If we conceive of natural kinds as those groupings that successfully feature in various epistemic practices, in principle every kind term that we use should be thought of as referring to a natural kind. The distinction between natural kinds and other kinds of kinds then becomes blurred to such an extent that it becomes unclear why there would be a need for a philosophical account of a particular category of kinds – natural kinds – that is to be distinguished from other kinds of kinds.12 Thus, while the metaphysical line of work involves a too limitative view of what natural kinds are, the epistemological line of work involves a too liberal view. Neither of the two approaches is “on target” and the principal contemporary challenge in attempts to devise an account of natural kinds is to navigate between the poles of extreme conservatism and extreme liberalism.

21.5 Conclusion: Toward Natural Kind Theory as a Tool for Philosophers of Science I have attempted to show that the dim view of the usefulness of natural kind theory, defended by Russell, Quine and a number of later authors, is not inevitable. The epistemological approach to the problem of natural kinds gives rise to a more optimistic view that could be able to do justice to the role that the notion of ‘natural kinds’ plays in many domains of philosophy that focus on a particular special

11

This already suggests that epistemological issues deserve priority over metaphysical ones. As Boyd acknowledged, “[a]lmost all sorts of kinds and kind terms except the most clearly arbitrary have been treated as natural kinds and kind terms” (1991: 128). 12

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science or cluster of sciences. But as the epistemological approach runs the risk of obscuring the difference between natural kinds and other kinds of kinds to such an extent that the account that it yields will no longer be a theory of natural kinds, at this point neither of the two approaches will be able to yield an account of natural kinds that is useful for the project of philosophy of science. A possible way out might be to approach the problem of natural kinds on a caseby-case basis, that is, by examining how the notion of ‘natural kinds’ functions in philosophical arguments about science, which epistemic roles reference to kinds plays in the various fields of science and what criteria kinds must meet in order to be able to perform these roles. A first step thus should be to look at how classifications of the subject matter of the various scientific disciplines into kinds are actually being used in these disciplines’ practices of investigation, knowledge production, reasoning, explanation, etc. Once this has been clarified, the metaphysics of the kinds involved can be examined. In this way it is possible to obtain a first approximation account of natural kinds in science that avoids the strictness of the metaphysical approach without immediately blurring the distinction between natural kinds and other kinds of kinds. This suggestion might strike some readers as unsatisfactory, as I have proposed a program for the development of a theory of natural kinds that can serve as a useful tool for philosophers of science rather than presenting a ready-for-use theory. But at least the preceding discussion has shown that the prospects for using the idea of natural kinds in the philosophical project of trying to understand what science is and how it works are better than some authors have suggested. Acknowledgement Research for this paper was funded by the German Research Council (DFG) under grants no. RE 2613/1–1 and RE 2613/1–2.

References Boyd RN (1991) Realism, anti-foundationalism and the enthusiasm for natural kinds. Philos Stud 61:127–148 Boyd RN (1999) Kinds, complexity and multiple realization. Philos Stud 95:67–98 Boyd RN (2000) Kinds as the “workmanship of men”: realism, constructivism, and natural kinds. In: Nida-R¨umelin J (ed) Rationalit¨at, Realismus, Revision: Vortr¨age des 3. Internationalen Kongresses der Gesellschaft f¨ur Analytische Philosophie. Walter de Gruyter, Berlin, pp 52–89 Churchland PM (1985) Conceptual progress and word/world relations: in search of the essence of natural kinds. Can J Philos 15:1–17 Dupr´e JA (2000) Natural kinds. In: Newton-Smith WH (ed) A companion to the philosophy of science. Blackwell, Oxford, pp 311–319 Elder CL (2008) Biological species are natural kinds. South J Philos 46:339–362 Ellis BD (2001) Scientific essentialism. Cambridge University Press, Cambridge Ellis BD (2002) The philosophy of nature: a guide to the new essentialism. McGill-Queen’s University Press, Montreal/Kingston Garvey B (2007) Philosophy of biology. Acumen, Stocksfield Hacking I (1991a) A tradition of natural kinds. Philos Stud 61:109–126 Hacking I (1991b) On Boyd. Philos Stud 61:149–154

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Hacking I (1995) The looping effects of human kinds. In: Sperber D, Premack D, Premack AJ (eds) Causal cognition: a multidisciplinary debate. Oxford University Press, New York, pp 351–394 Hacking I (2007) Natural kinds: rosy dawn, scholastic twilight. In: O’Hear A (ed) Philosophy of science (Philosophy – Royal Institute of Philosophy Supplement 61). Cambridge University Press, Cambridge, pp 203–239 Haddock A, Dupr´e JA (2006) Natural kinds. In: Borchert DM (ed) Encyclopedia of philosophy, 2nd edition, vol 6. Macmillan Reference, Detroit, pp 503–505 Oderberg DS (2007) Real essentialism. Routledge, London Quine WV (1969) Natural kinds. In: Rescher N (ed) Essays in honor of Carl G. Hempel. Reidel, Dordrecht, pp 5–23 Russell B (1948) Human knowledge: its scope and limits. George Allen & Unwin, London

Chapter 22

Whence Ontological Structural Realism? Juha Saatsi

22.1 Introduction In the scientific realism debate a distinction is made between epistemic and ontological varieties of structural realism. ‘Ontic’ Structural Realism (OSR) is motivated by considerations from the foundations of physics, and it is characterised as metaphysics. Epistemic Structural Realism (ESR), by contrast, represents a ‘mere’ epistemological refinement to ‘standard’ realism. I will focus on OSR’s motivations, and the claim that ESR doesn’t offer a structuralist alternative to standard realism that is far-reaching enough. I will argue that the advocates of OSR have failed to motivate it as an alternative to ESR and other ‘non-standard’ forms of realism. Although there’s incentive to move away from object-oriented standard realism, there’s no need to go as far as OSR.

22.2 What ESR Is (Not) There is a natural motivation for epistemic structural realism: the possibility of having ‘the best of both worlds’ (Worrall 1989) in the realism debate by combining the realist’s optimistic image of science with the historical fact of radical theory shifts. ESR purports to offer a principled way of identifying the structural content of a theory in such a way as to ensure cumulative continuity in the (structural) truth content of theories across radical theory shifts. The structuralist intuition springs from the fact that in various historical theoryshifts there are crucial mathematical equations that are carried over either intact or, more typically, as one set of equations being a limiting case of the other. Worrall’s

J. Saatsi () Department of Philosophy, University of Leeds, Leeds LS2 9JT, UK e-mail: [email protected]

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suggestion was to take the theoretical continuity manifested as such formal mathematical correspondence to be the locus of realist commitment. This is a cogent structuralist intuition. But there remains much to be clarified to turn the intuition into a credible argument. First of all, the structuralist needs to ensure that this kind of continuity really has to do with the realist rather than empiricist content (van Fraassen 2006). Worrall simply cites Fresnel’s equations for the amplitudes of reflected and refracted polarized light, to point out that they are identical to those resulting from Maxwell’s theory. But this is not enough. The motivation for going beyond empiricist commitments – the No Miracles argument – entails that we should be able to explain the success of the predecessor theory from the vantage point of the successor, in terms of truth-tracking theoretical content. This surely demands more than pointing out that the equations the two theories ultimately yield – the equations that are used to test the theory – are equivalent or stand in some limit-correspondence. What it demands, rather, is that we can account for the derivation of Fresnel’s equations in terms of Maxwell’s theory. For there is much to Fresnel’s theorising besides ‘Fresnel’s equations’ which represent only the very end result of his theorising, and the plausibility of the realist image, structural or otherwise, comes in part from fulfilling the intuition that success of a theory is connected to its approximate truth in a ‘non-miraculous’ fashion. This means that we should really be considering the relationship between the derivations by which the corresponding equations are arrived at in the respective theoretical frameworks. When these derivations are taken into account it is not clear that this relationship is best understood in structural terms (cf. Saatsi 2005, 2008). Another point to press the epistemic structural realist on concerns the sense in which one structure can be said to approximate another. Mere appeal to ‘the general correspondence principle’ leaves this too open. The worry is that without a precise sense in which one structure corresponds to another we end up finding mathematical continuity where we want it. Even in the cases of intuitively appealing limit-correspondence we often have grave mathematical discontinuities that mark a theoretical revolution (See Redhead 2001, p 346). Such discontinuities in the evolution of theoretical structures can perhaps be dismissed on the grounds that they are immaterial to the explanation of the success of the antecedent theory from the later perspective, but such claims need to be made on case-by-case basis and only after carefully scrutinising the nature of the particular structural (dis-)continuity in question. For these (and other) reasons the thesis of ESR needs sharpening. Nevertheless, the epistemological motivation for structural realism is valid. The project of first making the structuralist proposal more precise and then comparing it to various instances of historical theory change is well-defined and intuitively cogent one. According to this position, if successful, “all that we know of the world is its structure, as exemplified in our scientific theories, and the ‘nature’ of the underlying elements (physical objects) remains ‘hidden’ in some sense.” (Cei and French 2006, p 634) The ESR position has been recently misinterpreted by Cei and French (2006), who read Worrall’s ‘hidden natures’ as a kind of Ramseyan Humility that David

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Lewis (2009) advocates. According to Lewis even ‘the final theory’ of science, taken as fully true, would leave the true nature of things hidden from us. This reading creates certain problems for ESR that Cei and French then use to motivate the alternative OSR. Their argument for preferring OSR over ESR fails due to misinterpreting ESR’s sense of epistemic humility. The appropriate sense is the following. Our successful theories have often radically changed, so we are not in a position to commit to the full truth of our present theories. Rather, we should commit to our present theories being partially true in some ‘structural’ sense. With a suitable nature–structure distinction at hand we can say that our present theories, whether final or not, describe the structure of the world correctly, but not its nature. Our theories describe various properties of the worldly furniture and processes, and these properties describe a possible way the nature of these things could be. But we do not know that our world is a world of that kind. What we do know, however, is that the structure of our world – whatever its nature is – is such that it is correctly described by our theories. This sense of epistemic humility straightforwardly relates to the problem that rises from the history of science: most our current theories are probably not final ones – something that is also supported by the grand difficulties in making our theories fit together – and even if one of our theories is a final theory (for its domain) in some sense, we are simply not in a position to claim that we know that. I take ESR to be a well-motivated, somewhat programmatic realist alternative. The advocates of OSR take this as their starting point, and then offer two distinctive sources of motivation for going beyond ESR. One turns on a particular kind of underdetermination arguably exhibited by some of our best theories, seriously impeding any substantial realist commitments. The other source of inspiration comes from witnessing certain structuralist themes in the philosophy of physics, and develops into an argument by adopting a particular perspective on the relationship between metaphysics and epistemology. These two motivations for OSR are scrutinised in the next two sections.

22.3 Metaphysical Underdetermination James Ladyman asked about structural realism: ‘is it metaphysics or epistemology?’ (1998, p 410) As explicated above the answer seems clear: it is epistemology. There is, however, an interesting argument that at first seems to lead to a different conclusion.

22.3.1 The Argument Consider the challenge of providing a realist interpretation of quantum mechanics. Setting aside the problems with the collapse of the wave function to begin with, the realist should say of this most successful mature theory that it is probably

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approximately true in its claims about the unobservable world. So quantum particles, for example, are approximately like the theory tells us they are. But what does the theory tell us, exactly? Statistical behaviour of particles has been taken to be the key to their metaphysical nature. The behaviour of an assemblage of quantum particles is correctly described by either Bose–Einstein or Fermi-Dirac statistics, whilst Maxwell-Boltzmann statistics describes the behaviour of classical particles. What accounts for these differences in statistics? According to our best understanding of quantum theory these particles can just as well be individuals (‘cheese’) or non-individuals (‘chalk’), this metaphysical nature of the quantum objects being underdetermined by the theory. Both interpretations of the physics are equally compatible with the phenomena as well as the formalism. (French 1989; Huggett 1997; French and Krause 2006) So the realist is arguably in a pickle: she wants to say that the nature of quantum particles is as the theory says it is, but the theory doesn’t say what it is! We need to recognise the failure of our best theories to determine even the most fundamental ontological characteristic of the purported entities they feature. It is an ersatz form of realism that recommends belief in the existence of entities that have such ambiguous metaphysical status. What is required is a shift to a different ontological basis altogether, one for which questions of individuality simply do not arise. (Ladyman 1998, p 419–420)

I will now try to unpack this argument, assuming that there indeed is such metaphysical underdetermination at least with respect to some entities featured in our best physical theories.1 How should the realist react? Also, I follow Ladyman and French in taking standard realism to have the following metaphysical dimension: the ability to spell out our realist commitments in terms of objects, or entities, that exist.2 I do not take such metaphysical dimension to be a well-motivated part of realism. What I aim to show after explicating the argument from metaphysical underdetermination is that the move from standard realism to ontic structural realism is unnecessarily radical and not supported by the premise of metaphysical underdetermination. It is natural to respond to the challenge by reducing the metaphysical dimension of standard realism, instead of adopting radically alternative structuralist ontology. But first, let’s clarify the challenge itself: what is metaphysical underdetermination? For one thing, it is clearly different from the standard underdetermination objection to realism, according to which the realist cannot justify her commitment to any theoretical proposition P since there is always an empirically equivalent incompatible theory that says P  (incompatible with P ). The rampant nature of this kind of underdetermination (allegedly) makes it such a serious objection. If under-

1 Ladyman (1998), French and Ladyman (2003) and French and Rickles (2003) defend this premise particularly for quantum particles and quantum fields, and tentatively point towards the nature of spacetime. Pooley (2006) dissents, especially regarding the underdetermined status of spacetime points. See also Redhead and Teller (1992) and Saunders (2003b) for criticism of the underdetermination thesis, and French and Krause (2006) for further defence. 2 French and Ladyman read Psillos (1999), for example, as an advocate of standard realism thus characterised. French (2006) has called this ‘object oriented’ realism.

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determination was more limited in scope, so that only some theoretical propositions had empirically equivalent competitors, then realism about those parts of theories that are not thus underdetermined would be an option, at least prima facie (Psillos 1999, p 167). Metaphysical underdetermination is different from empirical underdetermination by virtue of not being rampant. Rather, the former has a very limited scope: only the metaphysical nature of quantum particles (and, perhaps, spacetime points) is underdetermined. So, prima facie, we should focus realist commitments to the common denominator, to whatever is common to both individuals-based and non-individuals-based interpretations of quantum physics, say. But this strategy, the argument continues, is at a risk of leading to ‘ersatz’ realism: realist commitments cannot be spelled out if nothing is said of the metaphysical nature of particles. This follows from the metaphysical dimension of standard realism: to be a realist about such-and-such unobservable entities requires one to spell out what an entity is. So, for example, if one says that ‘According to QED there are spin-half particles with charge e’, one implicitly appeals to metaphysical imagery (extrapolated from our experience of the macroworld) of point-like objects with properties mass, spin, etc., to give cognitive content to one’s assertion. Assertions (S) There are spin-half particles with charge e and other properties as described by QED. (S0 ) There are hard elastic orange balls of the diameter of 24 cm, with a black stripe contouring around the ball. are read on a par according to standard realism: they both assert the existence of some objects with some properties. Basketballs are observable, electrons are not, but we have good reasons to believe in both. So far so good. But the ontic structuralist points out that our epistemic grasp of the very objecthood of electrons, according to metaphysical underdetermination, is on a shaky ground. Therefore, S expresses no cognitive content beyond the surface semantic analogy that only pays lip service to the curious symmetry properties of the mathematical representation of quantum particles. Hence, there is an acute challenge with theoretical posits the metaphysical nature of which is underdetermined by the physics: the content of prototypical realist assertions is deflated unless the realist is able to specify ‘the most fundamental metaphysical categories’ applicable. The standard realist, not willing to tackle these issues posed by the foundations of physics, is offering a cheap simulacrum of knowledge of the quantum world, based on an extraneous metaphysical image given in terms of categories derived from our experience of the macroworld. Such realism is arguably ‘ersatz’ in that it does not succeed in capturing any actual realist commitment regarding our best theories. What allegedly could save the realist, however, is ontological commitment to structure (as opposed to (non-)individual objects with properties) as the fundamental metaphysical category.

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22.3.2 Resisting the Argument There are several points to be made in response to the above argument.

22.3.2.1 Common Denominator: From Entities to Properties If the standard realist is unable to choose between the metaphysically underdetermined options, are her realist commitments really as empty as the ‘ersatz’ charge suggests? Is ontological structuralism a natural solution to her alleged predicament? French and Ladyman press the standard realist on the nature of quantum particles: [T]he (standard) realist is unable to give a full answer to [the question:]‘what is a quantum object?’, where a ‘full’ answer will involve the metaphysical nature explicated in terms of such fundamental categories as individuality, identity, etc. Van Fraassen rightly sees this as a challenge to standard realism (and it is regrettable that the standard realist has not seen fit to respond) expressing his conclusion as a waving ‘good-bye to metaphysics’ (Van Fraassen 1991, 480–482), leaving the field clear for constructive empiricism. (French and Ladyman 2003, p 36, my italics)

So realism without adequate metaphysics succumbs to anti-realism. But to demand a full answer is to demand too much. Van Fraassen (as I read him) sees the kind of metaphysical underdetermination at issue to challenge full-blown metaphysics, not realism per se. Various degrees of realist confidence regarding our inductive practices can be defended whilst sharing van Fraassen’s distaste for wholesale metaphysics. Nevertheless, French and Ladyman insist that ‘if the realist refuses to be drawn on the metaphysics at least at the level of individuality versus non-individuality then how are we supposed to make sense of the impact of quantum mechanics?’ (ibid., 50) I will look at the impact of quantum statistics below, but let’s first consider this challenge in the abstract. There is an ambiguity here: there are two separate explanatory endeavours at stake for the realist. How can she explain (E1) the success of the theory by its partial truth; and (E2) what the world could be like to make the theory true simpliciter? The latter challenge asks what the world could be like according to our theory read literally, whilst the former asks what the world must be like according to our theory in order for the success of science (and of that theory in particular) not to appear ‘miraculous’. Neither of these challenges is made insuperable by the metaphysical underdetermination at hand. Regarding (E2), the realist can take different metaphysical frameworks to paint different meaningful images of how the world could be. Whether we have (ever could have) grounds to choose between such images – the very possibility and limits of metaphysical knowledge – is a different question, of course. Regarding (E1), the realist’s response depends on her general characterisation of realist commitments. What does it take to philosophically explain the success of a scientific theory in the spirit of scientific realism? How is the explanatory, truth-tracking theoretical content to be delineated in the first place? Such questions surface in connection with the

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‘pessimistic induction’ where the realist appeals to some kind partial truth. I have urged elsewhere that this notion should be analysed in terms of theoretical properties responsible for successful derivations in science (Saatsi 2005). This conception of realist commitments is appropriate in the present context, too, since knowledge of these success-fuelling properties can be independent of having knowledge (or not) of the nature of reality in terms of the fundamental metaphysical categories relevant to the explanandum (E2) above. (I will illustrate this below with quantum statistics.) We can answer the question (E1) without taking a stance regarding the metaphysically underdetermined alternatives because the relevant explanatory, success-fuelling properties are shared by the competing metaphysical interpretations. We need to reject the intuition that the realist must engage in metaphysics to the extent that she can spell out her commitments in terms of fundamental metaphysical categories.

22.3.2.2 The Impact of Quantum Statistics What, then, can a realist claim to know of quantum particles? How can these realist commitments be spelled out without reference to fundamental metaphysical categories? Consider, to begin with, a feasible metaphysical underdetermination vis-`a-vis the nature of spacetime. The realist wants to explain the success of the General Theory of Relativity by claiming it to have correctly identified the curvature of spacetime as the source of gravitational phenomena. This explanation is independent of the metaphysical question of whether the spacetime points of the substantivalist interpretation of GTR are to be understood haecceitistically or antihaecceitistically.3 In both cases the theory is true about the crucial unobservable features of the world, so that the concepts of curvature and geodesic, for example, similarly apply to properties of substantival spacetime. This kind of metaphysical underdetermination is quite different from the usual empirical underdetermination regarding spacetime theories: one theory having a curved spacetime and the other having extra forces in its ontology. In the face of such empirical underdetermination we really may not know what to believe in. Not so in the case of metaphysical underdetermination: we just believe that the theory correctly describes motion in curved spacetime. This illustrates how metaphysical underdetermination can fall outside of natural realist commitments. But there is a crucial disanalogy to the case of quantum statistics: underdetermination in the spacetime case – haecceitism vs. anti-haecceitism with respect to spacetime points – concern the modal identity of spacetime points, not their individuality. (Pooley 2006) Nevertheless, the lesson generalises. We can

3 The realist explanation of this success actually is independent of the existence or otherwise of spacetime points altogether, as corresponding to points of the mathematical manifold of a GTR model. The realist can remain agnostic of the ‘fine-structure’ of spacetime at the Planck-scale, only maintaining that the coarse-grained macrofeatures that emerge from the ultimate quantum theory of gravity are correctly described by GTR.

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account for the success of quantum statistics without reference to the metaphysical nature of particles. The explanation is subtle, and I refer to Saunders (2006) for details. The gist of the explanation turns on the probability measure on quantum state space: the discreteness of this measure makes a crucial difference in how the states are counted under permutation symmetry. Saunders demonstrates how the difference between classical and quantum statistics arises from the fact that the probability measure is continuous for classical state space but discrete for quantum state space, even if both classical and quantum particles are assumed to be indistinguishable and permutation symmetry is applicable to both. The realist does not have to deny that there may be different metaphysical explanations, underdetermined by the physics, for this crucial difference between classical and quantum systems. But these metaphysical musings go beyond what is required by the realist to explain ‘the impact of quantum mechanics’, as far as the explanandum (E1) is concerned. Regarding this aspect of quantum mechanics, the realist is committed to the characteristic discreteness of the quantum world – a property of quantum systems. Although this undeniably only scratches the surface of what the realist needs to say about quantum mechanics, it does address the source of the argument from metaphysical underdetermination.

22.3.2.3 Is Metaphysical Underdetermination Coherent? Let’s return to the two explananda (E1) and (E2), above. It seems that even at the level of (E2) the underdetermination does not motivate the radical step to OSR, regarded as ‘offering a reconceptualisation of ontology, at the most basic metaphysical level, which effects a shift from objects to structures’ (ibid., p 37). Such a metaphysical project is in itself fully legitimate, of course, but cannot in my view gain any extra impetus from the metaphysical underdetermination. An ontological structuralist conclusion (regarding (E2)) could perhaps be argued for by saying that structuralist metaphysics provides the only way to make sense of the notion of objecthood at the level of quantum particles. (Saunders 2003a,b)4 But this is not the claim presently evaluated. Indeed, such a claim directly contradicts the underdetermination premise, which is conditional on both horns being intelligible bona fide possibilities. If anything, it seems that the structuralist proposal only makes matters worse, for with such an alternative structuralist ontology available there would be three instead of two to choose from!5 The choice between these would presumably be done on the grounds of general metaphysical preferences. This, indeed, is another difference between metaphysical and empirical underdetermination; if one

4 Ladyman and Ross (2007) perhaps also argue for this claim, having shifted away from the argument from metaphysical underdetermination. 5 It has been suggested that the individuals and non-individuals packages could be viewed as different representations of the common ‘structuralist core’ but this intuition must be substantiated in order to show how the underdetermined options go over and above the common core, instead of just being metaphysical alternatives.

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(pace van Fraassen) is optimistic about metaphysical reasoning in general, then arguably metaphysical underdetermination can be broken by considerations that go beyond physics and belong to philosophy simpliciter. I conclude that the motivation gained from the metaphysical underdetermination for structural realism, and for ontological structural realism in particular, is highly problematic. I will next briefly look at an oblique line of enquiry that is sometimes taken to provide further grounds for OSR, or even for taking OSR to supplant ESR.

22.4 Structuralism in Philosophy of Physics I now want to argue in more general terms for a distinction to be made between two levels of structuralist philosophy often run together in a synergistic fashion.6 One family of structuralist thought belongs to the philosophy of physics proper: the unifying theme is the conviction that the ontology of physics is best conceived in structural terms. Very broadly speaking this movement can be characterised as an attempt to shift one’s ontology away from objects, as traditionally conceived, and towards structures relationally understood. A different set of structuralist ideas belong to epistemology, and concern the question of what we can claim to know of the (mind independent) world. Although there are eminent historical figures to draw on (e.g. Russell 1927), in the contemporary context the epistemological motivation, as outlined in Section 22.2, boils down to something quite specific. On the face of it, it is not easy to say exactly how structuralism in the philosophy of physics should interact with this epistemological idea. One might at first think that if the preferred ontology of physics is structural – so that one is an ontological structural realist at the level of philosophy of physics – then one must also be a structuralist with respect to one’s epistemological scientific image, since all theoretical truths are ultimately truths about structure. But the connection isn’t this straightforward. After all, the structuralist ontology is inspired by metaphysical questions regarding a literal reading of our best theories – questions such as: what are the spacetime points quantified over in GTR like; how to understand the nature of quantum particles in the face of the permutation symmetry, or the gauge symmetry behind the Bohm-Aharonov effect. The epistemological humility of the realist image, on the other hand, is based on the belief that our theories may only be partially true. Therefore the notion of partial truth adopted by the realist can affect whether or not a literal reading of our present theories has input on the realist’s epistemic commitments. For example, it might be part of the realist image that there really is a curved spacetime and that free particles move along the shortest paths as mathematically represented by geodesics on a manifold – i.e. the theoretical terms

6 It is not always easy to prise apart the different motivations running in parallel, but in my view an illegitimately close connection between different structuralist motivations is implied in Ladyman (1998), French and Ladyman (2003), Saunders (2003b), Lyre (2004), and French (2006), for example.

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‘curvature of spacetime’ and ‘shortest path’ do refer – irrespective of whether the most fundamental spacetime ontology consists of dimensionless points or of something else completely. GTR might be a true representation of the curvature properties of spacetime whilst being a false representation of its ‘fine structure’. Indeed, being a classical (non-quantised) theory this is most probably the case, as acknowledged by an epistemically cautious realist. Whether or not there is an argument for interpreting GTR substantivalism in structuralist terms, it is not clear what ramifications this argument should have on such a realist. This example is enough to sever intimate link between ontological and epistemological structuralism. Structuralism in metaphysics might be appropriate for an interpretation of some theory T , but if the realist is only committed to T being partially true it is not clear what epistemological lessons we should draw from the metaphysics. The realist only needs the resources required to capture those aspects of the world that were latched onto by the scientific practice in producing the successes of T . I believe that those features can be described independently of the underlying ‘fundamental metaphysical categories’.

22.5 Conclusion Several considerations for various forms of structural realism have been recently advanced in the quickly burgeoning literature. There is growing need to draw critical distinctions in order to regiment the multifaceted debate: too often different senses of ‘structure’ and ‘structuralism’ are confusingly placed under one and the same heading. Here I have attempted to make some headway by focusing on different motivations for adopting a form of structural realism. If correctly interpreted, the original epistemic strand of structural realism is a well motivated, if still somewhat programmatic position. What has been hailed by some as the radical alternative – the ontic version of structural realism—is rather weakly motivated in comparison. Whilst there is most certainly room for various forms of structuralism in metaphysics and philosophy of physics, the links between the various considerations are more subtle than is currently acknowledged in the literature. Acknowledgements I wish to thank Steven French and Angelo Cei for helpful correspondence.

References Cei A, French S (2006) Looking for structure in all the wrong places: Ramsey sentences, multiple realizability, and structure. Stud Hist Philos Sci 37:633–655 French S (1989) Identity and individuality in classical and quantum physics. Aus J Philos 67: 432–446 French S (2006) Structure as a weapon of the realist. Proc Aristotel Soc 106:1–19

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French S, Krause D (2006) Identity and individuality in modern physics. Oxford University Press, Oxford French S, Ladyman J (2003) Remodelling structural realism: quantum physics and the metaphysics of structure. Synthese 136:31–56 French S, Rickles D (2006) Quantum gravity meets structuralism: interweaving relations in the foundations of physics. In Structural foundations of quantum gravity. Oxford University Press, Oxford Huggett N (1997) Identity, quantum mechanics and common sense. Monist 80:118–130 Ladyman J (1998) What is structural realism? Stud Hist Philos Sci 29A:409–424 Ladyman J, Ross D (2007) Every thing must go: metaphysics naturalized. Oxford University Press, Oxford Lewis D (2009) Ramseyan humility. In: Braddon-Mitchell D, Nola R (eds) Conceptual Analysis and Philosophical Naturalism. MIT Press Lyre H (2004) Holism and structuralismin U(1) gauge theory. Stud Hist Philos Modern Phys 35:597–624 Pooley O (2006) Points, particles, and structural realism. In: French S, Rickles D, Saatsi J (eds) The structural foundations of quantum gravity. Oxford University Press, Oxford Psillos S (1999) Scientific realism: how science tracks the truth. Routledge, London Redhead M (2001) The quest of a realist. Metascience 10:341–347 Redhead M, Teller P (1992) Particle labels and the theory of indistinguishable particles in quantum mechanics. Br J Philos Sci 43:201–218 Russell B (1927) The Analysis of Matter. Kegan Paul, London Saatsi J (2005) Reconsidering the Fresnel-Maxwell case study. Stud Hist Philos Sci 36:509–538 Saatsi J (2008) Eclectic realism – the proof of the pudding: a reply to Busch. Stud Hist Philos Sci 39:273–276 Saunders S (2003a) Physics and Leibniz’s principles. In: Brading K, Castellani E (eds) Symmetries in physics: philosophical reflections. Cambridge University Press, Cambridge, pp 289–308 Saunders S (2003b) Structural realism, again. Synthese 136:127–133 Saunders S (2006) On the explanation for quantum statistics. Stud Hist Philos Modern Phys 37:192–211 van Fraassen BC (1991) Quantum mechanics: an empiricist view. Oxford University Press, Oxford van Fraassen BC (2006) Structure: its shadow and substance. Br J Philos Sci 57:275–307 Worrall J (1989) Structural realism: the best of both worlds? Dialectica 43:99–124

Chapter 23

Local, General and Universal Prediction Methods: A Game-Theoretical Approach to the Problem of Induction Gerhard Schurz

23.1 The Problem of Induction: Local, General and Universal Prediction Methods In an inductive inference, a property, regularity, or frequency is transferred from the observed to the unobserved, or from the past to the future. How can we rationally justify inductive inferences? This is the famous problem of induction, or Hume’s problem. David Hume has shown that all standard methods of justification fail when applied to the task of justifying induction. Inductive inferences cannot be justified by deductive logic, since it is logically possible that the future is completely different from the past. Nor can they be justified by induction from observation, by arguing that induction has been successful in the past, whence – by induction – it will be successful in the future. For this argument is circular, and circular arguments are without any justificatory value. On these reasons Hume was led to the skeptical conclusion that induction cannot be rationally justified at all, but is merely the result of psychological habit. There have been several attempts to solve or dissolve Hume’s problem, which cannot be discussed here. It seems that so far, none of these attempts has been successful in providing a non-circular solution to the problem of induction. Given that it is impossible to demonstrate that induction must be successful (Hume’s lesson), and that there are various alternative prediction methods (reliance on instinct, clairvoyants, etc.), then it seems to follow that the only approach to Hume’s problem for which one can at least uphold the hope that it could succeed if it were adequately developed is Reichenbach’s best alternative approach (Reichenbach 1949, 91). This approach does not try to show that induction must be successful, i.e. reliable, but it attempts to establish that induction is an optimal prediction method – its success will be maximal among all competing methods in arbitrary possible worlds. Thereby, one must, of course, allow all possible worlds, in particular all kinds of para-normal worlds in which perfectly successful future-tellers do indeed exist.

G. Schurz () University of Duesseldorf, Germany e-mail: [email protected]

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Restricting the set of worlds to ‘normal’ ones would render our enterprise circular, for then we would have to justify inductively that our real world is one of these ‘normal’ worlds. The optimality of a prediction method is a much weaker property than its reliability: a method which is strictly or approximately reliable in a given world will also be strictly or approximately optimal in this world, but not vice versa: also a method which is unreliable (in a given world) can be optimal, provided there exist no better methods in this world. Reichenbach did not succeed in establishing an optimality argument with respect to the goal of single event predictions. He only demonstrated this argument with respect to the goal of inferring an event’s frequency limit in the long run (cf. Reichenbach 1949, 474f). However, our ability to infer approximately correct frequency limits is practically not significant. What is of practical significance is our success in true predictions. In this respect, Reichenbach’s approach fails: nothing in Reichenbach’s argument excludes the possibility that a perfect future-teller may have perfect success in predicting random tossings of a coin, while the inductivist can only have a predictive success of 0.5 in this case (cf. Reichenbach 1949, 476f; Skyrms 1975, ch. III.4). By object-induction (abbreviated as OI) I understand methods of induction applied at the level of events – the ‘object level’. Generally speaking, the problem of Reichenbach’s account lies in the fact that it is impossible to demonstrate that object-induction is an (approximately) optimal prediction method, because for every object-inductive method there exist ‘demonic’ worlds (event-sequences) which turn its success rate down to zero, though other methods exist which have non-zero success in these worlds (cf. Kelly 1996, 260f). In contrast to Reichenbach’s approach, my approach is based in the idea of meta-induction. The meta-inductivist (abbreviated as MI) applies the inductive method at the level of competing prediction methods. The simplest type of meta-inductivist predicts what the presently best prediction method predicts, but one can construct much more refined kinds of metainductivistic prediction strategies. Many philosophers are deeply skeptical concerning the possibility of a rational and non-circular justification of induction. In line with this skepticism, Gigerenzer et al. (1999) and Norton (2003) have argued that all methods of induction must be local (or ecological) in the sense that they can only be reliable, or optimal, in restricted classes of environments. Gigerenzer calls this view the paradigm of ‘bounded rationality’. In this paper I intend to show that this view is not generally true. I suggest to classify prediction methods according to their range of applicability into local, general and universal prediction methods. Note that this distinction can be made in terms of reliability as well as in terms of optimality: (1) Local prediction methods (or strategies) are those whose reliability and/or optimality is restricted to specific kinds of environments (or worlds) which are characterized by material conditions which figure as presuppositions of the success of these strategies. An example of a local strategy is Gigerenzer’s recognition heuristics (1999, p 37ff.): this strategy presupposes that the layman’s

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recognition frequency of events is statistically correlated with certain comparative properties of these events; e.g., with the size of recognized cities or with the success of recognized stocks. The advantage of local strategies is that they are very quick (and usually genetically determined), but their disadvantage is that they cannot learn, i.e., they cannot revise their presuppositions. It would be a bad recommendation to apply the recognition heuristics to domains where its presupposition fails, for example, to the mathematical intelligence of recognized persons or to the attractiveness of recognized tourist places in nature. (2) General prediction methods are object-inductive methods which can learn at the object-level: they change their beliefs about correlations and cues in the light of new evidence. Their reliability as well as their optimality is restricted to presuppositions which are not material but structural (or formal) in nature. In this sense, the reliability of object-inductive methods is restricted to worlds which are uniform (to some degree), and their optimality presupposes that no superior non-inductive methods exist in non-uniform worlds. The structural presuppositions of object-inductive methods are often explicated as axioms of ‘inductive logics’. Their presuppositions are much weaker than the presuppositions of local methods, whence they perform well in a much broader range of possible worlds. (3) Universal prediction methods, finally, would be ones which are reliable, or optimal, in a possible worlds. We have already argued that (a) prediction methods which are universally reliable do not exist (Hume’s insight), and (b) objectinductive prediction methods which are universally optimal do not exist either. It remains to see whether there exist universally optimal meta-inductive prediction methods. The latter question will be the central theme of the remaining part of this paper. The significance of this question for the problem of induction is this: if there do indeed exist universally optimal meta-inductive prediction methods, then at least meta-induction would have a rational and non-circular justification based on mathematical-analytic argument. But this a priori justification of meta-induction would at the same time yield an a posteriori justification of object-induction in our real word: for we know by experience that in our real world, non-inductive prediction strategies have not been successful so far, whence it would be meta-inductively justified to favor object-inductivistic strategies. This argument would no longer be circular, given that we had a non-circular justification of meta-induction. The optimality of a prediction method alone is compatible with the existence of other equally optimal methods. Nevertheless, the optimality of meta-induction would already be sufficient for its rational justification, because as Reichenbach (1949, 475f) has pointed out, meta-induction is the only prediction strategy for which optimality can be rationally demonstrated. Of course, it would be desirable to extend an optimality result for meta-induction (if we had it) to a weak dominance result (see 5). But in this paper I will concentrate on the question of optimality. Let me finally emphasize that my notion of optimality is restricted to accessible prediction methods. There might be possible worlds in which alternative players do not give away their predictions but keep them secret. What I intend to show is

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that among all prediction methods (or strategies) who’s output is accessible to a given person, the meta-inductivistic strategy is always the best choice. I argue that this restriction is not a drawback. For methods whose output is not accessible to a person are not among her possible actions and, hence, are without relevance for the optimality argument.

23.2 Prediction Games A prediction game consists of: (1) An infinite sequence .e/ WD .e1 ; e2 ; : : :/ of events en 2 Œ0; 1 which are coded by elements of the unit interval [0,1]; hence .8n  1 W/ en 2 Œ0; 1. For example, (e) may be a sequence of daily weather conditions, stock values, or coin tossings. (2) A set of players … D fP1 ; P2 ; : : : ; xMI .xMI1 ; xMI2 ; : : :/g, whose task is to predict future events of the event sequence. The players in … include: (2.1) One or several object-inductivists, abbreviated as OI .OI1 ; : : : ; OIr /. They have informational access to past events; their first prediction (at n D 1) is a guess. (2.2) A subset of alternative players PrC1 ; PrC2 ; : : :; for example, persons who rely on their instinct, God-guided future-tellers, etc. In para-normal worlds, these alternative players may have any success and any information you want, including information about future events and about the meta-inductivist’s favorites. – Players of type (2.1) or (2.2) are called non-MI-players. (2.3) One or several meta-inductivists, whose denotation has the form ‘xMI’, where ‘x’ is a variable (possibly empty) expression specifying the type of the metainductivist. The meta-inductivist has access to the past events and the past and present predictions of the non-MI-players. Further notation: pn .P/ denotes the prediction of player P for time n, which is delivered at time n  1. Also the admissible predictions pn are assumed to be elements of [0,1]. The deviation of the prediction pn from the event en is measured by a normalized loss function l.pn ; en / 2 Œ0; 1. The natural loss-function is defined as the absolute difference between prediction and event, l.pn ; en / WD jpn  en j. However, my theorems will not depend on natural loss functions but hold for arbitrary and in case of theorem 2 for convex loss-functions. My prediction games cover binary as well as real-valued prediction games. In binary prediction games, predictions as well as events must take one of the two values 0 and 1 which code instantiations of a binary event-type E (‘1’ for ‘E obtains’ and ‘0’ for ‘E does not obtain’). The score s.pn ; en / obtained by prediction pn given event en is defined as 1 minus loss, s.pn ; en / WD 1  l.pn ; en /; the absolute success an .P/ achieved by player P at time n is defined as P’s sum of scores until time n, an .P/ WD †1in s.pi .P/; ei /, and the success rate sucn .P/ of player P at time n is defined as sucn .P/ WD an .P/=n. For binary prediction games, sucn .P/ coincides with the relative frequency of P’s correct predictions until time n.

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The simplest type of meta-inductivist from which I start my inquiry is abbreviated as MI. At each time, MI predicts what the non-MI-player with the presently highest predictive success rate predicts. If P is this presently best player, then I say that P is MI’s present favorite. If there are several best players, MI chooses the first best player in an assumed ordering. MI changes his favorite player only if another player becomes strictly better. MI’s first favorite is OI. I assume that MI has always access to OI: even if no person different from MI plays OI, MI may constantly simulate OI’s predictions and use them their success rate is in favorite-position. MI belongs to the class of so-called one-favorite meta-inductivists, which choose at each time a non-MI-player as their favorite for the next time and predict what their favorite predicts. In contrast, multiple-favorite meta-inductivists base their predictions on the predictions of several ‘attractive’ non-MI-players. The simplest object-inductive prediction method, abbreviated as OI, is based on the so-called straight rule. In the case of real-valued events, OI transfers the so-far observed mean value to the next event, i.e. pnC1 .OI/ D eN n . In the case of binary events, the integer-rounding ŒNen  of eN n is taken instead, which this generates the prediction rule pnC1 .OI/ D 1 if fn .E/  1, and else D 0. OI’s prediction rule is provably optimal as long as the event sequence is a random sequence. For nonrandom sequences conditionalized object-inductivistic prediction strategies exist, whose success dominates OI’s success (cf. 5). I identify prediction games with possible worlds. Apart from the definition of a prediction game, I make no assumptions about these possible worlds. The stream of events (e) can be any sequence you like. I also do not assume a fixed list of players – the list of players may vary from world to world, except that it always contains xMI and the (virtual) OI. I make the realistic assumption that xMI has finite computational means, whence I restrict my investigation to prediction games with finitely many players.

23.3 Simple Meta-Induction, Take-the-Best, and Its Limitations The performance of a type of meta-inductivist has always two sides: (i) its long-run behavior and (ii) its short-run performance. Although one should be willing to buy some short-run losses of a prediction method for sake of its long-term optimality, these short-run losses should not be too large, and should be under rational control. In this section I investigate the performance of MI and its relative, Gigerenzer’s prediction rule TTB (for Take-the-Best). The central result about MI is theorem 1 which tells us that MI predicts (long-run) optimal whenever there exists a best nonMI-player. Theorem 1. For each prediction game ((e), fP1 ; : : : ; Pm ; MIg) whose player-set contains a best player B – in the sense that there exists a ‘winning time’ nB such that for all later times B’s success rate is greater than the success rate of all other nonMI-players – the following holds (where maxsucn D max.fsucn .Pi / W 1  i  mg/):

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(2.1) (Short-run:) .8n  1 W/ sucn .MI/  maxsucn  .nB =n/. (2.2) (Long-run:) MI’s success rate approximates the maximal success of the non-MI-players for n ! 1. Illustrations of the behavior of MI by computer simulations can be found in Schurz (2008). The proof of theorem 1 is just explained informally: after the time point nB MI’s favorite will be B forever, but until time nB MI’s success may be zero in the worst case, due to switching favorites (see below). This yields theorem (1.1) and (1.2) follows. In determining her favorites MI must buy some losses, compared to the best non-MI-method. These losses result from the fact that in order to predict for time n C 1, the meta-inductivist can only take into account the success rates until time n. Whenever MI recognizes that her present favorite P1 has earned a loss compared to some new best player P2 , then MI has also earned this loss, before MI decides to switch to P2 . So for each switch of favorites MI looses a score of 1 in the binary prediction game, and a non-zero score  1 in the real-valued game, compared to the best non-MI-player. These losses may accumulate. The assumption of theorem 1 excludes that MI can have more than finitely many losses due to switching favorites; so these losses must vanish in the limit, although until time nB , MI’s short-run loss be maximally high (i.e., 1) in the worst case. In conclusion, MI’s optimality is very general but not universal: it is restricted to prediction games which contain a best player whose ‘winning time’ nB doesn’t occur to late. The assumption of theorem 1 is violated whenever the success rates of two or more leading non-MI-players oscillate endlessly around each other. There exist two sorts of success-oscillations: convergent oscillations and non-convergent oscillations. Convergent oscillations are given when two (or more) leading players oscillate in their success-rate around each other with constant time-period and diminishing success-rate-amplitude; i.e. their success-difference converges against zero. The worst case is a binary prediction game in which two players oscillate around each other with the smallest possible period of 4 time units, in such a way that MI gets systematically deceived, because the alternative players predict incorrectly exactly when they are in the position of being MI’s favorite. In the result, the success rates of the two alternative players converges against 1/2, while the meta-inductivist’s success remains zero for all time. A computer simulation of this scenario is found in Schurz (2008, Fig. 2). My results on MI generalize to the prediction rule Take-the-Best (TTB) of Gigerenzer et al. (1999, chs. 2–4). Although TTB is usually treated as an objectinductive (rather than a meta-inductive) prediction method, this difference is just one of interpretation, and not of logical content. There are the following two differences between MI and TTB as it is used in Gigerenzer’s setting: (1) The predictions of the non-MI-players correspond to the cues in Gigerenzer’s setting. The TTB strategy works like MI except that it is assumed that the cues need not make a prediction at every time. Thus, TTB chooses that cue as her favorite for time n which delivers a prediction for time n and has the first-best success rate among those cues which have delivered a prediction for time n.

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(2) Gigerenzer assumes that all frequencies converge to limiting frequencies, i.e. probabilities, and moreover, that the success probabilities of the cues (the socalled ‘ecological validities’, see 1999, 130), are estimated by repeated random samplings from finite domains. Random sampling estimations are ‘inductively safe’ modulo random errors. This downplays the very problem of induction. In the situation of so-called online learning – which is the setting of our prediction games – one inductively infers from past events to future events. This is not random sampling, because you cannot sample from future events, but only from past events. If the future is different from the past, inductive inference leads to systematic failure.

Success Rate

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Gigerenzer has impressingly demonstrated that in spite of its simplicity, TTB is almost always as good as more refined prediction strategies such as weighted averaging of cues or Bayes rules. My results, however, reveal a restriction of TTB in scenarios of online learning: TTB will only perform well if the success rates of the cues converge sufficiently fast either towards a limit or at least towards a unique successordering among the cues. This is assumption is granted by the explained random sampling methods of the ABC-group (modulo random errors). But in scenarios of online learning with oscillating event frequencies and success rates, as for example in predictions of the stock market, ‘inductive safety’ cannot be assumed. In such a case it would be a bad recommendation to put all of one’s money always on the presently most successful stock, instead distributing it over several stocks in form of a stock portfolio (which corresponds to weighted average meta-induction in the next section). Figure 23.1 shows a computer simulation of the breakdown of TTB when playing against ‘deceiving’ cues with convergently oscillating success rates. In other papers I have tried to improve one-favorite meta-inductive strategies, but with limited success. For example, one improvement of MI is the so-called

4 convergently oscillating cues (non-MI-players)

TTB

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Fig. 23.1 Breakdown of TTB with convergently success-oscillating non-MI-players

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"-meta-inductivist ©MI: ©MI switches his favorite only if the success difference between his present favorite and a new better favorite exceeds a small threshold © which is considered as practically insignificant. ©MI can defend himself very well against convergently oscillating players, because as soon as their success difference becomes smaller than ©; ©MI stops to switch but sticks to one of the oscillating players, with the result that ©MI long-run approximates their success rates. However, the ©-approximate long-run optimality of ©MI breaks down in prediction games with non-convergent success-oscillations of the non-MI-players. The worst case are so-called systematic deceivers, which are assumed to know (e.g., by clairvoyance) whether the meta-inductivist will choose them as favorite for the next time: they deliver a worst (i.e. minimal-score) prediction whenever the meta-inductivist chooses them as their favorite, while they deliver a correct prediction whenever they are not chosen as a favorite. In the result, the success rates of two or more systematic deceivers oscillate around each other with a nondiminishing amplitude of • > ©, in a way such that ©MI gets permanently deceived. Theorems and computer simulations concerning ©MI are found in Schurz (2008, 5). The negative result concerning ©MI generalizes to all kinds of one-favorite metainductivists: they must fail to be optimal whenever they play against systematic deceivers. The only way for one-favorite meta-inductivists to deal with systematic deceivers is to avoid them: the so-called avoidance meta-inductivist aMI introduced in Schurz (2008, 6) is provably optimal in regard to non-deceivers, but not in regard to deceivers. In conclusion, one-favorite meta-inductive method cannot predict optimally in regard to deceivers. Do other kinds of meta-inductivists strategies exist which can even handle deceivers and, hence, are universally optimal? In the next section we will see that they do indeed exist: the so-called weighted average meta-inductive prediction methods. I have found these methods – although unrelated to the problem of induction – in the literature on (non-probabilistic) online prediction based on expert advice (cf. Bianchi and Lugosi 2006).

23.4 Weighted Average Meta-Induction A weighted average meta-inductivist predicts a weighted average of the predictions of the non-MI-players. The weighted average meta-inductivist is abbreviated as wMI and defined as follows. For every non-MI-player P we define atn .P/ WD sucn .P/  sucn .wMI/ as P’s attractiveness (as a favorite) at time n. Let PP(n) be the set of all non-MI-players with positive attractiveness at time n. Then wMI’s prediction for time 1 is set to 1/2, and for all times > 1 with non-empty PP.n/ ¤ ¿ it is defined as follows: P P2PP.n/ atn .P/ pn C 1 .P/ P 8n  1 W pnC1 .wMI/ D at .P/ P2PP.n/

n

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In words: wMI’s prediction for the next round is the attractiveness-weighted average of the attractive players’ predictions for the next round. (Should it happen that PP(n) gets empty, pnC1 .wMI/ is reset to 1/2.) Informally explained, the reason why wMI cannot be deceived is the following: a non-MI-player who tries to deceive wMI would be one who starts to predict incorrectly as soon as his attractiveness for wMI is higher than a certain threshold. The success rates of such wMI-adversaries must oscillate around each other. But wMI does not favor just one of them (who predicts incorrectly in turn), but wMI predicts according to an attractiveness-weighted average of correctly and incorrectly predicting adversaries, and therefore wMI’s long-run success must approximate the maximal long-run success of his adversaries. Theorem 2 establishes wMI’s long-run optimality under the (natural) assumption that loss functions l.pn ; en / are convex in pn . It is easy to see that the natural loss-function l.pn ; en / WD jpn  en j is convex, but there exist many other convex loss-functions, and theorem 2 applies to all of them (a proof of theorem 2 is found in Schurz 2008, 7, th. p4). Also wMI’s short-run performance is good, as the worst-case short-run loss m=n quickly vanishes for times n >> m. Theorem 2. For every real-valued prediction game ((e), fP1 ; : : : ; Pm ; wMIg) whose loss-function l.pn ; en / is convex in the argument pn , the following holds: p (2.1) (Short run:) .8n  1 W/ sucn .wMI/  maxsucn  m=n. (2.2) (Long-run:) sucn .wMI/ (strictly) approximates the non-MI-players’ maximal success for n ! 1. Theorem 2 does not apply to binary prediction games, because even under the assumption that the events and the non-MI-player’s predictions are binary, i.e. values 2 f0; 1g, wMI’s predictions will (usually) not be binary but some real values between 0 and 1. Nevertheless I found a way to apply theorem 2 indirectly also to the prediction of binary events, namely by means of assuming a collective of k metainductivists, abbreviated as cwMI1 ; : : : ; cwMIk , and by considering their mean success rate (‘cwMIi ’ stands short for ‘collective weighted-average meta-inductivist no. i’). wMI’s real-valued prediction is approximated by the mean value of the k binary predictions of the collective of cwMI-meta-inductivists as follows: Œpn  k cwMI’s predict 1, and k  Œpn  k cwMI’s predict 0, where [x] is the integer-rounding of x. In this way, one obtains an approximate optimality result for the mean success rate of collective of cwMI’s, abbreviated as sucn .cwMI/, which differs from the success rate of wMI’s ‘ideal’ real-valued prediction by an additional worst-case loss 1 , that reflects the maximal loss due to the integer-valued approximation of the of 2k real number pn by Œpn  k=k (see Schurz 2008, 8, th. 5). Figure 23.2 shows a computer simulation of a collective of ten cwMI’s playing against 4 specially designed cwMI-adversaries, who predict incorrectly as soon as their attractiveness gets higher than a variable threshold. Theorem 2 and its variant for binary prediction games establish that (collective) weighted-average meta-induction is indeed a universally optimal meta-inductive

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4 worst-case deceivers (thick-grey) 10 cwMIs (thin) cwMI's mean success (bold) approximates maximal success Event-sequence: binary

(logarithmic)

Fig. 23.2 Ten cwMI’s against four cwMI-adversaries

prediction method. In prediction games in which systematic deceivers are excluded, weighted average meta-induction converges to the method of one-favorite metainduction MI.

23.5 Applications to the Evolution of Cognition Meta-inductive methods are not (weakly) dominant in regard to all competing prediction methods; they are only (weakly) dominant in regard to so-called noninductive methods (cf. Schurz 2008, 9). The reason for this fact is the existence of refined conditionalized (meta-) inductive strategies, which exploit correlations in non-random worlds between the success-rates of the non-MI-methods and certain environmental conditions with help of Reichenbach’s principle of the narrowest reference class (1949, 72). Assume fR1 ; : : : ; Rr g is a partition of events (internal or external to the event-sequence) which are correlated with the success-rates of the non-MI methods, and R.n/ WD Rin is the partition’s cell realized at time n. Then at each time n, the conditionalized meta-inductivist xMI uses the conditional success rates of the players P, sucn .PjR.n//, as the basis of his meta-inductive method. While the unconditional xMI ©-approximates the maximal success always from below, the success rate of a conditionalized xMI may even become strictly greater than the success rates of all other players. This fact shows that xMI can improve his success by getting access to conditionalized meta-inductivist methods (which then have to be included in the class of non-MI-methods; thus “non-MI” means “nonconditionalized-MI”). The latter fact is of particular relevance for the application of meta-induction to the evolution of cognition. In the evolutionary setting, I consider inductive strategies as strategies of learning within an individual’s lifetime. In contrast, non-inductive strategies correspond to genetically determined strategies which cannot be modified

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Fig. 23.3 condMI in an evolutionary scenario with five changing environments

by individual learning. In particular, meta-inductivistic strategies are strategies of learning from the performance of other successful individuals of one’s population. Given this evolutionary interpretation of meta-induction, my optimality result provide a general argument for the advantage of populations which possess the capability of cultural evolution, by imitating the most successful members of one’s population (in the sense of Richard Dawkins concept of ‘memes’; cf. 1989, ch. 11). Of course, evolutionary organisms are never perfect – perfect clairvoyants (which have to be considered in the epistemological context) do not play any realistic evolutionary role. Therefore I assume the constraint of imperfection, which says that for each non-MI-strategy there exist some environmental conditions in which its success is low. Under this condition, conditionalized meta-inductive strategies turn out to be not only weakly but even strongly dominant – i.e., dominant in all prediction games satisfying the constraint of imperfection. Figure 23.3 illustrates a simulation of the performance of conditionalized MI, abbreviated as condMI, in a prediction game with five different environments which change after 50 rounds: conMI’s success rates climbs high above the success rates of the non-MI-players, because in each given environment condMI takes advantage of exactly that strategy which performs best in this environment. For sake of comparison, Fig. 23.3 informs also about success rate of the unconditional MI under the hypothetical assumption that condMI’s predictions are not accessible to MI – otherwise MI would of course predict equally good as conMI (apart from a small short-run loss).

References Cesa-Bianchi N, Lugosi G (2006) Prediction, learning, and games. Cambridge University Press, Cambridge Dawkins R (1989) The selfish gene, 2nd edn. Oxford University Press, Oxford

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Gigerenzer G et al. (1999) Simple heuristics that make us smart. Oxford University Press, New York Kelly KT (1996) The logic of reliable inquiry. Oxford University Press, New York Norton J (2003) A material theory of induction. Philos Sci 70:647–670 Reichenbach H (1949) The theory of probability. University of California Press, Berkeley, CA Schurz G (2008) The meta-inductivist’s winning strategy in the prediction game: a new approach to Hume’s problem. Philos Sci 75:278–305 Skyrms B (1975) Choice and chance, 4th edn 2000. Wadsworth, Dickenson, Encino

Chapter 24

Multiple Contraction Revisited Wolfgang Spohn

24.1 Introduction Belief revision theory studies three kinds of doxastic movements: expansions, revisions, and contractions. Expansions and revisions are about learning or acquiring new beliefs. Expansion is the unproblematic case where the new belief is consistent with the old ones and can hence be added without further ado. Revision is the problematic case where the new belief is inconsistent with the old ones and can hence be accepted only when some of the old beliefs are given up; the problem is to find rules for this process. Contractions are directly about giving up beliefs without adding new ones. If we require beliefs to be deductively closed, this is problematic, since we cannot simply delete the belief in question; the remaining beliefs would entail it in turn. So, again the problem is to find rules for this process. There is an argument over the priority of these doxastic movements. As I have presented them, revision seemed to be a composite process, a contraction followed by an expansion. This view is championed by Isaac Levi, e.g., in Levi (2004). Others wonder how there can be genuine contractions; even for giving up beliefs you need to get a reason, i.e., to learn something. There is no need to decide the argument. I think there are good reasons for taking revisions and contractions to be on a par, firmly connected by Levi’s and by Harper’s identity (cf., e.g., G¨ardenfors 1988, sect. 3.6). This paper will be mainly about contractions and mention revisions only supplementarily. I believe that the three movements are dealt with by the well-known AGM theory (Alchourr´on et al. 1985; G¨ardenfors 1988) in a completely satisfactory way; I shall state my main reason below. Of course, there is a big argument over the adequacy of the AGM postulates for revision and contraction; see, e.g., the many alternative postulates in Rott (2001, ch. 4). However, let us be content here with the standard AGM theory.

W. Spohn () Department of Philosophy, University of Konstanz, 78457 Konstanz, Germany e-mail: [email protected]

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Still, there are problems the standard theory cannot cope with. One kind of problem concerns the rules for making several movements. I state this so vaguely, because the problem takes at least two forms. The main form is the problem of iteration first raised in Spohn (1983, ch. 5). How should you revise or contract your beliefs several times? What are the rules for doing so? Some iterative postulates seem accepted, some are contested (see the overview in Rott 2009), and the issue is still very much under dispute. A minor form is a problem first discussed by Fuhrmann (1988); it is about multiple contraction, as he called it. There the issue is to give up several beliefs not one after the other, but at once. This is a relevant issue. Suppose you read a newspaper article, and you accept all details of its surprising story. In the next issue, the journalist apologizes; the article was a 1st April’s joke, a make-believe from the beginning to the end. In this way, it is not uncommon that several of your beliefs at once turn our not to be maintainable. In fact, Fuhrmann and Hansson (1994) distinguish two forms of multiple contraction. The contraction of a set fA1 ; : : : ; An g of beliefs may take the form of choice contraction where you are requested to give up at least one of the beliefs A1 ; : : : ; An . This form is probably uninteresting; in any case it has a simple solution: the request is the same as that for a single contraction of the conjunction of A1 ; : : : ; An ; if you give up the conjunction, you have to give up at least one of the conjuncts. Hence, this case is covered by standard AGM contraction. The other form is what they call package contraction where you are indeed asked to give up all the beliefs A1 ; : : : ; An , as it was in my example above. Now the answer is not obvious at all; we shall see below why the obvious attempts are inadequate. In fact, as far as I know, the problem has not found a satisfactory solution. Fuhrmann and Hansson (1994) propose some axioms partially characterizing package contraction, but they are quite tentative about these axioms and apparently not satisfied. Fuhrmann (1997) does not get beyond these axioms, and Hansson (1999, sect. 2.16) acquiesces in a weak axiomatization, which, however, he is able to show to be complete relative to the weak semantics he proposes. As far as I know, the problem became neglected afterwards. The goal of the paper is to present a complete and satisfactory solution. As observed by Hansson (1999, sect. 3.17) there is the parallel problem of multiple revision by a set fA1 ; : : : ; An g of beliefs. In package revision, you are asked to accept all of the new beliefs A1 ; : : : ; An . This is obviously the same as accepting their conjunction, and thus the case reduces to single AGM revision. In choice revision, you are requested to accept at least one of those beliefs, and again there is no obvious answer. (Note that you may accept their disjunction without accepting any of the disjuncts; so accepting their disjunction is no way to meet to request.) The problem is as difficult as that of package contraction. I assume it can be solved by similar means. However, I shall not pursue this case here, since it seems artificial and without natural applications, unlike the case of package contraction. The basis of my solution is ranking theory, as I have developed it in Spohn (1983, 1988); see also my survey in Spohn (2009). It proposes a general dynamics of belief which comprises expansions, revisions, and contractions as special cases,

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which is iterable, and which hence solves the problem of iterated belief revision and contraction. Hild and Spohn (2008) show which set of laws of iterated contraction is entailed by ranking theory and proves its completeness. Ranking theory also provides a plausible model of multiple contraction, as I hope to show below; the behavior of multiple contraction entailed by it will turn out to be quite simple. The issue is much less involved than the problem of iteration. The plan of the paper is straightforward. In Section 24.2 I shall explain the problem of package contraction in formal detail. Section 24.3 will introduce the ranking theoretic material as far as needed. Section 24.4, finally, will present the ranking theoretic account of package contraction.

24.2 The Problem of Multiple Contraction Let me first recall the AGM account of contraction, in an equivalent form. The standard way is to represent beliefs, or rather their contents, by sentences, presumably because one wanted to do logic. However, the formalism is much simpler when beliefs are represented by propositions; one need not worry then about logically equivalent sentences. This is the way I always preferred. Hence, let W be a non-empty set of possibilities or possible worlds, and A be an algebra of subsets of W . The members of A are propositions. For the sake of simplicity, I shall assume A to be finite; but nothing depends on this. The first notion we need is that of a belief set: Definition 1. K is a belief set iff K is a proper filter in A, i.e., iff, given the finiteness of A, there is a proposition C.K/ ¤ ¿, the core of K, such that KDfA 2 AjC.K/ Ag. By assuming C.K/ to be non-empty, I exclude inconsistent belief sets right away. Deductive closure of belief sets is built into definition 1 and into the propositional approach. In this approach the AGM theory of contraction looks thus: Definition 2. is a single contraction for the belief set K iff is a function from A – fW g into the set of belief sets such that: (a) K A K [Inclusion] (b) if A … K, then K A D K [Vacuity] (c) A … K A [Success] (d) if B 2 K, then A ! B 2 K A [Recovery] (where A ! B D AN [ B is the set-theoretic analogue to material implication) (e) K A \ K B K .A \ B/ [Intersection] (f) if A … K .A\B/, then K .A\B/ K A [Conjunction] These are the set-theoretic translations of the AGM contraction postulates. The closure postulate is part of my characterization of the range of , and the extensionality

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postulate is implicit in the propositional approach. The necessary proposition W cannot be given up and is hence excluded from the domain of ; one might certainly acknowledge more necessary propositions, as AGM actually do. AGM also assume the contraction function to work for all belief sets; here, it suffices to define it only for a given belief set K. So much is settled. Now, let B be any set of non-necessary propositions in A – fW g, and let K ŒB denote multiple contraction in the package sense. The intended meaning is clear; all the propositions in B, insofar they are believed in K, have to be given up. How and according to which rules is package contraction to be carried out? Is it definable in terms of single contractions? In order to develop a sense for the difficulty of the problem, let us look at the simplest genuine case where B D fA; Bg, i.e., at the contraction K ŒA; B of two propositions A and B from K. It may obviously not be explained as K A \ B. To contract by the conjunction guarantees only that at least one of the conjuncts has to go; but the other may be retained, and then the package reduction would be unsuccessful. Success, i.e. .K ŒB/ \ B D ¿, is, no doubt, a basic requirement. In other words: it would be wrong to equate package contraction with choice contraction. They agree only in the degenerate case of contraction by a singleton. Nor may package contraction K ŒA; B be explained as K .A [ B/. This would guarantee success; if the disjunction has to give way, the disjuncts have to do so, too. However, the proposal is clearly too strong. One may well give up both disjuncts while retaining the disjunction; in any case, this should not be excluded. Package contraction must also be distinguished from iterated contraction. The easiest way to see this is that iterated contractions need not commute; we may have .K A/ B ¤ .K B/ A. When one asks in such a case with which of the two terms K ŒA; B should be identified, the obvious answer is: with none. There is no such asymmetry in the idea of package contraction. Hansson (1993) gives a nice example in which commutativity of iterated contractions intuitively fails. In the ongoing conflict between India and Pakistan, troops have been sent to the border from both sides. A friend has told me that an agreement has been reached between the two countries to withdraw the troops. I believe in this. I also believe that each of the two governments will withdraw its troops if there is such an agreement, but for some reason my belief in the compliance of the Pakistan government is stronger than my belief in the compliance of the Indian government. Let s denote that there is an agreement to withdraw troops on both sides, p that the Pakistan government is going to withdraw its troops and q that the Indian government is going to withdraw its troops. Then (the relevant part of) my belief base is fs; s ! p; s ! qg. Case 1. The morning news on the radio contains one single sentence on the conflict: “The Indian Prime Minister has told journalists that India has not yet decided whether or not to withdraw its troops from the Pakistan border.” When contracting q, I have to choose between retaining s and s ! q. Since my belief in the latter is weaker, I let it go, and the resulting belief base is fs; s ! pg. The evening news also contains one single sentence on the conflict, namely: “The Pakistan government has officially denied that any decision has been taken on the possible withdrawal of Pakistan troops from the Indian border.” I now have to contract p. This involves a

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choice between retaining s and retaining s ! p. Because of my strong belief in the latter, I keep it, and the resulting belief base is fs ! pg. Case 2. The contents of the morning and evening news are interchanged. In the morning, when contracting p from the original belief base fs; s ! p; s ! qg, I retain s ! p rather than s, because of the strength of my belief in the former. The resulting belief base is fs ! p; s ! qg. The contraction by q that takes place in the evening leaves this set unchanged. (Hansson 1993, p 648)

Fuhrmann and Hansson (1994) discuss a final option, namely that K ŒA; B D K A \ K B. Then, even though package contraction is not an ordinary contraction, it might be explained in the latter terms and thus could be reduced away as an independent phenomenon. However, they are not happy with that option, either, because they believe to see its incompatibility with the approach they chose instead (cf. Fuhrmann and Hansson (1994), p 62). I believe they were mistaken, as we shall soon see. On the other hand, it is intuitively not fully perspicuous that this should be the right explanation. So, one must look for another approach, anyway. The only approach left for Fuhrmann and Hansson (1994) is the axiomatic one: if we cannot define package contraction, we can at least try to characterize it. And so they start appropriately generalizing the AGM postulates. This works convincingly for Inclusion, Vacuity, Success, and Recovery, and they even produce representation results for their generalization (see their theorem 9 on p 59). However, they are not sure what to do with Intersection and Conjunction; Sven Ove Hansson told me that he no longer believes in the proposals made there on p 56. Instead, in Hansson (1999, sect. 2.16) he offers a different axiomatic characterization in the AGM style. That is, he generalizes the notion of a selection function so basic to the AGM approach to the notion of what he calls a package selection function and then proposes to define package contraction as a partial meet package contraction relative to such a package selection function. The relevant axiomatization contains adaptations of Inclusion, Vacuity, and Success and a strengthening of Recovery called P-relevance; it does not contain, however, anything corresponding to Intersection and Conjunction that are so important to single contractions. Since, no progress seems to have made on this point.

24.3 Required Basics of Ranking Theory I believe that ranking theory can help here and provide a plausible account of multiple contraction in the package sense. In order to present it, I have to develop the relevant portion of ranking theory. The basic notion is this: Definition 3. › is a ranking function for A iff › is a function from A into N0 D N [ f1g such that (a) ›.W / D 0 and ›.¿/ D 1 (b) ›.A [ B/ D min f›.A/; ›.B/g

[the law of disjunction].

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Ranks are to be understood as degrees of disbelief. ›.A/ D 0 says that A is not disbelieved; ›.A/ > 0 says that A is disbelieved (to some degree); hence N > 0 expresses belief in A. (a) and (b) entail ›.A/ N D 0 or both (c) either ›.A/ D 0 or ›.A/

[the law of negation].

Of course, both may be 0, in which case › is neutral or unopinionated about A. N > 0g is indeed a The law of negation and the law disjunction ensure that fAj›.A/ consistent and deductively closed belief set. Let us denote this belief set by K.›/. A main reason for giving the basic role to disbelief rather than belief is the following definition of conditional ranks (that would be less perspicuous in terms of degrees of belief): Definition 4. If ›.A/ < 1, the rank of B 2 A given or conditional on A is defined as ›.BjA/ D ›.A \ B/  ›.A/. Equivalently, we have (d) ›.A \ B/ D ›.A/ C ›.BjA/

[the law of conjunction]

that says that your degree of disbelief in A-and-B is given by your degree of disbelief in A plus the additional degree of disbelief in B given A. This is intuitively most plausible. The dynamics of subjective probabilities is stated in various conditionalization rules in terms of conditional probabilities. Likewise, the definition of conditional ranks helps us stating a dynamics of belief and disbelief. The idea is not simply that by learning A you move to the ranks given A. This would assume that you learn A with maximal certainty that can never be undone. The idea is rather that you learn A with some, but not necessarily maximal firmness, as Jeffrey conditionalization (Jeffrey 1965, ch. 11) proposes in the probabilistic case. If, following Jeffrey, we assume, moreover, that by learning A your conditional ranks given A and given AN do not change, we are able to state our first rule of belief change: Definition 5. Let ›.A/ < 1 and n 2 N0 . Then, the A,n-conditionalization ›A;n of N the ranking function › is defined by ›A;n .B/ D min f›.BjA/; n C ›.BjA/g. It is easily checked that this preserves conditional ranks given A and given AN N D n so that A is believed with firmness n in and that ›A;n .A/ D 0 and ›A;n .A/ ›A;n . It is also clear that only ›A;n has these two properties. So, the idea is that, rationally, your posterior belief state is always some A,n-conditionalization of your prior belief state. Note that this form of conditionalization can be arbitrarily iterated. Thus ranking theory has no problem with iterated belief change. We shall need a slight generalization of definition 5. Jeffrey has already envisaged the possibility that experience or learning induces you to have changed probabilities for several propositions. We can copy this in ranking theory. Let E be any (experiential) subalgebra of A, and let œ be any ranking function for E expressing your experientially acquired degrees of disbelief for E. Then we have: Definition 6. The E; œ-conditionalization ›E;œ of › is defined by ›E;œ .B/ D min f›.BjA/ C œ.A/jA is an atom of Eg.

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(Here, the atoms of E are the logically strongest, i.e., smallest consistent propositions in E; they partition E.) This entails that ›E;œ .A/ D œ.A/ for all A 2 E and, again, that all conditional ranks given any atom of E are preserved; they do not change just by learning news about E. All these definitions are intuitively motivated and well entrenched in ranking theory, a point that can be hardly conveyed in such a brief sketch. For details, I refer the interested reader to the survey in Spohn (2009). A,n-conditionalization generalizes expansion, revision, and contraction. If you N D 0, then for any n > 0 the are initially unopinionated about A, i.e., ›.A/ D ›.A/ A,n-conditionalization of › obviously amounts to an expansion of your initial belief set K.›/ by A (and indeed for any n > 0 to the same expansion). If you initially disbelieve A, i.e., ›.A/ > 0, then for any n > 0 the A,n-conditionalization of › amounts to a revision of K.›/ by A (and again for any n > 0 to the same revision). The A,0-conditionalization of your initial › makes you unopinionated about A. If N you initially believe A, this change is a contraction by A; if you initially believe A, N it is a contraction by A. Thus, we may define: N < 1, then the contraction ›A of › by A is given by ›A D Definition 7. If ›.A/ N D 0, and ›A D ›A;0 , if ›.A/ N > 0. is a ranking contraction for K iff ›, if ›.A/ for some ranking function › K D K.›/ and K A D K.›A / for all A 2 A  fW g. As observed in Spohn (1988, footnote 20), expansion, revision, and contraction thus explained in a ranking theoretic way satisfy exactly the AGM postulates. In particular, is a single contraction according to definition 2 if and only if it is a ranking contraction. Since I am fond of ranking theory, this is my main reason for accepting all the AGM postulates. Conditionalization indeed generalizes these forms of belief change in several ways. One aspect is that the three forms do not exhaust all ways of A,n-conditionalization; for instance, A may be initially believed and thus the belief in it only be strengthened or weakened by learning. The other aspect is iteration. definition 7 can obviously be iterated and thus provide a model of iterated contraction. Hild and Spohn (2008) give a complete set of postulates governing iterated contraction thus construed. So, let us see how these ideas may help with our present problem of multiple contraction.

24.4 A Ranking Theoretic Account of Multiple Contraction We start with a ranking function › for A and a set B A of propositions, and we ask how to change › and its associated belief set K.›/ so that none of the propositions in B is still believed in ›. It is clear that we may restrict attention to B 0 D B \ K.›/, the propositions in B believed in ›, since contraction is vacuous for the other propositions in B. Section 24.2 has shown, moreover, that we may have to deal with

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logical combinations of propositions in B 0 . Let us focus hence on the algebra B  of propositions generated by B 0 . There is no reason why propositions outside B  should become relevant. T 0 Now we should proceed as follows. We should start with contracting B, the strongest proposition in B  believed; it must be given up in any case. This is the same as choice contraction by B 0 , and we have noted that it removes at least some beliefs in B 0 . If we are lucky, it even removes all beliefs in B 0 ; then we are done with the package reduction. This would be exceptional, though. Normally, we shall have moved from the prior belief set K.›/ D K0 to a smaller belief set K1 K0 which still believes some propositions in B 0 . So, in a second step, we again proceed as cautiously as possible and contract the strongest proposition in B  still believed, T i.e., fA 2 B  jA 2 K1 g. Possibly, package contraction is now completed. If not, we have arrived at a belief set K2 K1 that still holds on to some other beliefs in B 0 . Then we add a third step, and so on until all beliefs in B 0 are deleted. This procedure must stop after finitely many steps. The conception behind this procedure is the same as in ordinary contraction of a single proposition: change as little as possible till the contraction is successful, where minimal change translates here into giving up the weakest beliefs, the negations of which receive the lowest positive ranks. Let us cast thisTinto formal definition: Let fE0 ; : : : ; Ek g be the set of atoms of B  . Let E0 D B 0 . So, ›.E0 / D 0 and ›.Ei / > 0 for i D 1; : : : ; k. Hence, the first contraction informally described above is an E0 , 0-conditionalization. Thereby, some further atoms receive rank 0, say E1 and E2 , so that E3 [    [ Ek is still disbelieved. The second contraction outlined above then is an E1 [ E2 ,  0-conditionalization. And so on. Let R D f›.E/jE is an atom S of B g be the set  of ranks occupied by the atoms of B . Let m D min fn 2 Rj fEjE is an atom of B  and ›.E/ > ng AN for all A 2 B 0 g. If we set only all atoms E with ›.E/ < m to 0, contraction of the whole of B 0 is not yet completed; if we set all atoms E with ›.E/  m to 0, contraction of B 0 is successful, and if we set more atoms to 0, we have contracted more than necessary. So, m is the margin where our contraction procedure stops. Hence, define the ranking function œ on B  by œ.E/ D 0 if ›.E/  m and œ.E/ D ›.E/  m if ›.E/ > m (and œ.A/ for non-atoms A of B  according to the law of disjunction). My proposal for explicating package contraction thus results in the following Definition 8. Let ›; B; B , and œ be as just explained. Then, the package contraction ›ŒB of › by B is the B  ; œ-conditionalization of ›. And the package contraction K.›/ ŒB of the belief set K.›/ of › by B is the belief set of K.›ŒB /. In this way, package contraction turns out as a special case of generalized conditionalization specified in definition 6. Note that my intuitive explanation of package contraction was in terms of successive contractions; but in order to describe the result in one step we require the expressive power of generalized conditionalization.

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It easily checked that this model of package contraction satisfies all the postulates endorsed by Fuhrmann and Hansson (1994, pp 51–54). If we accept the explication, we can immediately complete their theory of package contraction. First, it is obvious from the construction above that: (1) if B C, then K.›/ ŒC K.›/ ŒB. A fortiori, we have (2) K.›/ ŒB \ K.›/ ŒC K.›/ ŒB \ C, which translates into the ranking framework what Fuhrmann and Hansson (1994, p 56) propose as generalization of Intersection. Moreover, it is obvious from our construction that: (3) if for all B 2 B B … K.›/ ŒC, then K.›/ ŒC K.›/ ŒB [ C. If by contracting S C the whole of B is contracted as well, our iterative procedure for contracting B C must stop at the same point as that for contracting C. (3) is what Fuhrmann and Hansson (1994, p 56) offer as generalization of Conjunction. Thus, their tentative proposals are in fact confirmed by our model. Indeed, the most illuminating result concerning our explication is: (4) K.›/ ŒA1 ; : : : ; An  D K.›/ A1 \    \ K.›/ An . Proof. (1) entails that K.›/ ŒA1 ; : : : ; An  K.›/ Ai for i D 1; : : : ; n. This proves one direction. Reversely, assume that K.›/ A1 \    \ K.›/ Ai 1 K.›/ ŒA1 ; : : : ; Ai 1 . If Ai … K.›/ ŒA1 ; : : : ; Ai 1 , then K.›/ ŒA1 ; : : : ; Ai  D K.›/ ŒA1 ; : : : ; Ai 1  and there is nothing more to show. If Ai 2 K.›/ ŒA1 ; : : : ; Ai 1 , then ›ŒA1;::: ;Ai 1  .ANi / > 0, and hence C.K.›/ ŒA1 ; : : : ; Ai / D C.K.›/ ŒA1 ; : : : ; Ai 1 / [ fw 2 ANi j›.w/  ›.w0 / for all w0 2 ANi g D C.K.›/ ŒA1 ; : : : ; Ai 1 / [ C.K.›/ Ai /. Thus, K.›/ A1 \    \ K.›/ Ai K.›/ ŒA1 ; : : : ; Ai . This inductively proves the reverse direction. I take this to be a desirable theorem. It might have been difficult to motivate it as a definition of package contraction; but if it is a consequence of a plausible explication, this establishes mutual support for the explication and the theorem. In some sense, the theorem may also be disappointing. It says that package contraction is reducible to ordinary single contraction, after all, and is not an independent general issue. I am not sure whether I am thereby contradicting Fuhrmann and Hansson (1994). They have doubts about (1) (see there p 62) and hence about the ensuing assertions. However, the doubts are raised only on their weaker axiomatic basis intended to leave room for denying (1)–(4). Hansson (1999) no longer comments on the properties (1)–(4). Thus, the only disagreement we may have is that I cannot share the doubts about (1), find my explication in definition 8 utterly plausible, and do not see any need, hence, to retreat to a weaker axiomatic characterization.

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References Alchourr´on CE, G¨ardenfors P, Makinson D (1985) On the logic of theory change: partial meet functions for contraction and revision. J Symbol Logic 50:510–530 Fuhrmann A (1988) Relevant logics, modal logics, and theory change. Ph.D. Thesis, Australian National University, Canberra Fuhrmann A (1997) An essay on contraction. CSLI, Stanford Fuhrmann A, Hansson SO (1994) A survey of multiple contractions. J Logic Lang Inform 3:39–76 G¨ardenfors P (1988) Knowledge in flux. Modeling the dynamics of epistemic states. MIT Press, Cambridge, MA Hansson SO (1993) Reversing the Levi identity. J Philos Logic 22:637–669 Hansson SO (1999) A textbook of belief dynamics. Theory change and database updating. Kluwer, Dordrecht Hild M, Spohn W (2008) The measurement of ranks and the laws of iterated contraction. Art Intelligence 172:1195–1218 Jeffrey RC (1965) The logic of decision, 2nd edition, 1983. University of Chicago Press, Chicago, IL Levi I (2004) Mild contraction: evaluating loss of information due to loss of belief. Oxford University Press, Oxford Rott H (2001) Change, choice and inference: a study of belief revision and nonmonotonic reasoning. Oxford University Press, Oxford Rott H (2009) Shifting priorities: simple representations for twenty seven iterated theory change operators. In: Makinson D, Malinowski J, Wansing H (eds) Towards mathematical philosophy. Springer, Dordrecht, pp 269–295 Spohn W (1983) Eine Theorie der Kausalit¨at, unpublished Habilitationsschrift, Universit¨at M¨unchen, pdf-version at: http://www.uni-konstanz.de/FuF/Philo/Philosophie/philosophie/ files/habilitation.pdf Spohn W (1988) Ordinal conditional functions. A dynamic theory of epistemic states. In: William LH, Skyrms B (eds) Causation in decision, belief change, and statistics, vol II. Kluwer, Dordrecht, pp 105–134 Spohn W (2009) A survey of ranking theory. In: Huber F, Schmidt-Petri C (eds) Degrees of belief. An anthology. Springer, Dordrecht, pp 185–228

Chapter 25

Statistical Inference Without Frequentist Justifications Jan Sprenger

25.1 Frequentist Statistics and Frequentist Justifications In modern science, inductive inference often amounts to statistical inference. Statistical techniques have steadily conquered terrain over the last decades and extended their scope of application to more and more disciplines. Explanations and predictions, in high-level as well as in low-level sciences, are nowadays fueled by statistical models. However, this development did not occur because scientists believe the underlying systems to be irreducibly stochastic. This might sometimes be the case, but certainly not in general. Rather, even traditionally “deterministic” sciences (such as several branches of physics, psychology and economics) use statistics to model noise and imperfect measurement and to express their uncertainty about the nature of the data-generating process. A wide spectrum of techniques can be used to draw valid conclusions from data: Hypothesis tests help scientists to see which of two competing hypotheses is better supported. Confidence intervals narrow down the set of values of an unknown model parameter which is compatible with the observations. And so on. The classical methodology to answering these questions is frequentist inference (cf. Cox 2006). For reasons that will soon become obvious, I believe the term “frequentism” to be a misnomer. Rather, as pointed out by Mayo (1996), that school of statistical inference is characterized by a focus on the probability of making an error in the inference to a certain hypothesis or in setting up a confidence interval – hence, the name error statistics. A statistical procedure is good if and only if the two probabilities of committing an error – accepting a hypothesis when it is false, rejecting it when it is true – are low. For instance, assume that you want to test whether in a culture of 10,000 cells, less than 5% have been infected with a certain virus. That is your working hypothesis. To perform the test, you draw a sample of 100 cells. Then you formulate a decision rule whether or not to accept that hypothesis, dependent on

J. Sprenger () Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands e-mail: [email protected]

M. Su´arez et al. (eds.), EPSA Epistemology and Methodology of Science: Launch of the European Philosophy of Science Association, DOI 10.1007/978-90-481-3263-8 25, c Springer Science+Business Media B.V. 2010 

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how many infected cells are in your sample. You calculate the error probabilities of that rule – i.e. the probability that you accept the hypothesis when more than 5% of all cells are infected, and the probability that you reject it when less than 5% are infected. The lower these probabilities, the more powerful and the better your test, in the sense that your conclusions are more reliably produced. Finally, you look at the data and come up with a conclusion according to your decision rule. This example can easily be transferred to other applications of statistics in science. The rationale behind these procedures is that the more sensitive a hypothesis test which suggests a certain conclusion, the more substantial and reliable the conclusion which the test yields (Neyman and Pearson 1967; Mayo 1996). The crucial question – the one this paper tries to answer – is why probabilistic properties of such a test should affect rational decisions and actions (i.e. to base the next experiment on hypothesis H rather than on :H ). What precisely does it mean that a test has error probabilities of, say, 0.01 and 0.034 for the two types of error? How do they relate to real life losses? And why are these values relevant for our decision to accept or to reject our working hypothesis in a specific, concrete problem?1 An answer is suggested by the popular repeated sampling rationale of statistical inference. Statistical data are considered to be a (small) sample out of a (large) population, and in principle, the sampling process could be replicated. Thus, the error probabilities of a test are interpreted as relative frequencies of making an error if the sampling procedure were repeated. For instance, if the probability of erroneous rejection is 0.01, then, if this test were repeated very often, we would erroneously reject our hypothesis only in about 1% of all cases where it is true. In particular, if the test were repeated infinitely often, the rate of erroneous rejection would almost surely settle at 0.01, due to the Strong Law of Large Numbers. This is supposed to justify our confidence in a particular inference: “We intend, of course, that this long-run behavior is some assurance that with our particular data currently under analysis sound conclusions are drawn.”2

We call this a frequentist justification of statistical inference – our actual inference is supported by the long-run properties of the procedure(s) we use in our inference. In other words, we can confidently endorse the result of our test because, if the test were repeated, we would rarely go wrong. In a similar vein, Neyman and Pearson, the founding fathers of the error-statistical approach, write: “Œ: : : we shall reject H when it is true not more, say, than once in a hundred times, and in addition we may have evidence that we shall reject H sufficiently often when it is false.”3

However, the frequentist justification of inductive inference is not limited to frequentist, error-statistical inference – it can be applied in Bayesian statistics as well. Bayesians aim at posterior probabilities of a hypothesis H conditional on evidence E which they calculate by means of Bayes’s Theorem: 1

See Baumann (2005) and Sprenger (2009) for a discussion of this issue with respect to the Monty Hall Problem. 2 Cox 2006, 8. 3 Neyman and Pearson 1967, 142.

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P .H jE/ D ŒP .H /P .EjH /=ŒP .H /P .EjH / C P .:H /P .Ej:H /:

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The values of P(H) and P .:H / are, on a Bayesian account, standardly interpreted as the subjective degrees of belief in the truth of hypothesis H. However, the other probabilities that occur – the so-called likelihoods P .EjH / and P .Ej:H / – fulfill the same role as error probabilities above: they are probabilities of certain events under specific hypotheses (H is true vs. H is false). Thus we can assign them a repeated sampling interpretation as well: if we draw a lot of samples out of a H -distributed population, the actual evidence will occur in a fraction of cases roughly equal to P .EjH /. What remains to argue is that these repeated sampling properties bear on the credences we have, and the inference we make. Although an answer seems obvious (“just set your credence to the computed probability”), it is hard to argue for this step without invoking circularity. Why should the non-subjective, statistical property P .EjH / affect our rational credences? Howson and Urbach (1993, chapter 9), in their philosophical monograph on Bayesian inference, make recourse to frequentist justifications: They (correctly) observe that the value of P .EjH / makes an assertion about the frequency of observing E in a long, potentially infinite run of scenarios where H is true. That said, they argue that our credences should be equal to each other for each element of such an infinite run, and therefore, they have to correspond to the limiting relative frequencies. Thus they give a frequentist justification of statistical inference in a single case. Hence, frequentist justifications do not only arise in frequentist statistics, but in all varieties of probabilistic inference. For this reason, I find the term “frequentist statistics” misleading.4 However, are frequentist justifications justified at all?

25.2 Against Frequentist Justifications The frequentist justification of statistical inference has been under pressure from various sides, some in the philosophy of statistics, others in the philosophy of probability. Objective (as opposed to purely subjective) probabilities have often been interpreted as limiting relative frequencies (von Mises 1928), i.e. the meaning of a probability statement such as P .EjH / D x was identified with the fact that in an infinite run of trials where H were the case, the limiting frequency of E would approach x in [0,1]. This account has been popular among scientists and philosophers alike because metaphysical assumptions about the nature of probability are avoided. However, Albert (2005) points out that a frequentist, repeated sampling interpretation of objective probability (and in particular, statistical probability) cannot support rational credences in single cases, i.e. our degree of belief that we have actually committed an error. The limiting relative frequency of, say, erroneous rejection 4 However, from a historical point of view it is certainly true that frequentist justifications emerged from the error-statistical school of statistical inference (in particular from Jerzy Neyman), and this explains why frequentist statistics got their name.

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does, as a matter of mathematical fact, not impose any constraints on the expectedness of erroneous rejection in a finite set of tests.5 Any result in a finite set of tests is compatible with any limiting frequency because in the limit, the “weight” of the finite segment will be zero.6 For instance, even if there are one million successes and no failures in a coin flip trial, this is still perfectly compatible with all limiting relative frequencies in (0, 1]. In other words, whether a test erroneously rejects a hypothesis under test is logically independent of the limiting frequency of rejection in the infinite run. Limiting relative frequencies cannot ground confidence in our inferences and following acceptance/rejection rules in a particular case. Albert intends to make a point against the connection between frequentist justifications based on a repeated sampling interpretation of probability and rational credences. That is not to be confused with the (false) claim that probability theory does not tell us anything about finite samples. For instance, with increasing sample size we increase the sensitivity of a hypothesis test, too. This is not contentious. Rather, Albert shows that, if all we assume about statistical probabilities is that they determine limiting relative frequencies, we cannot make meaningful assertions about finite samples. The point of frequentist justifications was to circumvent a difficult task: namely, to describe the link between mathematical, statistical probabilities and rational credences and decisions. The lesson of the above criticism is that we cannot avoid to address that question by invoking limiting frequencies. In other words, we need a bridge principle connecting objective statistical probabilities and rational beliefs and decisions. Standardly, the Principal Principle (Lewis 1980) has played this role. I do not want to bother with the technicalities of the various formulations of the Principal Principle, but it can be seen as the attempt to capture the idea that  if we know that the objective probability of E, given information H , is q  if we do not have any “inadmissible” information that affects these probabilities

then our rational credence that E, conditional on H , should be equal to q. Obviously, the Principal Principle serves as the desired bridge principle. The likelihoods P .EjH / and P .Ej:H / are probabilities of certain observations under fixed distributions H or :H , and so are the error probabilities P .reject H jH / and P .reject :H j:H / since the decision whether or not to reject depends exclusively on the observations. Thus, both types of probabilities are objective probabilities and the Principal Principle applies. However, Strevens (1999) has argued that it is difficult to justify the Principal Principle in a non-circular way; and claiming that it is “evidently true” seems to beg the question against those who don’t believe in bridge principles between objective and subjective probability. Therefore, invoking the Principal Principle is not a convincing way to justify statistical inference. Rather, we should address the following two questions:

5 I refer the reader to Albert (2005) for a detailed reply to the argument by Howson and Urbach (1993) sketched at the end of Section 25.1. 6 Strevens (1999) makes the same point with respect to “long-run propensity” interpretations.

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 What kind of objective probabilities are statistical probabilities – and more gen-

eral, probabilities in scientific modeling?  Why do these probabilities affect rational decisions?

25.3 Artefactual Probabilities At the end of his (2005), Albert mentions that due to the failure of repeated sampling interpretations to account for the normative force of statistical inference, we might be pressed to understand objective probabilities as propensities, i.e. irreducible causal tendencies to bring about a certain result. For instance, a Pb210 atom might have an irreducible tendency of 1/2 to decay in the next hour. However, this interpretation comes with several drawbacks that have been discussed extensively in the literature.7 For our problem, it is most salient that propensity interpretations take probabilities as features of the world, e.g. as a causal power or irreducible tendency to bring about a certain event. However, it is questionable that practicing statisticians need to accept such a strong, realist interpretation of objective probability. Maybe the world has no stochastic features at all. Even in such circumstances, our statistical inference ought to be meaningful, and if all objective probabilities have to be propensities, this desideratum might be lost. Instead, we require a minimal interpretation of objective probabilities – an interpretation that vindicates their normative force for probabilistic inference, without making too many metaphysical commitments. To my mind, the lack of distinction between objective and ontic probability (cf. Rosenthal 2004) is the culprit for the lack of an account of the normative force of statistical probability. Ontic theories understand probabilities, or at least certain types of probabilities, as features of the world, such as mass, charge or entropy. Probabilities become properties of a physical system or a certain experimental arrangement. Of course, all ontic accounts are objective: there is a fact of the matter about the true value of an ontic probability; thus, in case of disagreement at least one side is wrong. However, objective probabilities need not be ontic – there might be probabilities whose value is unanimously accepted but which are not grounded in the material world. I believe that statistical probabilities are of that type. My account of statistical probabilities is the artefactual interpretation (cf. Gillies 2000, 179). It is motivated by the very idea of statistical modeling. When we are modeling a physical system, we are not so presumptuous to believe that our (probabilistic) model will capture all aspects of the system, and that inconsistent observations are merely the result of measurement inaccuracies. Such a complete stochastic model is rather the exception than the rule – it might be found in some fundamental branches of science, but certainly not in complex disciplines as in economics, psychology, or geophysics. In those sciences, we know very well that most

7

See Eagle 2004 for a comprehensive critique.

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of the time, there is no “correct” statistical model, or at least, we will not be able to find it. So we should not understand our statistical model as outright guesses about the true model. Rather, we idealize the target system into a mathematical model and hope that we approximately caught the interesting and fundamental properties of the system. This will help us to understand the system’s dynamics and governing mechanisms as well as to make reasonable predictions. But in making inferences about the model, we are well aware of the imperfections of the model. In particular, conclusions about the model transfer to the target system only cum grano salis. Therefore I contend that, when we use probability as a scientific modeling tool, we do not take it literally, e.g. as the belief that the studied population is fundamentally, irreducibly normally or exponentially distributed. (Note that these two distributions are themselves mathematically convenient idealizations of discrete distributions!) Rather we reason like this: “OK, let’s assume for the sake of convenience that the random variables .X1 ; : : : ; Xn / are independent and all Normally distributed, and let’s see what we can infer about the population mean (e.g.  0 vs. > 0).”8 In other words, we act as if the suggested distributions – call them again H and :H – were the only two possible models of the underlying system. We imagine a world in which an event E were more expected if H were true than if :H were true, and we take this to be the meaning of P .EjH / (respectively P .Ej:H /) and the basis of our statistical inference. Of course, reality might be quite unlike that imagined worlds H and :H . Still, we can compare those models with the help of real data. Therefore I call the probabilities of observations which are calculated in such an imagined probability model artefactual probabilities – they are the offsprings of our mathematical artefact, the probability model.9 I believe that artefactual probabilities capture the way working statisticians and empirical scientists reason about probability. For them, (objective) probability is mainly a modeling tool, and it should not be taken to mean more than that.10 But can statisticians really dismiss the metaphysics of probability so easily? When an error statistician rejects a null hypothesis in favor of an alternative, isn’t she committed to accepting the claims the alternative makes? Aren’t we suspect to the realist argument that when a theory works well, we should have an account of the quantities it posits? Are theories where chances figure not similar to theories where electrons or quarks figure? I don’t think so. Probabilistic models are often used although it is crystal-

8 In that example, P . jH / and P . jH / are not uniquely determined because H and :H are composite hypotheses (  0 vs. > 0 with fixed or unknown variance). Bayesians rescue the objectivity of these probabilities by assigning a prior distribution over , and frequentists have their own sophisticated techniques to solve the problem; however, to explain them would go beyond the scope of this paper. 9 It might be argued that the artefactual interpretation, instead of giving a new account, rather argues that interpretation questions are irrelevant to the problem of justifying statistical inferences. But I believe that the above explanations help us to understand what happens when scientists use probability as a modeling tool. 10 The ongoing popularity of frequentist conceptions might be due to the history of modern statistics, where quite a lot of influential figures (such as Jerzy Neyman and Richard von Mises) have defended a frequentist justification or interpretation of statistics.

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clear that they are not literally true, but rather a refined prediction tool. They are just the only way to make sense of the apparently messy, biased and untidy data that we collect, apt to model sampling error even if the sampling process was not genuinely random. Some more explanations might help. Clearly, artefactual probabilities qualify as objective: typical statistical assertions as (%) “If a coin is fair, the chance of getting two ‘heads’ in two independent and identically distributed tosses is 1/4.” are objective and not open to subjective disagreement. Rather, it is part of the meaning of a fair coin that, if two i.i.d. tosses are performed, the chances of observing two times “heads” are 1/4. Artefactual probability statements are conditionals where the antecedens specifies a certain distribution and the consequence gives the probability of a particular event under that distribution. Therefore they avoid the conceptual confusion of frequentism as well as the metaphysical hazzles of propensity accounts. Note that statistical inference builds on conditional statements such as (%) and does not require giving meaning to unconditional assertions about probabilistic mechanics in the real world, such as (&) “That particular coin is fair”. Propensity accounts have, historically, been motivated by the need to explicate such sentences – e.g. what it means that a particular, material coin is fair. I do not doubt that this is a challenging semantical and ontological question and deserves serious philosophical scrutiny. I just believe that science does not need to bother with this business – for matters of inductive inferences, conditional assertions such as (%) are fully sufficient, regardless of the preferred school of statistical inference. Bayesians and error statisticians can, for this matter, happily agree – the only objective probabilities which they need are of type (%), not of type (&). Therefore statisticians can restrict themselves to artefactual probabilities. It remains to argue why artefactual probabilities are normatively compelling. Recall that Strevens (1999) pointed out the problem of justifying bridge principles between objective and subjective probability, such as the Principal Principle. Part of his argument was the observation that it is impossible to establish a logical or semantic connection between ontic probability and subjective degrees of belief: The ones are in the material world, the others in our head. If one accepts that all objective accounts of probability have to be ontic (unless they are beset with other difficulties), then the skeptical conclusion apparently follows. However, as argued above, there is no need to accept this identification. In particular, we have developed an objective, non-ontic account of conditional probability assertions in statistics. These conditional accounts make it possible to defend the transfer of objective probability to rational expectations on semantic grounds: When scientists work with artefactual probabilities, they use probability as a model for reasoning about uncertainty. They decide to act as if P .jH / (or P .j:H /) really gave the expectations for the observations which we make. In other words, the act of statistical modeling is free of

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ontological elements. All that they assume is that in this imagined model, some events are more expected than others. Our inductive inference builds on considerations that the observed event is more surprising under one distribution than under another, as witnessed by the key role of likelihood ratios both in frequentist statistics (Neyman-Pearson Lemma) and Bayesian inference. To repeat, when building and analyzing a statistical model we firstly abstract from a target system that is too complex to model in every nuance, and secondly, we interpret the different distributions in the model as making assertions about the expectedness of certain events. Models can then be compared each other in terms of how expected they render the real data, and the more expected our actual findings, the better the model, ceteris paribus. Thus, skepticism with respect to bridge principles between objective and subjective probability does not concern us: the act of statistical modeling itself creates the crucial link to rational expectations. The reader might find that the account which I sketched resembles Gillies’s own (2000) account of artefactual probabilities and Sober’s (2009) No-Theory Theory (NTT) of objective probability. But there are subtle, and important, differences. Gillies uses the term “artefactual probabilities” as a subclass of objective probability and distinguishes them from “fully objective” probabilities, as the probability that a uranium atom disintegrates in a given time interval. But he also claims that artefactual probabilities “can be considered as existing in the material world”.11 This is certainly nothing I would subscribe to because it is, to my mind, the very point of artefactual probabilities that they avoid reference to the material world and that they are mere artefactual objects, byproducts of scientific modeling – Sober, on the other hand, likens probability to intrinsic properties of physical objects, such as mass and charge, and claims that like the aforementioned concepts, probability cannot be reduced to anything else. Certainly, by considering conditional probability as an objective relation between pairs of propositions, he is quite close to parts of my own position. But his analysis misses the imaginative, artefactual character of probability in scientific modeling, and he goes on with an argument for the reality of certain probabilities in the world. Again, I am not interested in correspondence relations between probability and the material world.

25.4 Conclusion The failure of frequentist justifications of statistical inference – justifications that draw on the long-run properties of sampling distributions – triggers the question how to explicate the link between mathematical probability calculations and sound scientific inference. This task arises for Bayesian statisticians and error-statisticians alike. Certainly, statisticians need to link conditional probabilities – probabilities of evidence given a hypothesis – to their rational beliefs. I have argued that this

11

Gillies 2000, 179.

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connection can be established by adopting the artefactual interpretation of objective probability. Thereby we conceive statistical probabilities as rational expectations in imagined worlds. This gives an account of inductive reasoning in statistics that avoids metaphysical commitments and is thus close to the practice of empirical science. Moreover, skepticism with respect to bridge principles between subjective and objective probability, such as the Principal Principle, does not apply when the proposed artefactual interpretation is adopted. Acknowledgements I would like to thank Stephan Hartmann, Sebastian Lutz, Jacob Rosenthal, Gerhard Schurz, Jos Uffink, and the audience at the First Conference of the European Philosophy of Science Association in Madrid, (EPSA07) for helpful discussion and suggestions.

References Albert M (2005) Should Bayesians bet where frequentists fear to tread? Philos Sci 72:584–593 Baumann P (2005) Three doors, two players and single-case probabilities. Am Philos Q 42:71–79 Cox D (2006) Principles of statistical inference. Cambridge University Press, Cambridge Eagle A (2004) Twenty-one arguments against propensity analyses of probability. Erkenntnis 60:371–416 Gillies D (2000) Philosophical theories of probability. Routledge, London Howson C, Urbach P (1993) Scientific reasoning: the Bayesian approach, 2nd edn. Open Court, La Salle, IL Lewis D (1980) A subjectivist’s guide to objective chance. In: Richard CJ (ed) Studies in inductive logic and probability, vol II. University of California Press, Berkeley/Los Angeles Mayo DG (1996) Error and the growth of experimental knowledge. University of Chicago Press, Chicago, IL Mises R von (1928) Wahrscheinlichkeit, Statistik und Wahrheit. Springer, Wien Neyman J, Pearson E (1967) On the problem of the most efficient tests of statistical hypotheses. In: Neyman J, Pearson E (eds) Joint statistical papers. University of California Press, Berkeley. Originally published in 1933 Rosenthal J (2004) Wahrscheinlichkeiten als Tendenzen. Mentis, Paderborn Sober E (2009) Evolutionary theory and the reality of macro probabilities. In: Eells E, Fetzer J (eds) Probability in science. Open Court, La Salle, IL Sprenger J (2009) Probability, rational single-case decisions and the monty hall problem. Forthcoming in Synthese, doi:10.1007/s11229-008-9455-y Strevens M (1999) Objective probability as a guide to the world. Philos Stud 95:243–275

Chapter 26

Carnap and the Perils of Ramseyfication Thomas Uebel

26.1 Introduction Frank Ramsey’s proposed regimentation of the theoretical terms of scientific theories has been much discussed recently as an articulation of the position of “structural realism”, a position intended to take its place between scientific realism and its denials. My concern here is different. It is to consider what the now standard criticism of the method of “ramseyfication” – based on Newman’s objection to Russell’s structuralism – means for Rudolf Carnap’s adoption and development of that method from the perspective of Carnap’s own philosophical programme and whether it could accommodate the objection.

26.2 Carnap’s Method of Ramseyfication In papers and book chapters first published between 1959 and 1966, Carnap presented his final proposal for the reconstruction of scientific theories.1 Its first step followed Ramsey (1929) according to which all of the theoretical terms of a finitely axiomatized theory can be replaced by variables while retaining the same explanatory and predictive power of the original theory. This involves combining all the theoretical postulates (which define theoretical terms) and correspondence rules of a theory (which link some of these theoretical terms with observational ones) in one long sentence and then replacing all the theoretical predicates that occur in it. So let the conjunction of the theoretical postulates (call this “T”) and the conjunction of the correspondence rules (call this “C”) be conjoined to represent the original theory (call this “TC”) and then replace the theoretical terms in TC by bound higher-order variables (call this “R(TC)”, the “Ramsey sentence”). Since R(TC) and TC differ only in that the theoretical terms in TC are replaced by variables in R(TC), R(TC) T. Uebel () University of Manchester, Manchester, England e-mail: [email protected] 1

See Carnap (1959), (1963, 24C-D), (1966 [1995, Chs. 26 and 28]).

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“represents the full observational content of a theory” (Carnap 1966 [1995, 254]). In order to distinguish between analytic and synthetic statements in the theoretical language – which he had been unable to until then – Carnap proposed the following second step. Since R(TC) and TC are extensionally equivalent, let “R(TC) -> TC” express the purely analytic component of the theory, what he called its “A-postulate AT ” (nowadays called its “Carnap sentence”). In consequence, the original theory is best understood as reconstructed not just by its Ramsey sentence itself, but only by it together with its Carnap sentence, namely by “R(TC) & (R(TC) -> TC)”. As Carnap himself put it, the A-postulate R(TC) -> TC, “coupled with the Ramsey sentence itself, will then L-imply the entire theory” (ibid.; cf. 1963, 965). Note Carnap’s strategy: understood simply as the conjunction TC, an empirical theory did not allow for the separation of its synthetic and analytical components. Thus he “propose[d] another way in which the theory TC can be split into two sentences that, taken in conjunction, are equivalent to the theory” (1966 [1995, 270]), namely, the Ramsey and the Carnap sentences. So Carnap’s solution of the problem of analyticity in the theoretical language leaves the received view and its model of partial interpretation of theoretical terms undisturbed. Instead it turns on the original theory being represented by the conjunction of its Ramsey and the Carnap sentences. Yet how are we to understand the latter? First, the Carnap sentence provides only a conditional meaning specification. It says that if the ramseyfied theory is true, then so is the original theory with theoretical terms unreplaced.2 Second, the Carnap sentence operates holistically. It maps the system of bound higher-order variables (call these the “Ramsey variables”) into a certain set of non-logical terms of the original theoretical language. For Carnap, it identifies the set of denotata of theoretical terms as a set of nodes in a mathematical structure in which observable events are embedded. Carnap’s adoption of the Ramsey method met mainly with criticism. (When, by contrast, ramseyfications continue to be discussed approvingly as a method of characterising theoretical terms and determining a theory’s ontological commitment, they are understood as supplemented with conditions not yet introduced by Carnap.) It is important to establish just what the criticism of Carnap’s use of ramseyfications amounts to determine whether Carnap himself would have to accept it.

26.3 Carnap’s “Empirical Realism” and his Explicationist Programme Scientific realists typically hold that ramseyfication does not accord theoretical terms their full due: it does not respect their ontological independence from the observational base but reduces the truth of the theory to the truth of its observational consequences. For that to be a criticism that Carnap has to respect, he has to share its assumptions.

2

See Carnap (1966 [1995, 270–271]) for various formulations.

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Support for such an interpretive position appears to come from someone who should know. In his ground-breaking 1950 foray into scientific realism Herbert Feigl claimed Carnap for his side (1950a, 60; 1950b, 191–192 and 194). Notably, Feigl held the position, which in 1950 he dubbed “semantical realism”, to be identical in spirit with one he had earlier called “empirical realism”. Given this supposition, Feigl’s claim on Carnap appears not unreasonable, given that Carnap himself asserted allegiance to what he called “empirical realism” (Carnap 1945 [1949, 345n]). Yet when Carnap called Feigl’s position a “closely related point of view” in a footnote in his own “Empiricism, Semantics and Ontology” (1950b [1956, 214n]), he did so at the conclusion of a paragraph outlining the difference between internal and external questions.3 Carnap referred to Feigl’s own reservations against metaphysical “questions of reality”. However, Feigl seems to have understood by “metaphysics” only “the justification of the assertion of the ‘independent existence’ of the designata of hypothetical constructs” (1950a, 50, emphasis added). For Carnap, metaphysics started not only with the “justification” of such assertions but already with the reification of entire categories of such hypothetical constructs, as it were, independently of the theoretical language they formed part of Feigl (1950b [1956, 214]). To be sure, Feigl also conceded that, to begin with, the introduction of systems of entities as understood by semantical realism was not an issue of truth or falsity but one of pragmatic usefulness. But he concluded, as one recent discussion rightly notes, that whether an entity “should be considered real depends on whether or not this entity is an indispensible and irreducible element of the well-confirmed nomological framework of science” (Psillos 1999, 45). Feigl took one additional step that Carnap would not take: Feigl drew ontological consequences from pragmatic considerations. The agreement with “empirical realism” that Carnap noted himself only amounted to partial agreement with Feigl. When Carnap lauded the “great clarity and convincing arguments” with which Feigl (and Carl Gustav Hempel) “expounded” a view that was also his own, he meant the view that “terms like ‘temperature’ in physics or ‘anger’ and ‘belief’ in psychology are introduced as theoretical constructs rather than as intervening variables of the observation language” and that sentences containing them cannot be reduced to sentences of the latter (Carnap 1955 [1956, 230]). This suggests that we distinguish between “empirical realism” and “semantical realism”. Even though for Feigl they meant the same, they did not for Carnap. Empirical realism and semantical realism agree in conceding the irreducibility of disposition terms and terms for unobservables and that statements concerning such terms are fallibly truth-valuable. By contrast, semantical realism as understood by Feigl, but not empirical realism as understood by Carnap, takes quantification over variables of a given category to legitimate existence claims for the system of entities to which the given category belongs. Carnap’s “empirical realism”, however, does not exceed the bounds of answers to what he called “internal questions” (1950b). 3

Carnap (1950b) appeared independently of Feigl (1950a) and the exchange about the latter in Philosophy of Science.

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Thomas Mormann has aptly suggested that Carnap understood philosophy as a “science of possibilities” (2000, 133 and 210–211). For Carnap, it was not the business of philosophy to tell us what the world is really like (behind the veil of appearances, as it were). Nor was it its business to determine the essence of things (what they had to be if they were those kind of things at all). Telling us what the world is like was the business of science. Of course, Carnap was happy to investigate what characteristics we were entitled to expect from things falling under certain categories, but whatever such investigations turned up were not essences in the traditional sense at all. The reason was that these categories were themselves but part of larger conceptual frameworks, and of these there existed a great number not all of which were intertranslatable.4 Any putative essences could be counted essential only relative to the framework under investigation. Carnap was interested not so much in determining what we are constrained to say, come what may, but rather in demonstrating the possibilities that existed for expressing whatever we might find that wants expression. Carnap’s own name for his philosophical strategy was “explication”. Explicationism entails a pluralist attitude and frees up what in earlier years he called “rational reconstruction” from mapping an imaginary pre-given, essential structure: contested concepts may be reconstructed in a variety of ways with none of them being able to claim exclusivity in doing so.5 The consequences of these considerations for the assessment of Carnap’s adoption of ramseyfication are clear: whatever the value of scientific realism may be, it would be wrong to use it as a yardstick for an assessment from his own perspective. Rather, immanent criticism would have to show ramseyfications to be inconsistent with his empirical realism and the aims of his explicationist programme.

26.4 The Problem with Ramseyfication The problem with Carnap’s ramseyfications also is not that in ramseyfied theories “all the factual content is in : : : the Ramsey sentence” (1966 [1996, 270]). This might be taken to spell instrumentalism, but this would overlook not only the higher-order quantifiers, but also that the Ramsey sentence “expresses in an observation language extended to include all of mathematics, everything that the theory says about the actual world” (ibid., emphasis added). The mathematical structure in which the observable events are embedded is absolutely crucial for Carnap. Nor is the problem that the Ramsey variables are interpreted as representing “purely logico-mathematical entities, e.g. natural numbers, classes of such, classes of classes, etc.” (1963, 963). For Carnap the Ramsey sentence asserted that “observable events in the world are such that there are numbers, classes of such, etc., which are correlated with events in a prescribed way and which have among them4 Carnap’s awareness of the possibility of incommensurable frameworks was expressed fully explicitly in Carnap (1936), but it was already implicit in his Logische Syntax (1934). 5 See Carnap (1950a, 3–5) and Carus (2007) for further discussion.

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selves certain relations” and that this is “clearly a factual statement about the world” (ibid.). Carnap here had mathematical physics in mind where space-time points are represented by quadruples of real numbers and physical properties like electrical charge-density or mass-density are represented as functions of such quadruples of real numbers. While Feigl complained that such a strictly extensional interpretation of the Ramsey variables failed to specify an intensional interpretation and single out the intended interpretation of the theory, Carnap clearly thought it an advantage of the method that it remained suitably indeterminate.6 Whatever problems realists may have with this, it was not a problem Carnap shared. The problem properly focussed upon is that his proposal apears to fall foul of arguments deriving from M.H.A. Newman’s objection to Bertrand Russell’s structuralism in Analysis of Matter (rediscovered in 1985 by William Demopoulos and Michael Friedman). Newman’s objection says that once they are empirically adequate, ramseyfied theories are trivially true, given the mathematical nature of their reconstruction of the original theories. Russell held that “nothing but the structure of the external world is known”. But if nothing is known about the generating relation that produces the structure, then the claim that there exists such a structure is vacuous, Newman claimed. “Any collection of things can be organised so as to have the structure W , provided there are the right number of them.” (Newman 1928, 144) In other words, subject only to a cardinality constraint on its intended domain, any consistent theory is true if and only if all of its empirical consequences are true. Sometimes the Newman objection is taken to turn on the thought that more is involved in the truth of the theoretical sentences of an empirical theory than the mere satisfaction of a cardinality constraint (over and above empirical adequacy). But the problem goes deeper still. The problem is that, subject only to its empirical adequacy, the cardinality condition is fulfilled trivially. Given the amount of mathematics that went into expressing the ramseyfied theory via the “extended observation language” some such structure as demanded by the Ramsey-sentence is bound to be found among those entities presupposed by its representational apparatus. The cardinality constraint is no constraint at all. This consequence gives rise to the complaint that for ramseyfications generally “the truth of physical theory reduces to the truth of its observational consequences” (Demopoulos and Friedman 1985 [1994, 195]). For Carnap Newman’s result threatens still further consequences. If the reconstruction of empirical theories by ramseyfication is unacceptable, then all explications that build on this are called into question: explications of theoretical analyticity as much as explications of the experiential import of theories. Yet since Carnap himself appears to have been unaware of Newman’s criticism of Russell and its applicability to ramseyfications, it is up to his interpreters to adjudicate the case.

6

See Carnap (1961, 2000) and the discussion in Psillos (2000a, 157–8).

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26.5 Psillos’ Criticism It is to Stathis Psillos that we owe the story behind Carnap’s own “rediscovery” of the Ramsey method.7 But taking the position of scientific realism Psillos also argues that since the Newman objection applies to Carnap’s use of ramseyfication, it signals the end of his anti-realist road. Psillos has provided two arguments against Carnap’s position. Aware that defenders of Carnap would challenge his realist assumptions, he sought to show the untenability of his ramseyfications in other ways. Thus his first argument is directed against Carnap’s so-called neutralism with respect to the question of the existential implications of scientific theories: no ontological commitments to unobservable entities are dictated by scientific theories, but scientific theories are not merely instruments for ‘prediction and control’ either. (1999, 42; cf. 2000b, 255)

Given his view that “the difference between the Ramsey-sentence proponents and scientific realists is that the former stick to R(TC), while the latter also accept the meaning postulate R(TC)->(TC)” (1999, 60; cf. 2000b, 268–269) and that Carnap embraces both R(TC) and R(TC)->(TC), Psillos characterises Carnap’s neutralism also as one between “a realist or a Ramsey-sentence understanding of scientific theories” (2000b, 269).8 Psillos argues that Carnap betrayed his neutralism repeatedly. Carnap failed – even if, he claims, we grant the distinction between existential statements concerning individual facts and existential statements concerning classes of the denotata of conceptual frameworks, which underpins his distinction between legitimate internal and illegitimate external questions. “Carnap’s empiricism should be happy with internal existential claims concerning physical unobservable entities”; since instrumentalists would not accept this claim, however, “the alleged neutrality of Carnap’s empiricism is betrayed” (1999, 44; cf. 2000b, 256). More betrayals are said to follow from Carnap’s dual interpretation of the Ramsey-sentences. If he were to stick exclusively to the extensional interpretation, which take Ramsey-variables to refer to classes, classes of classes, etc., “theories are still taken to be nothing but mathematical models in which observable phenomena are embedded”, but with this contrast to scientific realism “Carnap seems to betray his neutralism once more” (1999, 55; cf. 2000b, 264). Yet if Carnap allows intensional interpretations he is no better of: “If an intensional language is admitted, he cannot escape existential commitments to unobservable entities (properties).” (1999, 57; cf. 2000b, 265). It is not impossible to resist these arguments. Carnap’s extensional and intensional interpretations of Ramsey-sentences represent two ways in which internal questions about scientific existence claims can be answered.9 To complain that 7

See Psillos (1999, Ch.3; 2000a,b). That the Carnap sentence R(TC)->(TC) is not happily represented as characterising scientific realism seems to have been recognised by Psillos since (see below). 9 Psillos (2009) argues that Carnap preferred intentional interpretations, but both are, for him, legitimate. 8

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either interpretation violates ontological neutrality is to overlook precisely this. For instance, why should internal questions be unacceptable to instrumentalists? Not because they are ontologically committing in a way that satisfies a realist. The point is that they are unacceptable to both realists and instrumentalists alike, for Carnap did not play their game. To dub Carnap’s position “neutralism” is to put a misleading slant on it. Carnap was not “neutral” between realism and antirealism: instead, he rejected both positions. His own stance was not one of indifference between the ontological commitments of the instrumentalist and the realist, but a position that even rejects the ontological commitments both of them share, namely, to observables.10 The neutralism that Psillos undermines was not Carnap’s – which remains undisturbed.11 More recently Psillos returned to the matter noting that the Newman result “might not have bothered Carnap” (Psillos 2006, 77). This second argument advanced by Psillos turns on his complaint that, according to Carnap, “[e]mpiricism can accommodate the claim that theories are true, without going a lot beyond empirical adequacy” (ibid.). In other words, Carnap’s take on ramseyfications is not different enough from instrumentalism. Psillos thus notes that Carnap “deflated the issue of the possible existential commitment to physical unobservable entities by taking the existentially bound Ramsey-variables to [range over] mathematical entities” (ibid.)12 This “extensional treatment of the theoretical discourse” which regards theories as “nothing but mathematical models in which observable events are embedded” (1999, 55) is deemed to be implausible. Yet as Psillos has shown by reference to Carnap’s correspondence with Feigl (1999, 54–5; 2000b, 263), this was but one of the possibilities that Carnap envisaged, namely, the extensional interpretation of the Ramsey-variables. Carnap was equally happy to allow for an intensional interpretation on which the Ramsey-variables range over physical entities or properties. Of course, for scientific realists this is too superficial, for they want such an interpretation not just to be available but to be obligatory. Psillos concludes that what there is to Carnap’s conception of the truth of theories over and above empirical adequacy are “non-empirical non-synthetic commitments to a meaning postulate” (Psillos, personal communication) – in other words, commitment to the Carnap-sentence of a theory. And he rightly complains that this “non-empirical non-synthetic” commitment is just too thin for a realist. (It may be wondered how to square this with Psillos’ claim that Carnap’s ramseyfication model “collaps[es] his empiricism to some form of structural realism” (2000b, 275), but it must be remembered that, for Psillos, structural realism is a form of realism manqu´e – and also does not represent enough of an improvement over instrumentalism.) Whatever its worth on its own accord, however, Psillos’ second argument also is not one whose conclusions Carnap himself would accept. Claiming that the

10

See Carnap (1950b [1956, 206–207]). Here I disregard certain formulations in (the first edition of) Philosophical Foundations of Physics that Carnap later withdrew as misleading (see Psillos 1999, 58–61). 12 Here “range over” replaces “extend beyond” in the published version; in so replacing the latter I follow Psillos’ personal communication. 11

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central role empirical adequacy plays in ramseyfication “trivialises the search for truth” in scientific theories (2006, 78), it presupposes the scientific realist perspective. (We can call it the “ontological version” of the Newman objection.)

26.6 Demopoulos’ Criticism Consider Demopoulos’ renewal of the charge first made with Friedman. “The Carnap-Ramsey reconstruction is unacceptable because it implies that the existence of an abstract model for [the theory] suffices for its truth over [the theory’s] intended domain.” (Demopoulos 2003, 388. orig. emphasis) Demopoulos’ charge is not that no unique interpretation is provided but that the existence of an abstract mathematical model suffices to render the empirical theory true (given consistency and empirical adequacy). Such a mathematical model is available all too easily: “We take the truth of [the theory] over its intended domain to be a significant truth, not one that is ensured by what is virtually a purely logical argument.” (Ibid., 388) Only restrictions of the cardinality of a domain could prevent the imposition of certain structures on that domain, but given Carnap’s preference for an extensional interpretation and his assumption of an extended observation language, no such restrictions on the domain can follow. Put differently, “the difficulty is that theoretical sentences, though factual, are almost logical truths and hence, in Carnap’s reconstruction, almost analytic” (Demopoulos 2007, 262, orig. emphasis). What’s “almost analytic” is the satisfaction of the claim that there exists a structure that satisfies the postulates laid down in R(TC) – due to its triviality just outlined. Since the diagnosis that ramseyfication misrepresents the synthetic nature of empirical theory does not trade on the critic’s adoption of or on the attribution to Carnap of a metaphysical scheme he did not subscribe to, it is not as easily deflected as the ontological version of the Newman objection. (We can call it its “epistemic” version.) Since there are two remarks in Carnap’s writings that may suggest ways of accomodating Newman’s result, I will now discuss their viability in turn. The first proposal recommends that Carnap should return to his 1956 position which allowed for a criterion of empirical significance for theoretical terms but not for the analytic/synthetic distinction to be sustained with regard to the theoretical language. All the same it promised to save the explicationist programme in that it appeared possible to distinguish narrow logical truth from factual truth in the theoretical language. Indeed, this was Carnap’s own fall-back position before he hit upon ramseyfication: For a while I thought we would perhaps have to resign ourselves to taking a sentence that contained theoretical terms and no observation terms as analytic only under the most narrow and almost trivial conditions that it is L-true. For example: ‘Either a particle is an electron or it is not an electron.’ (1966 [1995, 273–4])

To return to this position, of course, means to abandon the Ramsey method altogether.

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It is important to note that even in this reduced form, explications could still be given that draw significant distinctions between closely related but different empirical theories and determine what has been called the “relative a priori” of a given theory: logico-linguistic presuppositions not amenable to direct testing.13 To do so, all Carnap needs to be able to do is draw distinctions between basic logical terms and descriptive terms. To see what this involves, consider how Carnap was able to distinguish between the status of geometry in special and in general relativity (1934, 50). Carnap was able to show that the semantic status of the term for the metrical fundamental tensor is different in each. In the context of geometries of constant curvature (as in special relativity), that term constitutes a logical term in what can be called the extended sense: its value is determinable by the physical and mathematical laws (and the transformation rules of the language) alone.14 By contrast, in the context of geometries of variable, mass-energy-dependent curvature (as in general relativity) the term for the metric constitutes a descriptive expression: its value is not determinable by the physical and mathematical laws (and the transformation rules of the language) alone, but also the distribution of matter in space-time must be known. Given that, by contrast, both Schlick and Reichenbach appear misled about the epistemic status of geometry in general relativity (their reconstructions rendered it conventional),15 this analysis shows that the distinction between descriptive and logical terms in this extended sense can do important work in the explication of scientific theories. Unfortunately, however, it is not unproblematic to want to classify statements as analytic on the basis of vocabulary alone.16 It is possible to construct sentences using only logical terms that could be classified as synthetic. (Consider the example “Every two things differ in at least thirty respects”.) Such sentences are only strictly speaking synthetic, for they are logically true except for cardinality constraints on their domain. (The problem of these statements is similar to that of ramseyfied theories, but in this case it is their analytic character, not their synthetic one, that is under pressure.) If this objection is granted, then Carnap’s fall-back position becomes still more minimal than at first envisaged. To be sure, Carnap would retain the basic distinction between the logical (in their basic and extended sense) and the factual – albeit drawn in terms of vocabulary alone (and then only with reference to lists of logical terms). But while the explicationist project would by no means have ground to a total halt (as our example shows), it would be radically reduced. The crucial distinction that Carnap’s explicationist programme has to retain is that between framework and content. Typically this is drawn in terms of statements – analytical and synthetic ones – but this now no longer seems possible. It is difficult to avoid thinking that this strategy of meeting the epistemic Newman objection admits of defeat in all but name.

13

On the notion of the relative a priori in early logical empiricism, see Friedman (1994). Carnap only used the unqualified expression “logical term”. 15 See Ryckman (1992). 16 I am indebted to Bill Demopoulos for spelling out this objection to me in correspondence. 14

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Here’s an alternative proposal. We may consider following another advice Carnap once gave, namely, that theoretical terms can be given a direct interpretation: We can, of course, state a rule for any term, no matter what its degree of abstractness, in a form like the: ‘the term “te” designates temperature’, provided the metalanguage used contains a corresponding expression (here the word ‘temperature’) to specify the designatum of the term in question. (Carnap 1939, 62)

In this case one could determine the analytical sentences of the observation as well as the theoretical language to be simply those that follow from the logical and semantical rules of the language in question. This would circumvent the possibility that due to the reliance on reduction sentences, correspondence rules or even theoretical postulates, the characterisation of analytical statements in the theoretical language is compromised by their factual meaning components (which was where the trouble started). This proposal suggests that Carnap did not have to look to the Ramsey method for a characterisation of analyticity in the theoretical language, but that he had available the resources needed for that all along. There are worries, however, even supposing that the standard one that correspondence rules and theoretical postulates ruin the sharp analytic/synthetic distinction due to their own partly empirical, partly meaning-constitutive nature could be allayed. Thus Hempel discounted the possibility of giving direct interpretations as besides the point for they “will be intelligible only to those who understand the metalanguage in which they are expressed” (Hempel 1963, 696; cf. 1958 [1963, 217]). Hempel’s worry was that, since assigning a direct interpretation presupposes an antecedent grasp of the terms to be interpreted, it is useless for anyone who does not yet understand the theoretical terms in question. Carnap himself endorsed Hempel’s criticism, indeed anticipated it, for he followed his own suggestion for direct interpretations of theoretical terms with the remark that they “would not do” for the purpose of enabling laypersons to connect their observations to the system of physics so as to arrive at predictions and explanations (1939, 62). Carnap seems to have considered everyone’s epistemic position vis-`a-vis theoretical terms like that of the layperson learner. Unlike these, of course, physicists also know about the implicit definitions that link all the theoretical terms into a system, but that system, he stressed, remains wholly uninterpreted as long as no connection to observable states of affairs is established via the correspondence rules (ibid., 60–61, 67). Years later Carnap stated categorically: “There is no independent interpretation for LT . The system T is in itself an uninterpreted postulate system.” (Carnap 1956, 47) Since “all the interpretation (in the strict sense of the term, i.e., observational interpretation) that can be given for LT is in the C-rules”, direct interpretations (in the non-strict sense) were only a “didactic help : : :” for understanding the theory expressed by LT (ibid., 46). Since the second proposal for “saving” Carnap from the seeming “misadventure” of his adoption of ramseyfication would involve abandoning the partial interpretation model, it must be considered uncongenial to Carnap’s project as well. It would shift his position much more closely to semantic realists like Feigl than he would have been comfortable with.

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26.7 Conclusion Championing a deflationist interpretation of Carnap’s philosophy, I argued that he turned to the method of ramseyfying the theoretical terms of empirical theories to uphold a semantical distinction that was central to his entire programme. Saving Carnap from the Newman objection is very much demanded, therefore, if Carnap’s explicationist programme is to be considered as a still viable candidate programme for philosophy of science. I suggested that a distinction can be drawn between an ontological and an epistemic reading of the Newman objection. On the former, the complaint is that ramseyfications trivialise existence claims associated with theoretical statements, on the latter, that they misrepresent the empirical nature of the theoretical statements at issue. On the ontological reading, the Newman objection presupposes the position of scientific realism, on the epistemic reading it does not but also challenges deflationists who wish to respect the empirical nature of the theoretical claims. I argued that while Carnap may reasonably reject the ontological Newman objection, given his perspective, he is unable to accommodate its epistemological reading without compromising his explicationism. This leaves but one radical option. But whether Carnap and latter-day Carnapians would be well advised now to reject the Newman objection also on the epistemic reading – and thus could indeed remain “unbothered” – must be investigated on another occasion.17

References Carnap R (1934) Logische Syntax der Sprache. Springer, Wien. Revised ed. transl. The logical syntax of language. Kegan, Paul, Trench Teubner & Cie, London, 1937. Reprinted Open Court, Chicago, IL, 2003 Carnap R (1936) Wahrheit und Bew¨ahrung. Actes du Congres Internationale de Philosophie Scientifique, Sorbonne, Paris 1935. Facs. IV, Induction et Probabilit´e. Hermann & Cie, Paris, pp 18–23, transl. with additions as Carnap, Truth and Confirmation. In: Readings in philosophical analysis. Appleton-Century-Crofts, New York, pp 119–127 Carnap R (1939) Foundations of logic and mathematics. University of Chicago Press, Chicago Carnap R (1945) Two concepts of probability. Philosophy and phenomenological research 5: 513–532. Reprinted in Readings in philosophical analysis. Appleton-Century-Crofts, New York, pp 330–348 Carnap R (1950a) Logical foundations of probability. University of Chicago Press. Chicago Carnap R (1950b) Empiricism, semantics and ontology. Revue International de Philosophie 4: 20–40. Reprinted in Meaning and necessity, 2nd edn. University of Chicago Press, Chicago, IL, 1956, pp 205–221 Carnap R (1955) On belief-sentences. In: McDonald M (ed) Philosophy and analysis. Blackwell, Oxford, pp 128–131. Reprinted in Meaning and necessity, 2nd edition. University of Chicago Press, Chicago, IL, 1956, pp 230–232

17 For discussion and correspondence I wish to thank Richard Creath, William Demopoulos, Michael Friedman and Stathis Psillos.

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Carnap R (1956) The methodological character of theoretical concepts. In: Feigl H, Scriven M (eds) The foundations of science and the concepts of science and psychology. University of Minneapolis Press, Minnesota, pp 38–76 Carnap R (1959) Beobachtungssprache und theoretische Sprache. Dialectica 12:236–248. Trans. “Observational language and theoretical language”, In Hintikka J (ed) Rudolf Carnap, Logical Empiricist. Reidel. Dordrecht, 1975, pp 75–85 Carnap R (1961) On the use of Hilbert’s epsilon-operator in Scientific Theories. In: Bar-Hillel Y (ed) Essays on the foundations of mathematics. Magnes, Hebrew University, Jerusalem, pp 156–164 Carnap R (1963) Replies and expositions. In: The philosophy of Rudolf Carnap. Open Court, La Salle, IL, pp 859–1016 Carnap R (1966) Philosophical foundations of physics, 2nd revised edn. Basic Books, New York. An introduction to the philosophy of science, 1974. Reprinted Dover, New York, 1995 Carnap R (2000) Theoretical concepts in science. In: Psillos S (ed) Rudolf Carnap’s ‘theoretical concepts in science’. Stud Hist Philos Sci 31:158–172 Carus A (2007) Carnap and explication. Cambridge University Press, Cambridge Demopoulos W (2003) On the rational reconstruction of our theoretical knowledge. Br J Philos Sci 54:371–403 Demopoulos W (2007) Carnap on the rational reconstruction of scientific theories. In: Creath R, Friedman M (eds) Cambridge companion to Carnap. University of Cambridge Press, Cambridge, pp 248–272 Demopoulos W, Friedman M (1985) Critical notice: Bertrand Russell’s The Analysis of Matter: Its historical context and contemporary interest. Philos Sci 52:621–639. Reprinted as “The concept of structure in The Analysis of Matter.” In: Savage CW and Anderson CA (eds) Rereading Russell. Essays on Betrand Russell’s metaphysics and epistemology. University of Minnesota Press, Minneapolis, MN, 1989, pp 183–199 Feigl H (1950a) Existential hypotheses. Realistic versus phenomenalistic interpretations. Philos Sci 17:32–62 Feigl H (1950b) Logical reconstruction, realism and pure semiotic. Philos Sci 17:186–195 Feigl H, Sellars W (eds) (1949) Readings in philosophical analysis. Appleton-Century-Crofts, New York Friedman M (1994) Geometry, convention, and the relativized a priori: Reichenbach, Schlick, and Carnap. In: Salmon W, Wolters G (eds) Logic, language and the structure of scientific theories. University of Pittsburgh Press, Pittsburgh, pp 21–43. Reprinted in Friedman (1999) Reconsidering logical positivism. Cambridge University Press, Cambridge, pp 59–71 Hempel CG (1958) The theoretician’s dilemma. In: Feigl H, Scriven M, Maxwell G (eds) Minnesota studies in the philosophy of science II. University of Minnesota Press, Minneapolis. Reprinted in Hempel (1965) Aspects of scientific explanation. Free Press, New York, pp 173–227 Hempel CG (1963) Implications of Carnap’s work for the philosophy of science. In: The philosophy of Rudolf Carnap. Open Court, La Salle, IL, pp 685–710 Mormann T (2000) Rudolf Carnap. Munich, Beck Newman MHA (1928) Mr Russell’s ‘causal theory of perception’. Mind 37:137–148 Psillos S (1999) Scientific realism. Routledge, London Psillos S (2000a) Rudolf Carnap’s ‘theoretical concepts in science’. Stud Hist Philos Sci 31: 151–172 Psillos S (2000b) Carnap, the Ramsey-Sentence and realistic empiricism. Erkenntnis 52:253–279 Psillos S (2006) Ramsey’s Ramsey-Sentences. In: Galavotti MC (ed) Vienna and Cambridge. Frank P. Ramsey and the Vienna Circle. Springer, Dordrecht, pp 67–90 Psillos S (2009) Carnap and incommensurability. Philos Inq (in press) Ramsey FP (1929) Theories. Reprinted in Ramsey (1978) Foundations: essays in philosophy, logic, mathematics and economics. In: Mellor DH (ed). Routledge, London, 1978, pp 101–125 Ryckman T (1992) P(oint)-C(oincidence) thinking: the ironical attachment of logical empiricism to general relativity (and some lingering consequences). Stud Hist Philos Sci 23:471–497 Schilpp PA (ed) (1963) The philosophy of Rudolf Carnap. Open Court, La Salle, IL

Chapter 27

Naturalizing Meaning Through Epistemology: Some Critical Notes Nicla Vassallo and Claudia Bianchi

27.1 Introduction Wittgenstein’s slogan “meaning is use” may be seen as a way to re-interpret Frege’s context principle. According to Frege, the meaning of a word must be given not in isolation but only in the context of an utterance.1 In a similar vein, Wittgenstein claims that a word has a meaning only in its context of use: in this antipsychologistic perspective (today we would call it “anti-naturalistic”), meaning is interpreted as a non-mental object; it is a matter of use, and therefore something we cannot investigate by scientific means. As is well known, Wittgenstein’s slogan has been variously interpreted. In the Philosophische Grammatik (I, 40) Wittgenstein claims: “It is what is regarded as the justification of an assertion that constitutes the sense of the assertion”. Dummett understands this as a theory of meaning as justification: the meaning of an assertion (or utterance) is given by the justification one may offer for the assertion (or utterance).2 This theory – that Dummett takes as deeply anti-naturalistic – is accepted by various philosophers, in particular Sellars and Brandom.3 Anti-naturalism in semantics parallels anti-naturalism in epistemology: epistemology cannot be replaced by science (as happened with alchemy, which was replaced by chemistry). Epistemology lies on a normative level, science on a descriptive one; epistemology tries to answer the question (i) how should we form justified beliefs and scientific theories? while science (cognitive, psychological,

N. Vassallo () Department of Philosophy, University of Genova, via Balbi 4, I-16126 Genova, Italy e-mail: [email protected] C. Bianchi University Vita-Salute San Raffaele, Faculty of Philosophy, Palazzo Borromeo, I-20031 Cesano Maderno (MI), Italy e-mail: [email protected] 1

Cf. Frege (1884). Cf. Dummett (1979). 3 Cf. Sellars (1963); Brandom (1994 and 2000). 2

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sociological, etc.) tries to answer the question (ii) how do we actually form our beliefs and scientific theories? However, this anti-naturalistic interpretation has been disputed. We will evaluate three main challenges, focusing on (a) the interaction between context of justification and context of discovery; (b) Quine’s naturalized epistemology; (c) the naturalization of logic. In this paper, we explore a different way of naturalizing meaning: we endorse a theory of meaning as justification and try to naturalize epistemic justification.4 We show that this method is bound to failure: it is impossible to naturalize the notion of justification. We then present a first argument against the naturalization of the notion of meaning; in the final section we propose a second argument. In philosophy of language one may claim that the meaning of an utterance amounts to the justification for the utterance, while in epistemology one may claim that the different theories of justification are set to clarify the meaning of the term “justification”. We are therefore confronted with a circularity: the theory of meaning depends on the theory of justification and the theory of justification depends on the theory of meaning. We conclude that the naturalization of semantics through epistemology cannot be pursued.

27.2 Discovery and Justification According to Reichenbach (1938), epistemology investigates the context of justification, whereas psychology investigates the context of discovery: if this distinction is clear cut, epistemology is an enterprise completely independent from science. The distinction, however, has been variously challenged: let us examine two different critiques, the first claiming that the context of discovery affects the context of justification, the second that the context of justification affects the context of discovery.5 Herbert Feigl writes: There is a fair measure of agreement today on how to conceive of philosophy of science as contrasted with the history, the psychology, or the sociology of science. All these disciplines are about science, but they are ‘about’ it in different ways Œ: : : In the widely accepted terminology of Hans Reichenbach, studies of this sort pertain to the context of discovery, whereas the analysis pursued by philosophers of science pertain to the context of justification. It is one thing to ask how we arrive at our scientific knowledge claims and what socio-cultural factors contribute to their acceptance or rejection; and it is another thing to ask what sort of evidence and what general, objective rules and standards govern the testing, the confirmation or disconfirmation and the acceptance or rejection of knowledge claims of science.6

4

On the naturalization of semantics, cf. Loewer (1997). For the distinction between context of justification and context of discovery, see Schickore and Steinle (2006), and Nickles (2008). 6 Feigl (1965), p 472. 5

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Feigl is arguing more or less explicitly that discovery is involved with the genesis of beliefs and scientific theories and hypotheses, whereas justification is involved with their evaluation: while the notion of discovery is descriptive, the notion of justification is normative. Yet Feigl is too optimistic in thinking that there is an uncontroversial divide between philosophy of science on the one hand, and history, psychology and sociology of science on the other. Logical empiricists and Popper have emphasized the distinction; Popper writes: The question how it happens that a new idea occurs to a man – whether it is a musical theme, a dramatic conflict, or a scientific theory – may be of great interest to empirical psychology; but it is irrelevant to the logical analysis of scientific knowledge.7

But at the time that Feigl wrote (1965) logical empiricism was already losing its force, and post-Popperian epistemologists had begun casting doubts on Popper’s theory. In The Structure of Scientific Revolutions, Thomas Kuhn underlines the role of history, sociology, and psychology in philosophical reflection on science. Moreover, he subsequently challenges the distinction between context of justification and context of discovery by means of two arguments: (1) Traditional philosophy of science takes a controversial stance concerning the choice of a scientific theory: crucial experiments, for example, are considered a good reason to opt for a particular scientific theory. But if we look at the history of science, we realize that, when crucial experiments are undertaken, scientists have already made their choice. Crucial experiments “scarcely illuminate the character of the choices that scientists are called upon to make”.8 (2) Traditional philosophy of science presents only the arguments supporting the dominant scientific theory. It claims, for example, that the theory of combustion based on oxygen – but not the one based on phlogiston – justifies the law of proportions; but it does not present the arguments in favor of the theory of phlogiston. To argue for the superiority of the theory of combustion based on oxygen is to oversimplify the scientists’ position concerning the choice between the two theories: “There are always at least some good reasons for each possible choice”.9 Kuhn uses (1) and (2) in order to claim that: Considerations relevant to the context of discovery are then relevant to the justification as well; scientists who share the concerns and sensibilities of the individual who discovers a new theory are ipso facto likely to appear disproportionately frequently among that theory’s first supporters.10

7

Popper (1934), p 31. Kuhn (1977), p 328. 9 Kuhn (1977), p 328. 10 Kuhn (1977), p 328. 8

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This amounts to saying that psychological, sociological and historical concerns affect the level of justification, introducing descriptive considerations in a normative enterprise. Feigl could reply that Kuhn fails to distinguish “how we arrive at our scientific knowledge claims and what socio-cultural factors contribute to their acceptance or rejection” from “what sort of evidence and what general, objective rules and standards govern the testing, the confirmation or disconfirmation and the acceptance or rejection of knowledge claims of science”.11 Kuhn, in other words, fails to distinguish context of justification from context of discovery.12 As far as (1) is concerned, we may agree with Kuhn that the scientists’ choice of a theory precedes the so-called crucial experiments. However, we must discriminate between the scientists’ decision (context of decision) and the justification of that decision (context of justification): in other words, we must distinguish between the question of how a scientist or a scientific community makes a choice, and the question of whether this very choice is justified. Psychological, sociological and historical factors affect the first issue, but not the second one (“is this choice supported by good epistemic reasons?). As far as (2) is concerned, we may agree with Kuhn that choosing between two competing theories may be a much more complicated matter than usually described by philosophical accounts: as Kuhn puts it, “there are always at least some good reasons for each possible choice”. Granted, two competing theories sometimes appear equally justified, and scientists choose between them taking into consideration not the epistemically good reasons supporting them but aspects (psychological, sociological and historical) of the context of discovery. But taking two opposing beliefs or theories as equally justified at a certain time does not amount to saying that they are in fact equally justified. And even if two opposing beliefs or theories do appear to be equally justified at a certain time, the epistemological advice should not be “choose your theory taking into account psychological, sociological and historical factors”, but “suspend your judgement until you have more evidence in favour of a belief or theory”. Kuhn has shown, then, that questions concerning the context of discovery are relevant not for the context of justification, but only for the context of decision. Nonetheless, the importance of the context of decision cannot be underestimated.13 Moreover, it is possible to define the context of discovery and of decision in terms of precise procedures; Sober writes: A discovery procedure must take sentences which characterize the evidence as inputs and yield theories and hypotheses as outputs. A decision procedure must take the evidence and a single hypothesis as input and then determine whether or not that hypothesis is the best explanation, or the most acceptable hypothesis, relative to the evidence.14

11

Feigl (1965), p 472, already quoted. On this point, cf. Siegel (1980), pp 309–313. 13 Our remarks thus far may appear less than completely fair to Kuhn; on this point, cf. HoyningenHuene (2006). 14 Sober (1978), pp 171–172. 12

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We may well be inclined to say that human reasoning calls for inter-subjective heuristic principles. But this does not undermine the distinction between context of discovery and context of justification. Discovery and decision procedures clarify how we discover and decide, but not how we should discover and decide: we must keep our discoveries and decisions distinct from their epistemic status. The goal of epistemology is to answer the question (i) how should we form our justified beliefs and scientific theories?; while the goal of science (cognitive, psychological, sociological sciences etc.) is to answer the question (ii) how do we actually form our beliefs and scientific theories? However, in our procedures of discovery and decision we take evidence into account, and evidence is a form of justification: this seems to imply that some issues pertaining to justification affect discovery. Does the distinction still hold? According to Kordig (1978), when we talk about real discoveries we are talking about something – at least partially – justified: we cannot say that we have discovered that UFOs exist if the hypothesis that UFOs exist isn’t somehow justified. Saying that real discoveries must be at least partially justified in order to be real means that the distinction between the context of discovery and context of justification is vague. Kordig proposes to replace it with new distinctions: initial conception of a hypothesis (where the formulation of a hypothesis may be a causal process); plausibility of a hypothesis (when we judge a hypothesis to be plausible, i.e. testable, because we may offer reasons supporting it); acceptability of a hypothesis (based on its empirical confirmation, logical fertility, extensibility, simplicity, etc.). How should we evaluate this proposal? As is well known, a passionate epistemologicalmethodological debate tries to understand whether reasons invoked by scientists are actually good reasons. In any case, for Kordig acceptability is justification: “Scientists believe that hypotheses are true. They believe that hypotheses are empirically confirmed. They infer hypotheses from data. They propose reasons”.15 But believing that hypotheses are true does not imply knowing that they are true; believing that hypotheses are empirically confirmed does not imply knowing that they are empirically confirmed: in order to know, one must have at least justified true beliefs. Inferring hypotheses from data does not imply inferring hypotheses from data in a proper way: proposing reasons and taking them as good reasons does not imply that they actually are good reasons. By identifying acceptability with justification, Kordig traces the latter back to the former: justification loses its normative force. Even if we agree that the distinction between discovery and justification is ambiguous – every real discovery being justified – we cannot replace question (i) (how should we form our justified beliefs and scientific theories?) with question (ii) (how do we actually form our beliefs and scientific theories?). Kordig does not offer a crucial argument for this replacement: it’s time to examine Quine’s argument.

15

Kordig (1978), p 115.

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27.3 Quine’s Epistemology According to Quine, “epistemology, or something like it, simply falls into place as a chapter of psychology and hence of natural science”.16 The normative dimension of epistemology fades away into the descriptive dimension of science, and the context of justification into the context of discovery. Yet, if we give up the normative dimension, we no longer have an epistemological enterprise; as Kim claims, “Quine’s naturalized epistemology, while it may be a legitimate scientific inquiry, it is not a kind of epistemology, and, therefore, Œ: : : the question whether it is a better kind of epistemology cannot arise”.17 If Quine’s is not an epistemological enterprise, it may disregard the context of justification – which is nonetheless the main object of epistemology. It may be objected that “epistemology, or something like it, simply falls into place as a chapter of psychology and hence of natural science” has two different interpretations: a strong one, where question (i) has no meaning at all, and a weak one, where question (i) has an answer only in relation to question (ii). In the weak interpretation, epistemology still has a role to play, in deep connection, or continuity, with science, while in the strong one there is no space for any epistemological endeavour. Quine claims that he does not want to give up the normative character of epistemology; but it is difficult to understand how it could be maintained if epistemology is reduced to science – an enterprise devoted to description and explanation, not to justification. The notion of justification guarantees the normativity of epistemology, and it is a wholly epistemological notion, difficult to account for from a scientific perspective. In his naturalized epistemology, therefore, Quine coherently doesn’t endorse any theory of justification: the strong interpretation is the plausible one. In fact, according to Quine, epistemologists are simply empirical psychologists investigating human acquisition of science,18 aiming to explain the causal functioning of human knowledge of the external world,19 endorsing a naturalistic perspective where epistemology is assimilated to empirical psychology.20 Question (i) loses any meaning: epistemology is replaced by science. Is this fate inevitable? In Quine’s opinion, epistemology – in its non-naturalistic version – “is concerned with the foundations of science”.21 As far as mathematics is concerned, for example, he writes: “Reduction in the foundations of mathematics remains mathematically and philosophically fascinating, but it does not do what the epistemologist would like of it: it does not reveal the ground of mathematical knowledge, it does not show how mathematical certainty is possible”.22 And as far as natural science is concerned, Quine takes into consideration only the foundation-

16

Quine (1969), p 82. Kim (1988), p 392. 18 Cf. Quine (1973), p. 3. 19 Cf. Quine (1970), p 2. 20 Cf. Quine (1981), p 72. 21 Quine (1969), p 69. 22 Quine (1969), p 70. 17

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alist model – re-interpreted by logical empiricists (especially Carnap) in order to rationally reconstruct our empirical beliefs as logical constructions based on sensedata: “The hopelessness of grounding natural science upon immediate experience in a firmly logical way was acknowledged. The Cartesian quest for certainty had been the remote motivation of epistemology Œ: : : but that quest was seen as a lost cause”.23 In a word, Quine’s naturalized epistemology is motivated by his dissatisfaction with traditional foundationalism, and its quest for certainty. But Quine’s dissatisfaction is largely insufficient to give up epistemology. In fact, foundationalist proposals have by now abandoned the quest for certainty. They are still valuable as structural proposals – concerning the structure of the justification and not the content of the beliefs to be justified: rationalists as well as empiricists may endorse foundationalism as a structural proposal. According to this kind of foundationalism, beliefs are basic if and only if they are not derived and justified inferentially – in other words if they are immediately justified; beliefs are derived if and only if their justification is derived inferentially and is founded on some basic beliefs. Giving up the quest for certainty does not amount to giving up foundationalism – which, according to Alston (a contemporary foundationalist), may be summarized as follows: “Every mediately justified belief stands at the base of a (more or less) multiply branching tree structure at the tip of each branch of which is an immediately justified belief”.24 The essential tenet of foundationalism – there are immediately justified beliefs and mediately justified beliefs based on the first ones – is still promising and unaffected by Quine’s criticism of traditional foundationalism25 : we are not necessarily forced to give up epistemology.

27.4 Logic We have said that from a foundationalist perspective, justification is transmitted inferentially from basic beliefs to derived ones. Inferences may be logico-deductive or inductive. Restricting our attention to logico-deductive inferences, foundationalism could be naturalized by naturalizing deductive logic. Thagard, for example, claims: The logician Œ: : : is concerned to develop a set of principles which is inferentially optimal given the cognitive limitations of reasoners. This requires reference to background psychological and philosophical theories and to the goals of inferential behavior.26

23

Quine (1969), p 74. Alston (1976, 1989), p 42. 25 For a different point of view, more sympathetic to Quine’s epistemology, and focused on the relationship between empiricism and naturalism, cf. Roth (2008). 26 Thagard (1982), p 35. 24

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According to Thagard, the aim of logic is to describe human deductive competence, and psychology must investigate our cognitive limitations. To give a description of logical inferential principles, we must seek a wide reflective equilibrium of many factors: human inferential practice, normative logical principles, psychological and philosophical theories concerning human cognitive competences and limitations, psychological and philosophical theories concerning objectives of human inferential behavior. Logic may be naturalized. Therefore, foundationalism – which proposes a normative analysis of justification – could be naturalized for its employment of logico-deductive inferences: the naturalization of foundationalism is based on the naturalization of logic. This, however, is a tricky approach. Resnik, for example, writes: Psychological reports Œ: : : have the same degree of relevance to the enterprise of building models of deductive inference as surveys of attitudes towards capital punishment have to the construction of moral theories.27

According to Resnik, then, psychological accounts have little relevance for the construction of theories of deductive inference. Goldman is even more explicit: “Validity or invalidity of arguments Œ: : : is not a matter of psychology. Truths of model theory, proof theory, and recursive function theory – the main branches of logic – do not depend on psychological truths”.28 Following a long tradition in philosophy of logic, one may argue that logic cannot be naturalized, because its principles are normative and not descriptive, contrary to human inferential practices. This notion of logic is essential to psychology itself: without a normative logic, there would be no psychology, no science of human deductive reasoning. As a matter of fact, the main goal of psychologists is to describe deviations from norms – norms of deductive reasoning provided by logic. Another way of rejecting the naturalization of logic is suggested by Goldman himself: logic is descriptive, but it does not describe human inferential practices: “Truths of logic are purely descriptive, factual statements. They formulate certain facts – presumably necessary facts – concerning semantic and syntactic properties and relations”.29 In closing, the naturalization of logic may be rejected by an additional remark. What all logic does is to preserve truth30 : it is a device producing all and only the truth-preserving inferences. The centrality of truth in logic casts doubts on any serious attempt to naturalize logic: being true is not a factual property or the object of a natural science. We must conclude that the naturalization of foundationalism based on the naturalization of logic is a far from promising project.

27

Resnik (1985), p 234. Goldman (1986), p 7. 29 Goldman (1986), p 82. 30 Better, logic preserves truth-value. 28

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27.5 Towards Semantic Naturalism? We have concisely presented three approaches to the naturalization of epistemology31 : (a) the interaction between justification and discovery; (b) Quine’s naturalized epistemology, replacing epistemology with science; (c) the naturalization of logic, where deductive logic depends on psychology. We have shown that all three approaches are confronted with major problems, casting serious doubts on the success of any attempt to naturalize epistemology. A theory of justification cannot be linked with sciences; therefore a theory of meaning (where meaning is interpreted as justification) cannot be linked to the sciences – namely meaning cannot be naturalized. This is, in itself, a fairly important point. It is also important if we agree with Bertolet when he writes that “the central topic in the philosophy of language that impinges on work in philosophy of science is the theory of meaning”.32 In fact, if we were to succeed in naturalizing the theory of meaning and replacing it with some science, we would be subscribing to a sort of nonsense, that is that the central topic in the philosophy of language that impinges on work in philosophy of science is the theory of science. Fortunately, we did not succeed in naturalizing the theory of meaning. Of course the three attempts examined above are not the only ones possible. Naturalization of epistemology is nowadays enjoying an intense development.33 But our worries with regard to the overall plausibility of the project of engaging science in the analysis of justification and meaning are exacerbated by another consideration. All theories of justification aim precisely to clarify the meaning of the expression ‘justification’, in spite of the well-known problems affecting the very notion of meaning. In this regard, what Goldman states is paradigmatic: First, while there are doubtless severe theoretical problems concerning the notions of meaning and synonymy, there must be some substance to the commonsense notions suggested by these terms. Certainly we can distinguish better and worse definitions of a given word, whether dictionary definitions or definitions offered by casual speakers Œ: : : So there must be some phenomenon of meaning that remains to be clearly elucidated. Second, although many philosophers preach the abandonment of analyticity, their practice sometimes belies their preaching. People do things very much like conceptual analysis even if they officially reject it. It is hard to do much in epistemology (or other branches of philosophy) without feeling constrained to do something like conceptual analysis.34

31 We have no space here to go into detail and clarify, for example, the relations between a descriptive and a normative stance, or between explanation and justification. For a fuller account, cf. Baumslag (2000), Bunge (1998), Kantorovich (1988). 32 Bertolet (2008), p 36. 33 Feldman (2001) and Goldman (2002) are useful in understanding the rich variety of naturalized epistemologies and the complexity of the relations between epistemology and science. It goes without saying that in this paper we basically took into consideration a radical naturalization of epistemology, i.e. the possibility to replace epistemology with science. There are of course moderate attempts to naturalize epistemology, i.e. to restructure it with the help of science. 34 Goldman (1986), p 38.

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In philosophy of language one may claim that the meaning of an utterance is given by its justification; in epistemology one may claim that all theories of justification aim precisely to clarify the meaning of the expression ‘justification’. There is a manifest circularity: the theory of meaning depends on the theory of justification, and the theory of justification depends on the theory of meaning. This circularity casts more doubts on the connection between theory of meaning and theory of justification. To conclude, the attempt to naturalize the notion of meaning through the naturalization of the epistemology seems bound to failure. We are left with a problem: shall we abandon the notion of meaning as justification, or the project of clarifying the meaning of ‘justification’? In epistemology, giving necessary and sufficient conditions for the term ‘justification’ is a crucial goal in order to understand the notion of knowledge: justification is a necessary condition for knowledge. Epistemologists try to analyse a concept (the analysandum) expressed by the schema “S knows that p” or “S is justified in believing that p”, where “S” is the knowing subject and “p” the proposition known or justified. The analysis is expressed by the schema “S knows that p if and only if: : :” or “S is justified in believing that p if and only if : : :”, where the dots must be replaced by the analysans, i.e. a list of necessary and sufficient conditions. This analysis “can be regarded as a first approximation to a better way of treating [the] meaning”35 of the main epistemic terms. In order to avoid the circularity described above, we must give up the notion of meaning as justification: luckily, this does not imply giving up every notion of meaning, since we can endorse a classical notion of meaning as truth-conditions. As a result, in any case, we must give up the attempt to naturalize meaning through the naturalization of justification.

References Alston WP (1976) Has foundationalism been refuted? Philos Stud 29:287–305. Now in Alston WP (1989) Epistemic justification – essays in the theory of knowledge. Cornell University Press, Ithaca/London, pp 39–56 Baumslag D (2000) How to test normative theories of science. J Gen Philos Sci 2:267–275 Bertolet R (2008) Philosophy of language. In: Psillos S, Curd M (eds) The Routledge companion to philosophy of science. Routledge, Abingdon, pp 36–46 Brandom RB (1994) Making it explicit. In: Reasoning, representing and discursive commitment. Harvard University Press, Cambridge, MA Brandom RB (2000) Articulating reasons. In: An introduction to inferentialism. Harvard University Press, Cambridge, MA Bunge M (1998) Philosophy of science: from explanation to justification. Transaction, Edison, NJ Carnap R (1928) Der logische Aufbau der Welt. Weltkreis, Berlin Dummett M (1979) What does the appeal to use do for the theory of meaning? In: Margalit A (ed) Meaning and use. Reidel, Dordrecht Feigl H (1965) Philosophy of science. In: Chisholm RM et al. (eds) Philosophy. Prentice-Hall, Englewood Cliff, NJ

35

Goldman (1986), p 39.

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Feldman R (2001) Naturalized epistemology. Stanford encyclopedia of philosophy. http:// plato.stanford.edu/entries/epistemology-naturalized/ Frege G (1884) Die Grundlagen der Arithmetik – Eine logisch-mathematische Untersuchung uber den Begriff der Zahl. Koebner, Breslavia Goldman AI (1986) Epistemology and cognition. Harvard University Press, Cambridge, MA Goldman AI (2002) The sciences and epistemology. In: Moser PK (ed) The Oxford handbook of epistemology. Oxford University Press, Oxford, pp 144–176 Hanna R (2006) Rationality and logic. Bradford Books, MIT, Cambridge, MA Hoyningen-Huene P (2006) Context of discovery versus context of justification and Thomas Kuhn. In: Schickore J, Steinle F (eds) Revisiting discovery and justification. Historical and philosophical perspectives on the context distinction. Springer, Berlin, pp 119–131 Kantorovich A (1988) Philosophy of science: form justification to explanation. Br J Philos Sci 39:469–494 Kim J (1988) What is ‘naturalized epistemology’? In: Tomberlin JE (ed) Philosophical perspectives, 2, epistemology. Ridgeview, Atascadero, CA, pp 381–405 Kordig CR (1978) Discovery and justification. Philos Sci 45:110–117 Kuhn TS (1962, 1970) The structure of scientific revolutions. The University of Chicago Press, Chicago, IL Kuhn TS (1977) The essential tension. The University of Chicago Press, Chicago, IL Loewer B (1997) A guide to naturalizing semantics. In: Hale B, Wright C (eds) A companion to the philosophy of language. Blackwell, Oxford, pp 108–126 Nickles T (2008) Scientific discovery. In: Psillos S, Curd M (eds) The Routledge companion to philosophy of science. Routledge, Abingdon, pp 442–451 Popper KR (1934) The logic of scientific discovery. Basic Books, New York Quine WVO (1969) Epistemology naturalized. In: Ontological relativity and other essays. Columbia University Press, New York, pp 69–90 Quine WVO (1970) Grades of theoreticity. In: Foster L, Swanson JW (eds) Experience and theory. University of Massachusetts Press, Amherst, MA Quine WVO (1973) The roots of reference. Open Court, La Salle, IL Quine WVO (1981) Theories and things. Harvard University Press, Cambridge, MA Reichenbach H (1938) Experience and prediction. An analysis of the foundations and the structure of knowledge. The University of Chicago Press, Chicago, IL Resnik MD (1985) Logic: normative or descriptive? The ethics of belief or a branch of psychology? Philos Sci 52:221–238 Roth PA (2008) The epistemology of science after Quine. In: Psillos S, Curd M (eds) The Routledge companion to philosophy of science. Routledge, Abingdon, pp 3–14 Schickore J, Steinle F (eds) (2006) Revisiting discovery and justification. Historical and philosophical perspectives on the context distinction. Springer, Berlin Sellars WF (1963) Science, perception and reality. Routledge, London Siegel H (1980) Justification, discovery and the naturalizing of epistemology. Philos Sci 47: 297–321 Sober E (1978) Psychologism. J Theory Soc Behav 8:165–191 Thagard P (1982) From the descriptive to the normative in psychology and logic. Philos Sci 49: 24–42 Wittgenstein L (1953) Philosophische Untersuchungen. Basil Blackwell, Oxford Wittgenstein L (1969) Philosophische Grammatik. Basil Blackwell, Oxford

Chapter 28

What Games Do Scientists Play? Rationality and Objectivity in a Game-Theoretic Approach to the Social Construction of Scientific Knowledge Jesus ´ Zamora-Bonilla

28.1 Introduction In a series of papers (Zamora Bonilla 1999, 2002a, 2006a, b, c; Ferreira and Zamora Bonilla 2006). I have been defending an economic, game-theoretic approach to the understanding of the social construction of scientific knowledge; such an approach would complement the traditional efforts in using insights and techniques from other social sciences (esp. sociology and anthropology) to the idiosyncratic epistemic aspects of science, but would also have two fundamental virtues from a ‘rationalist’ point of view: in the first place, the game-theoretic, rational-choice approach allows to model in an explicit way the factors determining the scientists’ decisions, as well as the interdependences between them, without dressing all this in a mystifying rhetoric which tends to obscure the analysis more than to illuminate it (many will say that the economic jargon can be no less mystifying and obscurantist than the Foucauldian one so often employed in post-modern studies of science, but the difficulty of rational-choice analysis is of the same kind as that of mathematics and logic: it serves, when used properly, the goal of making the inferential links of our reasoning explicit and subject to criticism); secondly, instead of launching a non-contestable accusation of lack of objectivity and rationality to the products and methods of scientific research, economic models allow to clearly see what are the specific shortcomings of certain ways research can be carried out (i.e., they permit us to identify specific inefficiencies), and point towards those changes in the modelled situations that would effectively improve the results that scientists are getting. Stated in other words, a game theoretic analysis of the social construction of scientific knowledge allows us not to renounce to the thesis that science is a pretty good method of finding out objective and significant truths about the world, nor to the claim that science is the product of typically human and social forces, nor to the goal of discovering the possible shortcomings of science and, more importantly, of discovering also some ways of overcoming them. I think the focus on the necessary

J. Zamora-Bonilla () UNED, Madrid, Spain e-mail: [email protected]

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formalisms I had to use in the papers quoted at the beginning may have precluded these virtues being well appreciated enough, so I would like to take this opportunity to state them in a clearer way.

28.2 The Elements of a Game-Theoretic Model of Science Understanding the construction of scientific knowledge with the help of game theory demands to adopt a cognitive style which is not frequent in science studies (though it is employed more often in some areas of philosophy of science, in particular in the more formal ones, like, e.g., Bayesianism). I am referring to the design of abstract models. A formal model is an encapsulated argument, with which we just try to prove that certain interesting conclusions follow (or do not follow) from certain reasonable premises. This argumentative style strongly contrasts with the more usual practice of case studies, one that has flooded the literature in philosophy and sociology of science for the last three decades. I have of course nothing to oppose to that practice, and I recognise that a detailed view of how science is and has actually been done is a precondition for a proper understanding of scientific knowledge, but the case-study technology is essentially inductive, not too appropriate to illuminate the regular mechanisms that make science to be the way it is, and the claims we reach with it can hardly be generalised, as the diversity of conflicting views that have actually been defended by means of case studies shows. However, I do not propose to consider the game-theoretic approach to the social construction of scientific knowledge as an alternative to case studies, but as a complement of it; the idea is merely to take the case based literature as a corpus of descriptive, empirical facts about science, using rational choice considerations as a tool for discovering theoretical mechanisms (i.e., abstract models) that help us explain (partially, at least) why science is the way those empirical descriptions say it is. The basic principles that such an approach offers for our attempt to discover this type of explanations are the following. In the first place, it points to scientists’ actions as the basic elements of what has to be explained, i.e., why do scientists do what they do, and in the way they do it; this does not mean that other aspects of scientific constructs (e.g., the structure of theories, the connections between models and observations) fall out of the scope of a game-theoretic explanations, for we can ask, say, why do scientists choose theories with a certain structure, or value models according to some connections with empirical facts. Secondly, a rational choice approach forces to explicitly consider the goals scientists are pursuing through their actions, as well as the information, capabilities and social mechanisms that allow them to reach those goals to the extent they do it. Lastly, what a game theoretic approach more characteristically adds to this is the idea that, as long as the actions of other colleagues (or other relevant actors) influence the possible gains a scientist can expect from her own decisions, the social situations that we will expect to

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observe will be what is traditionally known as a Nash equilibrium, i.e., a situation in which the strategy each agent is choosing is a best response to the decisions the other agents are making. Just to illustrate the way in which a game theoretic approach can be applied to traditional problems in philosophy of science, here are some examples of the kind of questions we can pose: Scientific standards: many philosophers have longly discussed the virtues a scientific claim must have in order to become acceptable (e.g., ‘degree of confirmation’, ‘corroboration’, ‘verisimilitude’, ‘simplicity’, ‘predictive capacity’, and so on), but, since these properties come in degrees, we can reasonably ask how do scientists actually determine the minimum level of those virtues a claim must have so that its acceptance by the community becomes ‘compulsory’; or, stated otherwise, when will a ‘competing’ scientists be ‘forced’ to recognise that the claim proposed by a rival is ‘right’. A game theoretic analysis will show that the fact that every possible standard (or ‘quality level’) determines the chances a researcher has of ‘winning’ the race for a discovery, is a sufficient reason for scientists to have a preference for some particular standard over the other alternatives (cf. Zamora Bonilla 2002a). ‘Theory’ choice: Not all scientific claims within a field are ‘compulsory’ (in the sense that, if you do not accept them, you will not be given your degree in chemistry, say; there are also claims it is compulsory not to accept them, in this sense), but many are a matter of choice to some level. The famous ‘underdetermination of theories’ thesis is just a formal justification of that practice, though its name is misleading in that it does not only apply to real theories, but to any type of scientific claim, from experimental reports to megaparadigms. The problem is that saying that logic is not sufficient to determine the choice of a theory does not help us to know what do these choices depend actually on: are these factors ‘social interests’, ‘cognitive biases’, or just a matter of ‘mob psychology’? The game theoretic approach allows to say that, as long as the profitability for a researcher of accepting a claim depends on who else in her community is also accepting it, then the only stable situations will be those that constitute an equilibrium, in the sense that everybody is making her best choice given the ones made by the rest. In general, there will only be a few equilibria in each case, and sudden changes from a situation to other are possible (‘scientific revolutions’?), but it is also possible to proof that, as long as the profitability of accepting a claim depends even very partially on how good the claim is according to the epistemic standards, then it can be expected that ‘better’ claims will have a tendency to become more ‘popular’ as their epistemic quality improves (cf. Zamora Bonilla 1999, 2006a, sec. 3). The ‘construction’ of an empirical fact: It is almost a platitude from science studies that the way in which empirical ‘discoveries’ are presented is the result of a ‘negotiation’. This entails, at least, that an empirical finding can be presented in more than one way. But this does not entail in any sense that all those ways are equally good for every agent engaged in the ‘negotiation’; rather on the contrary, if they were equally good, there will be no negotiation at all (which is usually costly), for the

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mere flip of a coin will be enough to select an interpretation or other. Game theoretical modelling of the situation allows to see how the interests and preferences of the different ‘negotiators’ induce a distinction between those interpretations that cannot be the outcome of the negotiation, and those that can; it also shows some ways in which the outcome can be judged as efficient or not, and, furthermore, it allows to devise institutions that may improve those outcomes (cf. Zamora Bonilla 2006c).

28.3 The Epistemic Quality of Scientific Products What makes a scientific theory, or model, or hypothesis, a good one from the scientific point of view? The economic approach to the social construction of scientific knowledge has just two insights to offer as a way to the answer of this question; they are not very deep insights (as a matter of fact, they are nearly trivial), but they are also controversial when examined from several philosophical or sociological approaches to the matter, and furthermore, there is even a certain amount of tension between both ideas. The first insight consists in the claim that, since in the game theoretic analysis we are assuming that scientists do rationally pursue their goals (whatever these happen to be), we are then forced to assume that they will also have a non negligible capacity for understanding what ‘sound reasoning’ is. In other words: if they are wise enough to know how to navigate the ocean of their social relationships in pursuit of resources, publications, and honours, they must not be necessarily inept when trying to discover the laws governing a physical phenomenon. The second, more important insight, is that the definition of the epistemic quality of scientific products is basically not a question for the philosopher of science (nor, for that case, for the sociologist or the economist of science), but for scientists themselves, or, dare we to say, for citizens in general; i.e. de epistemicibus gustibus non est disputandum. Real scientists will have some ‘epistemic utility function’, probably not everyone the same function, and the first role of the analyst of science is, rather than that of proposing what this utility function should be, that of discovering which one it is. The point is not to deny that many interesting things can be analysed from a philosophical point of view about the epistemic virtues of scientific items: what our approach precludes is just adopting a patronising attitude towards these questions. After all, scientists are the society’s best experts in the production and use of knowledge, and so, if some people know what knowledge consists in and how to discriminate ‘good’ pieces of knowledge from not so good ones, these are scientists. Perhaps they are not particularly good in making this practical knowledge explicit (actually, when scientists say what good science consists in, they tend to do it worse than philosophers). We should concentrate, hence, on the way that scientists’ behaviour ‘reveals’ what their actual criteria of ‘good scientific practice’ are. But, how to do that? As a matter of fact, all the theories that have been proposed by philosophers in order to explain the nature of scientific knowledge, its virtues and its progress, and so that some methodological rules of ‘good science’ can be derived from those theories, have been ‘refuted’ by showing that, in real scientific

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practice, researchers often do not behave as if they were pursuing those epistemic goals and the methodologies derivable from them; for example, scientists are usually not ‘falsificationist’, nor ‘confirmationist’, but they also are not ‘anarchist’, nor strict followers of the Lakatosian methodology of research programmes. A big part of the debates of the last 50 years between the different schools in philosophy of science has consisted in showing through historical or contemporary examples that scientists don’t do what other rival philosophical theories assume they should be doing. My suggestion is that, in these debates, almost all parts were right when they were criticising the theses of the rivals (more or less like in politics), but partially wrong when they were proposing a philosophical explanation of scientific practice. So, the outcome of the debate must be seen as a rich corpus of empirical evidence about how science is practiced, in which we should try to find out some regularities about what scientists actually consider as good practices. The fact that scientists behave in many different, often conflicting ways, is not an argument against this goal: in every society there can be conflicting practices and conflicting norms, both because people have different interests, values, and preferences, and because they face different situations, incentives, and constraints. In the case of science, it is not necessary to discover many norms that all scientists in all times and places have considered appropriate; it would also be interesting to show that, when certain specific conditions are given, then such and such norms of ‘good practice’ tend to be accepted. Our main goal as students of science should be, once the historical evidence is organised in such a way, that of trying to answer the following question: what hypothetical utility function explains in the best possible way the acceptance of precisely these ideas of ‘good practice’ by part of real scientits? Every economic model starts by making some reasonable assumptions about the agents’ preferences, and game-theoretic models of science are not unlike the rest. My hypothesis (obviously a very simplified one, for it is applied to very simple models, and also not too original) is that a typical scientist’s utility function has two main components: a ‘social’ one, and an ‘epistemic’ one. The social component can contain many different variables (income, control over resources, class interests, political or human values, and so on), but the most important one is ‘recognition’: scientists strive for being recognised by their colleagues as good, or even ‘excellent’ practitioners of their disciplines; this creates an incentive to agree, within a scientific community, on how a ‘good practice’ is defined, i.e., to agree on the ‘rules of the game’, for, if such an agreement is lacking, ‘recognition’ becomes simply impossible. The question (for scientists, nor for philosophers) is: what criteria to use in order to determine those rules? I think that the more general, more basic rules, i.e., those that allow to say that it is really a type of ‘science’ the game a community of researchers are playing, and not literature, or music, or football, or car mechanics, or politics, must be rather similar in all scientific communities (though they may have very strong differences in the details), and must not suffer very significant changes with the passing of time; so, by accepting these rules, scientists can not take into account their own social goals (or at least, their private social goals; things like ‘social justice’ will be different, and perhaps also ‘class interests’, but I doubt it), for it is impossible to know how the adoption of some methodological rules instead of

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others will affect their individual chances of getting recognition and things like that. Stated differently, the more basic a scientific norm is, the more it will be chosen by scientists ‘behind a veil of ignorance’, to use this well known Rawlsian metaphor. Here it is, then, where the epistemic elements of the scientists’ utility function enter, in determining the choice of what an appropriate criterion of ‘good science’ is. A hypothetical epistemic utility function, that tries to explain the prevalence of certain very basic and general criteria of preference over ‘theories’ (criteria that, as we have seen above, are in apparent mutual conflict), is the one I offered in my own research on verisimilitude, where this notion was explained not as ‘objective closeness to the full truth’, but as ‘perceived closeness to what we empirically know about the truth, weighted by the perceived amount of information this empirical knowledge contains’. In formulae: Vs(H,E) D [p(H&E)/p(HvE)][1/p(E)] D p(H,E)/p(HvE), where H is a model or theory, E is the relevant empirical evidence, and p is a Bayesian, subjective probability function, which allows for different scientists attaching different degrees of verisimilitude to the same theories; this does not condemn scientists to relativism, for the shared form of their epistemic utility function guarantees that they will agree on certain conditions under which a theory is necessarily better than another (e.g., if H entails H 0 , and both entail E, then H 0 will be judged to be better than H ), and these conditions will give us the ‘criteria’ of epistemic preference we were looking for. A more sophisticated measure assumes that E is structured as a set of known empirical regularities, and verisimilitude is defined then as the maximum perceived closeness to one subset of those regularities. (Cf. Zamora Bonilla 1996, 2000 and 2002b).

28.4 Epistemic Efficiency and Scientific Institutions One thing is to define what the quality of a scientific item consists in, and a very different thing is to determine how good that item is according to that definition of quality. The point made in the previous section amounts to saying that scientists will know better than the rest of us the answers to those questions (though they will not tell us those answers: we shall have to get them by studying scientists’ behaviour), but, even if they agree on what a good theory, model, hypothesis, experiment, etc., is, this does not guarantee by itself that the actual outputs of society’s investment in scientific research are of a ‘high epistemic quality’. This depends on a number of variables, the effort and talent of individual scientists not being the least, but an essential factor is also the efficiency of the scientific institutions. I will not refer here to their economic efficiency, though I admit this is a topic of fundamental importance, but will restrict myself to discuss the epistemic efficiency: do scientific institutions work in such a way that ‘high quality’ outputs tend to be produced? In order to illustrate how the game-theoretic approach can offer some answers to this question, I will briefly examine in turn the three examples given at the end of Section 28.2.

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Scientific standards: The process of collectively choosing a model, hypothesis, etc., as the right solution of a scientific problem demands, as we have seen, that the relevant community has agreed on certain standards specifying the minimum level of epistemic quality the solution must have. Will scientists choose a ‘low’ standard, or a ‘high’ one? Of course, this question only makes sense in comparison with some independent criterion of ‘lowness’ or ‘highness’, and the most helpful one is just that of individual scientists’ epistemic preferences: imagine that an ‘individual’ researcher (in the sense that she is not competing with other colleagues for the solution of her problem, but wants just to find out the solution for its own cognitive sake) has to decide when will she be satisfied with the number and variety of tests a solution has passed in order to be accepted by her; so, her choice in this ‘isolated’ situation will give us a certain epistemic benchmark (I would suggest to science students, and particularly to those more sympathetic to relativism, to ask themselves what standard would they choose in a similar situation : : : perhaps it is not very different from the scientists’ standard, but, even if it is, it would be nice to have some arguments about why both standards are not the same). The interesting thing about the models presented in Zamora Bonilla (2002a) and Ferreira and Zamora Bonilla (2006) is that they show that the collective choice in the case of a competitive search for the solution generates a standard of quality that is higher than the one that most individual scientists would have chosen if they only cared about epistemic considerations, not about recognition! That is, the search of solutions in a competitive environment ends in having solutions epistemically better (according to scientists’ own criteria of epistemic goodness) that those that would have been chosen in the absence of a competitive pressure. By the way, perhaps they are ‘too’ good, in the sense that we, citizens, would be content with a little bit worse solutions, if this allowed to have solutions to more problems. But the point of my argument is just showing that, from an epistemic point of view, there is no point in saying that the pursuit of recognition leads to scientific claims that are not ‘good enough’ on the average. Theory choice: As we saw in Section 28.3, if the acceptance of a scientific claim by an individual scientists depends on which ones of her colleagues also accept the same claim, it can be the case that more than one ‘social situation’ (i.e., a description of who accepts and who rejects the claim) is possible. For example, it can be the case that the hypothesis H being accepted by a 20% of the community is an equilibrium (i.e., everybody is happy with her choice, given the choices of the colleagues) and that a 70% is also an equilibrium; which one of both equilibria is the actual one will depend on historical causes. This seems to constitute, by itself, a reason in favour of certain degree of relativism: the scientific consensus is what it is, but with the same amount of information and the same social relations it could have been a different one (it is, however, a limited relativism, for there are more states that are not an equilibrium, than states that are possible equilibria). But the situation is still worse: for imagine that H 0 is a hypothesis that all the members of the community agree that is better than H . It can be proof that, in a case like this, for every equilibrium of the worse hypothesis there will be an equilibrium of the better one which is more inclusive than the former; so, it can be the case that the equilibria for H 0 are 30%

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and 80% respectively. So, H might be accepted by a 70% of the community, and H 0 by a 30%, in spite of everybody agreeing that H 0 is better. Contrarily to the analysis of the past example, this is a case where the game theoretic analysis can show that the interaction between researchers can lead to an epistemic inefficiency. The good news are that it can also be proved that, the better becomes a hypothesis (e.g., for having been confirmed by new data), it does not only happen that its equilibria go upwards, but smaller of them are disappearing, till in the end only one equilibrium, close to unanimity, remains. So, the growth of empirical knowledge can solve by itself those epistemic inefficiencies. The ‘construction’ of an empirical fact: Suppose you have performed an experiment, and are planning to report its result in a paper. It is now a platitude within science studies that you will have at least some possible choices, for ‘facts do not speak for themselves’, but need to be ‘interpreted’. For example, you can report the result as a ‘very important’, unexpected finding, which forces your community to look for a novel explanation, or you can present it as something uncontroversial. The problem you face is that, the more ‘radically’ you interpret your result, the less ‘credible’ it will be, i.e., the less ‘well confirmed’ by the experimental data you present will be from the point of view of your colleagues. As we saw above, the mere existence of many alternatives does not show that ‘all of them are equal’: it can certainly be the case that some of them are ‘better’ than others in specific senses; for example, some can be better from the epistemic point of view, whereas others (or, if scientists are fortunate enough, the same ones) are better from the point of view of the social elements of the researchers’ preferences; it can also be the case that some options are clearly better for some researchers, whereas other claims are better from the point of view of other colleagues. This plurality of valuations has not to be confused with some kind of ‘fundamental indifference’: game-theoretic models analyse precisely those situations in which people have different interests, and determine what choice they will make in those cases; and, by comparing the outcome determined by these choices with the value that other outcomes would have had for the agents themselves, the models allow to evaluate the efficiency of the interaction. It is also possible for the analyst to select the values or preferences she would like to be enhanced in that interaction (think of her as a science policy maker, for example, or just as a mere epistemologist), and then to think about ways of changing the way the agents interact, so that the chance of getting a ‘better’ result is bigger. In the case I’m discussing now, what can be proved is that, as long as the ‘readers’ of the paper the experimentalist is writing value her claim according to a positive function both of the result’s ‘novelty’ and of its ‘credibility’, but the author of the paper simply wants that the most possible novel claim is accepted, and as long as there is a negative correlation between novelty and credibility, then authors will have an incentive to interpret the results of their experiments in the least possible credible way that is compatible with the results’ acceptance. This means that, if authors were given a full liberty to describe their experiment in the way they preferred (do not forget we are assuming that they are choosing only between descriptions which are legitimate according to the methodological rules of the community), all the ‘gains’ to the

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scientific community from the interaction between authors and readers would go to the authors, and these gains will be in the form of ‘social’, not ‘epistemic’ values. It is reasonable to expect that communities will have designed some institutional ways of framing that interaction in such a way that epistemic gains are higher, e.g., by standardising the forms of interpreting experimental results, or by making peer review processes more severe.

28.5 Conclusion Is science ‘rational’? Is scientific knowledge ‘objective’? The game theoretic approach suggests that these questions can be better rephrased in the following way: Are scientific methods and scientific institutions efficiently ‘designed’ (or have they appropriately evolved) to provide us the best possible knowledge of the world, according to scientists’ epistemic values? And, do you find the epistemic goals of scientists appropriate? If the answer to the last question is ‘yes’, then a positive answer to the first question must be enough for satisfying (to a reasonable extent) our doubts about the rationality and objectivity of science; if the question to the first answer where negative, then we might employ the game theoretic approach to find where is that scientific institutions are failing, and how they can be improved. On the other hand, if your answer to the second question is not, i.e., if you think that scientist should pursue a different set of epistemic goals, then what you owe us is a specification of what these other goals should be, and game theoretical models of science can help you to discover how science should be organised in order to promote the epistemic values that you prefer. My own judgment is that, if I am right in my hypothesis that something similar to the verisimilitude function I summarised in Section 28.3 rightly describes the epistemic values of real scientists, then most branches of science are leading us to have progressively more and more theories and models that describe, predict and understand better and better an increasing number of empirical facts about the world, and this is the maximum I personally can ask from the epistemic point of view.

References Ferreira JL, Zamora Bonilla JP (2006) An economic theory of scientific rules. Econ Philos 22: 191–212 Zamora Bonilla JP (1996) Verisimilitude, structuralism and scientific progress. Erkenntnis 44: 25–47 Zamora Bonilla JP (1999) The elementary economics of scientific consensus. Theoria 14:461–488 Zamora Bonilla JP (2000) Truthlikeness, rationality and scientific method. Synthese 122:321–335 Zamora Bonilla JP (2002a) Scientific inference and the pursuit of fame: a contractarian approach. Philos Sci 69:300–323

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Zamora Bonilla JP (2002b) Verisimilitude and the dynamics of scientific research programmes. J Gen Philos Sci 33:349–368 Zamora Bonilla JP (2006a) Science studies and the theory of games. Perspect Sci 14:639–671 Zamora Bonilla JP (2006b) Science as a persuasion game. Episteme 2:189–201 Zamora Bonilla JP (2006c) Rhetoric, induction, and the free speech dilemma. Philos Sci 73: 175–193

Index

A AAAS. See American Association for the Advancement of Science (AAAS) Abstract models, 324 Academic patents. See Patents Academic research commodification, 130, 135 patenting of, 225–229 privatization of, 227–228 Academic science, commercialization of, 221 AGM rules for theory change, 47 AGM theory of belief change, 52–54 applying to propositional theories, 54–55 Grove’s method, reference to expansion, 54 road to verisimilitude, 56–61 proof of theorem, 58–61 theorems, investigating problem, 56–58 Albert, M., 291–293 Alchourr´on, C., 47 Alston, W.P., 317 American Association for the Advancement of Science (AAAS), 163 Anderson, E., 14 Andler, D., 1, 9 Anthropology, 5 Anti-naturalism in semantics, 311 Application innovation, 31–32. See also Science policy Applied research local models in, 26–27 conceptual structure of models, 26 giant magnetoresistance, 27 qualitative explanation, 27 quantum theory, 27 uses of understanding in, 27–29 Armstrong, D., 122 Artefactual probability(ies), 293–296 Aspirin, 25

Aunger, R., 9 Auyang, S.Y., 6

B Baade, W., 113, 114 Baltzer, U., 15 Balzer, W., 191, 192 Baringhaus, L., 65 Barnes, S.B., 223 Basic research and technological development, 24 Baumann, C.M., 13 Baumann, P., 290 Baumslag, D., 319 Bayesian confirmation measures, 74, 75 theory, 74, 77 Bayesian framework, 73 Bayesian incremental confirmation, 76 basic, derived and structural conditions, relationships, 87 Bayesian probability kinematics, 192 Bealer, G., 120 Behaviouristic roles, 124 Belief revision (BR) theory, 191 doxastic movement study, 279 truth likeness and, 195–198 Belief system(s), study of, 192 Bertolet, R., 319 Bianchi, C., 311 Bifurcationism, 1, 3, 5 Binary prediction games, 270 Biological phenomenon, 126 Bio-naturalistic research programs, 7 Bittner, R., 17, 18 Boghossian, P., 166–169, 171 Bounded rationality, 268 Boyd, R.N., 9, 245, 248, 249, 252 Brandom, R.B., 311

333

334 Brier’s rule, 99 weather forecasting, 98 Broad epistemic research, 24 Brown, J.R., 221 BR theory. See Belief revision (BR) theory Buchanan, B.G., 75 Bunge, M., 319 Bush, V., 24 Buss, L., 141 Buttasi, C., 73

C Calandra, F., 47 Carnap, R., 234–237, 240, 299–305, 307, 308 Carnap’s method of ramseyfication, 299–300 Demopoulos’ criticism, 306–308 problem with, 302–303 Psillos’ criticism, 304–306 Carrier, M., 23 Carruthers, P., 9 Cartwright, N.D., 9, 178, 212, 215, 216 Carus, A., 302 Cascade model vs. emergentism, 24–26 for research, 24 Causal Markov condition, 63 CCO. See Confirmation complementarity condition (CCO) Cei, A., 35, 39, 256 Cevolani, G., 47, 50, 54–56, 58 Cheng, M., 150 Chlaß, N., 63 Choice revision, 280 Chomsky, N., 5 Churchland, P.M., 120, 246 Cognition, application for evolution, 276–277 Cognitive sciences, 5, 9 Cognitive-scientific community, 9 Cognitive sirens, 6 Commercial academic science, consequences of, 221 Commercialization, benefits and costs, 132–136 of academic science, 135 negative impact on, 132 in research, 133 threatening social norms, 134 Communalism, 134, 136 Communism, 151 secrecy and publicity, 152 timely publication, 152–153

Index Communism, Universalism, Disinterestedness, and Organized Skepticism (CUDOS-norms), 150–151 Computer science, 131 Concept analysis; 320 Conditional independence, nonparametric tests for, 64–66 functions defined as, 66 multivariate distribution, 64 null hypothesis, 64 product kernel estimators, 65 p-value, estimation, 66 Confirmation complementarity condition (CCO), 88 Constraint of imperfection, 277 ‘Construction,’ of empirical fact, 325–326 Convergent oscillations, 272 Copyrights, 130 Cosmides, L., 9 Cox, D., 290 Cross-disciplinary computational templates, 146 Crupi, V., 73, 75, 81, 86 CUDOS-norms. See Communism, Universalism, Disinterestedness, and Organized Skepticism (CUDOS-norms)

D D’Agostino, M., 95, 103 Dardanoni, V., 103 De Caro, M., 4 Deontological ethics, 150 Descriptive adequacy, 25 Disambiguation, 35 Discovery vs. invention, 136–137 justification and, 312–315 Disinterestedness challenges before, 155–156 building of network, 161 citations number, 158–159 publication number, for assessing individual and group scientists, 157–158 research proposals, assessment of, 160–161 Dolby, R.G.A, 223 Dowe, P., 202 Dretske, F., 5 Dummett, M., 311 Dupr´e, J., 4 Durham, W.H., 9

Index E Ecological validity, 273 Economic competitiveness, 129 Economics, 5, 6, 147 Eells, E., 79, 86 Elastic Ether theory, 37 Ellis, B.D., 246, 247, 250 Elster, J., 14 Emergentists, 25 Empirical investigation, 120 Empirical realism Carnap’s ‘empirical realism’, 301–302 Ramsey and Carnap sentences, 300 Feigel’s ‘semantical realism’, 301 Enc¸, B., 120 Entrepreneurial academia, rise of, 221 Epidemiology, 9 Epiphenomenalism, 125 Epistemic accuracy, 96 Epistemic efficiency and scientific institutions, 328–331 Epistemic entrenchment, 54 Epistemic quality of scientific products, 326–328 Epistemic research, 23 Epistemic structural realism (ESR), 255 misinterpretation of position, 256 Epistemic thesis, 2 Epistemological justification of indirect representation, 147 Essay Concerning Human Understanding, 248 Evolutionary biology, 5 The Evolution of Individuality, 141

F Faithfulness condition, 63 Fallibilism, 39 Faye, J., 107 Feigl, H., 301, 312–314 Feldman, R., 319 Ferreira, J.L., 329 Festa, R., 47, 50, 73, 74, 82, 192 Fictitious infallible forecaster, 99 Final probability incrementality (FPI), 77 Financial interests of scientists. See Commercialization, benefits and costs Financial support, 23 Finch, H.A., 82 Fitelson, B., 79, 82–84, 86 Fodor, J., 5 Forecasters, 99 goal, 97

335 vectors, measuring distance between, 100 belief-vector, 100 error replication, 104 linear scoring rule, 103 properties, 100–103 theorem, 103 Fowler, W., 114 FPI. See Final probability incrementality (FPI) Franz, C., 65 Frege, G., 311 Frege’s context principle, re-interpretation, 311 French, S., 39, 256, 258, 263 Frequentism, 289 Frequentist inference, 289 Frequentist justification, 290–293 Fresnel’s equations, 256 Fresnel’s optical theory, 37 Friedman, M., 307 Frigg, R., 212 Fuhrmann, A., 280, 283, 287 Full belief, 96 Fundamental research practical challenges, 25 strategy to conduct, 24

G Galison, P., 4 Game-theoretic model of science, 324–326 G¨ardenfors, P., 47, 48, 53, 192 G¨ardenfors postulates, 53. See also AGM theory of belief change Gelman, S.A., 9 Gene-culture co-evolution, 9 General prediction methods, 269 Generative entrenchment, 9 Genetic engineering, 131, 136 Giant magnetoresistance, 27 Giere, R.N., 139, 144 Gigerenzer, G., 268, 272 Gilbertian JCs, 15 as social practices, 19 Gilbertian joint actions, 17 Gilbertian rights and obligations, 18–19 Gilbert, M., 14–18, 21 Gilbert’s account of social rules and norms, 19 argument, 19–20 circularity in social rules, 21–22 constitutive rules, 20 rules governing JCs, 20 Gilbert’s analysis of social norms, 13 JCs formation, 14 notion of social rule/social convention, 14

336 Gilbert’s permission point, 17 Gilbert’s strategy, social rules in JCs, 19 Gillies, D., 296 Godfrey-Smith, P., 139, 141 Goldman, A.I., 9, 318, 319 Good, I.J., 75 Gozzano, S., 119 Graded belief, 96 Grammar sorting, structural properties confirmation complementarity, 85–86 proof of theorems, 92 theorems, 85 confirmation measure, 83 disconfirmability, 84 equiconfirmability, 84 equidisconfirmability, 84 laws of likelihood, 82–83 proof of theorems, 91 theorems, 83 ordinal vs. quantitative level, 81–82 Graphical models, 63 causal model specification, 64 Grove, A., 54, 196

H Hacking, I., 247, 248 Hansson, S.O., 47, 280, 282, 283, 287 Harman, G., 165, 173 Harper’s identity, 279 Heat receptors, 124. See also Receptors Hempel, C.G., 204 Hermeneutic component, 3 Hild, M., 281, 285 Hirschfeld, L.A., 9 Hooker, C., 120 Horwich, P., 79 Howson, C., 291, 292 Hoyle, F., 114 Hoyningen-Huene, P., 314 Human and social sciences (HSS), 7 displaced by biology, 8 Human cognitive competences and limitations, 318 Human inferential practice, 318 Humanities, 6, 31, 109–111 Human reasoning, 251 Humility thesis, 35, 40 and structuralist intuitions, 41–43 Humphreys, P., 140

Index I ICSU. See International Committee of Scientific Unions (ICSU) Identity statements, 121 IFPD. See Initial and final probability dependence (IFPD) Imagined system, 145 Incremental confirmation basic properties, 76–78 equineutrality (EN), 78 final probability incrementality (FPI), 77 initial and final probability dependence (IFPD), 77 initial probability incrementality (IPI), 77–78 derived properties, 78–81 proofs of theorems, 89–91 qualitative discrimination (QD), 78–79 theorems for, 79–80 Indirect reasoning, 145, 146 Indirect representation, thesis of, 140–142 epistemological justification, 147 Induction, problem of, 267–270 Information technologies, 131 Initial and final probability dependence (IFPD), 77 Initial probability incrementality (IPI), 77–78 Institutional imperatives, 222 Integer-valued approximation, 275 Intellectual circles of Red Vienna, 237–242 Intentional properties, 120 Interest(s), kinds of, 151 International Committee of Scientific Unions (ICSU), 163 Interpretations characterization, 108 define, 108–109 forms of, 111–113 investigative, 112–113 as response to representational question, 115–116 in science, 109–111 standard wisdom of, 108–109 and what-questions, 113–115 interpretative inquiry, 115 something like, 114 theory of supernovas, 113 why-question, 113 Interpreter’s selection, 116 Investigative interpretations. See Interpretations IPI. See Initial probability incrementality (IPI)

Index Irzik, G., 129, 221 Isomorphism, 143

J Jackson, F., 9 Jeffrey, R., 190 Joint commitment (JC), 13 Joyce, J.M., 83, 96 Justification, meaning of, 312

K Kaiser, M., 152 Kantian humility, 43 diverges from Lewis’s view, 44 Kant, interpretation, 43. See also Interpretations Kantorovich, A., 319 Keeping Science Open, 135 Kellert, S.H., 4 Kemeny, J., 84, 86, 92 Keynes, J., 74 Kim, J., 5, 120, 316 Kitcher, P., 1, 4, 8 Knobe, J., 9 Knowledge, 38 commodification of, 130 Knowledge economy, 129 competitiveness in, 131 Knuuttila, T., 139, 142, 225 K¨obben, A, 159 Koertge, N., 134 Kordig, C.R., 315 Kraft, V., 237 Krantz, D.H., 101 Krause, D., 258 Krimsky, S., 137 Kripke’s argumentation, 120 Kuhn, T.S., 313 Kuipers, T.A.F., 76, 80, 149, 192 Kusch, M., 8, 165

L Ladyman, J., 257, 258, 262, 263 Langton, R., 43 Laudan, L., 190, 195 Law of likelihood (LL), 82, 88 Lawrence, S., 5 LEDs. See Light emitting diodes (LEDs) LESC. See Logic and Epistemology of Scientific Change (LESC) Levi, I., 190, 192, 194, 279

337 Levinson, J., 108 Levi’s identity, 279 Levy, N., 6 Lewis, D.K., 14, 40, 191, 193, 196, 256–257 Lewisian conventions, 14–15 Licensing, 130 Light emitting diodes (LEDs), 23 Linear scoring rule, 97 LL. See Law of likelihood (LL) Local prediction methods, 268–269 Loewer, B., 312 Logic, 317–318 Logical positivist view, 212 Logical theory of inductive inference, 190 Logic and Epistemology of Scientific Change (LESC), 90 programmes of philosophy, 191 Logico-deductive inferences, 317, 318 The Logic of Chance, 248 Longino, H.E., 4, 224 Lyre, H., 263

M Macarthur, D., 4 Macfarlane, B., 150 Machamer-Darden-Craver account (MDC) activities and actualization of, 202–203 argument by different actualization, 207–208 perfectly balancing casual contributors, 206–207 polygenic activities and activities of organization, 203–204 reason for construction, 201 Machamer, P., 202, 203 The Major Transitions in Evolution, 141 M¨aki, U., 177, 216 Margolis, E., 5 Massive modularity, 9 Mathematical formulation, 38–39 Maxwell, G., 39 Maxwell’s electromagnetic theory, 37 Maxwell theory, 256 Mayo, D.G., 289 McMullin, E., 216 MDC. See Machamer-Darden-Craver account (MDC) Mean absolute error, 97 Mertonian norms and values, 221 communism, 151, 222, 224, 227 secrecy and publicity, 152 timely publication, 152–153

338 when conceived as ‘default-norms,’ 150–151 disinterestedness and its challenges, 155–156, 222–223, 226, 228 assessment of research proposals, 160–161 networks, 161 number of citations, 158–159 number of publications, 157–158 writing research proposals, 159–160 and ethos of science, 222–223 organized skepticism, 154–155, 224, 225, 228 patenting of results of academic research, 225–229 scientific norms and, 223–225 universalism, 153–154, 222, 223, 224, 226 Merton, R.K., 134, 150, 221–223 Metaphysical underdetermination, of structural realism argument, 257–259 resistance for argument coherency of metaphysical underdetermination, 262–263 common denominator, 260–261 impact of quantum statistics, 261–262 Miller, D., 47 Mill, J.S., 204, 205 Mind-reading, 9 Model-enabled reasoning, 148 Model(s) representations, as, 178–181 truth and, 181–183 Model-theoretic view, 212 challenges to, 219 identification of class of models, 213 inadequacy of, 216–219 misconstrues model concretization characterization, 213–216 Modern science, perspective of, 38 Moneta, A., 63 Monism, 1 Monte Carlo study results Cramer test, 70 energy test, 69 Fisher’s z test, 70 Hellinger test, 70 proportion of rejection of H0 ; 69–71 rejection frequencies, 69 simulation design, 66–68 Moral sciences, 3 Morgan, M.S., 142, 216 Mormann, T., 302

Index Morrison, M., 142, 212, 216 Motion, 171 Moulines, C.U., 191, 195 Mulkay, M., 150, 223 Multiple contraction forms of, 280 problem of, 281–283 Multiple realizability definition, effected, 40–41 language, 40 Lewis constrains, 41 Lewis’s RS, 40 realization formula of T, 41 use of Scott’s denotationless term, 41 Multiple realizability argument, 120 Mura, A., 75

N Nash equilibrium, 325 Natural kind theory enthusiasm for, 245 importance of notion of, 246 problem of, 248–250 approaches to, 251–252 role in philosophical science, 245 uselessness of, 246–248 Natural sciences, 4, 109 radical changes in, 36 Natural-scientific component, 3 Neoliberalism, 131 Neo-naturalism, 4 Neo-naturalist unification, 4–6 Neurath ‘invented’ descriptive philosophy, 10 Neurath, O., 9 Neuroscientific theories of pain, 126 Neyman, J., 290 Niche construction, 9 Nichols, S., 9 Nickles, T., 312 Niiniluoto, I., 47, 48, 54, 56, 57, 162, 189, 192, 196 Normative logical principles, 318 Normativity of social norms, 17 Norton, J., 268 No-Theory Theory (NTT), 296 Nowak, L., 178, 216 Nozick, R., 81

O Oddie, G., 56, 192, 197 One-dimensional value-sensitivity, 112 Online learning, 273

Index Ontic probability, 293 Ontic structural realism (OSR), 255 Ontological thesis, 2 Oppenheim, P., 84, 86, 92 Orchestration, for social sciences, 11 Organic unitarianism, 2, 4 Organized skepticism, 154–155 Orthodoxy, 9 OSR. See Ontic structural realism (OSR) Over-intellectualisation, 15–17

P Package contraction, 280 Paparoditis, E., 66 Papineau, D., 4 Para-normal worlds, 267 Patents, 130 of academic research, 225–229 discovery-invention and, 137 increase in overall number of, 132 neo-Mertonian analysis of, 230 primary criteria for, 228 PCR. See Polymerase chain reaction (PCR) Pearson, E., 290 Permission point, 17 Persson, J., 201 Pettit, Ph., 163 Pharmacological research, 25, 28 Phenomenal consciousness, 119 Phenomenological argument, 120 Philosophical naturalism, 4 Philosophische Grammatik, 311 Philosophy of science, developments in, 25 The Philosophy of the Inductive Sciences, 248 Physicalism, 2 Physical life, 124 Physical phenomenon, 126 Physical sciences, 3 Pinker, S., 5 Poincar`e, H.J., 37 Politis, D.N., 66 Polygeny 1, 205 Polygeny 2 consequences of, 205–206 effects, 208 Polygeny, kinds of, 204–205 Polymerase chain reaction (PCR), 32 Pooley, O., 258 Popper, K.R., 47, 190, 313 Portides, D., 211, 218 Positivism, 3 Post-industrial capitalism, 129 Post-modern philosophers, 108

339 Post-Popperian theories of verisimilitude, 48–50 applying to propositional theories, 50–52 Prediction games, 270–271 Principal Principle, 292 Privatization, 131 Probabilistic laws, 95 Probability ratio, 74 Probability theory, 75 Pseudorationalism, 10 Psillos, S., 37, 303–305 Psychological properties, 119 Psychological truths, 318

Q QD. See Qualitative discrimination (QD) Qualitative discrimination (QD), 78–79 Quantitative and formal social science (QFSS) arguments in favor of, 8 minority within, 9 and NSS, rivalry between, 8 official representative within, 7 reasonably claim to, 6–7 social realm, 7 unproblematically scientific in, 8 Quantitative social science, 7 Quantum theory, 219 Quine’s epistemology, 316–317 Quine, W.V.O., 5, 246, 316, 317

R Radder, H., 135, 136, 221, 223, 225, 227 Ramseyan Humility, 42, 43, 256 Ramsey, F.P., 299 Random sampling estimations, 273 Ranking theory, 280, 285–287 required basis of, 283–285 Realistic optimism, regarding science, 36 Real-valued prediction games, 270, 275 Received wisdom, 108. See also Interpretations Receptors, 124–126. See also Sensations of pain, 127 Recognition heuristics, 268 Redhead, M., 258 Reductive unitarianism, 2 Regionalism, 2 Reichenbach, H., 267, 269, 276, 312 Relational features, 38 Rentetzi, M., 233 Replacement relativism, 165 Boghossian’s criticism, 167

340 solving problem of, 171–175 physics vs. philosophy, in, 167–168 Rescher, N., 75 Resnik, D., 136 Resnik, M.D., 318 Results-drivenness in modeling and indirect reasoning, 145–147 Results-driven theoretical activity, 146 Reydon, T.A.C., 245 Richerson, P.J., 9 Rigid designators, 122 Rizzo, M.L., 65 Rorty, R., 190 Ross, D., 262 Ross, W.D., 203 Roth, P.A., 317 Russell, B., 246 Ryckman, T., 307

S Saatsi, J., 255 Saliency, 125 Saunders, S., 258, 262, 263 Schickore, J., 312 Schlick, M., 235–237, 239–243, 307 Schurz, G., 267, 272, 274, 275 Science ethics and, 149 initiatives to shape up interaction between, 150 as Neurath, 10 Science for sale, 130–132 economico-political, 131 ideological, 131 legal Diamond v. Chakrabarty, 131 patents on genes, 131 scientific, 131–132 Science policy, 23 sponsor thorough, 24 and technological benefits, 31–32 Scientific accreditation, 6 Scientific development, 10 Scientific institutions, epistemic efficiency and, 328–331 Scientific integrity and openness, 136 Scientific knowledge, 30 and commodification, 130 Scientific naturalism, 4 Scientific products, epistemic quality of, 326–328 Scientific representation, 142–145 Scientific research, 23, 130, 132–134

Index Scientific revolution, 24 Scoring rules, 4 and epistemic accuracy, 96–99 Searle, J., 5 Selective realism, 38 Self-training, 126 Sellars, W.F., 311 Semantic naturalism, 319–320 Semantic theory of truth, 190 Sensations, 123 feature of, 124–125 participating in causal structure of, 124 Shortliffe, E.H., 75 Siegel, H., 314 Sigman, J., 110 Simple induction method, 271–274 Single event predictions, 268 Sinigaglia, C., 95 Sismondo, S., 223 Smith, J.M., 141 Sneed, J.D., 191 Sober, E., 74, 296, 314 Social cognition, 9 Social construction of scientific knowledge, 323 Social conventions, 14 Social norms commercialization threatening, 134 and function of science, 130 and joint commitments, 13–15 normativity of, 15 of science, 135, 136 Social psychology, 5 Social rule, 15 Social sanctioning system, 14 Social-scientific component, 3 Sociology, 4–7, 134 Solomon, M., 152 Sperber, D., 5, 9 Spirtes, P., 63, 64, 67, 69 Spohn, W., 279–281, 285 Sprenger, J., 289, 290 Statement, essential element, 121–122 Steel, D., 80–82 Stegm¨uller, W., 191 Sterelny, K., 9 Stich, S., 9 Strevens, M., 292, 295 Strong regionalism, 2 Structural ambiguity, 36 Structural correctness, 37 Structuralism in philosophy of physics, 263–264 Structuralism (STR) programme, 191

Index scientific realism and, 193 truthlikeness and, 194–195 Structural realism argument over, 257–259 resisting of, 260–263 position of, 299 Stump, D.J., 4 Su´arez, M., 143, 144, 180, 212 Sugden, R., 17 Su, L., 65, 66 Suppe, F., 213 Sure-thing principle, 99 Systematic educational disadvantage, 234 A System of Logic, 248 Szathm´ary, E., 141 Szekely, G.J., 65 T Take-the-Best (TTB), 271, 273 Taussky-Todd, O., 238 Technological changes, 24. See also Technologies independent of progress in basic science, 25 and scientific progress, 29 Technologies. See also Applied research advancement of, 23 determinants of pathways of, 30 and established knowledge, 30 science policy and benefits, 31–32 understanding in development of, 29–31 application innovation, 31 use-oriented projects in life sciences, 31 Technosciences, 131 commercialization, 132 Teller, P., 258 Tentori, K., 81 Thagard, P., 317 Theoretical identifications, 119 Theoretical knowledge, 24 Therapeutic efficacy, 29 Three-sex biology, 146 Tich´y, P., 47, 193 Tickle sensation, 124. See also Sensations Tissue test systems, effective substances, 25 TL programme. See Truthlikeness (TL) programme Tollefsen, D.P., 15, 21 Tooby, J., 9 Tromp, H., 159 Truth locus and stuff of, 184

341 model and, 181–183 Truthlikeness (TL) programme, 193–194 TTB. See Take-the-Best (TTB) Tuomela, R., 21 Turing, A.M., 5 Tuunainen, J., 225 Tverski, A., 101

U Uebel, T., 237, 299 Unification programs, 2 Unitarianism, 2 Unity of Science Program, 1 Universalism, 153–154 meaning of, 222 Universal prediction methods, 269 Urbach, P., 291, 292 U.S. Patent and Trade-mark Office (USPTO), 131 Utilitarian ethics, 150

V van Fraassen, B., 110 Vassallo, N., 311 von Th¨unen, J.H., 185

W Waters, C.K., 4 Weak regionalism, 2 Weighted average meta-induction, 274–276 Weisberg, M., 139, 140, 144, 146 White, H., 65, 66 Wilson, E.O., 4 Wilson, M., 120 Wimsatt, W.C., 9, 178 Withaar, H., 159 Wolff, P., 204 Workmanship of men, 249 Worrall, J., 35, 36, 39

Y Yatchew, A., 68

Z Zamora Bonilla, J.P., 323, 329 Zandvoort, H., 163 Ziman, J., 150 Zwicky, F., 113, 114