The Courage of Doing Philosophy: Essays Presented to Leszek Nowak

The Courage of Doing Philosophy

The Courage of Doing Philosophy Essays Presented to Leszek Nowak

edited by

Jerzy Brzeziński, Andrzej Klawiter, Theo A.F. Kuipers, Krzysztof Łastowski, Katarzyna Paprzycka & Piotr Przybysz

Amsterdam - New York, NY 2007

The paper on which this book is printed meets the requirements of “ISO 9706:1994, Information and documentation - Paper for documents - Requirements for permanence”. ISBN: 978-90-420-2336-9 ©Editions Rodopi B.V., Amsterdam – New York, NY 2007 Printed in The Netherlands

TABLE OF CONTENTS Andrzej Klawiter, Krzysztof àastowski — Introduction: Originality, Courage, and Responsibility. . . . . . . . . . . . . . . .

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List of Books by Leszek Nowak . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Selected Bibliography of Leszek Nowak’s Writings . . . . . . . . . . .

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SCIENCE AND IDEALIZATION

Theo A. F. Kuipers — On Two Types of Idealization and Concretization: The Case of Truth Approximation . . . . . . . .

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Ilkka Niiniluoto — Idealization, Counterfactuals, and Truthlikeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 R. F. Hendry, Stathis Psillos — How to Do Things with Theories: An Interactive View of Language and Models in Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Izabella Nowakowa — The Method of Ideal Types versus the Method of Idealization . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Igor Hanzel — Leszek Nowak on Scientific Laws and Scientific Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Michael J. Shaffer — Idealization, Counterfactuals, and the Correspondence Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Krzysztof àastowski — Synthetic and Neutralist Theory of Evolution: The Issue of Methodological Correlations. . . . . . 205 Adolfo García de la Sienra — Idealization in the Labor Theory of Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Krzysztof Brzechczyn — On the Application of the nonMarxian Historical Materialism to the Development of Non-European Societies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

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Contents

SCIENCE AND ONTOLOGY

C. Ulises Moulines — Model Construction, Idealization, and Scientific Ontology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Thomas Mormann — Representations, Possible Worlds, and the Idealizational Approach to Science . . . . . . . . . . . . . 273 Evandro Agazzi — Idealization, Intellectual Intuition, Interpretation, and Ontology in Science . . . . . . . . . . . . . . . . . . . . 303 Piotr Przybysz — What does to Be Mean in Leszek Nowak’s Conception of Unitarian Metaphysics? . . . . . . . . . . . . . . . . 315 Roberto Poli — Formal and Ontological Roundabouts . . . . . . 325 Jan WoleĔski — Metalogic and Ontology . . . . . . . . . . . . . . . . . 337 SCIENCE, PHILOSOPHY AND VALUES

Max Urchs — On the Structure of Deceptive Speech Acts: Lying as an Element of Communication . . . . . . . . . . . . . . . . 355 Jerzy Perzanowski — In Praise of Philosophy . . . . . . . . . . . . 375 Roman Kubicki — Love: In the Search for the First Philosophy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 Bert Hamminga — Is the Enlightened Worldview on Retreat? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Martti Kuokkanen — Boxing and Violence . . . . . . . . . . . . . . . 445 Katarzyna Paprzycka — On Willfully Contrarious Beliefs . . . 461

INTRODUCTION: ORIGINALITY, COURAGE, AND RESPONSIBILITY

Leszek Nowak’s Ways of Doing Philosophy This introduction makes no claim to neutrality. We have no desire to write about Leszek simply as a thinker, teacher and man of upright character. We leave that task to someone else, to someone who can keep some distance from their subject. We feel as if we were his spiritual children and we find ourselves unable to stop enumerating his merits and accomplishments. We had the fortune to experience something incredible and unique: we met a master who was not only willing to teach us, work with us and become our true friend, but who, through each of his texts or seminars, filled us with admiration and sheepish embarrassment. Admiration because, after over thirty years of acquaintance, we are still unable to predict his next move. Although illness has prevented him from giving lectures and hosting seminars, he still manages to work just as hard as ever, and we, waiting for his next text, wonder what stifling habit of thought Leszek will boisterously grapple with this time, and whether he will once again come up with the kind of thought that just does not become respectable professors — those custodians of timeworn traditions and

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 7-21. Amsterdam/New York, NY: Rodopi, 2007.

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guardians of philosophical mantras. In this respect Leszek is the youngest among us. Unfortunately, this source of admiration is also a cause of embarrassment. What is an eager student to do when their master continually demonstrates, with such ease and grace, ever new and increasingly complicated figures of thought, and they — a mere apprentice to the trade — have yet to fully master the figures from the first lessons? Our frustration was made worse by the fact that Leszek refused to treat us as assistants who filled in the gaps and smoothed down any rough edges in the system created by the boss. He expected us to be as bursting with thought as he was. Presenting a new text at a seminar every week was like water off a duck’s back for him. For us, his doctoral students, with whom he had regular tutorials, this was an ordeal of fire. Once a week, at a specified time, we had to arrive at Leszek’s house with a new idea (as well as something he took for granted — our work on the task set the previous week). Time and time again each of us would come to him full of remorse, explaining that, unfortunately, that week we had not managed to meet our quotas because no new ideas whatsoever had come into our heads. Then Leszek would comfort the wrongdoer, sit them down in an armchair and steer the conversation in such a way that, as it unfolded, it became clear that the many days of wracking our brains for an interesting idea had not been in vain, not by any means. The delighted doctoral student would discover that the idea had been on its way all the time, that it was their own little brainchild, and Leszek only gave his expert help in bringing it out into the world. Leszek Nowak is such a multifaceted and productive person that it is impossible to provide an exhaustive account of his achievements to date. So we shall focus instead upon what makes him, in our opinion, one of the most original thinkers in Polish philosophy after the Second World War. We will present the main strands of his academic work and draw attention to some of the other fields he has been active in. Concentrating on the essentials, we will begin by looking at the most important — his research activity. We shall also discuss Leszek’s accomplishments as a publisher (the creator and editor-in-chief of PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, the first philosophy book series after the World War II that was led by

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a Polish scholar and which promoted Polish philosophy among an English speaking audience), his role as organizer of academic life and teacher of young philosophers. To round off, we outline his political activities and his work as an essayist and political commentator.

Biographical Note Leszek Nowak was born on the 7th of January 1943, in the town of WiĊckowice, which can be found in the region of Maáopolska, in the south of Poland. He studied law at Adam Mickiewicz University (19611965), and then philosophy at Warsaw University (1966). From his student days to the present, he has been connected with Adam Mickiewicz University in PoznaĔ, first in the Department of Law, and later in the Institute of Philosophy. He took part in the seminars of Czesáaw Znamierowski, Zygmunt ZiembiĔski and Jerzy Giedymin. He wrote his doctoral thesis on the theory of law, entitled Problems of the Meaning and Validity of Legal Norms and the Semiotic Function of Language, under the supervision of Professor Zygmunt ZiembiĔski, in 1967. He gained his habilitation in general methodology in 1970, on the basis of the work The Methodological Foundations of Karl Marx’s Capital. He became a professor without chair in 1976 and a professor with chair in 1990. In 1985, Professor Nowak was expelled from the university for his involvement with underground publishing (the Minister Science of Higher Education who signed the decision had previously been the rector at Adam Mickiewicz University, so he effectively fired a former colleague). In 1989, he was invited back to work and took up his former position again. He has been a correspondent member of the Polish Academy of Sciences since 1994. Leszek Nowak was also: Visiting-professor in several Western universities, a fellow of the Institute of Advanced Research in Wassenaar and Berlin; the founder (in 1975) and editor-in-chief of the international book series PoznaĔ Studies in the Philosophy of the Sciences and the Humanities (Amsterdam: Rodopi; 92 volumes had been published by the end of 2006 ) as well as the series, published in

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Polish (from 1976) PoznaĔskie Studia z Filozofii Nauki, which changed its title in 1992 to PoznaĔskie Studia z Filozofii Humanistyki (20 volumes). Professor Nowak was a member of PZPR, the Polish United Workers’ Party, from 1962 to 29 August 1980. He was interned under the martial law on 13 December 1981 and held in prison to December 1982. He was also a member of Solidarity from 1980 to 1994. Even during his imprisonment, Professor Nowak did not cease his educational and journalistic activities. He gave lectures in the various places in which he was held prisoner and prepared written versions of his speeches. He did not belong to those who meekly submitted to the repressive regime: he made many protests, including a long-term hunger strike. It was during the time of his imprisonment that the first serious problems with his health arose; problems which have intensified in recent years. The early period of Leszek Nowak’s research activity coincided with the later years of the outstanding Polish philosophers who had learnt their craft in the period before World War II. He always tried to process their input in his own unique way and transform it through critique. At first he was a positivist, then a Marxist. He has maintained a deep respect for both these theoretical orientations to this day. Professor Nowak is the author of three original philosophical conceptions: the idealizational conception of science (philosophy of science); non-Marxian historical materialism (social philosophy) and negativist unitarian metaphysics. Among the most important of his interpretative treatises in which he commented upon the works of other philosophers one should mention: an analytic reconstruction of Marxian philosophy (the idealizational interpretation of the method of Marx’s Capital, a categorical interpretation of the dialectic, an adaptational interpretation of Marxian historical materialism), an interpretation of the social philosophy of Witold Gombrowicz, and an interpretation of the metaphysics in Bolesáaw LeĞmian’s poetry. Professor Nowak is the author of approximately 350 academic works, including 21 books.

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Professor Leszek Nowak raised numerous academic foster children. He promoted 13 doctors of philosophy: Wojciech Patryas, Jerzy BrzeziĔski, Krzysztof àastowski, Barbara TuchaĔska, Andrzej Klawiter, Jolanta Burbelka, Sáawomir Magala, Renata ZieliĔska, Jadwiga Wais, Piotr Buczkowski, Grzegorz Banaszak, Krzysztof Brzechczyn, Piotr Przybysz. The majority of them now work as professors at Polish Universities (Sáawomir Magala is a professor at Erasmus University in Rotterdam).

Our Master It is not particularly difficult to describe Leszek’s diverse accomplishments or enumerate his achievements in research and teaching. However, it is somewhat harder to convey how much his exploits helped us at a time when we were fledgling philosophers, when we considered it a landmark in our professional careers to have managed to get our first article printed, or be awarded our doctoral degrees. For it was necessary to sweat a great deal before our taskmaster would finally announce that he would “buy” the next section of our thesis. However, it was not just a matter of perfecting the technical skills of those under his care. Leszek strove to prepare us for the philosophical work. His texts and lectures showed us how not to be afraid of bold hypotheses, how to be sensitive to the criticisms of others, and how to make genuinely thoughtful responses. He endeavored to instill certain modes of conduct into us. When, in the late seventies, we met at “counsels,” i.e. regular workshops at the Department of the Dialectics of Cognition (at present the Department of Epistemology and Cognitive Science) at the Institute of Philosophy at Adam Mickiewicz University, it was every participant’s duty to find a weak spot in the paper presented, and to suggest how that weakness could be dealt with. Leszek intended this to be a gesture of good will toward our colleagues, to help them with the difficulties they were having with their research. Leszek’s guiding principle, adopted from the Popperian tradition, has always been a firm conviction in the great value of criticism. This

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is the source of his positive attitude toward colleagues who criticized his theoretical propositions. He was convinced that thanks to critics it is easier to see the weak sides of one’s own conceptions and to overcome one’s own limitations in this way. Having developed such an outlook, being so hungry for criticism, he began to urge us, his own pupils, to look for holes in his theories. We learnt much from this, though it must have looked odd, when we, together with our supervisor, tried to identify errors in his work. He was so generous that he excused even those who, at the time when Leszek was imprisoned or expelled from the university, criticized his dissident views to gain promotion to a higher academic position. Because he appreciated another’s criticisms, Leszek was of the belief that others would react kindly to his critical comments. He soon found out that, in the real world of academia, criticism is treated with the same hostility as it is in the real world of politics. To an outside observer, it could seem that the ease with which Leszek comes up with ideas, and his prolific output of articles and books, is just the result of a gift of nature. However, although this gift undoubtedly exists, it is fueled by an extraordinary motivation and a punishing work regime. He can work in any situation and at any hour. He did not even change his working habits in prison, where he was held during the Martial Law from December 1981 to December 1982. His neighbor joked that for Leszek to be deprived of his freedom was not such a big thing, because he had already relinquished his freedom of his own free will, by devoting himself to his work to such an extent that, to all intents and purposes, he had become a prisoner in his own home.

Original Philosophical Conceptions The central idea of Leszek Nowak’s philosophical work was, and is, to take up philosophical challenges whose significance is not dictated by fleeting intellectual fashion or by a temporary epistemic need. This can be seen in his publications, and in his seminars and lectures. He shocks not only with the way in which he grasps problems, but also — and

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maybe most importantly — the courageous way he questions the received modes of thought. His own propositions are based on a thorough understanding of the subject matter, but they are never limited to reports about existing solutions. He seeks solutions to problems which go against the current of popular research intuitions and common conviction. Starting from a preliminary sketch, he develops it to such a point that it takes on the shape of an entire philosophical conception or methodological doctrine.

1. Methodology and the Philosophy of Science Leszek Nowak began his career under the supervision of Professor Zygmunt ZiembiĔski in the Department of the Applications of Logic to Law in the Faculty of Law at the University of Adam Mickiewicz. His early work concerned the theory of law and analytical philosophy. His doctoral thesis proposed a conception of the rational legislator, and was entitled An Attempt at a Methodological Characterization of Jurisprudence (in Polish, 1968). At this time, he worked closely with Jerzy Kmita, with whom he co-published A Study on the Theoretical Foundations of the Humanities (in Polish, 1968). The appearance of this book marked the beginning of the intellectual movement which would later become known as “the PoznaĔ School in Methodology”. Next, Leszek Nowak embarked on an in-depth study of the methodological structure of Marx’s Capital, attempting to discover the research procedure used to construct the theory of surplus value and the theory of profit. In Foundations of the Marxian Methodology of Science (in Polish, 1971), he revealed the methodological basis for this economic theory of social phenomena. The author showed that Marx’s theory of capital was based on counterfactual assumptions used to construct models and describe situations which do not occur in real economical systems. To explain the nature of this operation, Leszek Nowak proposed the systematic conception of idealization and demonstrated how Marx applied the idealizational method in Capital. According to Leszek Nowak’s argument, Marx formulated the law of surplus value just as Galileo formulated the law of free fall. The

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introduction of idealizing assumptions allowed him to neglect secondary factors (those which are of lesser importance), and to consider only those factors which are the most essential to the phenomenon under investigation. The fact that Marx applied idealization means that the method of research in the social sciences does not differ, in this regard, from the method which is used in the natural sciences. Starting from a detailed analysis of this method Leszek Nowak developed a systematic methodological conception, which later became known as The Idealization Theory of Science (ITS). One of the most important works in his oeuvre is The Principles of Marxist Philosophy of Science. An Attempt at a Systematic Reconstruction (in Polish, 1974). The author reveals that scientific theories are a sequence of idealizational models. This claim is true both for advanced and for less advanced natural and social sciences. The Idealizational Theory of Science enables the reconstruction of the structure of various scientific theories and of various relations between them (the problem of correspondence and reduction between theories), and it also supplies the conceptual tools for investigating and discovering new aspects of science. An important feature of the Idealizational Theory of Science is that it is itself an idealizational theory. The textbook study of this conception can be found in An Introduction to the Idealizational Theory of Science (in Polish, 1977). In English, ITS was first presented in a book form in The Structure of Idealization: Towards a Systematic Interpretation of the Marxian Idea of Science (1980), published by the Synthese Library. The development and application of the main ideas of ITS were presented in the article entitled “The Idealizational Approach to Science. A New Survey” published in the book The Richness of Idealization (Rodopi 2000), by Izabella and Leszek Nowak. This book is the most extensive presentation of the Idealizational Theory of Science.

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2. Social Philosophy 2.1. An Adaptational Interpretation of Historical Materialism Analyses of the statements formulated in the social sciences reveal that, apart from their idealizational character, they have another important property, namely some of them refer to specific forms of social regularities. This is the case with, for example, statements about the determination of consciousness by social being, how the superstructure is determined by the base, and how productive relations are determined by productive forces. The structure of these statements is reconstructed in the article “The Theory of Socio-Economic Formation as an Adaptational Theory” (in Polish, 1973; in English, 1975), which shows that these statements describe the relationships between social categories in an adaptational manner rather than a causal one. Focusing his attention on the specific relations described in these statements led Professor Nowak to make a far-reaching revision of the theory of the structure of social formation. On this conception, there is an adaptational not a causal relationship between the social structures in question, which means that the relation is not understood as that of “causal production” but that of “survival” and dissemination. These statements are known as “adaptational statements.” They indicate that it is productive forces that determine which productive relations dominate (i.e. survive and become most disseminated) in a given social formation; they also show how the social-political superstructure is determined by the economic base; and how social being determines which ideas are disseminated in such a way that that they dominate the social consciousness. In the course of the next few years, from 1974-79, when the adaptational approach to social regularities was systematically studied, Leszek Nowak carried out critical research into the foundations of Marxian and Marxist historical materialism. The result of this work was a generalized historical materialism. The conception led to a series of publications that drew less and less inspiration from Marx’s original ideas and were increasingly focused on the systematic construction of

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the idealizational-adaptational social theory. This became in fact Nowak’s, not Marx’s, theory.

2.2. Non-Marxian Historical Materialism: The Theory of Socialism as a Supra-Class System of TripleMaster rule; the Non-Christian Model of Human; the Idealizational Theory of Power. In the second half of the seventies, Leszek Nowak demonstrated how limited was the scope of application of Marxian historical materialism. First, he showed that Marxian historical materialism, in its original form, is only suitable for describing and explaining processes occurring in class societies, and that these societies are only found in one epoch of social development, in the so-called “economic epoch” (“Epochs and Formations: An Attempt at a non-Marxian Generalization of Historical Materialism,” 1979). Second, he demonstrated that economic factors are not the only material factors. These criticisms gave birth to the notion of the “material momentum,” according to which a social theory is a theory of material factors and not just economic factors (“The Notion of Material Momentum,” 1980). At the same time, Leszek Nowak put the ability of historical materialism to the test, by seeing if it could explain the social phenomena occurring in the societies of the so-called “real socialism.” In September 1979, Leszek Nowak published a samizdat typescript entitled: The Foundations of a Theory of Historical Process (in Polish). In the same year, the text was smuggled to Paris and submitted to Kultura, which was not, however, interested in publishing it. The typescript contained the framework for a non-Marxian conception of historical materialism and, based on this, a theory of real-socialist society. An abridged version of this work, entitled Freedom and Power, appeared shortly before the proclamation of the martial law in Poland (in Polish, 1981). Leszek Nowak’s theory was published in its complete, unabridged form in 1991, in the threevolume work Foundations of the Theory of Socialism (in Polish). Among other things, the theory consists of four more specific theories and conceptions. (1) The conception of a supra-class society. It

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is argued that there are three basic spheres of social activity: economic, political and spiritual. Each of these spheres generates its own division of the society into two basic social classes, respectively: owners and direct producers, rulers and citizens, and priests and those who are indoctrinated by priests. Class societies are those in which the ruling classes are separated, whereas supra-class societies are those in which at least two of the ruling classes merge. On this view, totalitarianism can be classified as a double class system of ruler-owners, fascism as a double class system of ruler-priests, and socialism as a tripartite class system of owner-ruler-priests, or, in other words, triple-masters. According to Leszek Nowak, real socialism is the most oppressive social system, since power is concentrated in the hands of triplemasters. (2) The thesis about the dominance of the supra-class social systems throughout history as well as the thesis about the uniqueness of the single-class, the (Western) European, line of development (in Polish: vol. I. Property and Power. On the Necessity of Socialism, 1991; in English: Property and Power: Towards a non-Marxian Historical Materialism, 1983). (3) The thesis about the necessity of socialism in Russia (in Polish: vol. II. The Road to Socialism. On the Necessity of Socialism in Russia, 1991; in English: Power and Civil Society: Toward a Dynamic Theory of Real Socialism, 1991). (4) The non-Christian model of human. According to Leszek Nowak, the principle to respond to kindness with kindness and to hostility with hostility, has limited scope for application. In fact, we also react with hostility to kindness in cases of “satanization,” and with kindness to hostility in cases of “enslavement,” when we come to love our oppressors more and more (in Polish: vol. III. The Dynamics of Power. On the Structure and Necessity of Socialism’s Demise, 1991; in English: Power and Civil Society, 1991). (5) The Idealizational Theory of Power (in Polish vol. III; in English: Power and Civil Society, 1991).

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3. Metaphysics Leszek Nowak’s views on metaphysics underwent a clear evolution. At first they constituted a supplement to his idealizational conception of science. From the second half of the 1980s, metaphysics became an area of his fundamental concern. The crowning work in this area is the multiple volume work Being and Thought. To date two volumes have been published: Volume I : N o t h i n g n e s s a n d E x i s t e n c e (in Polish, 1998), in which the conception of the negativist unitarian metaphysics was formulated; and Volume II: Eternity and Change (in Polish, 2004), in which he continues his critique of metaphysical stereotypes and adds consecutive models to his conception, proposing an original view of change, time and eternity. He has recently finished working on Volume III, which will appear later this year (2007).

3.1. Metaphysical Essentialism and the Conception of Categorical Dialectics While working on the idealizational conception of science, Leszek Nowak came to the conclusion that his conception is not based on the metaphysical assumptions shared by the majority of twentieth century conceptions of science. What he proposed was based on the metaphysical essentialism already present in the philosophy of Karl Marx. In contrast to phenomenalism, Leszek Nowak assumed that reality is differentiated in terms of significance (essentiality). Scientific laws do not describe what is directly observed, but this is not so much because they contain theoretical terms that refer to postulated, non-empirical objects, but rather because they are descriptions of what Nowak calls regularities, i.e. the pure dependences of the investigated factor on only the most essential (significant) factors. Leszek Nowak also proposed an original interpretation of the dialectics. This was presented in the book Foundations of Marxian Dialectics. Toward a Categorial Interpretation (in Polish, 1977). It was a systematic construction of the philosophical system which could be built on the basis of Marx and Engels’ statements concerning dialectics. The “categorial dialectics” was formulated as the ontological and

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epistemological basis for the method of idealization and as a conception revealing the “homomorphism” between the systemichistorical structure of reality (the objective categories) and the systemic-historical structure of thought (the mental categories) .

3.2. Negativist Unitarian Metaphysics The Unitarian Metaphysics presented in the book Being and Thought (1998; 2004) is a new and uncommon philosophical conception, which is continually being perfected. Unitarian Metaphysics is an attempt to unify two philosophical traditions which appear to be irreconcilable at first glance: the Hegelian tradition, in which courage, depth and passion for creating a system lead to results which force one to revise the commonsense view of the world; and the Frege-Wittgensteinian tradition, in which the only permissible questions are those to which a clear answer can be given. Leszek Nowak builds his metaphysical project on the thesis about the negativity of existence, thus rejecting the dogma of standard metaphysics, i.e. the positivity of existence. On the one hand, his metaphysical conception is a critique of the philosophical idea of reality as a totality of objects that possess properties, with each property taking only a positive value. On the other hand, it is a consistent project, according to which reality is viewed as a complex system of metaphysical structures (worlds), whose basic components are not objects but attributes (properties), which can take on positive or negative values. A central place in so conceived Unitarian Metaphysics is occupied by the thesis on the negativity of existence: the view that to exist is to have a certain lack. Leszek Nowak claims that only those beings exist that possess negative properties. Unitarian Metaphysics proposes a language for the description of being (the totality of all possible situations: positive, negative and neutral), which is composed of the so-called worldly sphere (comprised by worlds subject to logic) as well as the so-called enigmatic sphere (the “enigma of being” includes contradictory situations that do not belong to any of the worlds), which cannot be described in a standard language of logic, but which is sensed and partly revealed in the works of art, in religion

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and in myths. One can explicate various metaphysical structures in these terms. In the first volume of Being and Thought, Leszek Nowak offers a systematic reconstruction of them in three models. The first model describes the basic structures of being, the second model offers a reconstruction of what exists and the third model – a negativist conception of the causal relationship.

Political Activist & Commentator The theoretical work on non-Marxian historical materialism was increasingly accompanied by a committed involvement in the process, which led to the formation of the Solidarity movement. Leszek Nowak participated in the first Solidarity convention, was an expert and consultant for Solidarity for the Wielkopolska region, he gave speeches in factories and at the meetings of self-government organizations. He was not, however, an uncritical observer of the subsequent transformation, which took place in Poland after 1989, as he made clear, and continues to make clear, in numerous articles and columns. He always took, and continues to take, the position of rational criticism, never yielding to fleeting political tendencies or allowing himself to be bound by the current fashion of political correctness. As an advisor and commentator, he gave intellectual support to the independent social movement of Solidarity when its organizational structure was being formed, and in the 1980s when Solidarity activists were being persecuted. At this time he published, among other things, “The Myth of Credibility,” “Anti-Rakowski” and “On Christ, the Church and Revolution.” The evolution of Solidarity led him to draw the conclusion that the movement had given birth to a political elite, whose main aim had become the seizure of power. A critical analysis of these processes found expression in his later commentaries. Articles revealing the petrified structure of the new leadership and its symbiotic links with the Catholic Church are published in journals hosting independent thinkers such as Bez Dogmatu, DziĞ and Res humana. It is our firm conviction that Leszek Nowak’s place in Polish philosophy in the second half of the twentieth century is defined by the

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following qualities: a bold search for new and original ideas, laborious work to organize them in a system and a readiness to risk the secure position of a scholar by defending them against the oppressive political and intellectual rulers. For us, his pupils and friends, Leszek’s accomplishments act on us like a guilty conscience. His persistent and indomitable output enables us to see that which is normally obscured by the hustle and bustle of everyday professional life: courage in attacking fundamental problems, originality in attempting to solve them, and finally the responsibility required in the service of philosophy. These are the principles which he obeys, unfailingly, without surrendering to intellectual fashion, changing political circumstances, or to the pressures and afflictions of everyday life, which have been particularly overwhelming and acute for him in recent years. Translated by Stephen Dersley

Andrzej Klawiter Uniwersytet im. A. Mickiewicza Department of Logic and Cognitive Science ul. Szamarzewskiego 89a 60-568 PoznaĔ Poland e-mail: [email protected]

Krzysztof àastowski Uniwersytet im. A. Mickiewicza Department of Philosophy ul. Szamarzewskiego 89c 60-568 PoznaĔ Poland e-mail: [email protected]

LIST OF BOOKS BY LESZEK NOWAK

1. Próba metodologicznej charakterystyki prawoznawstwa [An Attempt at a Methodological Characterization of Jurisprudence]. PoznaĔ: Wydawnictwo UAM, 1968. Pp. 205. 2. (with J. Kmita) Studia nad teoretycznymi podstawami humanistyki [A Study on the Theoretical Foundations of the Humanities]. PoznaĔ: Wydawnictwo UAM, 1968. Pp. 327. 3. U podstaw Marksowskiej metodologii nauki [Foundations of the Marxian Methodology of Science]. Warszawa: PWN, 1971. Pp. 252. 4. Model ekonomiczny. Studium z metodologii ekonomii politycznej [Economic Models. A Study in the Methodology of Political Economics]. Warszawa: PWE, 1972. Pp. 243. 5. Anatomia krytyki marksizmu [An Anatomy of the Critique of Marxism]. Warszawa: KsiąĪka i Wiedza, 1973. Pp. 117. 6. Interpretacja prawnicza. Studium z metodologii prawoznawstwa [Juridical Interpretation. A Study in the Methodology of Jurisprudence]. Warszawa: PWN, 1973. Pp. 219. 7. U podstaw aksjologii marksistowskiej [The Foundations of Marxian Axiology]. Warszawa: PWN, 1974. Pp. 159. 8. Zasady marksistowskiej filozofii nauki. Próba systematycznej rekonstrukcji [The Principles of Marxist Philosophy of Science. An Attempt at a Systematic Reconstruction]. Warszawa: PWN, 1974. Pp. 294. 9. Wykáady z filozofii marksistowskiej, tom I: Dialektyka [Lectures in Marxist Philosophy, vol. I: Dialectics]. PoznaĔ: Wyd. UAM, 1976. Pp. 158.

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10. Scienza come idealizzazione: i fondamenti della metodologia Marxiana. Bologna: Il Mulino, 1977. Pp. 369. 11. U podstaw dialektyki Marksowskiej. Próba interpretacji kategorialnej [Foundations of Marxian Dialectics. Towards a Categorial Interpretation]. Warszawa: PWN, 1977. Pp. 299. 12. WstĊp do idealizacyjnej teorii nauki [An Introduction to the Idealizational Theory of Science]. Warszawa: PWN, 1977. Pp. 243. 13. Wykáady z filozofii marksistowskiej; vol. II: Ontologia i epistemologia [Lectures in Marxist Philosophy, vol. II: Ontology and Epistemology]. PoznaĔ: Wyd. UAM, 1978. Pp. 166. 14. Osnovi na marksistkata aksjologia [Foundations of Marian Axiology (in Bulgarian)]. Sofia: Nauka i mysl, 1979. Pp. 147. 15. The Structure of Idealization: Towards a Systematic Interpretation of the Marxian Idea of Science. Synthese Library, vol. 139. Dordrecht: Reidel, 1980. Pp. 277. 16. WolnoĞü i wáadza. Przyczynek do nie-Marksowskiego materializmu historycznego [Freedom and Power. Contribution to a nonMarxian Historical Materialism]. PoznaĔ: Wydawnictwo NZS AR, 1981. Pp. 263. 17. Trzy wykáady z nie-Marksowskiego materializmu historycznego [Three Lectures from non-Marxian Historical Materialism]. Kraków: Wyd. NZS UJ, 1981. Pp. 52. 18. O koniecznoĞci socjalizmu i koniecznoĞci jego zaniku [On the Necessity of Socialism and Necessity of Its Disappearance]. Kwidzyn: Samodzielna Oficyna Wydawnicza Zakáadu Karnego, 1982. Pp. 46. 19. Property and Power: Towards a non-Marxian Historical Materialism. Theory and Decision Library, vol. 27. Dordrecht: Reidel, 1983. Pp. 384. 20. Oltre Marx: Per un materialismo storico non-marxiano. Roma: Armando, 1987. Pp. 317. 21. Wáadza: Próba teorii idealizacyjnej [Power: Towards Idealizational Theory]. Warszawa: In Plus, 1988. Pp. 192.

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22. Power and Civil Society: Towards a Dynamic Theory of Real Socialism. New York/London: Greenwood Press, 1991. Pp. 233. 23. U podstaw teorii socjalizmu [Foundations of the Theory of Socialism]. Vol. 1: WáasnoĞü i wáadza. O koniecznoĞci socjalizmu [Property and Power. On the Necessity of Socialism]. Vol. 2: Droga do socjalizmu. O koniecznoĞci socjalizmu w Rosji [The Road to Socialism. On the Necessity of Socialism in Russia]. Vol. 3: Dynamika wáadzy. O strukturze i koniecznoĞci zaniku socjalizmu [Dynamics of Power. On the Structure and Necessity of Disappearance of Socialism]. PoznaĔ: Nakom, 1991. Pp. 995 (359+311+325). 24. Byt i myĞl. U podstaw negatywistycznej metafizyki unitarnej [Being and Thought. Foundations of Negativistic Unitarian Metaphysics]. Vol. I: NicoĞü i istnienie [Nothingness and Existence]. PoznaĔ: Zysk i s-ka, 1998. Pp. 494. 25. Gombrowicz: Czáowiek wobec ludzi [A Person vis-à-vis Others]. Filozofia polska XX w. Warszawa: PrószyĔski i S-ka, 2000. Pp. 239. 26. (with I. Nowakowa) Idealization X: The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam/Atlanta: Rodopi, 2000. Pp. 519. 27. Byt i myĞl: U podstaw negatywistycznej metafizyki unitarnej [Being and Thought: Foundations of Negativistic Unitarian Metaphysics], vol. II: WiecznoĞü i zmiana [Eternity and Change]. PoznaĔ: Zysk i S-ka, 2004. Pp. 528. 28. Byt i myĞl: U podstaw negatywistycznej metafizyki unitarnej [Being and Thought: Foundations of Negativistic Unitarian Metaphysics], vol. III: Enigma i rzeczywistoĞci [Enigma and Realities]. PoznaĔ: Zysk i S-ka, 2007. Pp. 491.

SELECTED BIBLIOGRAPHY OF LESZEK NOWAK’S WRITINGS

The following principles were accepted in preparing this bibliography: 1 bibliographical positions were ordered according to three criteria: the primary criterion was the date of publication, the secondary one — the type of publication (authorship of a book, editorship of a collection, authorship of an academic paper published in a journal or a collection), and the tertiary one — alphabetical order; 2 in years 1980-81, some papers of professor Leszek Nowak were published in the form of separate brochures — in this bibliography they were classified as “papers”; 3 modified or expanded versions of particular articles and books are treated as separate bibliographical positions; 4 if a paper originally published in Polish appeared later in English, it is first listed under the year of its publication in English and the reference to the original date of publication is made underneath (following the words ‘Reprinted from’). The full bibliography of Leszek Nowak writing’s including essays (as well as their collections), encyclopedia entries, reviews, etc., are presented in: “Bibliografia prac profesora Leszka Nowaka za lata 19632003,” published in: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), Odwaga filozofowania. Leszkowi Nowakowi w darze. PoznaĔ: Wydawnictwo Humaniora, 2002, pp. 23-63. Krzysztof Brzechczyn

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Selected Bibliography of L. Nowak’s Writings

1963 Papers 1. Wybrane pojĊcia semiotyczne w koncepcji Kazimierza Ajdukiewicza [Selected Semiotic Notions in Kazimierz Ajdukiewicz’s Conception]. In: Materiaáy na Studencką SesjĊ Naukową poĞwiĊconą pamiĊci profesora Kazimierza Ajdukiewicza, pp. 67-93. PoznaĔ.

1964 Papers 2. Postulat jasnoĞci i pojĊcie analizy jĊzykowej w polskiej literaturze logicznej [The Postulate of Clarity and Concept of Linguistic Analysis in Polish Logical Literature]. In: Logika w Polsce Ludowej. Materiaáy na studencką sesjĊ naukową z okazji XX-lecia PRL, pp. 51-79. PoznaĔ.

1966 Papers 3. Cztery koncepcje obowiązywania prawa [Four Concepts of the Validity of Law]. Ruch Prawniczy, Ekonomiczny i Socjologiczny 2: 95-104. 4. Koncepcja racjonalnego stanowienia norm [The Concept of Rational Proclaiming of Norms]. Studia Metodologiczne 2: 19-33. 5. O znaczeniu wypowiedzi normatywnych. Problem rozstrzygalnoĞci empirycznej twierdzeĔ opartych na rozumieniu tekstów normatywnych [On the Meaning of Normative Statements. The Problem of Empirical Verification of Statements based on the Understanding of Normative Texts]. In: Naturalistyczne i antynaturalistyczne interpretacje humanistyki. Materiaáy na studenckie seminarium naukowe, pp. 27-52. PoznaĔ.

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6. Problem wartoĞci logicznej wypowiedzi oceniających [The Problem of the Logical Value of Value Statements]. Studenckie Prace Prawnicze, no. 2, pp. 19-37. Wrocáaw.

1967 Papers 7. PojĊcie obowiązywania prawa jako teoretyczne pojĊcie prawoznawstwa [The Concept of the Validity of Law as a Theoretical Concept of Jurisprudence]. Studia Metodologiczne 3: 45-65.

1968 Books 8. Próba metodologicznej charakterystyki prawoznawstwa [An Attempt at a Methodological Characterization of Jurisprudence]. PoznaĔ: Wydawnictwo UAM. Pp. 205. 9. (with J. Kmita) Studia nad teoretycznymi podstawami humanistyki [A Study on the Theoretical Foundations of the Humanities]. PoznaĔ: Wydawnictwo UAM. Pp. 327. Papers 10. Performatywy a jĊzyk prawny i etyczny [Performatives in Legal and Ethical Language]. Etyka 3: 148-158. 11. (with S. Wronkowska), Zagadnienie integracji nauk prawnych w polskiej literaturze teoretyczno-prawnej [The Issue of Integration of Jurisprudence in Polish Theoretical and Legal Literature]. Studia Metodologiczne 5: 107-112.

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Selected Bibliography of L. Nowak’s Writings

1969 Papers 12. Analiza pojĊcia prawdy wzglĊdnej i pojĊcia prawdy absolutnej [An Analysis of the Concepts of Relative and Absolute Truth]. Ruch Filozoficzny 26: 343-348. 13. Historical Generalizations and the Problems of Idiographism and Historicism. The Polish Sociological Bulletin 2: 48-55. Reprinted from: Studia Socjologiczne 3: 215-225 (in Polish). 14. Metodologiczna analiza pojĊcia ustawodawcy [Methodological Analysis of the Notion of Legislator]. Ruch Filozoficzny 26: 341-343. 15. De la rationalité du législateur comme élément d’interprétation juridique. Logique et Analyse 45: 65-86. Reprinted in: Studia Metodologiczne 6: 157-180 (in Polish); and in: Ch. Perelman (ed.), Contributions polonaise à la théorie du droit et de la interprétation juridique, pp. 75–86. Bruxelles: Bruylant (in French). 16. Spór o definicje legalne a sposób pojmowania “prawodawcy” [Controversy Over the Legal Definitions and the Way of Understanding of “Legislator”]. PaĔstwo i Prawo 3: 510-515. 17. Uwagi o sensownoĞci sporów Ğwiatopoglądowych [Remarks on the Sense of Worldview Controversies]. Studia Filozoficzne (suppl. vol.): 435-445. 18. (with J. Kmita), O racjonalizującym charakterze badaĔ humanistycznych [On Rationalist Character of Research in the Humanities]. Studia Filozoficzne 5: 49-77.

1970 Papers 19. Analiza logicznej struktury modelu ekonomicznego [An Analysis of the Logical Structure of Economic Models]. Ekonomista 6: 1231-1251.

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20. Kilka uwag o postulacie jasnoĞci i pojĊciu analizy jĊzykowej [Some Remarks on the Postulate of Clarity and the Concept of Linguistic Analysis]. Studia Semiotyczne 3: 109-122. 21. O prawomocnoĞci prawniczych rozumowaĔ subsumpcyjnych [On the Status of Juridical Subsumptive Arguments]. Ruch Prawniczy, Ekonomiczny i Socjologiczny 2: 163-173. 22. O zasadzie abstrakcji i stopniowej konkretyzacji [On the Principle of Abstraction and Gradual Concretization]. In: ZaáoĪenia metodologiczne “Kapitaáu” Marksa, pp. 123-218. Warszawa: KiW. 23. Przyczynek do kwestii statusu ocen w jĊzyku nauki [A Contribution towards Issue of the Status of Values in the Language of Science]. Etyka 7: 145-158. 24. Teorie racjonalnego zachowania jako teorie modelowe [Theories of Rational Behavior as Modeling Theories]. Studia Metodologiczne 7: 59-89. 25. (with J. Kmita), The Rationality Assumption in Human Sciences. The Polish Sociological Bulletin 1: 43-68. 26. (with S. Wronkowska, M. ZieliĔski and Z. ZiembiĔski) O “Zagadnieniach teorii prawa” [On the “Issues of Theory of Law”]. Ruch Prawniczy, Ekonomiczny i Socjologiczny 4: 49-63.

1971 Books 27. U podstaw Marksowskiej metodologii nauki [Foundations of the Marxian Methodology of Science]. Warszawa: PWN. Pp. 252. Papers 28. Oceny w naukach spoáecznych w koncepcji twórców marksizmu [Value-judgments in the Social Sciences in light of the Conceptions by the Creators of Marxism]. Studia Socjologiczne 3: 5-18. 29. O pojĊciu wyraĪania [On the Concept of Expressing]. Studia Semiotyczne 2: 89-98.

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30. O wáaĞciwe rozumienie metodologicznych badaĔ nad Marksem [On the Proper Understanding of the Methodological Research on Marx]. Czáowiek i ĝwiatopogląd 12: 113-115. 31. The Problem of Explanation in Carl Marx’s Capital. Quality & Quantity: European Journal of Methodology 5(2): 311-330. Reprinted in: The Polish Sociological Bulletin 2 (1971): 47-64; Revolutionary World: An International Journal of Social Philosophy 8 (1974): 13-35; Filosofskije Nauki 4 (1974): 108-121 (in Russian); J. Ritsert (ed.), Zur Wissenschaftslogik einer kritischen Soziologie (Frankfurt/Main: Suhrkam, 1976), pp. 13-45 (in German); J.J. Wiatr (ed.), Polish Essays in the Methodology of the Social Sciences (Boston Studies in the Philosophy of Science, vol. 29) (Dordrecht: Reidel, 1979), pp. 49-73.

32. W sprawie empirycznego charakteru ekonomii politycznej [On the Empirical Character of Political Economy]. Ekonomista 5: 813-818. 33. W sprawie empirycznego charakteru prawoznawstwa [On the Empirical Character of Juriprudence]. Studia Metodologiczne 8: 117-129. 34. Zasada konstrukcji praw naukowych w Kapitale Karola Marksa [The Principle of Constructing Scientific Laws in Carl Marx’ Capital]. In: S. Nowak (ed.), Metodologiczne problemy teorii socjologicznych (Warszawa: PWN), pp. 15-65.

1972 Books 35. Model ekonomiczny. Studium z metodologii ekonomii politycznej [Economic Models. A Study in the Methodology of Political Economics]. Warszawa: PWE. Pp. 243. Papers 36. Abstraction, Idealization, Model. Zagadnienia Naukoznawstwa 4: 467-480. Reprinted in: Teoria a Metoda 7(4): 26-39 (in English).

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37. Marksowska zasada wprowadzania pojĊü teoretycznych [Marxian Principle of Introducing Theoretical Concepts]. Czáowiek i ĝwiatopogląd 6: 22-44. 38. Marksowski model struktury klasowej spoáeczeĔstwa kapitalistycznego [The Marxian Model of Class Structure of the Capitalist Society], Studia Socjologiczne 2: 5-47. 39. Theories, Idealization, Measurement. Philosophy of Science 39(4): 533-547. Reprinted in: Czáowiek i ĝwiatopogląd 2 (1972): 158-185 (in Polish); T.A.F. Kuipers (ed.), Idealization and Concretization (Groningen: University Press, 1980), pp. 15-23. 40. Social Action versus Individual Action. The Polish Sociological Bulletin 2: 84-93. Reprinted from: Studia Filozoficzne 3 (1970): 126135 (in Polish). Reprinted in: T.A.F. Kuipers (ed.), Idealization and Concretization (Groningen: University Press, 1980), pp. 148-153. 41. ZaáoĪenia o racjonalnoĞci w ekonomii marksistowskiej i Marksowskiej [The Assumption of Rationality in Marxist and Marxian Economics]. Ruch Prawniczy, Ekonomiczny i Socjologiczny 4: 163-173. 42. (with M. Chmara) Zasada historyzmu w teorii marksistowskiej i Marksowskiej [The Principle of Historicism in the Marxist and Marxian Theory]. Studia Socjologiczne 3: 4-43. 43. (with A. Malinowski) Problemy modelowania w teorii prawa [Problems of Modeling in the Theory of Law]. PaĔstwo i Prawo 2: 86-95.

1973 Books 44. Anatomia krytyki marksizmu [An Anatomy of the Critique of Marxism]. Warszawa: KsiąĪka i Wiedza. Pp. 117. 45. Interpretacja prawnicza. Studium z metodologii prawoznawstwa [Juridical Interpretation. A Study in the Methodology of Jurisprudence]. Warszawa: PWN. Pp. 219.

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Selected Bibliography of L. Nowak’s Writings

Papers 46. Budowa prawa idealizacyjnego [The Construction of an Idealizational Law]. In: J. Kmita (ed.), Elementy marksistowskiej metodologii humanistyki, pp. 42-62. PoznaĔ: Wydawnictwo PoznaĔskie. 47. Cztery pytania z materializmu historycznego [Four Questions from Historical Materialism]. Czáowiek i ĝwiatopogląd 4: 112-118. 48. Filozoficzne podstawy teorii naukowej [Philosophical Foundations of a Scientific Theory]. Studia Filozoficzne 3: 159-168. 49. Idealizational Laws and Explanation. Logique et Analyse 60: 527545. 50. Konkretyzacja prawa idealizacyjnego (rozwijanie abstrakcji) w koncepcji Karola Marksa [Concretization of an Idealizational Law (the Development of Abstraction) in Karl Marx’s Conception]. In: J. Kmita (ed.), Elementy marksistowskiej metodologii humanistyki, pp. 63-97. PoznaĔ: Wydawnictwo PoznaĔskie. 51. Marksowska dyrektywa konstrukcji teorii [The Marxian Directive of Theory Construction]. In: J. Kmita (ed.), Elementy marksistowskiej metodologii humanistyki, pp. 98-110. PoznaĔ: Wydawnictwo PoznaĔskie. 52. Marksowski model wyjaĞniania [A Marxian Model of Explanation]. In: J. Kmita (ed.), Elementy marksistowskiej metodologii humanistyki, pp. 111-137. PoznaĔ: Wydawnictwo PoznaĔskie. 53. Popperowska koncepcja praw i sprawdzania [Popper’s Conception of Laws and Testing]. In: J. Kmita (ed.), Elementy marksistowskiej metodologii humanistyki, pp. 302-324. PoznaĔ: Wydawnictwo PoznaĔskie. 54. Pozorne i rzeczywiste trudnoĞci zasady falsyfikacji [Apparent and Real Difficulties of Principle of Falsification]. Studia Metodologiczne 10: 47-57. 55. Problemy metody idealizacji [Problems of the Metod of Idealization]. Studia Filozoficzne 4: 153-169. 56. Pozytywistyczna koncepcja praw i wyjaĞniania [The Positivist Conception of Laws and Explanation]. In: J. Kmita (ed.), Elementy

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marksistowskiej metodologii humanistyki, pp. 277-302. PoznaĔ: Wydawnictwo PoznaĔskie. 57. Uwagi o stosunku logiki do jĊzykoznawstwa [Remarks on the Relationship of Logic to Linguistics]. Studia Semiotyczne 3: 75-84. 58. (with I. Nowakowa) Dyrektywa dialektycznej korespondencji praw idealizacyjnych [The Directive of Dialectical Correspondence of Idealizational Laws]. In: J. Kmita (ed.), Elementy marksistowskiej metodologii humanistyki, pp. 168-180. PoznaĔ: Wydawnictwo PoznaĔskie. 59. (with I. Nowakowa) W sprawie zasady korespondencji w fizyce [On the Principle of Correspondence in Physics]. Kwartalnik Historii Nauki i Techniki 2: 33-43.

1974 Books 60. U podstaw aksjologii marksistowskiej [The Foundations of Marxian Axiology]. Warszawa: PWN. Pp. 159. 61. Zasady marksistowskiej filozofii nauki. Próba systematycznej rekonstrukcji [The Principles of Marxist Philosophy of Science. An Attempt at a Systematic Reconstruction]. Warszawa: PWN. Pp. 294. Papers 62. Aproksymacja i idealizacja [Approximation and Idealization]. In: J. Kmita (ed.), Metodologiczne implikacje epistemologii marksistowskiej, pp. 84-87. Warszawa. 63. Eclecticism and Tolerance. Revolutionary World: An International Journal of Social Philosophy 8: 91-99. 64. Essence-Idealization-Praxis. An Attempt at a Certain Interpretation of the Marxist Concept of Science. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2(3): 1-28. Reprinted in Studia Filozoficzne 7 (1974): 57-81 (in Polish); Dijalektika 2-3 (1978): 39-69 (in Serbian).

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Selected Bibliography of L. Nowak’s Writings

65. Fenomenalizm a esencjalizm [Phenomenalism and Essentialism]. In: J. Kmita (ed.), Metodologiczne implikacje epistemologii marksistowskiej, pp. 68-77. Warszawa. 66. Galileo of the Social Sciences. Revolutionary World: An International Journal of Social Philosophy 8: 5-12. 67. The Methodological Origins of Certain Ideological Criticisms of Karl Marx’s Capital. Revolutionary World: An International Journal of Social Philosophy 8: 37-51. 68. MoĪliwoĞü i typ idealny. Przyczynek do kwestii ontologicznych zaáoĪeĔ jĊzyka nauki [Possibility and Ideal Type. Contributions toward Ontological Assumptions of Language of Science]. Studia Metodologiczne 12: 49-59. 69. The Nature of Marxist Dialectics. Dialectics and Humanism 1: 129-145. Reprinted in: Studia Filozoficzne 3 (1974): 3-20 (in Polish). 70. O dalszych problemach metody idealizacji [On Further Problems of the Method of Idealization]. Studia Filozoficzne 9: 83-101. 71. O jednorodnoĞci pojĊcia modelu [On Homogeneity of the Notion of Model]. Neodidagmata 6: 61-69. 72. On Some Modifications of the Concept of Dialectical Correspondence. Dialectics and Humanism 1(3): 73-78. Reprinted in: J. Kmita (ed.), Metodologiczne implikacje epistemologii marksistowskiej (Warszawa, 1974), pp. 274-279 (in Polish). 73. An Outline of the Idealizational Concept of Science. Teoria a Metoda 6: 5-26. Reprinted in: Revolutionary World: An International Journal of Social Philosophy 8 (1974), pp. 53-70. 74. Philosophy of Dialectic Negation. Revolutionary World. An International Journal of Social Philosophy 8: 1-4. 75. Podmiot wiedzy w epistemologii marksistowskiej [Subject of Knowledge in Marxist Epistemology]. Czáowiek i ĝwiatopogląd 5: 116125. 76. Praktyka i prawda [Praxis and Truth]. In: J. Kmita (ed.), Metodologiczne implikacje epistemologii marksistowskiej, pp. 336-340. Warszawa.

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77. Prawda wzglĊdna – prawda absolutna – praktyka [Relative Truth – Absolute Truth – Praxis]. In: W. Krajewski, W. Mejbaum, J. Such (eds.), Zasada korespondencji w fizyce a rozwój nauki, pp. 147-178. Warszawa: PWN. 78. Science, Philosophy and Classes. Revolutionary World: An International Journal of Social Philosophy 8: 85-90. 79. Value, Idealization, and Valuation. Quality & Quantity: European Journal of Methodology 7(2): 107-119. Reprinted from: Studia Filozoficzne 6 (1973): 153-163 (in Polish). Reprinted in: I. Lazari-Pawáowska (ed.), Metaetyka (Warszawa: PWN, 1978), pp. 353-365 (in Polish); T.A.F. Kuipers (ed.), Idealization and Concretization (Groningen: University Press, 1980), pp. 153-159. 80. ZaáoĪenia prawniczego pojĊcia czynu [The Presuppositions of the Juridicial Concept of Action]. Prakseologia 2: 129-146.

1975 Edition of Collective Works 81. Polish Contributions to Historical Materialism. Amsterdam: Grüner. Pp. 129. Papers 82. Abstraction, Idealization and Model. Teorie a Metoda 7(4): 23-36. 83. The Anatomy of Anti-Marxist Criticism. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 1(3): 30-74. 84. Idealization: A Reconstruction of Marx’s Ideas. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 1(1): 25-42. 85. Idealizacja i interpretacja humanistyczna [Idealization and Humanistic Interpretation]. Studia Filozoficzne 4: 153-163. 86. O interpretacji adaptacyjnej [On Adaptational Interpretation]. In: J. Kmita (ed.), WartoĞü – dzieáo – sens, pp. 211-227. Warszawa: KiW. 87. Relative Truth, the Correspondence Principle, Absolute Truth, Philosophy of Science 42(2): 187-201. Reprinted in: T.A.F. Kuipers

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(ed.), Idealization and Concretization (Groningen: University Press, 1980), pp. 182-190. 88. The Theory of Socio-Economic Formation as an Adaptational Theory. In: L. Nowak (ed.), Polish Contributions to Historical Materialism, pp. 85-102. Amsterdam: Grüner. Reprinted from: Studia Socjologiczne 4 (1973): 5-21 (in Polish). Reprinted in: T.A. F. Kuipers (ed.), Idealization and Concretization (Groningen: University Press, 1980), pp. 65-74. 89. (with A. JasiĔska) Foundations of Marx’s Theory of Class: A Reconstruction. In: P.K. Crosser, D.H. DeGrood, D. Riepe (eds.), EastWest Dialogues: Foundations and Problems of Revolutionary Praxis (Amsterdam: Grüner), pp. 141-169. Reprinted in: J. Ritsert (ed.), Zur Wissenschaftslogik einer kritischen Soziologie (Frankfurt/Main: Suhrkamp, 1976), pp. 175-213 (in Germain); J.J. Wiatr (ed.), Polish Essays in the Methodology of the Social Sciences (Boston Studies in the Philosophy of Science, vol. 29) (Dordrecht: Reidel, 1979), pp. 75-104. 90. (with J. Kmita and J. Topolski) On False Alternatives. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 1(2): 1-10. Reprinted from: Nowe Drogi 10 (1975): 102-112 (in Polish).

1976 Books 91. Wykáady z filozofii marksistowskiej, tom I: Dialektyka [Lectures in Marxist Philosophy, vol. I: Dialectics]. PoznaĔ: Wyd. UAM. Pp. 158. Edition of Collective Works 92. The Categorial Interpretation of Dialectics. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2(4). Amsterdam: Rodopi. Pp. 130. 93. The Idealizational Conception of Science. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2(3). Amsterdam: Rodopi. Pp. 126.

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94. Teoria i rzeczywistoĞü [Theory and Reality]. PoznaĔskie Studia z Filozofii Nauki 1. Warszawa/PoznaĔ: PWN. Pp. 319. Papers 95. Evaluation and Cognition. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2(1): 42-63. 96. Jeszcze o metodzie idealizacji [More on the Method of Idealization]. In: L. Nowak (ed.), Teoria i rzeczywistoĞü, pp. 273-307. Warszawa/PoznaĔ: PWN. 97. Modele pracy badawczej [Models of Research]. In: L. Leja (ed.), Rola promotora w kierowaniu kadrą naukową, pp. 33-41. PoznaĔ: Wyd. UAM. 98. A Note on Simplicity. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2: 115-119. 99. Ontologiczne zaáoĪenia teorii [Ontological Presuppositions of a Theory]. In: L. Nowak (ed.), Teoria i rzeczywistoĞü, pp. 5-11. Warszawa/PoznaĔ: PWN. 100. Das Problem der Erklärung in Karl Marx’s Kapital. In: J. Ritsert (ed.), Zur Wissenschaftslogik einer Kritischen Soziologie, pp. 13-45. Frankfurt a. Main: Suhrkamp Verlag. 101. (with J. BrzeziĔski, J. Burbelka, A. Klawiter, K. àastowski, S. Magala and W. Patryas) Prawo, teoria, sprawdzanie. Przyczynek do marksistowskiej metodologii nauki [Law, Theory, Testing. A Contribution to the Marxian Methodology of Science]. In: L. Nowak (ed.), Teoria i rzeczywistoĞü, pp. 107-133. Warszawa/PoznaĔ: PWN. 102. (with J. BrzeziĔski, J. Burbelka, A. Klawiter, K. àastowski, and S. Magala) Law and Theory. A Contribution to the Idealizational Interpretation of Marxist Methodology. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2: 61-80. Reprinted from: Studia Filozoficzne 2 (1975): 61-80 (in Polish). 103. (with P. Chwalisz, P. Kowalik, W. Patryas and M. StefaĔski) The Peculiarities of Practical Research. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2: 81-100. Reprinted in: L. Nowak

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(ed.) Teoria i rzeczywistoĞü (Warszawa/PoznaĔ: PWN), pp. 189-213 (in Polish).

1977 Books 104. Scienza come idealizzazione: i fondamenti della metodologia Marxiana. Bologna: Il Mulino. Pp. 369. 105. U podstaw dialektyki Marksowskiej. Próba interpretacji kategorialnej [Foundations of Marxian Dialectics. Towards a Categorial Interpretation]. Warszawa: PWN. Pp. 299. 106. WstĊp do idealizacyjnej teorii nauki [An Introduction to the Idealizational Theory of Science]. Warszawa: PWN. Pp. 243. Edition of Collective Works 107. ZaáoĪenia dialektyki [Assumptions of Dialectics] (PoznaĔskie Studia z Filozofii Nauki 2). Warszawa/PoznaĔ: PWN. Pp. 262. Papers 108. The Classical and the Essentialist Concepts of Truth. In: M. de May, R. Pinxten, M. Poriau, F. Vandamme (eds.), The Cognitive Viewpoint, pp. 344-353. Ghent: University Press. Reprinted in: A. Klawiter, L. Nowak (eds.), Odkrycie, abstrakcja, prawda, empiria, historia – a idealizacja (Warszawa-PoznaĔ: PWN, 1979), pp. 115-124 (in Polish). 109. Koncepcja historii w kategorialnej interpretacji dialektyki [A Conception of History in Categorial Interpretation of Dialectics]. In: L. Nowak (ed.), ZaáoĪenia dialektyki, pp. 73-104. Warszawa/PoznaĔ: PWN. 110. Marx’s Concept of Laws of Science. In: M. PrzeáĊcki, K. Szaniawski, R. Wójcicki (eds.), Formal Methods in the Methodology of Empirical Sciences, pp. 399-416. Wrocáaw/Dordrecht: Ossolineum/Reidel. Reprinted from: Czáowiek i ĝwiatopogląd 7 (1972): 151-174 (in Polish). 111. The Model of Empirical Science in the Writings of Founders of Marxism. In: M. PrzeáĊcki, R. Wójcicki (eds.), Twenty Five Years of

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Logical Methodology in Poland, pp. 499-539. Warsaw/Dordrecht: PWN/Reidel. Reprinted from: Studia Filozoficzne 2 (1972): 35-64 (in Polish). Reprinted in: J. Kmita, (ed.), Metodologiczne implikacje epistemologii marksistowskiej (Warszawa: PWN, 1974), pp. 109-141 (in Polish); Laboratorio 10-11 (1983): 6-19 (in Italian). 112. On the Categorial Interpretation of History. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities 2-4: 1-27. Reprinted in: Communication and Cognition 12(2) (1979): 171-199. 113. On Some Interpretation of the Marxist Methodology. Zeitschrift für Allgemeine Wissenschaftstheorie 7(1): 141-183. Reprinted in: T.A.F. Kuipers (ed.), Idealization and Concretization (Groningen: University Press, 1980), pp. 75-96. 114. On the Structure of Marxist Dialectics. An Attempt at Categorial Interpretation. Erkenntnis 11(3): 341-361. Reprinted in: J. Kmita (ed.), ZaáoĪenia teoretyczne badaĔ nad rozwojem historycznym (Warszawa: PWN, 1977), pp. 61-118 (in Polish). 115. O tzw. formalnologicznej koncepcji dialektyki [On So-Called Formal Conception of Dialectics]. In: J. Kmita (ed.), ZaáoĪenia teoretyczne badaĔ nad rozwojem historycznym, pp. 407-414. Warszawa: PWN. 116. O wieloĞci materializmów historycznych [On the Plurality of Historical Materialisms]. In: J. Kmita (ed.), ZaáoĪenia teoretyczne badaĔ nad rozwojem historycznym, pp. 250-256. Warszawa: PWN. 117. Prawda jest tam, gdzie nikt jej nie oczekuje [The Truth Is Where Nobody Expects It]. Znak 11-12: 1348-1352. 118. RacjonalnoĞü i poznanie naukowe [Rationality and Scientific Knowledge]. In: J. Kmita (ed.), ZaáoĪenia teoretyczne badaĔ nad rozwojem historycznym, pp. 310-356. Warszawa: PWN. 119. Rola abstrakcji i modeli teoretycznych w procesie poznania [The Role of Abstraction and Theoretical Models in the Process of Cognition]. OĞwiata i Wychowanie 12: 209-216.

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1978 Books 120. Wykáady z filozofii marksistowskiej; vol. II: Ontologia i epistemologia [Lectures in Marxist Philosophy, vol. II: Ontology and Epistemology]. PoznaĔ: Wyd. UAM. Pp. 166. Edition of Collective Works 121. ZaáoĪenia materializmu historycznego [Assumptions of Historical Materialism]. PoznaĔskie Studia z Filozofii Nauki, vol. 3. Warszawa/PoznaĔ: PWN. Pp. 280. 122. (with P. Buczkowski) Teoria ekonomiczna: Metodologia i rekonstrukcje. [Economic Theory: Its Methodology and Reconstructions]. PoznaĔ: Wyd. Akademii Ekonomicznej. Pp. 147. Papers 123. Dialectics as the Basis of Scientific Rationality. In: 16 Weltkongress für Philosophie 1978, pp. 467-470. Düsseldorf. 124. Humanistyka a przyrodoznawstwo. Próba analizy programu antynaturalistycznego [Humanities and Science. An Attempt of Analysis of Anti-Naturalistic Programme]. Przegląd Antropologiczny 44(1): 119125. 125. On the Structure of Marxist Dialectics: An Attempt at Categorial Interpretation. Erkenntniss 11(3): 341-363. Reprinted in: T.A.F. Kuipers (ed.), Idealization and Concretization (Groningen: University Press, 1980), pp. 191-202. 126. O strukturze modelu ekonomicznego [On the Structure of an Economic Model]. In: P. Buczkowski, L. Nowak, (eds.), Teoria ekonomiczna: metodologia i rekonstrukcje, pp. 45-58. PoznaĔ: Wyd. Akademii Ekonomicznej. 127. Teoria formacji spoáeczno-ekonomicznej jako teoria adaptacyjna [Theory of Social-Economic Formation as Adaptational Theory]. In: L.

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Nowak (ed.), ZaáoĪenia materializmu historycznego, pp. 59-75. Warszawa/PoznaĔ: PWN. 128. Weber’s Ideal Types and Marx’s Abstraction. In: R. Bubner (ed.), Marx’ Methodologie (Neue Hefte für Philosophie, vol. 13), pp. 81-91. Goettingen: Ruprecht. Reprinted from: J. Kmita (ed.), Elementy marksistowskiej metodologii humanistyki (PoznaĔ: Wydawnictwo PoznaĔskie, 1973), pp. 350-361 (in Polish). 129. (with P. Buczkowski) Nauka ekonomii i jej metodologia [Science of Economy and Its Methodology]. In: P. Buczkowski, L. Nowak (eds.), Teoria ekonomiczna: Metodologia i rekonstrukcje, pp. 5-8. PoznaĔ: Wyd. Akademii Ekonomicznej. 130. (with P. Buczkowski) O strukturze materializmu historycznego [On the Structure of Historical Materialism]. Studia Socjologiczne 2: 5-33. 131. (with P. Buczkowski) Some Remarks on Political Sciences. Polish Round Table 9: 19-32. Reprinted in: Studia Nauk Politycznych 4 (1978): 17-33 (in Polish).

1979 Books 132. Osnovi na marksistkata aksjologia [Foundations of Marian Axiology (in Bulgarian)]. Sofia: Nauka i mysl. Pp. 147. Edition of Collective Works 133. (with A. Klawiter) Odkrycie, abstrakcja, prawda, empiria, historia – a idealizacja [Discovery, Abstraction, Truth, Experience, History – and Idealization]. Warszawa/PoznaĔ: PWN. Pp. 225. 134. (with K. àastowski) Konfrontacje i parafrazy [Confrontations and Paraphases]. PoznaĔskie Studia z Filozofii Nauki, vol. 4. Warszawa/ PoznaĔ: PWN. Pp. 306.

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Papers 135. Epochs and Formations: An Attempt at a non-Marxian Generalization of Historical Materialism. In: E. Leinfellner, A. Huebner, W. Leinfellner (eds.), Wittgenstein, the Vienna Circle, and Critical Rationalism (Proceedings of the 3rd Wittgenstein Symposium: 13-18 August 1978), pp. 435-444. Vienna: Hoelder-Pichler-Tempsky. 136. Historical Momentums and Historical Epochs: An Attempt at a non-Marxian Historical Materialism. Kritik und Analyse 1: 60-76. 137. Historyzm metodologiczny w kategorialnej interpretacji dialektyki [Methodological Historicism in the Categorial Interpretation of Dialectics]. In: Z. Cackowski, J. Kmita, (eds.), Spoáeczny kontekst poznania, pp. 119-148. Wrocáaw: Ossolineum. 138. Idealization and Rationalization: An Analysis of the Anti-Naturalist Programme. Epistemologia 2: 83-105. 139. Ist der Erkenntniss-processs ein dialektischer Process? In: B. Waldenfels, J. H. Broekman, A. Pazanin (eds.), Phaenomenologie und Marxismus, z. 4, pp. 128-141. Frankfurt/Main: Suhrkamp. Reprinted from: Zagadnienia Naukoznawstwa 1: 24-33 (in Polish). 140. Kategoria przedmiotowa, struktura, postĊp: Idee strukturalistyczne w kategorialnej interpretacji dialektyki [Object Category, Structure, Progress. Structuralist Ideas in the Categorial Interpretation of Dialectics]. In: K. àastowski, L. Nowak (eds.), Konfrontacje i parafrazy, pp. 57-89. Warszawa/PoznaĔ: PWN. 141. O Leninowskiej teorii odbicia. Próba interpretacji kategorialnej [On Lenin’s Theory of Reflection. An Attempt of Categorial Interpretation]. In: K. àastowski, L. Nowak (eds.), Konfrontacje i parafrazy, pp. 73-86. Warszawa/PoznaĔ: PWN. 142. (with P. Buczkowski) Idealizacja a istotnoĞü: studium przypadku [Idealization and Essence: A Case Study]. In: A. Klawiter, L. Nowak (eds.), Odkrycie, abstrakcja, prawda, empiria, historia – a idealizacja, pp. 59-86. Warszawa/PoznaĔ: PWN. 143. (with A. Klawiter) Idealizacja a odkrycie, abstrakcja, prawda, empiria, historia [Idealization and Discovery, Abstraction, Truth, Experi-

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ence, History]. In: A. Klawiter, L. Nowak (eds), Odkrycie, abstrakcja, prawda, empiria, historia – a idealizacja, pp. 3-9. Warszawa/PoznaĔ: PWN. 144. (with A. Klawiter, K. àastowski, and W. Patryas) Adaptacja, uczenie siĊ, praktyka. Próby zastosowaĔ adaptacyjnego aparatu pojĊciowego [Adaptation, Learning and Practice. An Attempt at an Application of the Adaptational Conceptual Apparatus]. In: K. àastowski, L. Nowak (eds.), Konfrontacje i parafrazy, pp. 91-99. Warszawa/PoznaĔ: PWN. 145. (with I. Nowakowa) Marxism and Positivism: The Idea of Scientific Philosophy. In: W. Krajewski (ed.), Aspects of the Growth of Science (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 4), pp. 210-232. Amsterdam: Rodopi. 146. (with I. Nowakowa) Zasada wszechzwiązku i systemowoĞü prawdy [The Principle of Interconnectness and an Idea of Truth as a System]. In: A. Klawiter, L. Nowak (eds.), Odkrycie, abstrakcja, prawda, empiria, historia – a idealizacja, pp. 125-142. Warszawa/PoznaĔ: PWN. 147. (with Z. ZiembiĔski) Positivistic Trends versus Trends of Natural Law in Modern Comprehension of Law. In: A. àopatka (ed.), Contemporary Conceptions of Law, pp. 109-120. Warszawa. Reprinted in: Archiv für Rechts- und Sozialphilosophie 1 (1980): 559-573 (in German).

1980 Books 148. The Structure of Idealization: Towards a Systematic Interpretation of the Marxian Idea of Science. Synthese Library, vol. 139. Dordrecht: Reidel. Pp. 277. Papers 149. Gáos klasy ludowej: polska droga od socjalizmu [The Voice of the People Class: The Polish Road from Socialism onward] (PoznaĔskie

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Broszury Spoáeczne). PoznaĔ: Wielkopolska Inicjatywa Wydawnicza. Pp. 17. 150. The Methodological Status of the Rationality Assumption. In: T.A.F. Kuipers (ed.), Idealization and Concretization, pp. 139-148. Groningen: University Press. Reprinted from: Studia Metodologiczne, 11 (1974): 111-126 (in Polish). 151. The Notion of Material Momentum. Towards the Adaptational Interpretation of Historical Materialism. The Polish Sociological Bulletin 2: 17-42. 152. Prawodawca doskonaáy i optymalizacja prawa. Kilka uwag korygujących [Ideal Legislator and Optimalization of Law. Some Corrections]. Studia Metodologiczne 20: 143-153. 153. Socjalistyczny sposób panowania czáowieka nad czáowiekiem [The Socialistic Way of Domination of a Human over another Human] (PoznaĔskie Broszury Spoáeczne). PoznaĔ: Wielkopolska Inicjatywa Wydawnicza. Pp. 23. 154. (with P. Buczkowski) Values and Social Classes. The Unitarian Interpretation of the Marxist Axiology in the Light of the Adaptational Interpretation of Historical Materialism. In: A. Honneth, U. Jaeggi (eds.), Arbeit, Handlung, Normativität (Theorien des Historischen Materialismus 2) , pp. 365-401. Frankfurt/Main: Suhrkamp. Reprinted from: Etyka 17 (1979): 93-121 (in Polish).

1981 Books 155. WolnoĞü i wáadza. Przyczynek do nie-Marksowskiego materializmu historycznego [Freedom and Power. Contribution to a nonMarxian Historical Materialism]. PoznaĔ: Wydawnictwo NZS AR. Pp. 263. 156. Trzy wykáady z nie-Marksowskiego materializmu historycznego [Three Lectures from non-Marxian Historical Materialism]. Kraków: Wyd. NZS UJ. Pp. 52.

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Papers 157. BáĊdy Lenina, czyli o koniecznoĞci socjalizmu w Rosji [Errors of Lenin that is on Necessity of Socialism in Russia]. PoznaĔ: Wyd. NZS PP. Pp. 15. 158. Dwa szkice z nie-Marksowskiego materializmu historycznego [Two Papers on non-Marxian Historical Materialism] (PoznaĔskie Broszury Spoáeczne). PoznaĔ: Wielkopolska Inicjatywa Wydawnicza. Pp. 24. 159. Fundamentalny báąd Marksa czyli o koniecznoĞci socjalizmu [Fundamental Error of Marx that is on Necessity of Socialism]. PoznaĔ: Wielkopolska Inicjatywa Wydawnicza. Pp. 35. 160. Marksizm jako faászywa ĞwiadomoĞü socjalizmu [Marxism as False Consciousness of Socialism]. Wolna Polska. PoznaĔski Biuletyn Spoáeczno-Polityczny 1: 15-26. 161. Moment materialny i epoka historyczna. O pewnej moĪliwoĞci uogólnienia Marksowskiego materializmu historycznego [Material Moment and Historical Epoch. On Certain Possibility of Generalization of Marxian Historical Materialism]. Tematy: Kwartalnik myĞli alternatywnej 3: 85-119. 162. Nie wiemy z dziejów akurat tego, co jest konieczne aby zrozumieü Ğwiat w jakim Īyjemy [We Do Not Know from History Just It What Is Necessary to Understand World We Live]. Aplauz 2: 6-10. 163. Przeciw ekonomistom. Przyczynek do analizy ideologicznej roli ekonomii politycznej w spoáeczeĔstwach supraklasowych [Against Economists. A Contribution to the Analysis of Ideological Role of Political Economy in Supra-class Societies]. In: W. Balicki (ed.), Polska 81: Odnowa czy rewolucja, pp. 1-16. PoznaĔ.

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1982 Books 164. O koniecznoĞci socjalizmu i koniecznoĞci jego zaniku [On the Necessity of Socialism and Necessity of Its Disappearance]. Kwidzyn: Samodzielna Oficyna Wydawnicza Zakáadu Karnego. Pp. 46. Edition of Collective Works 165. Social Classes Action and Historical Materialism. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 6. Amsterdam: Rodopi. Pp. 439. Papers 166. Adaptation and Revolution: The Problem of Motion of the SocioEconomic Formation in the Adaptational Interpretation of Historical Materialism. In: L. Nowak (ed.), Social Classes, Action and Historical Materialism, pp. 346-381. Amsterdam: Rodopi. 167. Marxian Methodology Leads to the Generalization of Marxian Historical Materialism. In: H. R. Alker (ed.), Dialectical Logics for the Political Sciences (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 7), pp. 9-30. Amsterdam: Rodopi. 168. Problem dialektyki przyrody [The Problem of Dialectics of Nature]. In: K. àastowski, J. Strzaáko (eds.), Filozofia i biologia (PoznaĔskie Studia z Filozofii Nauki, vol. 7), pp. 167-185. Warszawa-PoznaĔ: PWN. 169. The Theory of Socio-Economic Formations as a Theory of Adaptation Processes. In: L. Nowak (ed.), Social Classes Action and Historical Materialism, pp. 110-121. Amsterdam: Rodopi. 170. (with P. Buczkowski and A. Klawiter) Historical Materialism as a Theory of Social Whole. In: L. Nowak (ed.), Social Classes Action and Historical Materialism, pp. 236-280. Amsterdam: Rodopi. 171. (with K. àastowski), Galileusz nauk biologicznych [Galileo of the Biological Sciences]. Kosmos 31: 195-210.

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1983 Books 172. Property and Power: Towards a non-Marxian Historical Materialism. Theory and Decision Library, vol. 27. Dordrecht: Reidel. Pp. 384. Papers 173. Né rivoluzione né evoluzione. Il problema della transizione in un materialismo storico non marxiano. Rinascita 23(50-51): 31-32. 174. On Marxist Social Philosophy. In: G. Floystadt (ed.), Contemporary Philosophy: A New Survey, vol. 3: The Philosophy of Action, pp. 243-275. Hague/Boston/London: Nijthoff. 175. La scienza come progressiva caricatura, Laboratorio 12: 36-49. 176. La struttura delle scienze empiriche come concepita da i fondatori del Marxismo. Laboratorio 10/11.

1984 Edition of Collective Works 177. (with J. BrzeziĔski) ĝwiadomoĞü jednostkowa i spoáeczna [Individual Consciousness and Social Consciousness]. PoznaĔskie Studia z Filozofii Nauki, vol. 8. Warszawa-PoznaĔ: PWN. Pp. 251. Papers 178. Pop-marksizm: Rozprawka o anatomii ideologii [Pop-marxism: An Essay on Anatomy of Ideology]. ObecnoĞü 6: 16-21. 179. SpoáeczeĔstwo Orwellowskie: Próba analizy przy zaáoĪeniu nieMarksowskiego materializmu historycznego [Orwellian Society: An Attempt at Analysis in the Light of non-Marxian Historical Materialism]. Veto 13.

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1985 Papers 180. Czáowiek i ludzie, czyli o tym, ile utopii spoáecznej da siĊ wyprowadziü na obecnym poziomie konkretyzacji z nie-Marksowskiego materializmu historycznego [A Persona and People, that is, How Much of Social Utopia One May Derive at the Present Level of Concretization of non-Marxian Historical Materialism]. ObecnoĞü 9: 45-54. 181. Marksizm w socjalizmie: studium ideologii dysfunkcjonalnej [Marxism In Socialism: a Study of Dysfunctional Ideology]. Przyjaciel Nauk: Studia z teorii i krytyki spoáecznej 1-2 (1984/85): 21-43. 182. Marxian Historical Materialism: The Case of Dialectical Retardation. In: B. Chavance (ed.), Marx en perspective, pp. 77-94. ParyĪ: Editions de l’Ecole des Hautes Etudes en Sciences Sociales. 183. Marxism and Positivism or Dialectics in Books and Dialectics in Action. Studies in Soviet Thought 30: 195-218. 184. On Idealization: A Reply to prof. Kirschenmann. Studies in Soviet Thought 30: 237-245. 185. O koniecznoĞci socjalizmu i koniecznoĞci jego zaniku [On Necessity of Socialism and Necessity of its Disappearance]. Przyjaciel Nauk: Studia z teorii i krytyki spoáecznej 1-2 (1984/85): 105-151. 186. (with S. Magala) The Problem of Historicity of Cognition in the Idealizational Conception of Science. In: J. BrzeziĔski (ed.), Consciousness: Methodological and Psychological Approaches (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 8), pp. 1835. Amsterdam: Rodopi. Reprinted from: A. Klawiter, L. Nowak (eds.), Odkrycie, abstrakcja, prawda, empiria, historia – a idealizacja. (Warszawa-PoznaĔ: PWN, 1979), pp. 211-225 (in Polish). 187. (with I. Nowakowa) The Position of the Theory of Mind in the Categorial Interpretation of Dialectics. In: R.M. Chisholm, J.Chr. Marek, J.T. Blackmore, A. Huebner (eds.), Philosophy of Mind: Philosophy of Psychology, pp. 264-270. Vienna: Hoelder-Pichler-Tempsky. Reprinted from: Z. Cackowski (ed.), Poznanie – umysá – kultura (Lublin: Wyd. Lubelskie, 1983), pp. 71-83 (in Polish).

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1986 Papers 188. Ideology versus Utopia: A Contributions to the Analysis of the Role of Social Consciousness in the Movement of Socio-Economic Formation. In: P. Buczkowski, A. Klawiter (eds.), The Theory of Ideology and Ideology of Theories (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 9), pp. 24-52. Amsterdam: Rodopi. Reprinted from: J. BrzeziĔski, L. Nowak (eds.), ĝwiadomoĞü jednostkowa i spoáeczna (Warszawa/PoznaĔ: PWN, 1984), pp. 37-68 (in Polish). 189. Né rivoluzione né evoluzione: Il problema della transizione al socialismo nel materialismo storico non-Marxiano. In: C. Mancina (ed.), Marx e il mondo contemporaneo, pp. 235-262. Roma: Editori Riuniti. 190. Science, that is, Domination through Truth. In: P. Buczkowski, A. Klawiter (eds.), The Theory of Ideology and Ideology of Theories (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 9), pp. 106-122. Amsterdam: Rodopi. Reprinted in: M. Blancato, G. Boscarino (ed.), Scienze, epistemologia, arte (Catania, 1986), pp. 9-28 (in Italian).

1987 Books 191. Oltre Marx: Per un materialismo storico non-marxiano. Roma: Armando. Pp. 317. Papers 192. Class and Individual in the Historical Process. Philosophy of the Social Sciences 17(3): 76-93. Reprinted from: Bez debitu 1 (1984): 51-65 (in Polish).

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193. A Concept of Rational Legislator. In: Z. ZiembiĔski (ed.), Polish Contributions to the Theory and Philosophy of Law (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 12), pp. 137146. Amsterdam: Rodopi. 194. Man and People: The Problem of the Individual in non-Marxian Historical Materialism. Social Theory and Practice 13(1): 1-16. 195. A Model of Socialist Society. Studies in Soviet Thought 34: 1-55. 196. O historiozofii, antropologii, utopii i gnozie [On Historiosophy, Anthropology and Gnosis]. Przegląd polityczny 8: 132-161. 197. O antropologicznym i historiozoficznym wymiarze kategorii pokolenia [On Anthropological and Historiosophic Dimension of the Category of Generation]. In: J. GáuszyĔski (ed.), Teoretyczno-metodologiczne problemy badaĔ nad máodzieĪą, pp. 135-181. PoznaĔ: OĞrodek Analiz Spoáecznych ZMW. 198. On Homogeneity of the Notion of Model. Polish Psychological Bulletin 18(4): 243-249. 199. O podwójnej herezji w filozofii spoáecznej [On Double Heresy in Social Philosophy]. TwórczoĞü 11: 27-54. 200. PĊtla pracownicza i kontrpĊtla ideowa. Próba konkretyzacji modelu kapitalizmu [Labor Loop and Ideological Counter-Loop. An Attempt at Concretization of Model of Capitalism]. Przyjaciel Nauk: Studia z teorii i krytyki spoáecznej 3-4: 41-55. 201. (with P. Buczkowski and A. Klawiter) Religia jako struktura klasowa: Przyczynek do nie-Marksowskiego materializmu historycznego [Religion as a Class Structure: A Contribution to nonMarxian Historical Materialism]. Studia Religiologica 20: 79-128. 202. (with S. Wronkowska, M. ZieliĔski and Z. ZiembiĔski) Conventional Acts in Law. In: Z. ZiembiĔski (ed.), Polish Contributions to the Philosophy and Theory of Law (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 12), pp. 162-187. Amsterdam: Rodopi. Reprinted from: Studia Prawnicze 33 (1972): 73-99 (in Polish).

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1988 Books 203. Wáadza: Próba teorii idealizacyjnej [Power: Towards Idealizational Theory]. Warszawa: In Plus. Pp. 192. Papers 204. The Coming Revolution. Research in Social Movements, Conflicts and Change 10: 107-125. 205. Imperium socjalistyczne: Próba modelu [Socialist Empire: An Attempt at Model]. Notatnik historyczny 1: 9-87. 206. Intellectuals in the Age of Revolution: The Case of Socialist World. In: J.-D. Nackmayr (ed.), Die Herausforderungen der Wissenschaftvol. Essays zum 40. Grundjahr Freie Universität Berlin, pp. 7178. Berlin. Reprinted in: Thesis Eleven 27 (1990): 167-172. 207. Spiritual Domination as a Class Oppression: A Contribution to the Theory of Culture in non-Marxian Historical Materialism. Philosophy of the Social Sciences 18(2): 231-238.

1989 Edition of Collective Works 208. Dimensions of the Historical Process. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 13. Amsterdam: Rodopi. Pp. 317. Papers 209. Byt i myĞl: Przyczynek do metafizyki unitarnej [Being and Thought: A Contribution to Unitarian Metaphysics]. Studia Filozoficzne 1: 3-21.

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210. Hegel i liberalizm: zagadnienie natury historiozofii [Hegel and Liberalism: The Problem of the Nature of Historiosophy]. Pismo 11-12: 126-146. 211. An Idealizational Model of Capitalist Society. In: L. Nowak (ed.), Dimensions of the Historical Process, pp. 217-258. Amsterdam: Rodopi. 212. It is the Revolutions that Work for the Perestroikas. Merkourios 3: 21-29. 213. Jednostka a system spoáeczny [The Individual and the Social System]. In: P. Buczkowski, R. Cichocki (eds.), PodmiotowoĞü: moĪliwoĞü, rzeczywistoĞü, koniecznoĞü, pp. 71-108. PoznaĔ: Nakom. 214. MyĞl o czymĞ jest tym wáaĞnie: Nie ma wiĊc teorii bytu i teorii poznania – jest metafizyka [A Thought Is What It Is about: There Is Not a Theory of Being and a Theory of Knowledge – there is Metaphysics]. Pismo literacko-artystyczne 7-8: 78-112. 215. A New Model of Aggression. International Relations: Society and Politics 28(1-2): 46-56. 216. On the (Idealizational) Nature of Economic Theories. Erkenntnis 30: 225-246. Reprinted in: W. Balzer, B. Hamminga (eds.), Philosophy of Economics (Dordrecht/Boston/London: Kluwer, 1992), pp. 225-246. 217. Remarks on the Christian Model of Man and the Nature of Interpretation. Social Theory and Practice 15(1): 107-117. 218. Some Remarks on the Place of Logical Empiricism in the 20th Century Philosophy. In: K. Szaniawski (ed.), The Vienna Circle and the Lvov-Warsaw School, pp. 375-390. Dordrecht: Kluwer. Reprinted in: R. Egiert, A. Klawiter and P. Przybysz, (eds.), Oblicza idealizacji (PoznaĔskie Studia z Filozofii Humanistyki, vol. 15) (PoznaĔ: Wyd. UAM, 1996), pp. 293-30 (in Polish). 219. (with K. Paprzycka) On the Social Nature of Colonization. In: L. Nowak (ed.), Dimensions of the Historical Process, pp. 299-312. Amsterdam: Rodopi. Reprinted from: Przyjaciel Nauk: Studia z teorii i krytyki spoáecznej 3-4 (1987): 57-66 (in Polish). Reprinted in: Studia Socjologiczne 2: 161-174 (in Polish).

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1990 Edition of Collective Works 220. (with J. BrzeziĔski, F. Coniglione, T.A.F. Kuipers) Idealization I: General Problems. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 16. Amsterdam/Atlanta: Rodopi. Pp. 286. 221. (with J. BrzeziĔski, F. Coniglione, T.A.F. Kuipers) Idealization II: Forms and Applications. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 17. Amsterdam/Atlanta: Rodopi. Pp. 193. Papers 222. Abstracts Are Not Our Constructs. The Mental Constructs Are Abstracts. In: J. BrzeziĔski, F. Coniglione, T.A.F. Kuipers, L. Nowak, (eds.), Idealization I: General Problems, pp. 193-206. Amsterdam/ Atlanta: Rodopi. 223. MyĞli są sytuacjami [Thoughts Are Situations]. ĩycie Katolickie 2: 83-95. 224. On Theories, Half-Theories, One-Fourth Theories, etc.: The Requirement of Formalization and the Results of the Inability to Fulfill It. In: J. BrzeziĔski, T. Marek (eds.), Action and Performance: Models and Tests. Contributions to the Qualitative Psychology and Methodology (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 14), pp. 39-53. Amsterdam/Atlanta: Rodopi. 225. (with I. Nowakowa) Approximation and the Two Ideas of Truth. In: P. Weingartner, G.J.W. Dorn (ed.), Studies on Marlo Bunge’s Treatise (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 19), pp. 79-93. Amsterdam/Atlanta: Rodopi.

1991 Books 226. Power and Civil Society: Towards a Dynamic Theory of Real Socialism. New York/London: Greenwood Press. Pp. 233.

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227. U podstaw teorii socjalizmu [Foundations of the Theory of Socialism]. Vol. 1: WáasnoĞü i wáadza. O koniecznoĞci socjalizmu [Property and Power. On the Necessity of Socialism]. Vol. 2: Droga do socjalizmu. O koniecznoĞci socjalizmu w Rosji [The Road to Socialism. On the Necessity of Socialism in Russia]. Vol. 3: Dynamika wáadzy. O strukturze i koniecznoĞci zaniku socjalizmu [Dynamics of Power. On the Structure and Necessity of Disappearance of Socialism]. PoznaĔ: Nakom. Pp. 995 (359+311+325). Papers 228. The Collapse of Communism? An Analysis of a Myth. Polish Western Affairs 32(1): 77-87. Reprinted in: W. Zapf (ed.), Die Modernisierung moderner Gesellschaften (Frankfurt a. Main)/New York), pp. 449-454 (in German). 229. Czáowiek wobec ludzi. Przyczynek do problematyki związków mikro- i makrospoáecznych [A Person and Other People. A Contribution to the Problems of Micro- and Macro-Social Relations.] In: A. Suáek, W. Wincáawski (eds.), Przeáom i wyzwanie: PamiĊtnik VIII Ogólnopolskiego Zjazdu Socjologicznego. ToruĔ, 19-22 wrzeĞnia 1990, pp. 61-69. Warszawa/ToruĔ: PTS/UMK. 230. The Defense of a Socialist System against Its Ideology: A Case Study. In: P. Buczkowski (ed.), The Social Horizon of Knowledge (PoznaĔ Studies in the Philosophy of Science and the Humanities, vol. 22), pp. 59-85. Amsterdam/Atlanta: Rodopi. 231. Kilka tez o wspóáczesnym spoáeczeĔstwie polskim [Some Theses on Present Polish Society]. In: Zmiany Stosunków WáasnoĞciowych w Polsce i ich Konsekwencje Spoáeczne (Materiaáy na ogólnopolską konferencjĊ naukową. PoznaĔ 23-24 XI 1990), pp. 64-75. PoznaĔ: Zakáad Filozofii i Socjologii INS AR w Poznaniu. 232. Man vis-à-vis Others. A Contribution to the Critique of Liberal Social Philosophy. The Polish Sociological Bulletin 4: 289-297. 233. The Method of Relevant Variables and Idealization. In: E. Eells, T. Maruszewski (eds.), Probability and Rationality (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, 21) , pp. 41-63.

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Amsterdam/Atlanta: Rodopi. Reprinted in: Filozofia Nauki 1 (1993): 67-88 (in Polish). 234. The Post-Communist Society? An Attempt at Theoretical Analysis. In: D. Herzog, A. Predetto, H. Wagner (eds.), Revolution und Rekonstruktion. Der Aufbau freiheitlicher Demokration in Ostmitteleuropa, pp. 59-73. Berlin: Politische Wissenschaft. 235. Thoughts are Facts in Possible Worlds, Truths are Facts of a Given World. Dialectica 45: 273-287.

1992 Edition of Collective Works 236. (with J. BrzeziĔski) Idealization III: Approximation and Truth. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 25. Amsterdam/Atlanta: Rodopi. Pp. 288. Papers 237. The Idealizational Approach to Science: A Survey. In: J. BrzeziĔski, L. Nowak (eds.), Idealization III: Approximation and Truth (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 25), pp. 9-63. Amsterdam/Atlanta: Rodopi. Reprinted in: R. Egiert, A. Klawiter, P. Przybysz (eds.), Oblicza idealizacji (PoznaĔskie Studia z Filozofii Humanistyki, vol. 15) (PoznaĔ: Wyd. UAM, 1996), pp. 10-74 (in Polish); F. Coniglione, R. Poli (eds.), La Realtà Modellata: L’approccio idealizzazionale e le sue applicazioni nelle scienze umane (Milan: FrancoAngeli, 2004), pp. 37-97 (in Italian). 238. MyĞl o czymĞ jest tym wáaĞnie. Nie ma wiĊc teorii bytu i teorii poznania: jest metafizyka. [A Thought Is What It Is about: There Is Not a Theory of Being and a Theory of Knowledge – there is Metaphysics] In: J. BrzeziĔski, K. àastowski, T. Maruszewski (eds.), O związkach teoretycznych w filozofii nauki i psychologii (PoznaĔskie Studia z Filozofii Nauki 12), pp. 7-63. Warszawa-PoznaĔ: PWN.

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239. Metaphor, Creativity and the Metaphysics of Deformation. In: J. BrzeziĔski, F. Coniglione, T. Marek (eds.), Science: Between Algorithm and Creativity, pp. 11-28. Delft: Eburon. 240. On the Concept of Adequacy of Law: An Idealization Explication. In: J. BrzeziĔski, L. Nowak (eds.), Idealization III: Approximation and Truth, pp. 245-254. Amsterdam/Atlanta: Rodopi. Reprinted from: K. àastowski, L. Nowak (eds.), Konfrontacje i parafrazy (Warszawa/ PoznaĔ: PWN, 1979), pp. 29–38 (in Polish). 241. Paradoxes of Social Conscioussnes under Socialism. Studies in Soviet Thought 42: 159-168. 242. (with I. Nowakowa) “Truth is a System”: An Explication. In: J. BrzeziĔski, L. Nowak (eds.), Idealization III: Approximation and Truth (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 25), pp. 215-235. Amsterdam/Atlanta: Rodopi.

1993 Edition of Collective Works 243. (with M. Paprzycki) Social System, Rationality and Revolution. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 33. Amsterdam/Atlanta: Rodopi. Pp. 456. Papers 244. The Downfall of Real Socialism? An Analysis of a Myth. In: S-E. Liedman, M. Peterson, P. Rudny (eds.), Ideological Changes in Europe on the 1990s: Working Report from Inter-European Research Symposium in Goteborg on May 8-9 1992, pp. 119-138. Goteborg: University of Goteborg. 245. The Hidden Sense of Clericalization: The Case of Eastern Europe. The Centennial Review (special issue: Poland from Real Socialism to Democracy, edited by P. L. Esquith and M. WilczyĔski) 37: 105-114. 246. On Creativity in Theory-Building. In: J. BrzeziĔski, P. di Nuovo, T. Marek, T. Maruszewski (eds.), Creativity and Consciousness.

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Philosophical and Psychological Dimensions (PoznaĔ Studies in the Philosophy of Science and the Humanities, vol. 31), pp. 131-142. Amsterdam/ Atlanta: Rodopi. 247. O tak zwanym paradygmacie koincydentalnym w filozofii: Dyskusja dwóch najnowszych polskich opracowaĔ problemu [On the SoCalled Co-Incidental Paradigm in Philosophy: Discussion of Two Newest Polish Approaches to this Problem]. Edukacja Filozoficzna 15: 49-59. 248. Post-Communist Society? An Attempt at Theoretical Analysis. Social Theory and Practice 19: 249-272. 249. Postmodernizm: Pewna próba wykáadni metafizycznej i wyjaĞnienia historycznego [Postmodernism: A Certain Attempt of Metaphysical Interpretation and Historical Explanation], pp. 39-51. In: L. GrudziĔski (ed.), Wobec kryzysu kultury. GdaĔsk: Wyd. UG. 250. Real Marxism in Real Socialism. The Centennial Review (special issue: Poland from Real Socialism to Democracy, edited by P. L. Esquith and M. WilczyĔski) 37: 39-59. 251. Revolution is an Opaque Progress but a Progress Nonetheless. In: L. Nowak, M. Paprzycki (eds.), Social System, Rationality and Revolution, pp. 237-250. Amsterdam/Atlanta: Rodopi. 252. The Totalitarian Approach and the History of Socialism. In: J. Frentzel-Zagórska (ed.), From a One-Party State to Democracy: Transition in Eastern Europe (PoznaĔ Studies in the Philosophy of Science and the Humanities, vol. 32), pp. 45-66. Amsterdam/Atlanta: Rodopi. 253. Two Inter-Human Limits to the Rationality of Man. In: L. Nowak, M. Paprzycki (eds.), Social System, Rationality and Revolution, pp. 197-204. Amsterdam/Atlanta: Rodopi. Reprinted from: Due limiti interumani alla razionalitá dell’uomo, Cifra 38 (1989): 189-195 (in Italian). 254. Wychowanie w Ğwietle nie-Ewangelicznego modelu czáowieka [Education in the Light of the non-Christian of A Human]. Socjologia wychowania 5: 31-55.

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255. (with K. Paprzycka and M. Paprzycki) On Multilinearity of Socialism. In: L. Nowak, M. Paprzycki (eds.), Social System, Rationality and Revolution, pp. 355-370. Amsterdam/Atlanta: Rodopi.

1994 Papers 256. Czy nasza ĞwiadomoĞü jest wolna? Próba parafrazy unitarnej [Is Our Consciousness Free? An Attempt at Unitarian Metaphysics]. Zeszyty KarmelitaĔskie 3-4: 23-36. 257. The Idealizational Methodology of Economics: Replies to Diederich, Hoover, Janssen, Jorland and Mäki. In: B. Hamminga, N. de Marchi (eds.), Idealization VI: Idealization in Economics (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 38), pp. 303-336. Amsterdam/Atlanta: Rodopi. 258. Lewica, prawica, teoria spoáeczna. Esej raczej ideowy niĪ naukowy [The Left, The Right. An Essay]. In: J. BrzeziĔski, L. Witkowski (eds.), Edukacja wobec zmiany spoáecznej, pp. 177-194. PoznaĔ/ToruĔ: Edytor. 259. On Ontological Assumptions of Idealizational Theory. Theoria (San Sebastian) 20: 19-28. 260. O speánieniu siĊ czáowieka wobec ludzi [On the Fulfillment of a Human with respect to People]. Zeszyty KarmelitaĔskie 2: 129-132. 261. O zagadnieniu tak zwanej transformacji ustrojowej [On the SoCalled Systemic Transformation]. In: K. Zamiara (ed.), Spoáeczna transformacja w refleksji humanistycznej, pp. 117-129. PoznaĔ. 262. Political Theory and Socialism: On the Main Paradigms of Political Power and their Methodological and Historical Legitimization. In: M. Krygier (ed.), Marxism and Communism: Posthuman Reflection on Politics, Society and Law (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 36), pp. 77-97. Amsterdam/Atlanta: Rodopi.

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263. (with I. Nowakowa) On Correspondence between Economic Theories. In: B. Hamminga, N. de Marchi (eds.), Idealization VI: Idealization in Economics (PoznaĔ Studies in the Philosophy of Science and the Humanities, vol. 38), pp. 135-146. Amsterdam/Atlanta: Rodopi. Reprinted from: P. Buczkowski, L. Nowak (eds.), Teoria ekonomiczna: Metodologia i rekonstrukcje (PoznaĔ: Wyd. Akademii Ekonomicznej, 1978), pp. 63-73 (in Polish).

1995 Papers 264. Ajdukiewicz and the Status of Logical Theory of Language. In: V. Sinisi, J. WoleĔski (eds.), The Heritage of Kazimierz Ajdukiewicz (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 40), pp. 111-126. Amsterdam/Atlanta: Rodopi. 265. Anty-cogito, magia, unitarna koncepcja metafizyki [Anti-Cogito, Magic, Unitarian Concept of Metaphysics]. Kultura Wspóáczesna 1-2: 5-34. 266. Antirealism, (Supra-)Realism and Idealization. In: W. E. Herfel, W. Krajewski, I. Niiniluoto, R. Wójcicki (eds.), Theories and Models in Scientific Processes (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 44), pp. 225-241. Amsterdam/Atlanta: Rodopi. Reprinted in: K. Zamiara (ed.), O nauce i filozofii nauki: KsiĊga pamiątkowa poĞwiĊcona pamiĊci Jerzego Giedymina (PoznaĔ: Humaniora, 1995), pp. 111-126 (in Polish). 267. ChrzeĞcijaĔstwo versus liberalizm [Christianity versus Liberalism]. In: B. Stanosz (ed.), Z punktu widzenia humanizmu (Biblioteka “Bez Dogmatu”, vol. 1), pp. 83-99. Warszawa: KsiąĪka i Wiedza. 268. The Intelligentsia and the Problem of Transition: The Case of Poland. In: Ch. Hahn (ed.), The Perspectives for Poland, pp. 67-72. New York: Cambridge University Press. 269. JĊzyk logików i jĊzyk jĊzykoznawców [Language of Logicians and Language of Linguists] In: J. Pogonowski (ed.), Eufonia i logos: KsiĊga Pamiątkowa oferowana Profesor Marii Steffen-Batogowej

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oraz Profesorowi Tadeuszowi Batogowi, pp. 483-496. PoznaĔ: Wyd. UAM. 270. KoĞcióá i lud ziemski [The Church and the Earthly People]. In: B. Stanosz (ed.), Z punktu widzenia humanizmu (Biblioteka “Bez Dogmatu”, vol. 1), pp. 218-228. Warszawa: KsiąĪka i Wiedza. 271. Le mythe des racines marxistes du socialisme réellement existant. In: Utopie, Théologie de la libération. Philosophie de l’émancipation, pp. 2-37. Paris: Presses Universitaires de France. 272. National Independence: A Model for Central Europe. In: H. Timmerman (ed.), Die Kontinentwerdung Europas. Festschrift für Helmut Wagner zum 65 Geburstag, pp. 335-348. Berlin: Duncker Humboldt. 273. O ponowoczesnoĞci, “prawdzie absolutnej” i micie tej ostatniej w pierwszej jak równieĪ o racjonalnym jądrze tego mitu [On Postmodernity, “Absolute Truth” and Myth of the Latter in the First and Rational Kernel of this Myth]. In: J. Sójka (ed.), Horyzonty ponowoczesnoĞci: Rozmowy z Zygmuntem Baumanem, part II, pp. 35-57. PoznaĔ: Humaniora. 274. Remarks on the Nature of Galileo’s Methodological Revolution. In: M. Kuokkanen (ed.), Idealization VII: Structuralism, Idealization and Approximation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 42), pp. 111-126. Amsterdam/Atlanta: Rodopi.

1996 Edition of Collective Works 275. (with z A. Falkiewicz) Przestrzenie ĞwiadomoĞci: Studia z Filozofii Literatury [The Spaces of Consciousness: Studies from Philosophy of Literature]. PoznaĔskie Studia z Filozofii Humanistyki, vol. 16. PoznaĔ: Zysk i S-ka. Pp. 231.

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Papers 276. Byt i nicoĞü: Dogmat Parmenidesa i pewne jego metafizyczne implikacje [Being and Nothingness: Parmenides’ Dogma and Its Certain Metaphysical Implications]. In: J. Perzanowski, A. JĊdruszczak (eds.), Byt, Logos, matematyka: KsiĊga pamiątkowa bloku ontologiczno-logicznego VI Polskiego Zjazdu Filozoficznego, pp. 95-112. ToruĔ. 277. Gombrowicza model ĞwiadomoĞci (miĊdzy)ludzkiej [Gombrowicz’s Model of InterHuman Consciousness]. In: A. Falkiewicz, L. Nowak (eds.), Przestrzenie ĞwiadomoĞci: Studia z filozofii, pp. 139-192. PoznaĔ: Zysk i S-ka. 278. Koniec historii czy jej powtórka [The End of History or Its Repetition]. In: W. Heller (ed.), ĝwiat jako proces, pp. 31-40. PoznaĔ: Wyd. IF UAM. 279. O polskich paradoksach Socjaldemokratyczna 4: 7-20.

[On

Polish

Paradoxes].

MyĞl

280. O pozornoĞci podziaáu filozofii na analityczną i syntetyczną [On an Apparent Division of Philosophy into Analytic and Synthetic]. Principia 13: 2-4. 281. O supozycja i sądach [On Suppositions and Judgments]. In: J.J. Jadacki, W. StrawiĔski (eds.), W Ğwiecie znaków: KsiĊga Pamiątkowa ku czci Profesora Jerzego Pelca, pp. 81-88. Warszawa: PTF. 282. On the Limits of the Rationalistic Paradigm. In: A. Zeidler-Janiszewska (ed.), Epistemology of History: Humanities as a Philosophical Problem and Jerzy Kmita’s Approach to It (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 47), pp. 267-282. Amsterdam/Atlanta: Rodopi. Reprinted from: K. Zamiara (ed.), Humanistyka jako autorefleksja kultury (PoznaĔ: CIA Books, 1995), pp. 207-219 (in Polish). 283. Rewolucje i ich Ğlady w ĞwiadomoĞci narodowej [Revolutions and their Signs in National Consciousness]. In: A. Górny (ed.), PoznaĔski Czerwiec w ĞwiadomoĞci i historii, pp. 11-14. PoznaĔ: WiS. 284. (Unitarna) metafizyka Bolesáawa LeĞmiana [Unitarian Metaphysics of Bolesáaw LeĞmian]. In: A. Falkiewicz, L. Nowak (eds.), Prze-

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strzenie ĞwiadomoĞci: Studia z filozofii literatury, pp. 73-124. PoznaĔ: Zysk i S-ka. 285. Z metafizyki idealizacji [From the Metaphysics of Idealization]. Principia 15: 81-98.

1997 Edition of Collective Works 286. (with J. BrzeziĔski) The Idea of University. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 50. Amsterdam/ Atlanta: Rodopi. Pp. 221. 287. (with P. Przybysz) Marksizm, liberalizm, próby wyjĞcia [Marxism, Liberalism, Attempts to Go Out]. PoznaĔskie Studia z Filozofii Humanistyki, vol. 17. PoznaĔ: Zysk i S-ka. Pp. 404. Papers 288. Efekt kresowy w procesie historycznym [The Limit Effect in the Historical Process]. In: L. Nowak, P. Przybysz (eds.), Marksizm, liberalizm, próby wyjĞcia, pp. 307-319. PoznaĔ: Zysk i S-ka. 289. Marksizm versus liberalizm: Pewien paradoks [Marxism versus Liberalism: A Certain Paradox]. In: L. Nowak, P. Przybysz (eds.), Marksizm, liberalizm, próby wyjĞcia, pp. 7-19. PoznaĔ: Zysk i S-ka. 290. Na poáy filozoficzny, a na poáy naukoznawczy esej o postmodernizmie [Half-Philosophical and Half-Scientific Essay on Postmodernism]. In: J. BrzeziĔski, Z. KwieciĔski (eds.), Polacy u progu (Forum oĞwiatowe, vol. 16-17), pp. 305-330. ToruĔ: Edytor. 291. O twórczoĞci w nauce teoretycznej [On Creativity in Theoretical Science]. In: J. Goükowski, M. Sikora (eds.), Porozumiewanie siĊ i wspóápraca uczonych, pp. 213-220. Kraków: Secesja. 292. On Common-sense and (Para-) Idealization. In: J. BrzeziĔski, B. Krause, T. Maruszewski (eds.), Idealization VIII: Modelling in Psychology (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 56), pp. 289-292. Amsterdam/Atlanta: Rodopi.

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293. On the Concept of Nothingness. Axiomathes 1-3: 381-394. Reprinted from: J. PaĞniczek (ed.), MiĊdzy logiką a etyką: Studia z logiki, ontologii, epistemologii, metodologii, semiotyki i etyki: Prace ofiarowane Profesorowi Leonowi Kojowi (Lublin: Wyd. UMCS, 1995), pp. 107-121 (in Polish). 294. On Postmodernist Philosophy: An Attempt to Identify Its Historical Sense. In: P.-E. Liedman (ed.), The Postmodernist Critique of the Project of Enlightenment (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 58), pp. 123-134. Amsterdam/Atlanta: Rodopi. Reprinted from: Wijsgerig perspectief 31 (1991): 172-180. 295. The Personality of Researchers and the Necessity of Schools in Science. In: J. BrzeziĔski, L. Nowak (ed.), The Idea of University (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 50), pp. 191-197. Amsterdam/Atlanta: Rodopi. Reprinted from: E. Rodziewicz (ed.), Inspiracje, otwarcia, krytyki – w edukacji (GdaĔsk: Wyd. UG, 1995), pp. 17-23 (in Polish). 296. Polskie paradoksy: próba materialistycznego wyjaĞnienia [Polish Paradoxes: An Attempt at a Materialist Explanation]. PaĔstwo i Kultura Polityczna 18: 9-24. 297. Struktura dogmatu [The Structure of a Dogma]. Bez Dogmatu 31: 10-12. Reprinted in: B. Stanosz (ed.), Humanistyczna wizja zjednoczonej Europy (Warszawa: Federacja Polskich StowarzyszeĔ Humanistycznych, 1998), pp. 101-109 (in Polish). 298. Uwagi o tak zwanej metodzie izolacji [On the So-Called Method of Isolation]. In: J. Mrozek (ed.), MiĊdzy filozofią nauki a filozofią historii, pp. 29-38. GdaĔsk: Wyd. UG.

1998 Books 299. Byt i myĞl. U podstaw negatywistycznej metafizyki unitarnej [Being and Thought. Foundations of Negativistic Unitarian Metaphysics]. Vol. I: NicoĞü i istnienie [Nothingness and Existence]. PoznaĔ: Zysk i s-ka. Pp. 494.

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Edition of Collective Works 300. (with R. Panasiuk) Marx’s Theories Today. PoznaĔ Studies in the Philosophy of Science and the Humanities, vol. 58. Amsterdam/Atlanta: Rodopi. Pp. 457. Papers 301. The Adaptational Interpretation of Historical Materialism: A Survey: On a Contribution to Polish Analytical Marxism. In: L. Nowak, R. Panasiuk (eds.), Marx’s Theories Today, pp. 201-236. Amsterdam/ Atlanta: Rodopi. Reprinted from: L. Nowak, P. Przybysz (eds.), Marksizm, liberalizm, próby wyjĞcia (PoznaĔ: Zysk i s-ka, 1997), pp. 29-69 (in Polish). 302. A Conception that is Supposed to Correspond to the Totalitarian Approach to Real Socialism. In: A. Siegel (ed.), The Totalitarian Paradigm after the End of Communism. Towards a Theoretical Reassessment (PoznaĔ Studies in the Philosophy of Science and the Humanities, vol. 65), pp. 91-108. Amsterdam/Atlanta: Rodopi. Reprinted in: A. Siegel (ed.), Totalitarismus Theorien nach dem Ende des Kommunismus (Köln/Wimar: Bohlan Verlag 1998), pp. 81-103 (in German). 303. O metaforze [On Metaphor]. In: W. Wrzosek (ed.), ĝwiat historii, metodologii historii i historii historiografii dedykowane Jerzemu Topolskiemu z okazji siedemdziesiĊciolecia urodzin, pp. 341-345. PoznaĔ: IH UAM. 304. Struktura myĞli prowincjonalnej [The Structure of Provincial Thought]. Przegląd Bydgoski 9: 8-20. 305. (with I. Nowakowa) Model(s)’ and Experiment(s) as Homogenous Families of Notions. In: N. Shanks (ed.) Idealization IX: Idealization in Contemporary Physics (PoznaĔ Studies in the Philosophy of Science and the Humanities, vol. 65), pp. 35-50. Amsterdam/Atlanta: Rodopi.

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1999 Edition of Collective Works 306. (with A. Klawiter and P. Przybysz) Umysá i rzeczywistoĞü [Mind and Reality]. PoznaĔskie Studia z Filozofii Humanistyki, vol. 18. PoznaĔ: Zysk i S-ka. Pp. 455. Papers 307. Unifikacja liberalnego i Marksowskiego modelu czáowieka [Unification of Liberal and Marxian Model of a Human]. In: J. Kozielecki (ed.), Humanistyka przeáomu wieków, pp. 162-180. Warszawa: Wyd. Akademickie ĩAK. 308. Zagadka punktu wyjĞcia [The Puzzle of the Point of Departure]. In: A. Klawiter, L. Nowak, P. Przybysz (eds.), Umysá i rzeczywistoĞü, pp. 43-71. PoznaĔ: Zysk i S-ka. 309. Zygmunta ZiembiĔskiego koncepcja interpretacji: Pewne komentarze, dopeánienia i aplikacje [Zygmunt ZiembiĔski’s Conception of Interpretation: Some Comments, Additions and Applications]. In: A. Klawiter, L. Nowak, P. Przybysz (eds.), Umysá i rzeczywistoĞü, pp. 423435. PoznaĔ: Zysk i S-ka.

2000 Books 310. Gombrowicz: Czáowiek wobec ludzi [A Person vis-à-vis Others]. Filozofia polska XX w. Warszawa: PrószyĔski i S-ka. Pp. 239. 311. (with I. Nowakowa) Idealization X: The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam/Atlanta: Rodopi. Pp. 519.

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Papers 312. Commentary on M. Lance, “The Best is the Enemy of the Good: Bayesian Epistemology as a Case Study in Unhelpful Idealization”. In: N. Shanks, R.B. Gardner (ed.), Logic, Probability and Science (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 71), pp. 130-134. Amsterdam/Atlanta: Rodopi. 313. Hipoteza logicznej sprzecznoĞci zmiany: Próba parafrazy unitarnej [The Hypothesis of the Logical Contradiction of Change: An Attempt At a Unitarian Paraphrase]. In: MiĊdzy przyrodoznawstwem, matematyką a humanistyką: Profesorowi Janowi Suchowi w 70-lecie urodzin i 45 lecie pracy naukowej, pp. 219-225. PoznaĔ: Wyd. Naukowe IF UAM. 314. O Bogu i Ğwiatach boskich [On the God and Godly Worlds]. Preteksty (special issue: Teizm i ateizm w filozofii): 9-22. 315. On the Common Structure of Science and Religion. In: A. Garcia de la Sienra (ed.), The Rationality of Theism (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69), pp. 317-343. Amsterdam/Atlanta: Rodopi. 316. O dialektyce w metafizyce unitarnej [On Dialectics in Unitarian Metaphysics]. In: J. DĊbowski, M. HetmaĔski (ed.), Poznanie — czáowiek — wartoĞci: Prace ofiarowane Profesorowi Zdzisáawowi Cackowskiemu, pp. 37-49. Lublin: Wyd. UMCS. 317. O metodzie kwadratu logicznego w metafizyce (na przykáadzie metafizyki unitarnej) [On Method of Logical Square in Metaphysics (An Example of Unitarian Metaphysics]. In: J. Hartman (ed.), Filozofia i logika. W stronĊ Jana WoleĔskiego, pp. 40-54. Kraków: Aureus. 318. O stylach i dewiacjach filozofowania [On Styles and Deviations of Philosophizing]. In: J. Pelc (ed.), JĊzyk wspóáczesny i humanistyka (Biblioteka MyĞli Semiotycznej), pp. 233-240. Warszawa.

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2001 Papers 319. Chichot heglowski, czyli marksizm i liberalizm w polityce polskiej [Hegel’s Cackle that is Marxism and Liberalism in Polish Politics]. In: K.T. Toeplitz (ed.), Czáowiek, rynek, sprawiedliwoĞü, pp. 62-85. Warszawa: Tow. Wyd. Literackie. 320. Jak pojmowaü ĪyczliwoĞü wobec bliĨniego? [How to Understand Benevolence towards the Neighbor?]. Przegląd Filozoficzny 10(3): 312323. 321. O pluralizmie metafizycznym [On Metaphysical Pluralism]. In: W.P. Glinkowski, A. Nowaczyk, J. PiórczyĔski (eds.), Rozum w dziejach: KsiĊga Jubileuszowa Profesora Ryszarda Panasiuka, pp. 9-20. àódĨ: Wyd. Uà.

2003 Papers 322. O prognozie totalitaryzacji kapitalizmu. Próba oceny po dwudziestu latach [On Prognosis of Totalitarization of Capitalism. An Attempt at Evaluation After Twenty Years]. In: K. Brzechczyn (ed.), ĝcieĪki transformacji. UjĊcia teoretyczne i opisy empiryczne (PoznaĔskie Studia z Filozofii Humanistyki, vol. 19), pp. 361-401. PoznaĔ: Zysk i S-ka.

2004 Books 323. Byt i myĞl: U podstaw negatywistycznej metafizyki unitarnej [Being and Thought: Foundations of Negativistic Unitarian Metaphysics], vol. II: WiecznoĞü i zmiana [Eternity and Change]. PoznaĔ: Zysk i S-ka. Pp. 528.

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Papers 324. O metodologii Karola Darwina [On Methodology of Charles Darwin]. In: K. àastowski (ed.), Teoria i metoda w biologii ewolucyjnej (PoznaĔskie Studia z Filozofii Humanistyki, vol. 20), pp. 13-57. PoznaĔ: Zysk i S-ka. 325. O pewnej metafizycznej zagadce Leibniza [On Certain Metaphysical Puzzle of Leibniz]. In: J. Malinowski, A. Pietruszczak (eds.), Wokóá filozofii logicznej, pp. 179-191. ToruĔ: Wydawnictwo UMK. 326. La’ unità nascosta di scienze sociali e scienze naturali. In: F. Coniglione, R. Poli (eds.), La Realtà Modellata. L’approccio idealizzazionale e le sue applicazioni nelle scienze umane, pp. 237-273. Milan: FrancoAngeli. Reprinted from: Nauka 1 (1998): 11-42 (in Polish).

2005 Papers 327. On the Collective Subjects in Epistemology: The Marxist Case and a Problem for the African Viewpoint. In: B. Hamminga (ed.), Knowledge Cultures. Comparative Western and African Epistemology (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 88), pp. 117-128. Amsterdam/New York: Rodopi. 328. O interpretacji filozoficznej i historyczno-filozoficznej [On Philosophical and Philosophical-Historical Interpretation]. In: W. Krajewski (ed.), Nauka, Ğwiat, czáowiek, pp. 262-266. GdaĔsk: Wyd. UG. 329. O prawomocnych strategiach obrony prawa przed empiryczną refutacją [On Valid Strategies of Defense of Scientific Law before Empirical Refutation]. In: J. Kmita, B. Kotowa, J. Sójka (eds.), Nauka, Humanistyka, Czáowiek, pp. 125-138. PoznaĔ: Wyd. Naukowe UAM.

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2006 Papers 330. Kawaá(ecz)ek CaáoĞci w sensie metafizyki unitarnej [The Part of the Whole in the Sense of Unitarian Metaphysics]. In: P. Orlik (ed.), CaáoĞü – wizje, pejzaĪe, teorie (Problemy/dyskusje, vol. 6), pp. 17-39. PoznaĔ: Wyd. Naukowe. 331. O metafizyce unitarnej, CaáoĞci i filozofii – dyskusja [On Unitarian Metaphysics, the Whole and Philosophy]. In: P. Orlik (ed.), CaáoĞü – wizje, pejzaĪe, teorie (Problemy/dyskusje, vol. 6), pp. 40-64. PoznaĔ: Wyd. Naukowe.

2007 Books 332. Byt i myĞl: U podstaw negatywistycznej metafizyki unitarnej [Being and Thought: Foundations of Negativistic Unitarian Metaphysics], vol. III: Enigma i rzeczywistoĞci [Enigma and Realities]. PoznaĔ: Zysk i S-ka, 2007. Pp. 491.

SCIENCE AND IDEALIZATION

Theo A. F. Kuipers ON TWO TYPES OF IDEALIZATION AND CONCRETIZATION: THE CASE OF TRUTH APPROXIMATION*

Introduction In my view, Idealization and Concretization (henceforth I&C) is not only an important methodology in the empirical science (empirical I&C), but also in philosophy, at least as far as philosophy is engaged in “concept explication.” In concept explication one aims at the construction of a simple, precise and useful concept which is, in addition, similar to a given informal concept. According to the standard strategy of concept explication one tries to derive from the informal concept to be explicated and relevant empirical findings, if any, conditions of adequacy that the explicated concept will have to satisfy, and evident examples and counterexamples that the explicated

*

I like to thank the present members of the Promotion Club Cognitive Patterns (PCCP) of my home institution for their useful comments, in particular, Atocha Aliseda, David Atkinson, Fred Keijzer, Erik Krabbe, Jeanne Peijnenburg, Menno Rol and Jan-Willem Romeyn.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 75-101. Amsterdam/New York, NY: Rodopi, 2007.

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concept has to include or exclude.1 As in the empirical case, it may be very useful to start with an idealized way of catching cases and conditions, in order to make it gradually more realistic. This I will call “conceptual I&C.” Of course, conceptual I&C is useful not only for concept explication but also for concept formation in general. Moreover, explication may go further than the explication of informal concepts, it may also aim at the explication of intuitive judgments, i.e. intuitions, including their justification, demystification or even undermining. The strategy of “intuition explication” is a plausible extension of that of concept explication, and it may or may not make use of a plausible variant of conceptual I&C. Moreover, in case one aims at justifying an intuition concerning one or more concepts, this possibility becomes a condition of adequacy for their explication. Leszek Nowak has not only, rightly, highlighted empirical I&C, in his philosophical work, whether belonging to the philosophy of science, social philosophy or metaphysics, he has rightly practiced conceptual I&C. However, whereas I see both empirical and conceptual I&C primarily as a methodology, based on practical reasons, Nowak has argued in several publications, that there is also a kind of metaphysical foundation of this methodology, in particular of empirical I&C. Here I just raise the question whether such a foundation can also be given for conceptual I&C, and leave it at that. I will focus on (one of) the crossroads of the two methods. A typical cluster of examples of concept and intuition explication concerns truth approximation. In my From Instrumentalism to Constructive Realism (Kuipers 2000), henceforth ICR, I have presented a synthesis of a (qualitative, structuralist) theory of truth approximation that I have developed over the years. In this theory, three concepts and two intuitions play a crucial role. The concepts are confirmation, empirical progress, and (more) truthlikeness. The first intuition, the success intuition, amounts to the claim that empirical progress is, as a rule, functional for truth approximation, that is, an

1

See (Kuipers 2001, Ch. 1) for an elaboration of the idea that “explicative” programs form a fourth type of research programs, besides descriptive, explanatory, and design programs.

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empirically more successful theory is, as a rule, more truthlike or closer to the truth, and vice versa. The second intuition, the I&C intuition, is a kind of specification of the first. It starts from Nowak’s observation that empirical I&C is a dominant method in the empirical sciences and says that a proper explication should not only do justice to this observation, but also entail that this method is functional for truth approximation. Both intuitions function as condition of adequacy for the proper explication of all relevant concepts. Moreover, in the course of the development some additional intuitions come into play. Finally, the transition from the ideal gas law to the law of Van der Waals functions as one of the main evident examples of truth approximation in general and of truth approximation by empirical I&C in particular. The truth approximation theory has many conceptual I&C aspects and, on this occasion, I like to present the main lines of the theory from the I&C point of view. A main I&C aspect is that the first so-called “basic explication” satisfies already the first intuition, the success intuition, but not the second, the I&C intuition. Only the concretization leading to the so-called “refined explication” realizes the I&C intuition. This and some other I&C aspects will be elaborated in some detail, whereas yet other I&C aspects will merely be indicated. Since I have always been aware of the need of I&C thinking starting from my first reading of papers by Nowak in the mid-seventies, in both science and philosophy, I did not expect surprises in writing this paper. However, even for myself it was very instructive to find out which versions are matters of genuine, typically asymmetric, concretization and which are merely cases of symmetric variation. In this way, the truth approximation theory obtained a lot more transparency for myself. I will successively elaborate the I&C perspective on the ten conclusions of ICR, presented in Section 13.1 of ICR. I will do so in a couple of sections, following the division of ICR in four parts. ICR has an introductory chapter, on epistemological positions, in particular, instrumentalism,2 constructive empiricism, referential realism and

2

Instrumentalism as an epistemological position should be distinguished from the instrumentalist or evaluation methodology. The latter is claimed to serve also other epistemological positions.

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theory realism, and a concluding chapter (13), articulating “constructive realism,” a non-essentialist version of theory realism. The eleven chapters of ICR in between are grouped together into four parts, entitled “Confirmation” (I), “Empirical Progress” (II), “Basic Truth Approximation” (III), and “Refined Truth Approximation” (IV). These four parts tell a stepwise story that can be summarized in 9 conclusions, followed by an overall epistemological conclusion. Within the sections, each new topic begins with the relevant conclusion. The reader who prefers to read first a complete summary is referred to Section 13.1 of ICR. As a final terminological point, I will continue to speak of empirical I&C when relevant, but I will from now on refer to conceptual I&C simply by ‘I&C’.

1. Confirmation The first three conclusions deal with confirmation and empirical progress, and their relation. I will discuss them separately. (I) The first conclusion from Part I and II of ICR, is that a useful distinction can be made between two kinds of applying the Hypothetico-Deductive (HD) method, viz. testing of hypotheses in order to try to establish their truth-value, leading to falsification or confirmation, and evaluation of theories, in the first place, in order to establish their observational merits and failures. This brings us immediately to one of the main I&C aspects of the truth approximation theory. Put crudely, drawing the conclusion that empirical progress has been made when a new theory is persistently more successful than an old one, even if both are falsified, is the concretization of the idealized point of departure of observational induction, that is, drawing the conclusion that a theory is (observationally) true when it is persistently confirmed (or, for that matter, corroborated). Although testing for truth-values is crucial for test implications of theories, for the evaluation of theories themselves their comparative evaluation in terms of observational merits and

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failures is crucial. A major argument for this arises from empirical I&C. If Leszek Nowak’s main tale is right, that is, that empirical I&C plays a very important role in the development of the empirical sciences, and I have not the slightest doubt in this, even most of our concretized theories will not only be false, but known to be false beforehand. Hence, any falsificationist methodology for theories is inappropriate in such cases and all other cases of falsified theories that nevertheless seem better than other ones. This applies also to the so-called Bayesian methodology, for it throws all falsified theories on the scrap heap of “p-zero hypotheses.” I will investigate the further consequences in Section 2 but, first, I will turn to “confirmation.” (II) According to Part I of ICR, the notion of confirmation is primarily related to hypothesis testing, and can be given a direct qualitative explication, presented in Ch. 2, at least as far as deductive confirmation is concerned. Moreover, a quantitative, Bayesian, explication, given in Ch. 3, leads to a clear division of deductive and non-deductive confirmation. This quantitative explication indirectly generates a qualitative explication of confirmation in general and of non-deductive confirmation in particular. For the acceptance of observational hypotheses as true, fallible, inductive jumps have to be made in the sense of inductive generalizations. In Ch. 4 it is shown that inductive confirmation and inductive logic pertain to a particular kind of probability functions governing quantitative, deductive and nondeductive, confirmation. Let me start with deductive confirmation. The notion of “deductive confirmation” has met a number of objections. However, my claim is that “confirmation” can receive a highly plausible partial explication in terms of “deductive confirmation,” provided two concretizations are taken into account. More specifically, the idealized point of departure is the following “basic definition” of “deductive (d-)confirmation”: E d-confirms H iff H (logically) entails E. The first concretization concerns replacing this purely classificatory perspective by a (qualitative, classificatory-cum-) comparative pers-

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pective by enriching the basic definition with at least the following special principles: (S1) if H entails E and E entails E* then E d-confirms H more than E* (S2) if H* entails H and H entails E then E d-confirms H* as much as H The second concretization concerns the transition from “deductive confirmation” to “conditional deductive (cd-)confirmation.” In most cases of HD-testing of general hypotheses by individual test implications, the confirmation presupposes “initial conditions.” E cd-confirms H on the condition C iff H & C entails E Hence, d-confirmation is an extreme special case of cd-confirmation, where C is tautologous. With these two concretizations the famous paradoxes of Hempel and Goodman disappear, as well as a couple of other general objections, such as the “irrelevant conjunction” objection. The transition from Ch. 2 to Ch. 3 amounts to the transition from the idealization that all confirmation is deductive confirmation to the concretization of taking non-deductive confirmation also into account, such that the former is an extreme special case of the latter. The standard way of doing this is probabilistic, that is, assuming a probability function and defining confirmation by the condition p(H/E) > p(H), with the conditionalized version: p(H/E & C) > p(H/C). In the following, I will present diagrams that summarize the relevant conclusions. Simple arrows always indicate “I&C transitions,” where the tail of the arrow represents the idealized point of departure and the head the concretized result. unconditional

unconditional

deductive

non-deductive

confirmation

confirmation

conditional

conditional

deductive

non-deductive

confirmation

confirmation

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Although it is not a matter of concretization, I like to mention that my favorite version is in three ways non-standard: it is “reverse,” and therefore “inclusive,” and it is “pure.” That is, it reverses the definiens clause from “E makes H more plausible” (p(H/E) > p(H)) into “H makes E more plausible” (p(E/H) > p(E)), with the consequence that it includes the possibility of confirming “p-zero” hypotheses, provided p(E/H) can be plausibly defined (such as in the case of deductive confirmation when p(E/H) of course equals 1). It is pure in the sense that it is neutral in rewarding hypotheses of different plausibility for the same success: if p(E/H) = p(E/H*) their ratio degree of confirmation is equal: p(E/H)/p(E) = p(E/H*)/p(E). Note that this is a generalization of (S2). Note also that (S1) is satisfied by the ratio degree. Probabilistic confirmation can be inductive or merely structural. This depends on whether the relevant probability function is inductive, or ampliative, in the sense that an extra occurrence of, say, a black raven increases the chances that the next raven is again black. This property can be obtained in two different ways, and their combination: the standard Bayesian way with “inductive priors,” that is, positive prior probabilities for genuine universal generalizations, the Carnapian way of “inductive likelihoods,” that is, likelihoods having the ampliative character, and finally the Hintikkian way, which combines inductive priors with inductive likelihoods. Rejection of such inductive probability functions, such as Popper is assuming in his notion of “corroboration,” leaves open the option of a merely structural probability function and corresponding structural confirmation, or corroboration. This amounts to confirmation on the basis of vocabulary appropriate versions of Carnap’s non-inductive c+ function. A nice, objective case of structural confirmation is the claim that a high outcome of a fair dice (4, 5, 6) is confirmed by knowing that it is even (2, 4, 6); the evidence raises the objective probability of the hypothesis from 1/2 to 2/3. However, within Popper’s and Carnap’s approach alike, confirmation of genuine universal hypotheses requires the reverse definition of confirmation, mentioned above, for they will get zero probability. For the other approaches it makes no difference.

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The question remains whether inductive confirmation is a matter of concretization, relative to merely structural confirmation. I do not think this is the case in some objective sense. As I have stressed in ICR, the point of all these approaches is not so much a matter of what the correct one is, but a matter of which “confirmation language” one prefers. The only important point is that one should be explicit about one’s choice. In other words, if we assume that a genuine concretization is a refinement with an improvement claim, to be distinguished from a mere refinement, one confirmation language may be more refined than another, but this need not be a concretization. In this way, having an inductive character, whether in a Bayesian or in a Carnapian way, may be seen as a first explication of informal, inductive confirmation languages. Moreover, going “double inductive,” as Hintikka proposes, or including analogy considerations (for a survey, see Kuipers 1988) is a matter of further explication of more refined, inductive confirmation languages. In the next diagram, the arrows are dashed to indicate the special, non-objective, nature of the I&C-like relations.3 Popperian

Bayesian

corroboration

confirmation

Carnapian

Hintikkian

confirmation

confirmation

Although the role of confirmation and falsification is strongly relativized in ICR, it will also become clear in the next sections that the notions of confirmation and falsification remain of crucial importance

3

If we would take the practice of subjective probability assignments by scientists as our target, it may well be argued that the arrows in the diagram truly represent cases of (successive) concretization of reconstructing actually occurring confirmation languages.

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for testing three types of hypotheses, viz. general test implications of theories, comparative success hypotheses, and truth approximation hypotheses.

2. Empirical Progress We now get to the elaboration of one of the main I&C aspects of the truth approximation theory which has already been mentioned: empirical progress, including that among falsified theories, is the concretization of the idealized point of departure that a theory has persistently been confirmed by all experiments. (III) The evaluation of theories by the HD-method, studied in Part II of ICR, concerns, in the first place, the separate evaluation in terms of general successes and individual counterexamples, but immediately suggests a comparative sequel, leading to the establishment of empirical progress by applying the Rule of Success. The resulting evaluation methodology can be seen as an explication of the instrumentalist methodology, according to which counterexamples play a crucial role, but not the dramatic one that is associated with the falsificationist methodology. This explains and even justifies non-falsificationist, i.e., dogmatic, behavior of scientists. However, in contrast to pseudoscientists, scientists nevertheless aim at the improvement of their theories, which is frequently possible within a set of dogmas. Separate HD-evaluation of a theory, amounts to successive application of the HD-method to that theory, that is, deriving test implications and testing them, whether or not already falsified. This results in an evaluation report, counting on the positive side individual or general successes and on the negative side individual or general problems, that is counterexamples or “falsifying general facts.” Positive and negative individual outcomes result from deriving, first, general test implications from the theory and, second, individual test implications from the general ones and, third and finally, testing these. Both general cases result from inductive generalization of individual results.

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Important qualifications of the idealized picture of HD-evaluation arise from taking various complications into account (ICR, 5.2.3., which could also have been dealt with in Ch. 2), that is, factors that may lead to the questioning of a result as a genuine success or problem of the theory. The main points for questioning are the following: 1) hidden auxiliary hypotheses, 2) the logico-mathematical derivation of the general test implication, 3) observation theories, providing the link between higher and lower (e.g. scale reading) levels of observation, 4) initial conditions, 5) statistical and approximative decision criteria, 6) inductive generalizations. Not all of them typically qualify as concretization, but I will not go into this further. An immediate consequence of the comparative perspective is the arising of neutral results from the fact that a test implication of a certain theory may be merely compatible with another theory, provided the latter is incomplete in the logical sense. This generates a 3x3 comparative evaluation matrix for locating (individual or general) results. Comparative evaluation matrix of Y relative to X Y

X negative

neutral

positive

negative

B4: 0

B2: −

B1: −

neutral

B8: +

B5: 0

B3: −

positive

B9: +

B7: +

B6: 0

However, neutral results remain hidden in the strict definition of “being more successful,” of which I prefer to give here the asymmetric version in terms of general successes and individual problems (counterexamples). Theory Y is (at time t) at least as successful as theory X iff (at t) − all individual problems of Y are (individual) problems of X − all general successes of X are (general) successes of Y. Theory Y is (at time t) more successful than theory X iff (at t) − in addition: Y has extra general successes or X has extra individual problems.

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This so-called “basic definition” is a strict definition in the sense that no exceptions and, hence, no relative weights of problems and successes are taken into account. In ICR the latter is only done, implicitly, in Ch. 12 on quantitative truth approximation. For the rest, ICR is based on this strict definition, or a refined version of it, but refined in another than quantitative sense. In my (Kuipers 2001), Structures in Science, henceforth SiS, I have introduced a qualitative weakening of “more successful” to “almost more successful,” in particular by taking “Kuhn-losses” into account, that is, a success of an old theory that is neutral for the new one, such as the number of planets that could be explained by certain former cosmological theories. They can be compensated by “sufficient” new successes. However, both in ICR and SiS, I also explain that the strict definition should not be seen as a limitation, for in cases of “divided success,” where both theories have extra successes relative to each other, the proper behavior differs from the one, see below, that corresponds to strict cases of being more successful. In divided cases, we have to search for a third theory, maybe a genuine synthesis, that retains the successes of both and has at most the shared problems of both, and hence is more successful than both in the strict sense. Turning to the strict sense, the rest of the instrumentalist methodological story is the following. Suppose that Y is, at t, more successful than X. This suggests the Comparative Success Hypothesis: (CSH) Y (is and) remains more successful than X (CSH) has of course to be further tested, now by a comparative application of the HD-method. At last we may come to the conclusion that it has been sufficiently tested, with only positive results, which provides the condition for applying the Rule of Success: (RS) If (CSH) has been sufficiently confirmed to be accepted as true, i.e. if Y has so far proven to be more successful than X, then eliminate X, in favor of Y, for the time being.4

4

Note that (CSH) itself is without reserve, whereas “for the time being” represents a typical fallibilist element in (RS).

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Application of the rule of success amounts to the recognition of a case of genuine empirical progress, also in cases where the better theory is known to be false, a possibility that is attractive from the instrumentalist point of view. Note that if X is a tautology, the application of (RS) must be such that Y has not yet been falsified. In this case, switching to Y amounts to assuming, for the time being, that Y is (observationally) true, that is, observational induction of Y. Hence, the latter is an extreme special case of applying the Rule of Success. observational induction:

applying the Rule of Success:

as

asserting that empirical progress

(observationally) true on

has been made by replacing one

the basis of persistent

theory by another on the basis of

confirmation

being persistently more successful

accepting

a

theory

I will speak of basic empirical progress, since it is grounded in the basic definition of “more successful.” By denouncing falsified theories, the falsificationist methodology is inefficient in making empirical progress. However, by aiming at empirical progress, even within the boundaries of the dogmatic core of a research program, the instrumentalist methodology strongly deviates from pseudoscientific habits. So far, I implicitly assumed that our theories were dealing with a fixed common domain of phenomena and using a fixed common observational vocabulary. However, in the course of research, both may be adapted in order to obtain better results in some defensible sense. Although the ideal is to enlarge the domain of the theory while keeping its successes, without new problems, this is difficult to achieve. On the one hand, ad hoc changes of the domain are out of order when they merely want to avoid counterexamples. On the other hand, domain changes that merely lead to throwing out Kuhn-losses (see above) may be defensible. Similarly, reducing the observational vocabulary will only be defensible if it leads at most to setting Kuhnlosses aside. Again, the ideal is to enlarge the observational vocabulary such that the theory becomes more successful.

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It is plausible to assume that the strict definition of “more successful” can be extended to the case of an enlarged domain and/or observational vocabulary. However, in practice, simple enlargement of one or both, leading to an at least as successful theory, will be exceptional; the search for a combination of a suitable domain and observational vocabulary is a kind of interactive process, where the results play a steering role. Starting from the idealized picture of empirical progress given a fixed domain and observational vocabulary, we obtain in this way a more realistic, concretized, picture of empirical progress. There is one other type of concretization possible of empirical progress. It is directly related to empirical I&C. Despite the suggestion, perhaps, empirical progress cannot yet deal with empirical I&C. The reason is that in case of empirical I&C improvement of a theory is not obtained by removing counterexamples or even turning them into successes, but by replacing mistaken models by less problematic ones. Roughly speaking, a new theory may have (observational) models that are closer to, or more similar to, the model description of the counterexample than the old one. The best way of dealing with this type of concretization of empirical progress, however, is in the context of refined truth approximation to which I will turn in Section 4. However, it is important to keep in mind that, whereas refined truth approximation is a concretization of basic truth approximation, refined empirical progress is a concretization of basic empirical progress, a concretization that is already meaningful from the instrumentalist (methodological and epistemological) point of view.

3. Basic Truth Approximation Empirical progress and truth approximation are strongly related, although not in an I&C way. According to the success intuition of (many) scientists, my first leading condition of adequacy, empirical progress indicates, if not guarantees, truth approximation. It is perfectly possible to explicate this intuition in a first round on the basis of the fourth conclusion of ICR:

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(IV) Empirical progress cannot be seen only as an aim in itself; it can also be seen as a means to truth approximation, as argued from Ch. 7 onwards. Here, “the truth” is conceived as the nomic truth, provided by the so-called Nomic Postulate, i.e., the strongest true theory about what is nomically possible for a given domain of reality assuming a certain vocabulary. Using the structuralist approach to theories, the Nomic Postulate assures the existence of a subset of nomic possibilities within the set of conceptual possibilities generated by a vocabulary. Within this framework, a prima facie plausible definition of the idea that one theory is more truthlike than another can be given. A claim of the latter type can be seen as a hypothesis, the truth approximation hypothesis, which can be tested due to its prediction of empirical progress, which makes empirical progress functional for truth approximation. [This explicates the success intuition mentioned in the Introduction.] The indicated assumptions, namely: a given domain of reality and vocabulary, and the Nomic Postulate, enable the definition of “basic truthlikeness” and the clarification of its relation with basic empirical progress. For convenience, I will skip ‘basic’ all the time in the rest of this section, but it is always assumed until the next section. In terms of the set of structures generated by a vocabulary, also called conceptual possibilities or potential models, and assuming the mentioned Nomic Postulate, “the truth” T amounts to that subset that characterizes precisely all nomic possibilities belonging to the domain. Moreover, a theory amounts to a subset with the weak claim that it covers T, and the strong claim that it is identical to T. A model of theory X, i.e. a member of X, is a correct model when it is also a member of T, and it is a mistaken model when it is not. This enables the crucial definition: Theory Y is at least as similar (close) to the truth as theory X iff − all mistaken models of Y are (mistaken) models of X − all correct models of X are (correct) models of Y. Theory Y is more similar (closer) to the truth than theory X iff − in addition: Y has extra correct models or X has extra mistaken ones.

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Now it is possible to prove the Success Theorem, according to which, assuming correct data and some provisos, “more observational truthlikeness” entails “empirical progress.” More surprisingly perhaps is that the converse is also true, that is, “genuine empirical progress,” amounting to the assumption that (CSH) (the comparative success hypothesis) is true, entails, according to the Forward Theorem, “more observational truthlikeness.” This theorem is weaker than one might think at first sight, for the condition “(CSH) is true” is very strong indeed. The theorems together form the basic explication of the success intuition. To be sure, these results require a number of idealizations. To begin with, there are again the assumptions of a fixed domain and a fixed observational vocabulary. This may be concretized by taking vocabulary and domain changes into account. Here is still a lot of interesting work to do. Second, in addition to the Nomic Postulate, it is assumed that the postulated set of nomic possibilities can be characterized by the available vocabulary, which need not be the case. Besides looking in this case for more refined vocabularies, the theory can also be concretized by redefining the target of theorizing as (one of) the smallest characterizable superset(s) of the set of nomic possibilities, that is, (one of) the strongest true theories that can be formulated with the vocabulary. Third, the correct data assumption claims in the first place that the descriptions of experimentally realized possibilities are correct, at least in as far as the assessment as example or counterexample of the relevant theories is concerned. But the assumption also claims that the established observational laws on the basis of these realized possibilities are true. As a matter of fact, these realized possibilities will have partly been the result of testing hypothetical laws, and the latter apparently have “sufficiently been confirmed” in order to assume that they are true. They amount to what Popper calls “reproducible effects,” but they require, pace Popper, inductive jumps. Concretization of the main results by taking mistakes in descriptions and inductive generalizations into account does not seem to be easy. The remaining two idealizations to be mentioned allow concretization. The first removable idealization, all non-models, and hence all

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counterexamples, are equally bad, brings us to the refined truth approximation, presented in the next section. The second is the neglect of a distinction between observational and theoretical terms, which amounts in fact to assuming that all (non-logical) terms are observational, as I did above. The concretization of that assumption, that is, introducing the distinction, brings us to the stratified approach, but before that I will deal with the ICR-conclusions regarding the explication of some more intuitions of scientists and philosophers. (V) The idea of more truthlikeness and the aim of truth approximation have been shown, in Ch. 8, to be in accordance with a main point of scientific common sense about theory improvement, viz., more true consequences and more correct models. Moreover, they suggest intralevel explications of some persisting intuitions among philosophers, viz., the correspondence theory of truth and intuitions governing dialectical reasoning. As suggested, the first intuition, according to which truth approximation is a two-sided affair amounting to achieving “more true consequences and more correct models,” not only belongs to scientific common sense but can be proven to be equivalent to the basic definition. More precisely, we may replace the basic definition by: Theory Y is at least as similar (close) to the truth as theory X iff − all true consequences of X are (true) consequences of Y − all correct models of X are (correct) models of Y. Theory Y is more similar (closer) to the truth than theory X iff − in addition: Y has extra true consequences or extra correct models. However, another variant of the two-sided intuition, viz. “more true consequences and fewer false consequences,” also belongs to scientific common sense. The latter was Popper’s plausible but unhappy point of departure. In Ch. 8 of ICR, Popper’s bad luck is further explained. Moreover, it is shown that some other variants of the “correct intuition” are possible, among which a nuance of Popper’s point of departure by replacing “merely false” consequences by consequences

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that are “strongly false” in some unusual but well-definable sense. I do not think, however, that this can be reconstrued as a concretization. Regarding the other two, more typical philosopher’s intuitions, I will confine myself to the following claims. The main correspondence (theory of truth) intuitions, “true (false)” amounts to “(not) corresponding to the facts” and “closer to the truth” to “corresponds better to the facts,” can get a precise intralevel explication, as opposed to the usual, but problematic attempts at an interlevel explication. The dialectical intuitions, in particular those behind the notions of “dialectical negation,” “double negation” and “thesis-antithesissynthesis,” can also get precise explications in terms of truth approximation, even in various logical, methodological and ontological ways. In this conclusion, we came across three (sets of) intuitions that were not presented as conditions of adequacy. However, their unintended successful explication in terms of the basic definition, suggests to impose the keeping of these explications, perhaps in some adapted form, as conditions of adequacy for concretizations of the basic definition. Hence, the truth approximation explication of the three intuitions raises the question whether the concretizations of truth approximation to come, those of stratification and refinement, enable concretizations of the relevant intuitions. In ICR I have claimed in the relevant chapters this to be always the case and in a number of cases I have elaborated this. Refined truth approximation even enables (ICR, p. 270) the explication of the idea of “dialectical correspondence” (Nowakowa 1994), which is not yet possible in terms of basic truth approximation. In the meantime, I have been working on a fourth additional intuition, viz. the aesthetic intuition, mainly of scientists, according to which aesthetic criteria may not only be functional for obtaining empirical progress but even for truth approximation. McAllister (1996) inspired me with his notion of “aesthetic induction” to find a naturalized-cum-formal underpinning of this intuition (Kuipers 2002), contrary to my pre-1996 conviction that such a story could not be told and that scientists must make some basic mistake in their “aesthetic intuition.” To be sure, my explication is rather disenchanting, for it explains aesthetic appreciation of certain features of theories as a kind

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of recurrent exposure effect, well known in experimental psychology. According to this explication, there is no intrinsic relation between beauty and truth, but the psychophysiological mechanism generating aesthetic appreciation produces a connection, mediated by empirical success. Whether the explication of the aesthetic intuition can be concretized in the direction of refinement is a matter of further research, for it may now well be seen as an extra condition of adequacy for any concretization of the basic definition. However, although the aesthetic intuition may already come into play without a distinction between observational and theoretical terms, aesthetic criteria typically are put into play when this distinction is made since the intuition deals with non-empirical features of theories. For this reason, in the article referred to, the explication of the aesthetic intuition is already presented from the stratified perspective and hence does not need further concretization along the lines of the stratification concretization of truth approximation to which I now turn. (VI) The (shifting) distinction between observational and theoretical terms not only naturally leads, together with the Nomic Postulate, in Ch. 9, to the distinction between theoretical and observational truthlikeness, but also to definitions of reference, referential claims of theories, and referential truthlikeness. Whereas observational truthlikeness implies empirical progress, theoretical truthlikeness only implies observational truthlikeness as far as true consequences are concerned. This leads to a further relativization of the role of counterexamples. Whereas the loss of a true observational consequence is a genuine drawback of a new theory, an extra counterexample of a new theory may well be an accidental (observational) merit of the old one. Moreover, since there are no deductive relations between referential truthlikeness and the other comparative notions, other kinds of (theoretical and experimental) arguments may also have to be taken into account for the assessment of referential claims. From this conclusion, it is clear that the theorems connecting truthlikeness on both levels are not as straightforward as those

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connecting observational truthlikeness and empirical progress. In contrast to the Success Theorem, the Projection Theorem, conditionally inferring observational from theoretical truthlikeness, cannot exclude the possibility of “extra lucky hits” of a theory that is not as close to the theoretical truth as another. Similarly, in contrast to the Forward Theorem, the Upward Theorem, conditionally inferring theoretical from observational truthlikeness, has to take “extra lucky hits” into account. Of course, all this has everything to do with the many-one relation between theoretical models and observational models, that is, the underdetermination of “proper theories” by merely “observational theories” and hence “observational data.” This makes stratification a genuine concretization in the sense that purely “observational truth approximation” is an extreme special case of “theoretical truth approximation.” Moreover, in view of the conditional nature of the Projection and the Upward Theorem, it leads to a genuine concretization of the success intuition: the connection between “more truthlikeness” and “more successfulness” has to be relativized to some extent. In the diagram, normal arrows indicate conceptual concretization and the thick arrow deductive consequence; the dashed arrow also indicates deductive consequence, provided the basic empirical progress is genuine. observational induction

basic empirical

Forward Theorem

progress

more basic

more stratified

truthlikeness

truthlikeness

Success Theorem

Ch. 9 of ICR introduces a plausible definition of reference of theoretical terms in terms of the question whether or not a term plays a role in shaping the relevant set of nomic possibilities. It leads to plausible explications of “the referential truth,” of “the referential claim” of a theory and of the claim that one theory is closer to the referential truth than another. However, since there are no deductive relations between referential truthlikeness and the other comparative

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notions, other kinds of (theoretical and experimental) arguments usually have to be taken into account for the assessment of referential claims. This makes it also difficult to analyze the ICR theory of reference in terms of I&C.

4. Refined Truth Approximation So far, all mistaken models are assumed to be equally bad, with the consequence that one of the best arguments for taking falsified theories into account, viz. empirical I&C, cannot be dealt with, for it is essentially based on the idea that mistaken models can be improved by replacing them with models that are also mistaken, but less so. This brings us to the core of refined truth approximation, which not only captures empirical I&C, a recurring phenomenon in the empirical sciences highlighted so convincingly and persistently by Leszek Nowak, but also explicates the corresponding intuition according to which empirical I&C is functional for truth approximation. (VII) Although the analysis sketched above may come close to scientific common sense, it does not yet mean that the crucial notions are directly applicable to real-life scientific examples. However, in Ch. 10 it is shown to be perfectly possible to take into account that the improvement of theories is usually not a matter of replacing mistaken models by correct ones, but of replacing mistaken models by less mistaken ones, e.g., when using the method of idealization and concretization, as for instance Van der Waals did in two concretization steps. [Hence, the corresponding refined definitions of truthlikeness and empirical progress enable the explication of the I&C intuition, mentioned in the Introduction, as a special type of case.] This second major concretization, which is called refinement, and to be distinguished from stratification, typically can occur in the form of empirical I&C, that is, truth approximation by empirical I&C can be explicated in terms of a special kind of refinement. To be sure, the two major concretizations can be combined into refined stratified truthlikeness. The crucial idea of the refined version is to introduce the

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notion of “structurelikeness,” that is, one structure (potential model) may be at least as similar to a target structure as another. E.g. starting from an idealized structure, a concretized version of it may be more similar to a target structure, which is still more concretized. This will be called “I&C structurelikeness.” The refined definition of “Y is at least as truthlike as X” can be paraphrased by the clauses: − all relevant models of X are improved by (relevant) models of Y − extra mistaken models of Y are not redundant with plausible explications of “relevant model,” “one model improving another” and being “non-redundant,” all in terms of structurelikeness. Moreover, the corresponding refined definition of “Y is at least as successful as X” can be paraphrased, assuming suitable explications of the relevant terms, by: − all relevant successes of X are successes of Y − all counterexamples of Y are counterexamples of X accommodated by Y. This definition enables the refined explication, announced in Section 2, of the instrumentalist methodology in terms of refined definitions of the rule of success and of empirical progress, according which mistaken models are not so much removed, but replaced by less problematic ones. Moreover, by confronting the two definitions, refined versions of the Success Theorem and the Forward Theorem can be proved, together forming a refined explication of the success intuition. From this perspective, basic truthlikeness amounts to the extreme special case of refined truthlikeness, viz. when structurelikeness is trivial in the sense that the structures have to be identical for that purpose. In other words, refined truthlikeness is a genuine concretization of basic truthlikeness. Sjoerd Zwart (2001) argues that there is an important distinction between so-called content theories of truth approximation, such as my basic theory, and likeness theories, such as my refined theory. In his view, they are really competing. However, the concretization relation between the two makes clear, at least in my

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opinion, that these two types of theories should not be seen as competitors. Apart from these divergent opinions, Zwart’s analysis of a couple of content and likeness theories is extremely enriching. For example, Zwart is certainly right with the claim that although all kinds of truthlikeness discussed so far leave room for false theories being closer to the truth than other false ones, they do not leave room for a false theory being closer to the truth than a true one. He designs such a theory that combines aspects of a specific content theory and a specific likeness theory. My impression is that this synthesis can be seen as a concretization of both. Maybe, it is even possible to reconstrue it as a further concretization of refined truth approximation. Assuming a plausible I&C version of structurelikeness, I&C structurelikeness, it is not difficult to explicate now the second leading intuition, the I&C intuition, as was done for the first time in Kuipers (1992), according to which empirical I&C is functional for truth approximation. As mentioned in the seventh conclusion, it enables the reconstruction of a famous I&C case as an example of (potential, see below) truth approximation, viz. the Law of Van der Waals as a double (two-stage) concretization of the ideal gas law.5 Hence, refined truthlikeness leaves room for real-life examples of truth approximation. As a matter of fact the other two elaborated examples in ICR are based on I&C versions of refined truth approximation. (VIII) Ch. 11 demonstrates that the succession of the (old) quantum theories of the atom of Rutherford, Bohr and Sommerfeld provides an example of potential truth approximation, more specifically, by specialization followed by concretization. A succession of theories about the capital structure of firms, the theory of Kraus and Litzenberger, followed by that of Modigliani and Miller, illustrates a different kind of truth approximation, but one which is, formally speaking, again by double concretization. 5

See Kuipers (1985) for a detailed reconstruction of this paradigm example of concretization, of which it is shown in addition that the kinetic argument for the ideal gas law has also to be concretized to derive the Law of Van der Waals.

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Note that I speak in this conclusion of examples of “potential” truth approximation. The point is, of course, that we never know whether we are in possession of the final truth, so our target theory may at most be assumed to possibly be the truth. However, in most cases, such as the ones mentioned, this concerns in fact counterfactual conditions, for we know that the postulated target theories are false. Hence, the point of a potential truth approximation claim is the claim that if the postulated target theory were the relevant truth, another theory would be closer to that than a third theory. Now I am able to draw the diagram with the main I&C aspects of the (qualitative, structuralist) theory of truth approximation in combination with confirmation and empirical progress. conceptual I&C (tail→head)

observational induction

(tail) special case (head) success intuition (empirical) I&C intuition

basic empirical

more basic

more stratified

progress

truthlikeness

truthlikeness

refined empirical

more refined

more stratified

progress

truthlikeness

refined truthlikeness

I&C-type of

I&C-type of

I&C-type of more

empirical progress

more truthlikeness

stratified truthlikeness

Refined truth approximation does not only exclude that a false theory is closer to the truth than a true one, but it also does not account for the fact that successes may compensate failures and that successes and failures may have different weights. One plausible way to obtain such concretizations is by turning to a quantitative theory of truth approximation, for example, the one developed by Ilkka Niiniluoto (1987), or some alternative of it.

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(IX) Finally, speaking of distance from the truth and truth approximation easily suggests quantitative explications, as presented in Ch. 12. Although this is formally possible, assuming that there is some kind of distance function between the conceptual possibilities, it only seems to make sense in contexts where such a distance function is not rather arbitrary but plausible. As suggested, this type of concretization, with basic, stratified and refined versions, seems only plausible and desirable when there is some meaningful distance function between the structures for the domain. In this case, assuming, in addition, plausible probability assignments, even the notion of “estimated truthlikeness” makes sense and may govern the choice of theories. This notion essentially enables then a truth approximation laden quantitative idealization and concretization of empirical progress. However, in areas where only artificial distances and/or probabilities can be defined, this approach does not seem to make much sense, whereas a qualitative approach may still be very appropriate. In other words, in these areas, going quantitative seems to be merely a kind of refinement, but no genuine concretization. This concludes the unavoidably incomplete survey of I&C features of the theory of truth approximation and its relation to empirical progress and confirmation.

5. Epistemological Conclusions Recall that Ch. 1 of ICR introduces the main epistemological positions, instrumentalism, constructive empiricism, referential realism, constructive (theory) realism and essentialist (theory) realism, whereas Ch. 13 provides a further articulation of constructive realism. In the meantime the following conclusion was provisionally drawn at the end of Part III and was further strengthened in Part IV: (X) The instrumentalist methodology provides good reasons for the transition of epistemological positions from instrumentalism to constructive realism. Here, the intermediate step from

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constructive empiricism to referential realism turned out to be the hardest one, whereas the finally possible step from constructive to essentialist realism had to be rejected. As suggested, in the rest of Ch. 13 the main lines have been drawn of the resulting favorite epistemological position of constructive realism. It is a conceptually relative, non-essentialist, nomic truth approximation version of theory realism, accounting for objective truths. In all cases, “the truth” is not only determined by the chosen domain but also by the chosen vocabulary, which is constructed by scientists guided by previous findings and pragmatic concerns. Hence, there is no ideal languange, grasping essences, involved and hence no “myth of the given” presupposed. The truths can be approached by an intersubjective method, viz. the evaluation methodology for theories, in which the role of (truth-)testing of hypotheses primarily concerns testing test implications of theories as well as testing comparative success and truth approximation hypotheses between theories. The term ‘constructive realism’ has earlier been used by Giere (1985), and my conception of it is rather similar, except that I include in it, of course, truth approximation, whereas Giere still focuses on the true/false dichotomy, but he fully recognizes the nomic aim of theorizing. With respect to truth approximation, my position is rather similar to that of Niiniluoto (1987, see in particular Section 4.3.). The main difference between my and his position is, besides my primarily qualitative versus his straightforward quantitative approach, my emphasis on the nomic aim of theorizing. In sum, constructive realism reflects the combination of the deviating strengths of Giere and Niiniluoto by emphasizing nomic truth approximation as opposed to the actual truth-value of theories. The final question is of course whether the epistemological positions are related in an I&C way. Regarding the relation between constructive empiricism and constructive realism, this has at least some plausibility in the sense that the first, at least the nomic version of it, follows as a special case when all non-logical terms are observational. Regarding the other comparisons the situation is less

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clear. However, as concerns strength a linear ordering seems certainly possible. Hence, the following diagram emerges6: instrumentalism

constructive empiricism

referential realism

concretization

constructive realism

essentialistic realism

entailment

University of Groningen Faculty of Philosophy Oude Boteringestraat 52 9712 GL Groningen The Netherlands [email protected]

REFERENCES Giere, R. (1985). Constructive Realism. In: P. Churchland and C. Clifford (eds.), Images of Science, pp. 75-98. Chicago: The University of Chicago Press. Kuipers, T. (1985). The Paradigm of Concretization: The Law of Van der Waals. In: J. BrzeziĔski. Consciousness: Methodological and Psychological Approaches (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 8), pp. 185-199. Amsterdam: Rodopi. Kuipers, T. (1988). Inductive Analogy by Similarity and Proximity. In: D. Helman (ed.), Analogical reasoning, pp. 299-313. Dordrecht: Kluwer.

6

[Note added in proof:] The currently much debated position, called “structural realism,” according to which “(formal) structure” rather than “reference” forms the possibly realist aspect of theories, would occupy in the diagram a similar position as “referential realism.”

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Kuipers, T. (1992). Truth Approximation by Concretization. In: J. BrzeziĔski and L. Nowak (eds.), Idealization III: Approximation and Truth (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 25), pp. 159-179. Amsterdam: Rodopi. Kuipers, T. (2000/ICR). From Instrumentalism to Constructive Realism. On Some Relations Between Confirmation, Empirical Progress, and Truth Approximation. Synthese Library, vol. 287. Dordrecht: Kluwer Academic Publishers. Kuipers, T. (2001/SiS). Structures in Science. Heuristic Patterns Based on Cognitive Structures. An Advanced Textbook in Neo-Classical Philosophy of Science. Synthese Library, vol. 301. Dordrecht: Kluwer Academic Publishers. Kuipers, T. (2002). Beauty, a Road to The Truth? Synthese 131 (3): 291-328. McAllister, J. (1996). Beauty and Revolution in Science. Ithaca, NY: Cornell University Press. Niiniluoto, I. (1987). Truthlikeness. Synthese Library, vol. 185. Dordrecht: D. Reidel Publishing Company. Nowakowa, I. (1994). The Dynamics of Idealizations. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 34. Amsterdam: Rodopi. Zwart, S.D. (1998). Approach to The Truth. Verisimilitude and Truthlikeness. Dissertation Groningen, ILLC-Dissertation-Series-1998-02. Zwart, S.D. (2001). Refined Verisimilitude. Synthese Library, vol. 307. Dordrecht: Kluwer Academic Publishers.

Ilkka Niiniluoto IDEALIZATION, COUNTERFACTUALS, AND TRUTHLIKENESS

1. Introduction Professor Leszek Nowak’s work on idealization belongs to the most significant contributions to the philosophy of science within the twentieth century. Starting his studies in the late 1960s, he initially applied his treatment of idealization to Marx’s theory of value, but also claimed that the same method was used by Galileo in physics (see Nowak 1980). However, the mainstream analytic philosophers of science (Carl G. Hempel, Ernest Nagel), as well as their critics (Thomas Kuhn, Paul Feyerabend), failed to pay sufficient attention to issues of idealization. Together with his collaborators in the PoznaĔ School, Nowak gave a comprehensive account of the method of idealization and concretization. Wáadysáaw Krajewski (1977) formulated the approach in a general and easily readable form. The success of the program can be seen in the remarkable series of further studies it has stimulated: in the 1990s, the book series PoznaĔ Studies published nine volumes of essays on idealization. The tenth volume, The Richness of Idealization (2000), is an impressive collection of papers by Izabella Nowakowa and Leszek Nowak.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 103-122. Amsterdam/New York, NY: Rodopi, 2007.

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The work initiated by the PoznaĔ School has convincingly shown that idealization and concretization are widely used methods in the natural and social sciences — even though some disagreement may still remain about some details of historical illustrations (see, e.g., Hanzel 1999). However, there are debates about the best ways of reconstructing these methods in logical and philosophical terms. Nowak’s original formulation is primarily syntactical and extensional, while his ontological views are influenced by Marxist essentialism. Later he has elaborated his metaphysical ideas about the existence of “possibilia.” Nowak and Nowakowa have also suggested that the Hegelian notion of truth is a useful tool in analyzing the status of idealizational laws. Alternative reconstructive approaches include the structuralist view of theories (see Kuokkanen 1994) and the structuralist account of truthapproximation (see Kuipers 2000). My own proposal, given in Niiniluoto (1986, 1990, 1994), is to treat idealizational statements as counterfactual conditionals which have a truth-value within a Lewis-type possible worlds semantics. This also allows us to apply the notion of truthlikeness (Niiniluoto 1987, 1998) to idealized theories, and to study the conditions under which concretizations make progress towards the truth. In this way, the method of idealization and concretization can be interpreted in a manner which is in harmony with critical scientific realism (see Niiniluoto 1984, 1999a, 2002). In this paper, I reconsider some key issues in the realist interpretation of idealization in the light of recent publications by Nowak and Nowakowa. In particular, I shall consider the logical form of idealizational laws before and after concretization (Sections 2 and 3), the concepts of possibility and truth (Section 4), and the notion of truthlikeness (Section 5).

2. Idealization and Concretization in the PoznaĔ Way To summarize the PoznaĔ approach to idealization, consider an equation that expresses, for all objects x of a certain kind G(x), the functional dependence of a quantity F(x) on a finite number of other

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quantities q1(x), . . . , qn(x). Let us assume, for simplicity, that n = 1, so that the initial factual law has the form (T) (x) [G(x) → F(x) = f0(q(x))] where (x) is the universal quantifier and the arrow → is material implication. The assumption that laws are expressed by using material implication → is characteristic to Nowak (1980) and Krajewski (1977). According to Nowak’s terminology, q is the principal factor for quantity F, and T expresses the essence of F. However, it is known in advance, or discovered later, that T is false about empirical reality, since it excludes the influence of some other disturbing factors that are secondary relative to the principal one, q. Assuming that there are two such additional factors w1 and w2, the factual law T is then transformed into an idealizational law, which is conditional on the counterfactual assumption that the factors w1(x) and w2(x) have the extreme value zero: (T0) (x) [G(x) & w1(x) = 0 & w2(x) = 0 → F(x) = f0(q(x))] In the next phase, the idealizing assumptions are removed one by one by concretization (factualization), i.e., by adding the factors w1(x) and w2(x) to the equation and by modifying the function f0: (T1) (x)[G(x) & w1(x) ≠ 0 & w2(x) = 0 → F(x) = f1(q(x),w1(x))] (T2) (x)[G(x) & w1(x) ≠ 0 & w2(x) ≠ 0 → F(x) = f2(q(x),w1(x),w2(x))] Here the hierarchical ordering q q, w1 q, w1 , w2 is the scientist’s image of the essential structure for F, and the sequence of functions {f0, f1, f2} is the scientist’s image of the nomological structure for F. Assuming that → is material implication, we immediately see that T logically entails T0. On the other hand, there are no logical relations between T0, T1 and T2. If the factors w1 and w2 really do influence F, then both T1 and T2 are logically incompatible with T. According to Nowakowa, the concept of dialectical correspondence can be defined as the relative product of abstraction and concreti-

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zation: T0 is more abstract than T as it has more idealizing assumptions than T, and T0 is then concretized to T1 and T2 with respect to these idealizing assumptions (see Nowakowa and Nowak 2000, pp. 186-187). Even though Nowakowa defines dialectical correspondence as a relation between T and T0, it might be more natural to think about it as a relation between the original T and the concretized T2 (cf. Krajewski 1977, p. 48). For example, BoyleMariotte’s law (1) (x) [p(x)V(x) = RT(x)] can be abstracted to (2) (x) [a = 0 & b = 0 → p(x)V(x) = RT(x)] but it dialectically corresponds to van der Waals’ law (3) (x) (p(x) + a/V(x)2)(V(x) — b) = RT(x) When Nowakowa emphasizes anti-cumulativism and the logical incompatibility of the later system with the earlier (Nowakowa 1994, pp. 36, 115), she is in fact referring to the relations between T and T2. As we have seen, the step from T to T0 is, logically speaking, not very exciting, since it is a relation of entailment. Even though it may happen that T is false and T0 is true, T0 is still weak in the sense that it has the same consequent as T and does not specify the influence of factors w1 and w2 on F. Nowakowa also argues that the observational consequences of T2 are “more accurate” than those implied by T (p. 33). This may be the case if the concretization is successful, for example, if T is false and T2 is true. But without some extra assumption, concretization may lead us to very bad theories which do not improve the earlier ones. To take a simple example, suppose that the original theory T claims that the mass m(x) of an object x is a constant m0(x): (4) (x) [m(x) = m0(x)] and the true concretized theory expresses the dependence of m(x) on the velocity v(x) of x and on the constant velocity c of light: (5) (x) [m(x) = m0(x)/[1 — v(x)2/c2 ]1/2] However, if our hypothesis is, instead of (5), (6) (x) [m(x) = m0 (x)/ [1 + v(x)2/c 2 ]1/2]

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then we see that the curve defined by (6) is (for all possible values of v(x) > 0) farther from the true curve (5) than the line defined by (4). This is the case in spite of the fact that (6) is one of the possible concretizations of (4). Equations (5) and (6) illustrate the standard idea in science that the old theory should be obtained as a special case of the new theory, when some factors have a limiting value zero: if c grows without limit, or 1/c approaches the value zero, then both (5) and (6) reduce to (4). Similarly, if a = 0 and b = 0 in van der Waals’ law (3), it reduces to Boyle’s law (1). This is called Bohr’s Correspondence Principle (CP) (see Krajewski 1977). In the case of the concretizations T1 and T2, this means that f1(q(x), z) should approach f0(q(x)) as its limit, when z approaches 0, and f2(q(x), w1(x), z) should approach f1(q(x), w1(x)), when z approaches 0. Let us call concretization strong, if it satisfies CP, and weak otherwise. The example given by (5) and (6) shows that even strong concretization does not guarantee, without additional success conditions, that the new law is an improvement of the earlier one. A well-known difficulty for the PoznaĔ approach is that all idealizational statements are true in the classical sense (see Nowak 1980, p. 134). This arises from the assumption that these statements are formulated by using the material implication →. By classical logic, p → r (read: if it is the case that p then it is the case that r) is true if and only if p is false or r is true. Hence, idealizational laws of the form T0 and T1 are true, as their antecedents include false assumptions that are not satisfied by any actual objects. This seems to imply that the whole account is unable to make sense of idealization in realist terms: if B is the false condition that no other forces besides gravitation influence a freely falling body then both conditionals (7) B → s = gt2/2 B → s ≠ gt2/2 are true (Nowak 1994, p. 319; Nowakowa and Nowak 2000, p. 179). Nowak’s way out of this problem is to revise or reject the classical concept of truth; this idea is evaluated in the next sections. Another possible solution is to take seriously the point that the conditions in

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idealizational laws are counterfactual. This suggestion, made in Niiniluoto (1986, 1990), is discussed and defended in the next sections.

3. Idealizational Laws as Counterfactual Conditionals Subjunctive conditionals differ from indicative conditionals in their typical reading: if it were the case that p, then it would be the case that r. A counterfactual conditional p Ÿ r is a subjunctive conditional which presupposes that the antecedent p is false. Unlike indicative conditionals involving material implication →, this conditional need not be true, even though its antecedent p is false (see Nute 1984). Therefore, we may hope that a semantical analysis of counterfactuals could show that only the first of the conditionals (7) is true. (An antirealist alternative, suggested by Gärdenfors (1979), would be to define assertability conditions for counterfactual conditionals.) According to David Lewis (1973), a counterfactual conditional p Ÿ r is true in world M if and only if the p-worlds closest to M are also r-worlds. Thus, a counterfactual conditional may be true in the actual world, but this truth-value is based on (i) where the actual world is located relative to other possible worlds, and (ii) what happens in the closest possible worlds where the antecedent is true. Let us reformulate the idealizational law T0 by using the counterfactual conditional Ÿ: (C0) (x) [G(x) & w1(x) = 0 & w2(x) = 0 Ÿ F(x) = f0(q(x))] Then, instead of Nowak’s formulation of T1 where the “realistic” condition w1(x) ≠ 0 is included in the antecedent, it seems better to use the alternative (C1) (x) [G(x) & w2(x)= 0 Ÿ F(x) = f1(q(x), w1(x))] and similarly T2 can be formulated without the “realistic” conditions w1(x) ≠ 0 and w2(x) ≠ 0: (C2) (x) [Gx) Ÿ F(x) = f2(q(x), w1(x), w2(x))] (see Niiniluoto 1986, 1994). Then the law C2 is again factual like T, i.e. not relativized to explicitly stated idealizational conditions. As it

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asserts a law unconditionally, it entails Nowak’s material conditional T2. Similarly, C1 entails T1. Note that the counterfactual formulation applies to genuine cases where the idealizing assumption is never true. The situation is somewhat different with “quasi-idealizations” or “partial idealizations” where the idealizing assumption in T0 happens to be true (not counterfactual) for some members G0 of the domain defined by the predicate G (see Nowak 1980, p. 190; Kuokkanen and Tuomivaara 1992; Nowakowa and Nowak 2000, p. 161). For example, free fall sometimes happens in a void without resistance of air. In such cases, T0 expresses a subjunctive conditional which is a counterfactual conditional for the members of G-G0. Kuokkanen and Tuomivaara (1992, p. 92), argue that my C1 and C2 are no more concretizations or factualizations of T0 in the original sense of the PoznaĔ school, as the secondary factors w1 and w2 are lacking in their antecedents. I think this remark is not quite justified. First, Krajewski (1977, p. 24) uses a similar formulation (though with material implication). Secondly, C1 and C2 express the crucial idea of concretization by introducing the new factors w1 and w2 and by showing how their influence modifies the consequent of the idealizational law T0. In his reply to Diederich (1994), who also proposes the formulations C1 and C2 (without referring to Niiniluoto 1986, 1990), Nowak (1994) insists that concretization should not be understood as “an operation of deleting an idealizing condition,” but rather as “replacing it with an appropriate realistic condition” (Nowak 1994, p. 317; Nowakowa and Nowak 2000, pp. 129-130). However, he mistakenly takes Diederich to claim that concretization is the relation of entailment. Nowak has recently given two objections to my counterfactual reading of idealizational laws (see Nowakowa and Nowak 2000, pp. 118-119). His second objection is epistemological: if C2 can be directly justified, e.g. inductively, then there is no need to consider the idealizational statements, and then also concretization becomes cognitively superfluous. However, any inductive justification of my C2 would also be an inductive justification of Nowak’s weaker statement T2, so that Nowak’s own approach faces the same threat as mine. In

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fact, I am in complete agreement with Nowak that, in typical cases in science, the route to the discovery of the richer factual law T2 or C2 goes via idealization and concretization. Hence, Nowak’s epistemological objection does not drive a wedge between us. Nowak’s first objection is more important. He points out that semantically my C2 is not a factual statement in the same sense as his T2: it refers both to the empirical domain defined by the realistic condition G(x) & w1(x) ≠ 0 & w2(x) ≠ 0, but also to the idealized domains defined by G(x) & w1(x) ≠ 0 & w2(x) = 0 and G(x) & w1(x) = 0 & w2(x) = 0. Thus, C2 is a kind of “supra-factual” and “supra-idealizational” statement. I completely agree with this diagnosis. But I also think that this is just as it should be. There is an important distinction between accidental and lawlike generalizations: the former are extensional statements about the actual world (including its history, present, and future), while the latter are stronger in some sense. Some philosophers have attempted to give epistemological and methodological analyses of lawlikeness (e.g., lawlike statements are confirmable by their instances, laws are deductive consequences of scientific theories), but for most philosophers the hallmark of lawlikeness is the ability to sustain counterfactual conditionals. To make sense of this ability, the realist view of laws takes them to be intensional statements whose truth conditions refer to the actual world and to some alternative possible worlds (see Niiniluoto 1978; Fetzer 1993). One way of guaranteeing that laws entail counterfactuals is to analyze them as logically contingent but physically necessary implication statements: the law ‘All G’s are H’ is then formalized by (x) (G(x) → H(x)), where is the operator of physical necessity. This statement is true in a world M if and only if (x) (G(x) → H(x)) is true in all physically possible worlds relative to M, i.e., all G’s are H in those possible worlds where the laws prevailing in M hold (see Lewis 1973, p. 7; Niiniluoto 1978). It follows that all G’s are H also in those possible worlds which are closest to M, i.e. the physically necessary implication (x) (G(x) → H(x)) entails the counterfactual (x) (G(x) Ÿ H(x)), but not vice versa.

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In my view, quantitative laws of the form T and C2 should be understood in the strong sense that they entail counterfactuals. In Niiniluoto (1986, 1990), I suggest that the equations in such laws express all the physically possible combinations of their factors, and exclude other combinations as physically impossible. The law T does not express the dependence of F on only those values of q(x), which happen to be realized in the actual history, but also on the physically possible values of q(x). In this sense, T is indeed a kind of mixed statement which entails something about actual cases and something about counterfactual but possible cases. The same holds of C2, as Nowak in fact observes. But the same should hold of Nowak’s own factual T2 as well, if it claims to be a genuine law. A counterfactual p Ÿ r does not logically entail p & s Ÿ r for arbitrary s (see Lewis 1973, p. 31). In particular, r does not entail s Ÿ r for all s, since the actual truth of r does not guarantee the truth of r in any s-worlds. However, if r is lawlike, and thereby necessary in some sense, then this kind of entailment should hold. This has important consequences to the analysis of idealization. In the first place, it means that the original factual law T entails the idealizational law C0 (just as in the case of material implication). Secondly, the advantage of the counterfactual formulation is that C2 entails C1, and C1 entails C0, by the Correspondence Principle CP. Thus, strong concretization is the converse of entailment. This justifies Nowak’s practice of denoting concretization by the inverted sign of logical deduction Z . Thirdly, if C2 itself is a true law then C1 and C0 are true counterfactual conditionals. The fact that concretization and entailment are converse relations justifies Krajewski’s (1977) point that it is feasible to “renew” the implicative notion of correspondence, rejected by Nowakowa’s (1994) treatment of dialectical correspondence. Note, however, that here we still have the “dialectical” result that the new law C2 contradicts the original T. Note also that Krajewski (1977, pp. 49-50), states the deductive relations in a wrong way. In my notation, using Ÿ in the place of →, his claim is: C2 & w1(x) = 0 & w2(x) = 0 entails C0, whereas he should have stated that C2 & w1(x) = 0 & w2(x) = 0 entails T, and further C2 entails C0 by CP.

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4. Possible Worlds and Truth In several papers published in the 1990s, Leszek Nowak has elaborated his ontological views about abstracts and constructs (see Nowakowa and Nowak 2000, Ch. 28), thoughts and facts (see Nowak 1991), possibilia and ideas (see Nowak 1995). His version of ontological possibilism is presented as an alternative to David Lewis’ approach of possible worlds, and it is intended to provide a natural ontological framework for the method of idealization. Nowak distinguishes weak and strong form of deformational procedures (see also Ibarra and Mormann 1994). A weak deformation of an object X transforms it into an object XĻ which possesses some property P of X in a different degree. An important special case is ideation where XĻ possesses property P in the minimum or “zero” degree; in this case XĻ is called an “ideal type.” A strong deformation involves a change in the relevant space of properties: X is transformed into XĻ which lacks some properties of X (reduction) or adds some properties to those of X (transcendentalization). Idealization, which leads to “ideas,” is a combination of reduction and ideation. For example, mass points possess spatial dimensions in the zero degree and they lack altogether the remaining physical, chemical, geological, and climatic properties. Nowak correctly emphasizes the difference between the negation of a property P (e.g., replacing P with its alternative or extreme value) and the lacking of the property P. In the former case, claiming that the object has P is false, but in the latter case this claim is nonsense. Nowak’s standard syntax for formulating idealizational laws does not make this difference. But ontologically Nowak (1995) now prefers to formulate idealization as involving strong deformation: an idealizing assumption neglects a property W, so that the actual world M is transformed into its reduct M-W. The introduction of new idealizing assumptions leads us ever farther from M, while concretization again adds some properties and brings us to reducts less remote from M. Nowak suggests that his account is a generalization of the universe of possible worlds of Lewis (see Nowak 1995, p. 231), since it includes both reducts and transcendentales of the actual world. He makes the

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interesting point that idealized objects (like mass points and inertial systems) are not what “things could have been,” so that they are not members of possible worlds in Lewis’ sense, and hence ideal worlds are not possible worlds. If Nowak is right then the possible worlds semantics does not give a method for defining the truth-value of an idealizational law of the form C0, since its antecedent is not true in any possible world. This difficulty is comparable to troubles with counterfactuals with logically impossible antecedents (see Lewis 1969, p. 24). Another way of formulating this puzzle is the following: lawlike generalizations as physically necessary statements do not entail a counterfactual of the form C0, since its antecedent is not true in any physically possible world. Nowak’s criticism is forceful, since Lewis tends to assume that possible worlds are built up from the same individuals (or their counterparts) as the actual world. However, this “one domain” assumption need not accepted: in principle, possible worlds could include any kinds of objects as long as their existence is logically possible. In this broad sense, possible worlds would include Nowak’s ideal worlds as well, since his ideal objects are logically possible. But at the same time we should be cautious, since we do not wish to claim that laws of nature are logically necessary, i.e., true in all logically possible worlds. If Nowak’s ideal objects are physically possible then the proposed treatment of counterfactuals is after all feasible. So are mass points physically possible? The answer is negative if it is a law of nature that all physical objects must be spatially extended. I am inclined to think otherwise, but it is not easy to justify any strong conclusion about this issue. Therefore, we may admit Nowak’s point that possible worlds should be allowed to include logically possible ideal worlds which may fail to be physically possible. The operator should then be reinterpreted as nomic necessity whose range includes such ideal alternatives to the actual world. Physical theories are typically applied to such ideal cases, as we see from textbook exercises of classical mechanics; hence, scientific theories should be understood as nomically necessary generalizations which are able to entail idealizational counterfactual laws.

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It seems to me that Tarski’s model theory gives a natural framework for explicating Nowak’s possible worlds, including the ideal ones. An Lstructure is composed of a domain D of objects and, as interpretations of the non-logical constants of language L, some designated subsets, relations, and functions in D. By choosing the language L in an appropriate way, our L-structures contain precisely those factors that we wish to consider. If possible worlds are represented by the relational structures of Tarskian model theory, then we have counterparts of Nowak’s strong deformations: the notions of reduct (i.e., the elimination of some relations from a structure) and expansion (i.e., the addition of some relations to a structure) are familiar from model-theoretic literature. Hence, it seems to me that Nowak’s ontology could be formalized by assuming that his possible worlds are L-structures in the model-theoretic sense, where language L may be chosen in different ways — by allowing reductions and expansions of its vocabulary (see PrzeáĊcki 1969). It follows immediately that the notion of truth in the “free” sense, i.e., truth in a possible world (see Nowak 1995, p. 236), is explicated by the Tarskian model-theoretic notion of truth in a structure, while truth in the “rigid” sense is equal to Tarskian truth in the L-structure M*(L) representing the actual world relative to language L (see Niiniluoto 1999a, 1999b). A theory T in L is actually true if and only if M*(L) f T in the Tarskian sense. I agree with Nowak that scientific theories are like caricatures: they modify some properties of their objects, and neglect others (see Nowakowa 1992, p. 182; Nowak 1995, p. 228; Niiniluoto 1999a, p. 128). Sometimes idealizing assumptions seem to be only weak deformations: in the ideal gas law (5) the assumption that molecules are mass points (b = 0) does not neglect the property of having a volume entirely, as the gas container still has a positive volume V(x). The assumption in (2) that c is infinite does not mean that there is no velocity of light. In some other cases idealizing assumptions could indeed be treated as strong deformations: in (5) it is assumed that there are no forces between molecules (a = 0), so that the concept of intermolecular force is neglected. But even there the concept of force is not eliminated, so that it is still convenient to follow Nowak’s original

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device by stating this condition as an assignment of an extreme value zero to the parameter a referring to intermolecular force. Following this treatment, all the successive laws C0, C1, and C2 can be assumed to be expressed in the same language L (with function terms F, q, w1, and w2). In Niiniluoto (1986, 1990), the intended models of C0, C1, and C2 are defined as L-structures of the following form, respectively: M0 = ¢D0, f0(q0), q0, 0, 0² M1 = ¢D1, f1(q1, w11), q1, w11, 0² M2 = ¢D2, f2(q2, w12, w22), q2, w12, w22² where Di is the domain of objects with the property G, and qi, w1i, w2i are functions defined in Di (interpretations of the function terms q, w1, and w2 of L in the structures M0, M1, and M2), and 0 is a function in Di with the constant value zero. The intended models M0 and M1 thus satisfy both the antecedent and the consequent of the conditionals C0 and C1. (Note that such conditionals may be true also in other models besides their intended models.) It is now possible to define the distance between possible worlds — instead of taking it as a primitive notion like Lewis does. For example, the distance between structures of the form ¢D, F ² and ¢D,1FĻ² is defined by the Lp-metric: ª

F ( x ) − F ′( x ) «¦

(8) «

¬ x∈D

p

ºp » » ¼

(see Niiniluoto 1986, p. 272; 1987, p. 397). It follows immediately that the relative distances between the structures M0, M1, and M2 are minimal if they have the same domain and the function symbols q, w1, and w2 of L have the same interpretations in them (apart from the zero functions). If this is the case, then Correspondence principle CP guarantees that M1 is closer to M2 than M0 is. Strong concretization thus receives a natural interpretation in semantic terms: the intended models M0, M1, and M2 approach to the last member of this sequence (see the notion of approximate reduction in Niiniluoto 1986, 1987). This is the same result that Nowak wishes to establish for his ideal worlds by his notion of strong deformation. The intended models of the original law T have the form ¢D, f0(q), q². They can be expanded to L-structures of the form ¢D, f0(q), q,

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w1, w2², where functions w1 and w2 have no restrictions. The intended models of C0 belong to such models of T, since we may choose w1 and w2 as 0. (Recall that T entails C0.) On the other hand, the minimum distance of the model M2 of C2 to the models of T depends on the distance between the values f2(q2(a), w12(a), w22(a)) and f0(q2(a)) for a in D. Let M*(L) = ¢G*, F*, q*, w1 *, w2*² be the actual world relative to L, where G* consists of the objects of type G. With this machinery, we can define the factual law C2 to be actually true if and only if M*(L) f C2. Relative to M*(L), the closest L-structure where the idealizing assumption w1(x) = 0 & w2(x) = 0 holds is M2*= . With this distance between structures, we can now apply the Lewis-type semantics for counterfactuals in a precise way: the idealizational law C0 is true in the actual world M*(L) if and only if its consequent is true in the ideal world M2*: (9) M2* f F(x) = f0(q(x)) i.e., F*(a) = f0(q*(a)) for all a in G*. If the Correspondence Principle holds for C0 and C2, then f2(q*(a), 0, 0) = f0(q*(a)) for all a in G*. Hence, given CP, if C2 is actually true, then (9) holds and C0 is true in M*(L). As the antecedent and consequent of C0 are true in M2*, it follows that the counterfactual conditional C0 is true also in M2* (in addition to being true in M*(L)). In this sense, it is correct to say that a conditional like C0 is “a true description of some existing, ideal world” (Nowak 1995, p. 236), but it may be misleading to add that it is “fulfilled only in the ideal models” (Krajewski 1977, p. 26).

5. From Truth to Truthlikeness Nowak’s early approach to the problem of truth was based on the Marxist idea that science approaches the absolute truth through a series of relative truths (see Nowak 1980). His explication of this idea was based on the assumption that in mature science the scientists have

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succeeded in identifying correctly the essential structure of factors influencing the given magnitude. Nowakowa’s (1976) article developed a comparative notion of truth for idealization (see Nowakowa 1992; Nowakowa and Nowak 2000, Ch. 23). Her classification depends on the nature of the images of the essential structure for F and the nomological structure for F. If both of them are complete mistaken, we have absolute falsities; if both of them are completely correct, we have absolute truths. Between these extremes she includes relative truths (the principal factor and its nomological influence are correctly identified) and partial truths (some secondary factor and its influence are correctly identified). However, Nowakowa’s explication has the consequence that adequate concretization of an idealizational statement does not increase its “degree of essential truth” (Nowakowa 1992, p. 201, 212). Thus, this approach fails to show that concretization is a method of truth-approximation. Nowakowa makes a distinction between the classical definition of truth, based on the notion of satisfaction, and the essentialist conception, based on the concept of imitation (Nowakowa 1992, p. 209). In their joint article about Mario Bunge’s notion of degrees of truth, Nowakowa and Nowak (2000, Ch. 26) make a contrast between the Aristotelian or representationist notion of truth and the Hegelian or deformationalist notion of truth. They argue that the source of Bunge’s difficulties is his attempt to reconcile representativism with the phenomenon of approximation and idealization in science. But we have seen that Nowak’s own account of truth in free and rigid senses (see Nowak 1991, 1995) can be directly explicated by the Tarskian notion of truth in a structure. To say that idealized laws are true in the free sense, i.e. true descriptions of some existing ideal worlds, amounts only to the claim that they are nomically possible. Thus, in spite of their expressed interest in imitation and deformation, what seems to be lacking from Nowakowa’s and Nowak’s proposals is the idea of similarity (cf. Niiniluoto 1987, 1988), needed to make sense of the idea that some imitation or deformation may be better than another. For example, if we have correctly identified the principal factor q for F, our proposal for the law expressing the dependence of F on q may be more or less correct. In other words, it is possible to introduce an ordering of

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the laws in the nomological structure in terms of their closeness to the truth. This is, indeed, the basis move in the similarity approach to truthlikeness, as developed since the mid-seventies after the refutation of Popper’s (1963) definition (for details, see Niiniluoto 1987, 1998). The degree of truthlikeness of a statement or theory does not express its closeness to the whole truth about everything, but rather its closeness to a target t* which is the most informative truth within a chosen conceptual framework L. The similarity approach is very flexible in the sense that the target may be chosen in different ways in different cognitive problems, and there are also dynamic ways of changing cognitive problems, e.g. by enriching the language. For some purposes, the similarity account can be formulated by taking the target to be a real system (structure) M*(L) in the actual world, and a theory T is represented by a class of its models (see the preceding section). This may called the problem of verisimilitude, since the goal of science is then to identify all L-truths (Lat. verum) about the world. But if our interest is to find truth about laws of nature, understood as “nomic necessities” valid in all nomically possible worlds, rather than about contingent truths describing the actual world, then the cognitive problem is one of legisimilitude. The problem of legisimilitude can be solved by choosing as the target the strongest true lawlike statement in the relevant scientific language (see Niiniluoto, 1987, Ch. 11). For example, if there is a true law in language L of the form F(x) = f*(q(x), w1(x), w2(x)), then the degree of legisimilitude of the law C2 can be defined by the distance between the functions f* and f2. The original law T may be treated as a set of lawlike statements in the richer language L, and the distance of this set from the true law F* may be evaluated (see Niiniluoto 1986, 1990). We have already seen in formula (8) how such distances between functions can be defined. These geometrical distances were reinvented by Peter Smith (1998) without reference to Niiniluoto (1987). Distances between functions help also to make precise the idea that a factual law like T can be approximately true for some values of its arguments. For example, if we put v(x) ≈ 0 in (6), we obtain m(x) ≈ m0(x). Hence, if (6) is true, then (4) is approximately true for sufficiently small velocities v(x).

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When CP holds, C2 entails C0 and C1. If C2 is true, then also C0 and C1 are true. In this case, strong concretization is a method of truthapproximation, since steps from C0 to C1 and to C2 lead us to stronger truths, so that the latter theories in this sequence are more truthlike than the former ones (cf. principle M4 in Niiniluoto 1987, p. 233). The same conclusion holds typically, if C2 itself is only truthlike, but the truth is obtained from it by further concretization. More generally, the concept of legisimilitude can be applied to counterfactual conditionals like C0 in several alternative ways. First, the conditional C0 defines a restricted curve in the state space, and the distance of this curve from the true law F* may be evaluated by the geometrical measures (see Niiniluoto 1986, 1990), Secondly, we may apply the theory of truthlikeness in situations where the cognitive problem is defined relative to a counterfactual assumption B. In this case, the target t* can be chosen as the strongest statement which would be true if B were true (see Niiniluoto, 1987, pp. 259-262). This gives us a comparative notion of truthlikeness: conditional B Ÿ t1 is more truthlike than conditional B Ÿ t2 if and only if t1 is more truthlike than t2 relative to t*, i.e. relative to the B-world closest to the actual world. Thirdly, in a situation where the counterfactual conditional B Ÿ t* is true, we could define a modified cognitive problem where it is chosen as the target. It further seems to me that the similarity approach to truthlikeness, with a suitable choice of the target, gives a tool for assessing the essesimilitude of scientific theories. Uskali Mäki (1992, 1994), who has introduced this term, proposes that economic theories could be understood as expressing partial truths about the essences of economic phenomena. This proposal seems to be close what Nowakowa (1992) calls relative truth. Let L be the full language in which a theory T in economics can be expressed. A metaphysical realist, who advocates essences (cf. also Nowak 1980), should specify the sublanguage Le of L which contains only the essential or core attributes. Then the essesimilitude of T can be defined as its closeness to a target sentence in Le (see Niiniluoto 2002).

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These observations hopefully illustrate the power of realist notions of truth and truthlikeness to function as tools in analyzing the method of idealization and concretization in science. University of Helsinki Department of Philosophy P.O. Box 9 00014 Helsinki Finland e-mail: [email protected]

REFERENCES BrzeziĔski, J., F. Coniglione, T. Kuipers and L. Nowak, eds. (1990). Idealization I: General Problems. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 16. Amsterdam: Rodopi. BrzeziĔski, J. and L. Nowak, eds. (1992). Idealization III: Approximation and Truth. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 25. Amsterdam: Rodopi. Diederich, W. (1994). Nowak on Explanation and Idealization in Marx’s “Capital.” In: Hamminga and de Marchi (1994), pp. 255-264. Dilworth, C., Ed. (1992). Idealization IV: Intelligibility in Science. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 26. Amsterdam: Rodopi. Fetzer, J.H. (1993). Philosophy of Science. New York: Paragon House. Gärdenfors, P. (1979). Conditonals and Changes of Belief. In: I. Niiniluoto and R. Tuomela (eds.), The Logic and Epistemology of Scientific Change (Acta Philosophica Fennica), pp. 381-404. Helsinki: The Philosophical Society of Finland. Hamminga, B. and N. de Marchi, eds. (1994). Idealization VI: Idealization in Economics. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 38. Amsterdam: Rodopi. Hanzel, I. (1999). The Concept of Scientific Law in the Philosophy of Science and Epistemology. Dordrecht: Kluwer. Ibarra, A. and T. Mormann (1994). Counterfactual Deformation and Idealization in a Structuralist Framework. In: Kuokkanen (1994), pp.81-94. Krajewski, W. (1977). Correspondence Principle and the Growth of Knowledge. Dordrecht: Reidel. Kuipers, T. (2000). From Instrumentalism to Constructive Realism. Dordrecht: Kluwer.

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Kuokkanen, M., ed. (1994). Idealization VII: Structuralism, Idealization and Approximation. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 42. Amsterdam: Rodopi. Lewis, D. (1973). Counterfactuals. Oxford. Blackwell. Mäki, U. (1992). On the Method of Isolation in Economics. In: Dilworth (1992), pp. 317-351. Mäki, U. (1994). Isolation, Idealization and Truth in Economics. In: Hamminga and de Marchi (1994), pp. 147-168. Niiniluoto, I. (1978). Dretske on Laws of Nature. Philosophy of Science 45: 431-439. Niiniluoto, I. (1984). Is Science Progressive? Dordrecht. D. Reidel. Niiniluoto, I. (1986). Theories, Approximations, Idealizations. In: R. Barcan Marcus, G.J.W. Dorn and P. Weingartner (eds.), Logic, Methodology and Philosophy of Science VII, pp. 255-289. Amsterdam: North-Holland. Niiniluoto, I. (1987). Truthlikeness. Dordrecht: D. Reidel. Niiniluoto, I. (1988). Analogy and Similarity in Scientific Reasoning. In: D.H. Helman (ed.), Analogical Reasoning: Perspectives of Artificial Intelligence, Cognitive Science, and Philosophy. Dordrecht: Kluwer, pp. 271-298. Niiniluoto, I. (1990). Theories, Approximations, Idealizations. In: BrzeziĔski et al. (1990), pp. 9-57. (Enlarged version of Niiniluoto 1986.) Niiniluoto, I. (1994). Approximation in Applied Science. In: Kuokkanen (1994), pp. 127-139. Niiniluoto, I. (1998). Verisimilitude: The Third Period. The British Journal for the Philosophy of Science 49: 1-29. Niiniluoto, I. (1999a). Critical Scientific Realism. Oxford: Oxford University Press. Niiniluoto, I. (1999b). Tarskian Truth as Correspondence — Replies to Some Objections. In: J. Peregrin (ed.), Truth and its Nature (if any), pp. 91-104. Dordrecht: Kluwer. Niiniluoto, I. (2002). Truthlikeness and Economic Theories. In: U. Mäki (ed.), Fact or Fiction in Economics: Models, Realism, and Social Construction, pp. 214-228. Cambridge: Cambridge University Press. Nowak, L. (1980). The Structure of Idealization: Towards a Systematic Interpretation of the Marxian Idea of Science. Dordrecht: D. Reidel. Nowak, L. (1991). Thoughts are Facts in Possible Worlds, Truths are Facts of a Given World. Dialectica 45: 273-288. Nowak, L. (1994). The Idealizational Methodology and Economics: Replies to Diederich, Hoover, Janssen, Jorland and Mäki. In: Hamminga and de Marchi (1994), pp. 303-336. Nowak, L. (1995). Antirealism, (Supra-) Realism and Idealization. In: W.E. Herfel et al. (eds.), Theories and Models in Scientific Processes (PoznaĔ

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Studies in the Philosophy of the Sciences and the Humanities, vol. 44), pp. 225-242. Amsterdam: Rodopi. Nowak, L. and I. Nowakowa (2000). Idealization X: The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam: Rodopi. Nowakowa, I. (1992). A Notion of Truth for Idealization. In: BrzeziĔski and Nowak (1992), pp. 181-213. Nowakowa, I. (1994). Idealization V: The Dynamics of Idealizations. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 34. Amsterdam: Rodopi. Nute, D. (1984). Conditional Logic. In: D. Gabbay and F. Guenther (eds.), Handbook of Philosophical Logic II, pp. 387-439. Dordrecht: D. Reidel. Popper, K.R. (1963). Conjectures and Refutations. London: Routledge and Kegan Paul. PrzeáĊcki, M. (1969). The Logic of Empirical Theories. London: Routledge. Smith, P. (1998). Explaining Chaos. Cambridge: Cambridge University Press.

R. F. Hendry and Stathis Psillos HOW TO DO THINGS WITH THEORIES: AN INTERACTIVE VIEW OF LANGUAGE AND MODELS IN SCIENCE*

1. Introduction There are two major approaches to the individuation of scientific theories, that have been called syntactic and semantic. We prefer to call them the linguistic and non-linguistic conceptions. On the linguistic view, also known as the received view, theories are identified with (pieces of) languages. On the non-linguistic view, theories are identified with extra-linguistic structures, known as models. We would like to distinguish between strong and weak formulations of each approach. On the strong version of the linguistic approach, theories are identified with certain formal-syntactic calculi, whereas on a weaker reading, theories are merely analyzed as collections of claims or propositions. Correspondingly, the strong semantic approach identifies

*

An earlier version of this paper was presented at the Philosophy of Science Association meeting in Kansas City in November 1998. We should thank the participants of our session for their comments. We should particularly thank James Ladyman and Steven French for very useful and extended criticism of earlier drafts.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 123-157. Amsterdam/New York, NY: Rodopi, 2007.

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theories with families of models, whereas on a weaker reading the semantic conception merely shifts analytical focus, and the burden of representation, from language to models. To exploit a distinction drawn by Patrick Suppes, the strong version of the linguistic approach strives for an “intrinsic characterization” of theories, whereas the strong version of the non-linguistic approach strives for an “extrinsic characterization.” An “intrinsic characterization” of a theory characterizes it as the set of the logical consequences of a set of given axioms; and to give an “extrinsic characterization” is “simply to define the intended class of models of the theory” (Suppes 1967, pp. 1-9). After critically reviewing the two approaches in sections 2 and 3, we move on (in sections 4-6), to advance and defend an interactive view of theories. One of our main claims will be that arguments currently available are telling against the strong versions of the two standard approaches, and that their weak versions can happily coexist in our interactive approach.

2. Theories as Languages The so-called “syntactic” view of theories was not purely syntactic for it was consistent with, and made room for, the view that theories are interpreted linguistic frameworks. This approach, as developed by Rudolf Carnap (1939) brought together the Duhem-Poincaré view that theories are systems of hypotheses whose ultimate aim is to save the phenomena, and the Hilbert formalization program, according to which theories (mathematical theories, to be sure) should be reconstructed as formal axiomatic systems. The prima facie advantage of a Hilbert-style formalization of a scientific theory is that it lays bare logical structure and unambiguously identifies its content: the theory consists of the set of logical consequences of the axioms, or fundamental hypotheses of the theory. But formalization does not preclude questions of interpretation. In fact, a Hilbert-style characterization makes it possible to circumscribe the class of admissible interpretations of the theory: they are just those which satisfy its axioms. As such, it amounts to an implicit definition of its basic

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predicates. An implicit definition is a kind of indefinite description: it delineates a whole class of classes of entities which can realize the logical structure of the theory, as defined by the axioms. After Alfred Tarski’s work in model theory, the class of admissible interpretations can be identified with the class of models of the theory. Still, no purely linguistic — or syntactic — consideration can single out one class of models as the intended one. The intended interpretation gets singled out by application of the formal system to a certain domain: what, for example, makes a certain formal language a theory of mechanical phenomena is that it finds an interpretation in these phenomena. Carnap’s case is quite instructive. He took it to be the case that the “calculus of mechanics” — a fully syntactical axiomatic characterization of classical mechanics — could be interpreted via semantical rules so that it becomes a physical theory: one that states “physical laws.” But he added: [t]he relation of this theory [i.e. the interpreted physical theory of classical mechanics] to the calculus of mechanics is entirely analogous to the relation of physical to mathematical geometry. The customary division into theoretical and experimental physics corresponds roughly to the distinction between calculus and interpreted system (1939, p. 57).

Despite the qualifier ‘roughly’, it is clear, and obvious from the surrounding text, that Carnap conceived of the interpretation of the calculus (i.e., of the theory) to be made at the point of its application to the physical (and in particular, the observable) world. In light of this, the correct statement of the strong version of the linguistic view should be that theories are identified with formal languages (calculi), whose interpretation — what the calculus is a theory of — is fixed at the point of application. The upshot is that by identifying theories with formal languages, the strong version of the linguistic approach divorces the theory from its intended content: what a theory is a theory of need not be a feature of the theory, conceived by itself; rather it is tacked onto it at the point of application. This divorce is even more obvious if we take account of two further points. Firstly, although it is clear that for Carnap and other “syntacticists” the interpretation of the calculus is effected by means of semantical rules, the semantical rules were not taken to be

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part of what individuates a theory. Secondly, Carnap did not take to it be a requirement of having a theory of a domain X that this theory be fully interpreted. Consider the following quotation: To be sure, in order to pass judgement about the applicability of a given physical calculus we have to confront it in some way or other with observation, and for this purpose an interpretation is necessary. But we need no explicit interpretation of the axioms, nor even of any theorems. The empirical examination of a physical theory given in the form of a calculus with rules of interpretation is not made by interpreting and understanding the axioms and then considering whether they are true on the basis of our factual knowledge. (Carnap 1939, pp. 66-67)

Instead, Carnap explained, “[w]e construct derivations in the calculus with premises which are singular sentences describing the results of our observations, and with singular sentences which we can test by observations as conclusions” (1939, p. 67). So, the semantical rules need only apply to the singular sentences of the calculus which purport to refer to observations and predictions. As for the rest of the sentences of the theory, “we need not make their interpretation explicit in order to be able to construct the derivation [of a prediction] and to apply it” (p. 66). By identifying theories with formal languages, and first-order languages with identity in particular, the strong version of the linguistic approach drastically impoverished them as means of representation. How, for instance, can they reasonably be seen as able to represent the real-number continuum? And as Suppes (1967, pp. 1-11) has rightly stressed, it is often more practical, and even theoretically more plausible, to start with a class of models and then inquire whether there is a set of axioms such that the models in the given class are its models. By concentrating on clean axiomatic presentations of theories, the strong version of the linguistic approach centered on what can at best be refined analyses, rather than complicated and messy scientific theories. These objections to the strongly linguistic approach to theories are no longer news. But it is important that the baby should not be thrown out with the bath water, for the linguistic approach is right to assume that language is a central means by which theories represent their domain. Problems rather arise from two contingent features of the

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setting in which that insight was pursued: firstly that formalization was thought to be necessary for the adequate characterization of theories; and secondly that the epistemological doctrine of empiricism had come to be expressed in a peculiarly linguistic form. Although empiricists like Carnap never abandoned the quest for formalization, the demand for first-order formalization was relaxed: in mature formulations of the empiricist account of theories-as-languages (see Carnap 1956), the underlying logical apparatus is so strong as to include virtually the whole of set theory. Carnap and others found solace in formalization because it seemed to offer a way to study theories without being committed to any particular interpretation of the so-called theoretical terms and predicates, and hence without being committed to any unwanted implications about unobservable entities. Having identified a theory with a formal language, it was thought enough to interpret only part of it — that which is apt for the representation of observable phenomena when the theory is applied to a certain domain — leaving the rest uninterpreted. Faced with the objection that this would concede too much to instrumentalism, they appealed to correspondence rules in order to show how some meaning can be given to theoretical discourse, by means of fusion with the interpreted observational terms. Thus began the well-known problems of partial interpretation, the alleged dichotomy between observational and theoretical terms, and the analytic-synthetic distinction, which cannot in any case be maintained given that correspondence rules play a dual role, contributing to the meaning of theoretical terms, but also delineating the empirical content of the theory.1 More generally, the very idea of correspondence rules raised the question of what relation they bear to theories conceived as formal languages, a problem noted by Fred Suppe (1977, pp. 102-109): are they parts of theories or not? If the former, then modification of the correspondence rules entails modification of the theory, and conditions of theoretical identity become either vague or counterintuitive. If the latter, then theories become free-floaters, devoid of content.

1

For a statement of Carnap’s final views on these matters, see his (2000).

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Problems such as the above, which contributed so much to disillusionment with the linguistic approach and to the demise of its strong version, do not follow from the thought that language is a medium by which theories represent. Dissociated from the empiricist predicament and the quest for formalization, the linguistic conception is clearly consistent with the claim that theories are not merely formalaxiomatic calculi looking for (partial) interpretation, but collections of statements. Language here is a means of representing an extralinguistic domain (a collection of worldly phenomena and their causes), and constituent sentences are interpreted by understanding them literally. Perhaps the logical relationships among these statements can be investigated through formal features of their canonical linguistic formulations, or perhaps not. But this cannot be a condition of adequacy (or good scientific standing) of the representation offered by the theory. We identify this commonsense understanding of the linguistic approach as its “weak version.” It is at least arguable that practicing scientists who reflected on the nature of theories, such as Henri Poincaré and Pierre Duhem, understood theories in this way. This weak version of the linguistic approach seems immune to most of the problems that plagued its strong counterpart. Still, in so far as it focuses all attention on linguistic representation, it obscures some fundamental ways in which theories represent the world. Language is certainly a vehicle of representation, but not the only one, and not always the most important one. The weak view, for instance, neglects the role of models in scientific theorizing: it is no accident that proponents of the linguistic view struggled with the thought — or better, the fact — that theories represent by setting up and investigating iconic (or analogical) models of the physical systems they target (see Psillos 1995).2 It also neglects the fact, stressed rightly and repeatedly by Suppes (1969) and Suppe (1977; 1989), that theories confront not the phenomena themselves but models of the phenomena. Where the linguistic approach goes deeply wrong is in its implication

2

A case in point here is Duhem (1954 [1906]), whom we identified as one of the proponents of the weak linguistic view. His resistance to models as a means by which theories represent the world is notorious.

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that either a domain X satisfies theory T or it does not. The linguistic approach (in all its guises) cannot easily accommodate more complex representational relations that might hold between a domain and what the theory says about this domain. This needs to be stressed. Even the weak version of the linguistic approach seems committed to the following naïve view: a good theory, viewed as a collection of statements, directly represents the world in that the world (or a certain domain) directly satisfies the theory (i.e. makes it true, or empirically adequate or what have you). The naïveté of this view is apparent when one thinks of the idealizations, approximations, simplifications and ceteris paribus clauses that are so typical of scientific theorizing.3 Now, this is a naïveté that Leszek Nowak (2000) has done probably more than anyone else to highlight. His detailed study of the nature of idealization shows emphatically that, in the first instance, theories represent ideal systems which are constructed from real systems by eliminating factors that are thought to be secondary (see 2000, p. 117). According to Nowak’s insightful idea, a theory of a certain domain consists, in fact, of a series of theories, each being less abstract (or more concrete) than the other. The starting element of the series is an abstract version of the theory which applies to the idealized description of the phenomena under study, while its terminal element is a realistic (because de-idealized) description of the relevant phenomena — a description which has taken into account all, or most, of the secondary factors that the abstract version of the theory had neglected but which, nonetheless, influence the phenomena under study. Though this outline of Nowak’s view of idealization is very sketchy, we think it brings to light two important thoughts. Firstly, the way theories represent is much more complex than the linguistic approach has assumed. Secondly, idealization does not detract from representation. This last thought is strengthened by two further considerations: an idealized theory admits of concretizations, which enhance its representational capacity, and

3

Here Duhem (1954 [1906]) got it right. For though he worked within the weak linguistic approach, he did try to accommodate idealizations, approximations and the like.

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even without the concretizations, there is still a sense in which an idealized theory does represent the phenomena it studies. For, as Nowak (2000, pp. 117-118) puts it, a theory studies the behavior of real entities or magnitudes, even though it offers an idealized description of them.

3. Theories as Families of Models The single major advantage of the alternative non-linguistic approach is that it naturally accommodates all these more complex representational relations between the theory and the physical world. But, in so far as it strives for an “extrinsic characterization” of theories, it does so at the cost of neglecting the role of language in representation. On a strong reading of the non-linguistic approach, theories are identified with families of models, where the term ‘model’ is to be understood in the logician’s sense: a structure that makes some statement true. Thus Suppes has it that “the meaning of the concept of model is the same in mathematics and the empirical science” (1967, pp. 2-6), and Suppe has urged that “theories be construed as propounded abstract structures serving as models for sets of interpreted sentences that constitute the linguistic formulations,” where these structures are “metamathematical models of their linguistic formulations” (1989, p. 82).4 This identification of theories with extra-linguistic entities is supposedly suggested by a distinction between a theory and its formulations, a distinction which is the backbone of the non-linguistic approach. In its turn, that distinction is motivated by the “multiple formulations argument” (see Suppe 1977, pp. 204-205; 1989, p. 82). Suppose, the argument goes, that a theory formulated first in English is translated into French. If we would deny that a new theory had been offered in the French, we must identify the theory with something extra-linguistic 4 For some relevant thoughts, see also Lloyd (1988, p. 15) and van Fraassen (1989, p. 366, n. 4), who understand ‘models’ as mathematical structures, but distinguish the latter from the logician’s model-as-an-interpretation of a set of statements, which includes a mapping from the terms of the language in which the statements are made.

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that has been formulated in two languages. As more telling examples, Suppe cites the equivalent formulations of the quantum theory offered by matrix and wave mechanics (1977, p. 205) and of classical particle mechanics by its Lagrangian and Hamiltonian formulations (1989, p. 82). In all cases, Suppe concludes, since we must distinguish between a theory and its formulations, it follows that a theory should be identified with something extra-linguistic, that is with something which can admit of different linguistic formulations. And what else could this plausibly be, if not an abstract mathematical structure? Let us suppose that this argument does establish the distinction between theories and their formulations: even then the intended conclusion, that theories should be identified with abstract structures, does not follow. In case we think that sets of statements in two or more different languages constitute formulations of the same theory, the theory should not be identified with one particular set of statements, but rather with all those linguistic formulations which are theoretically equivalent. An analogy with the problem of meanings in the philosophy of language is irresistible. How shall we account for semantic relations between ‘snow is white’, ‘la neige est blanche’ and ‘der Schnee ist weiß’? We need not invoke an abstract extra-linguistic entity, but can merely say that there is something that can be said equivalently in the languages of the different formulations. If we do invoke something extra-linguistic, we appeal to identity of truth-conditions. Now matrix and wave mechanics are a case in point: here we have historically independent but “equivalent” formulations. But are they formulations of the same theory? On our view of the individuation of theories (see below), this is an open question. An intimate mathematical relationship between the two theories was proved by Schrödinger: that a (semantic) model of one could be turned into a model of the other. But mathematics aside, it is hard to imagine two theories that were further apart in what they had to say about the nature of the physical world, in their “fleshly clothing” (1928 [1926], p. 59) as Schrödinger himself once put it. If historical hindsight has deemed the two theories to be one, this may be as much a product of their joint mathematical

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subsumption under the later Hilbert-space formalism as it is a sign of equivalence in any sense wider than the mathematical. 5 Both Bas van Fraassen (1995/1996, pp. 5-6) and Ronald Giere (1988, p. 84) have employed the multiple formulations argument. However, van Fraassen’s (1989, p. 222) endorsement of the argument’s conclusion seems to be conditional: “[I]f the theory as such is to be identified with anything at all — if theories are to be reified — then a theory should be identified with its class of models.” If the proviso indicates a worry about whether theories have the well-defined identity conditions that identifying them with sets of models would entail, the point is well taken.6 But van Fraassen then goes on to claim that “the semantic view of theories makes language largely irrelevant to the subject [of theory structure]” (1989, 222). Of course, language cannot totally be neglected because “to present a theory, we must present it in and by language,” since “any effective communication proceeds by language” (1989, p. 222). But as we shall see in section 5, van Fraassen thinks that in the “discussion of the structure of theories it [i.e. language] can largely be ignored” (1989, p. 222). Two points are worth making here. Firstly, language is an ineliminable element in theoretical representation, and not just in the banal sense allowed by van Fraassen. Any theory of theories should include language in the account of how theories represent. These central thoughts will be taken up in sections 5 and 6. Secondly, to consider sets of models in isolation from language, or some other means of making a representational claim, as van Fraassen’s point seems to imply, is to render them unsuitable for representing, and the theories of which they are part devoid of empirical content. Let us see why this is so.

5

Indeed Müller (1997) argues that joint subsumption was achieved at the cost of “chopping” much “excess” mathematical structure from the two subsumed theories. Hendry (forthcoming) argues that Schrödinger himself thought that mathematical equivalence falls short of equivalence simpliciter.

6

See also Giere (2000), p. 524. More recently, van Fraassen (1995/1996, p. 6) has made the unconditional statement that “a theory can be identified through its class of models.” Although a theory is not identical with its class of models, the class of models would be sufficient to identify the theory.

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If theories are identified with, or even through, families of models, then the non-linguistic approach is committed to some distinction between theories themselves, and the claims that they can be used to make when applied to real-worldly systems. Classical mechanics, according to Giere’s elegant analysis (1988, Chapter 3) consists of hierarchically arranged clusters of models, picked out and ordered by Newton’s laws of motion plus the various force-functions. On Giere’s view (also endorsed by van Fraassen 1989, p. 222), the relationship between a law-statement and a model is a definitional one: a model is an abstract entity that satisfies the definition. But neither the definition itself nor the resulting model tells us which physical systems, if any, the model represents, or how. Construed as Giere suggests, classical mechanics makes no claims about physical systems. It only identifies a cluster of models: abstract mathematical entities that may or may not have physical counterparts. Giere reinstates the empirical content by means of what he calls “theoretical hypotheses,” linguistic items expressing representational relationships, in specified respects and to specified degrees, between abstract structures and given classes of real systems. Now this seems to imply that a detailed theoretical treatment of the processes that underlie some domain of phenomena must involve two linguistic components: the definition and the hypothesis. But Giere tries to resist this implication, as it would put “too much emphasis on matters linguistic” (1988, p. 85). Hence he substitutes “the models [i.e. the abstract structures] for the definitions” (p. 85). But this leads him to counter-intuitive results, in two ways. The first way is highlighted by Giere’s following dictum: “Thus, what one finds in the textbooks is not literally the theory itself, but statements defining the models that are part of the theory” (p. 85). To say that we find only theory-formulations in textbooks seems to us a strange category mistake: what we find in textbooks are statements that are being used to present the theory. The theory itself is inseparable from the statements that in any particular instance express it, and if it is not to be found where they are, we do not know where else to find it. The second way is highlighted by the following consideration. To define the

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class of models is not yet to say anything about the world: that requires something linguistic, a theoretical hypothesis.7 Although Giere insists that we have models “occupying center stage” (1988, p. 79), in the analysis of theories considered in isolation from their applications, he has to admit that a linguistic element is indispensable if models are to do any representational work. Note that the appearance of this distinction between ‘theoretical definition’ and ‘theoretical hypothesis’ is historically ironic: although the correspondence rules of the received view came in for much (justified) criticism from the founders of the semantic view, here we find theoretical hypotheses playing a parallel role of tying free-floating structures to the empirical world, albeit in the context of a more sophisticated and diverse account of theory-world relations. Giere resists this comparison, stressing that correspondence rules linked “terms with things or terms with other terms” (1988, p. 86). But this does not discredit the proposed parallel between theoretical hypotheses and correspondence rules. Not only must we interpret the elements of the abstract mathematical model so that they are apt for representing physical content (solving what Giere calls the “interpretation problem”, see his 1988, p. 75), we must also treat theoretical hypotheses as bridge principles which give the theory whatever empirical content it has (solving Giere’s “identification problem”). Our suggested parallel between correspondence rules and theoretical hypotheses might seem a bit too quick. Criticizing the appeal to correspondence rules made by the linguistic approach, Suppe (1989, pp. 69-72) suggests that a major advantage of the semantic view is its replacement of correspondence rules with a more sophisticated (and non-linguistic) characterization of how theories relate to phenomena. Correspondence rules, Suppe argues, were ill-motivated because they aimed to “eliminate the physical system,” purporting to link the

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‘Linguistic’ is used here in the sense intended in our formulation of the weak linguistic view of theories, to cover items that are of no one language, but are constitutively connected to language. Thus it includes, for instance, propositions and statements.

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postulates of the theory directly with observation reports. According to Suppe (1989, p. 67), a physical system is an abstract or idealized replica of the phenomena, described in the vocabulary of the theory. The role attributed to correspondence rules is replaced by a two-stage process. The first stage converts the “raw phenomena” (1989, p. 69) into “hard data” describing the behavior of a physical system, which involves correcting them and expressing them in the vocabulary of the theory. The second stage connects the “hard data” to the postulates of the theory. Suppe (1989, pp. 69, 71) notes that the second stage of the process, being essentially mathematical, is part of the theory, while the first stage is not. Instead, it constitutes the application of the theory to the phenomena and is therefore experimental or empirical. So for Suppe, the connection between theory and phenomena is not linguistic, as it is when made through correspondence rules. To use Giere’s terminology, the theoretical hypotheses connecting the models to physical systems are unlike correspondence rules in that (i) they are part of the theory; and (ii) they do not directly link the theory with observational reports. Although we do not agree with Suppe that the relationship between the systems studied by theories and the phenomena to which these systems somehow apply is one of replication (instead, as it will be shown in section 6, we take some notion of abstraction to be operative8), we do think that his main insight, that theories represent natural phenomena indirectly, is essentially correct. It is also true that, by focusing exclusively on linguistic representation, the linguistic approach obscured this fundamental aspect of representation. Yet it still does not follow from this that theoretical hypotheses are not, on Suppe’s account, the modern-day analogue of correspondence rules. The latter gave empirical content to the abstract linguistic calculus of the theory, and empirical content — at least on the empiricist account of those rules — was “cashed out” in terms of observational reports. Given Suppe’s insight that empirical content accrues through the theory’s descriptions of physical systems, it is easy to see that this 8

For more on the notion of “abstraction,” see Nowak and Nowakowa (2000, pp. 116ff ).

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reliance on observational reports is unnecessary and ill-motivated. But even on Suppe’s account, theories qua families of abstract entities are free-floaters, unless these abstract entities are suitably connected with concrete physical systems and phenomena. This is precisely what theoretical hypotheses do: anchor models to the world, by showing how their descriptions are relevantly true of empirical systems. In this sense, theoretical hypotheses do play the same role in the strong nonlinguistic view as did the correspondence rules in the strong linguistic view. So, unless appeal is made to theoretical hypotheses — which are essentially linguistic devices — the strong semantic view divorces the theory from its empirical content no less than the rival linguistic conception. Such a divorce would be mistaken, in our view, for two kinds of reason. Firstly, it is a curious use of the term ‘theory’ that allows a particular theory to be individuated independently of what it is a theory of. The models that are associated with a particular set of equations must naturally play an important role in delineating the content of theories that use them, but they cannot provide the entire story. Part of what individuates a theory, and determines its empirical content, is surely its intended domain of application. It was essential to Bohr’s 1913 theory, for instance, that it was a theory of the structure of atoms; if its subject-matter had been different, it would have been a different theory. Secondly, even if models do play an essential role in the representation of a theory’s content, it is a category mistake to infer that the models themselves constitute that content. Models are central to the theory of theories just because they are a means of theoretical representation: theories represent via models. In saying that (some part of) the world is some particular way, a theory may ipso facto invoke some representational relation between a model and part of the world. But in so far as the theory embodies a representational relationship between model and world, it must reach out beyond the model to the world itself. The content of a physical theory is what it has to say about real-worldly physical systems. We use equations to say these things, and the central insight of the semantic view is precisely in identifying models as the means by which equations convey their message. But the models themselves are not the message.

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The master argument for the semantic conception is that a focus on models allows a more perspicuous analysis of theories and theorizing than the linguistic view, one that is closer to the structure of theoretical texts, the practice of theorizing, and scientists’ usage of such central terms as ‘theory’ and ‘model’. As noted in the beginning of this section, it is to the credit of the semantic conception that it has indeed allowed more sophisticated accounts of relations between theory and data (Suppes 1969; van Fraassen 1980), approximation and idealization (Suppe 1989; French and Ladyman 1998), and illuminating analyses of particular theories (e.g. Lloyd 1988 on evolutionary theories; Giere 1988 on classical mechanics; van Fraassen 1991 on quantum mechanics). But these points speak only in favor of a weak version of the semantic view: that a focus on models must play an important part in any viable analysis of theories. As such, the weak version is consistent with the interactive conception which we will articulate and defend in the next three sections, according to which the central representational medium of the non-linguistic conception (models) must find a place alongside the central medium of the linguistic approach (language) in any viable account of how theories represent.

4. Varieties of Theoretical Representation In its theories, science provides representations of the world. Some of these are successful, others less so. That much is truism, for it is consistent with any mainstream philosophical view of science and scientific theories. Defenders of both linguistic and non-linguistic approaches to theories can agree on it, for both accept that theories can be used to explain and predict, and as such must represent parts of the world as being certain ways. Now mathematics is a central representational medium, at least for the physical sciences. In this section we will compare it, as a representational medium, to some others. Historians of science have documented the many roles that nonlinguistic modes of representation (diagrams, concrete physical models) have played in theoretical representation, and how they have been central to the development of physics, chemistry and biology.

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Nineteenth-century structural chemistry, for instance, coalesced around particular schemes of diagrammatic representation and balland-stick renderings of particular molecular structures.9 A few general points of relevance to our discussion emerge: diagrams and models are governed in use by evolving traditions of visual representation, by the practical limitations of the media for reproducing them, and by the broader aims and beliefs of those who use them. In short, they are creatures of the theory, technology and society of their time. In use, they appear in conjunction with text or speech. A written or spoken argument gives the diagram a representational role: to illustrate, motivate and support things that are said in the text.10 The partnership of text, tradition and image (or object) allows the effect achieved by a particular representation to transcend the inherent limitations of the medium of which it is an instance: suitably explained, or within a particular tradition of use, two-dimensional diagrams can, for instance, allow claims to be made about three-dimensional structures. It matters not whether the relevant traditions are thought of as (explicit or implicit) conventions, or as more diffuse constraints on right interpretation, issuing in a Tarski-style truth-theory for a language in use. If pictorial representation seems too peripheral, turn now to the iconic (or analogical) models of Hesse (1966), which directly involve the representational use of mathematics. One physical system (the Source) is a model of another (the Target) in virtue of positive analo-

9

Knight (1996) traces the development of the “visual language” of nineteenthcentury chemistry, considering portraits and illustrations in addition to theoretical diagrams. Francoeur (1997) gives a vivid account of the interplay of theoretical and practical constraints on the development of molecular modeling systems in the twentieth century. Knight (1985) argues that even in natural history texts, illustrations need to be read in conjunction with a rich cultural context that includes the accompanying text. See Hendry 2001, Sections 2 and 3 for an overview. 10 This is not to say that proper understanding of a diagram requires no work on the part of the reader or hearer. To the extent that diagrams or models can be used to say anything, or represent (part of) the world as being a certain way, their interpretation is constrained (see also van Fraassen and Sigman 1993, pp. 93ff ).

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gies between them. Given the positive analogies, fragments of mathematics that have been used to describe the behavior of the Source are transferred to the Target, along with (ideas about) causal structure, and attendant auxiliary assumptions in mathematical form (see also Hughes 1993). Thus did Bohr redescribe the hydrogen atom as a solar-system (albeit an atypical one), and the hydrogen atom inherit the solar-system’s mathematics (see Hendry 1999); the elasticsolid models of the luminiferous ether provide another case in point (see Psillos 1995). The benefits of this kind of analogical transfer can be both pragmatic and heuristic: equations with well-known solutions are used, and to the extent that the analogy is helpful, the user benefits from seeing the complex behavior of the Target in terms of the readilyinterpreted mathematics of the Source. Bohr, for instance, used the well understood equations of central-force mechanics, and was thereby able to separate electronic motions into well-understood components, opening up a detailed program of theoretical development starting with single electrons describing circular orbits, followed by precessing elliptical orbits, many-electron atoms, and perturbing fields. Along the way, he was able to account for unforeseen empirical anomalies (in the exchange with Fowler, see Lakatos 1970, pp. 140-154) in terms of some natural de-idealizations of his initial model: natural, that is, in the context of the analogical connection. In so far as Bohr used mathematics to represent, he relied on its prior uses. The upshot is that Bohr succeeded in saying some things, primarily about hydrogen atoms, and he said them using some text and some equations. Now the semantic view has an obvious way of accommodating all this: in so far as they determinately represent the world as being some way, diagram and text serve to pick out a model, or structure. In a cleaned-up analysis of a historical theory, this structure could also be picked out — using the language of mathematics, following Suppes’ and van Fraassen’s injunction — by a set-theoretic predicate. But in our view this could be misleading, for three reasons. Firstly it privileges mathematics, which is but one representational medium among many, and one whose central role in modern science is, after all, contingent. In any case, in some of the foregoing examples (the nineteenth-century molecular models, for instance), mathematics was

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not obviously involved. Secondly, in so far as “structures” are understood as abstract objects, diagrams and equations do not pick out structures; rather they pick out objects with structures (where a structure should now be thought of as a mode: a way for a concrete object to be). Many of the nineteenth-century diagrams and models — those employed by the realist-minded Kekulé and van t’Hoff, for instance11 — were intended to pick out three-dimensional structures, possible occupants of three-dimensional physical space, not mathematical structures, which are “three-dimensional” in a metaphorical sense at best (for our positive approach to this issue, see section 6). Thirdly, in so far as equations are items of mathematical language, they are as bound by tradition, and as much in need of interpretation, as other media. Where mathematics is used within object-level science, rather than its metalinguistic description, the trivially set-theoretic move from equation to structure obscures the need for interpretation. Our contention is not that Hessean analogy cannot be accommodated within the semantic view: it has been, and elegantly so, within the “partial structures” approach of da Costa and French (see da Costa and French 1990; French and Ladyman 1999).12 Rather, we claim that in concentrating on shared (set-theoretical) structure, the temptation is to reify structure, viewing the analogy as a relationship that Source and Target each bear to some third object. The analogical connection is the end of a long process, where theoretical assumptions, analogies and idealizations are orchestrated to lay bare a level of description of the two systems (Source and Target) in which they share structure.

11

For an account of the interplay between visual representations of molecular structure and the mathematics of quantum mechanics in the formation of quantum chemistry, see Hendry (2001). 12

Discussing Hesse’s critique of correspondence rules in the received view, Suppe (1977, pp. 95-102) questions whether Hesse establishes the indispensability of iconic models. This seems to us to get the burden of proof the wrong way round. Hesse and others give examples of iconic models at work: it is for the semantic view to show that every iconic model can be reduced to a semantic model, in a way that fully explains, rather than re-describes, the heuristic power of the iconic model.

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5. The Limits of Structural Representation The lesson we would draw from the Bohr atom is that Bohr’s mathematical equations, just like the earlier visual media, represent what they do only given their historical context. In this section we seek to generalize this conclusion and assimilate it into our understanding of how models represent. Considering representation under its most general description, as an intentional relation, we argue that paradox and error arise when models, conceived as abstract mathematical structures, are considered outside of the contexts in which they are capable of realizing their role in science, representation. Representation has two elements: success and denotation. To the extent that it can be evaluated in terms of faithfulness or unfaithfulness, representation should at least involve either some comparative criterion according to which (in stated respects) some representations are better than others, or perhaps some absolute criterion that only good representations meet. Let us call this the criterion of success: it is, we think, irresistible to take it to play a role like that of truth in semantics. Now, proponents of the semantic view have proposed isomorphism (Suppe), embeddability (van Fraassen), similarity (Giere) and partial truth (da Costa and French) as criteria of success. For van Fraassen, to claim empirical adequacy for a theory is to claim that a model of the appearances can be embedded in a model of the theory. Giere measures success in terms of similarity (in specified respects, and to specified degrees) between a real-worldly system and some specified model. But success can only be one dimension of representation, the other being denotation. Besides, representational success cannot be reduced to a purely structural relation. Long ago, Goodman (1968, Chapter 1) noted that to identify representation with resemblance is to trivialize it, for there are too many resemblances (that is, instances of the two-place relationship x resembles y).13 Firstly, any thing resembles any other thing in some

13

Hughes’ (1997) DDI account of theoretical representation invokes Goodman’s insight, and Suárez (1999) also argues for an intentional element to scientific representation.

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respect and to some degree. So it must already be understood which elements (and which of their features) are represented, and how: this is denotation. Secondly, resemblance is reflexive and symmetric, while representation is irreflexive and anti-symmetric: resemblance fails to capture the intentional element in representation. When A resembles B, it follows only that A might be used to represent B (and indeed vice versa), not that A represents B. Denotation is part of representation, and representation can admit of non-trivial success or failure only given prior relations of denotation. Of course Goodman went further, famously arguing that resemblance is not necessary for representation either. This sounds right when it comes to linguistic representation. But in general, denotation without some implied measure of representational success is empty. Perhaps any thing can be used to stand for any other thing regardless of their resemblance: thus can a pepper-pot represent the Duke of Wellington’s forces in a table-top re-enactment of the Battle of Waterloo. But “standing for” in this sense succeeds by stipulation: it cannot admit of failure. To the extent that representation in science can succeed or fail, it cannot be so established by mere denotation. When mathematics is used to represent some part of the world, the representation is partly a matter of denotation (that is, more-or-less implicit stipulation) and partly some other relation whose obtaining is a matter of empirical investigation. So there is more to representation than success. In fact, it makes no sense to speak of representational success unless denotational relations are already in place. To use the oft-paraphrased Kantian precept, representational success without denotation is blind, whereas denotation without representational success is empty. Goodman’s points about resemblance generalize to the structural notions of success favored by defenders of the semantic view. Representation cannot reduce to isomorphism, simply because there are too many isomorphisms. A particular relation-instance of isomorphism can be representational only in the context of a scheme of use that fixes what is to be related to what, and how. We think that these points have

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some grave implications for the structuralism14 that is sometimes associated with the semantic view of theories. For instance, van Fraassen (1997, p. 522) argues that since scientific representation comes down to isomorphism, and isomorphism preserves just structure, the semantic view is committed to the thought that “science’s description of its subject-matter is solely of structure.” Why isomorphism? Van Fraassen offers the following argument: models are mathematical objects, that is, not relevantly differentiated beyond isomorphism: qua mathematical entities, models possess only structure. So when we use a model to represent some part of the world, the resultant description of the world cannot “ ‘cut through’ structure” (1997, p. 522). But given what we said above, there are just too many isomorphisms, and all of them are equally good representations, if representation cannot “cut through” isomorphism. In fact there are two problems here. Firstly, qua structure, there is nothing to distinguish a data-model of the simple periodic motion of a pendulum from that of a suitably-described economic cycle. Secondly, even when the subject of the model is fixed, we can define a relational structure on its subject domain, cardinality permitting, in such a way as to guarantee isomorphism. If there is nothing more to empirical adequacy than isomorphism, we need pursue no empirical investigation to assure ourselves of the empirical adequacy of our theory (again, cardinality permitting). Now van Fraassen is well aware of these objections.15 He notes that “if one structure can represent the phenomena, then so can any isomorphic structure, mutatis mutandis” (1997, p. 522). The Latin clause is crucial. It seems to give, in two words, what van Fraassen misses: that other, non-structural, consid-

14 Structuralism is the view that science provides only structural (mathematical, or set-theoretic) information about processes in nature. One version of structuralism has it that it is possible to know only the truth of a theory’s Ramsey sentence, not the truth of the theory itself. For more on this, see Psillos (2001). 15

The second problem was first raised, in its essence, against Russell’s (1927) structuralism by M.H.A. Newman (1928); see Demopoulos and Friedman (1989, p. 189) and Psillos (1999, chapter 3).

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erations single out one among the many isomorphisms as that which is intended. Van Fraassen concedes that the structural relationship which on his version of the semantic view is constitutive of empirical adequacy is representational only in the particular context of use: “. . . in science models are used to represent nature, used by us, and of the many possible ways to use them, the actual way matters and fixes the relevant relation between model and nature — relevant, that is, to the evaluation as well as application of that theory” (1997, p. 523). Moreover, that context is conditioned by history and theory. This concession arose in the context of an acknowledgement qualifying (but not, he insists, weakening) the structuralist commitment of the nonlinguistic view. But in view of this concession, does van Fraassen’s structuralist conclusion still follow from his premise, the semantic view? That conclusion depends on two erroneous assumptions about scientific uses of mathematics: firstly, that mathematical descriptions provide only structural information about the objects they pick out (because these objects are “structures” in the technical sense); secondly, that descriptions of families of models are all there is to scientific theories (this is just the strong non-linguistic view of theories). But these assumptions have already lapsed in van Fraassen’s attempt to come to terms with the fact that isomorphism is too weak a representational relation. It is instructive to see why. To overcome the ubiquity of isomorphism, van Fraassen appeals to pragmatics, and the specific denotative relations that are part of a language in use, admitting that structures represent non-trivially only in contexts that are partly determined by these relations. If invocation of the denotative context is to dissolve the “too-many-isomorphisms” problem, context must be sufficient to determine that the subjectmatter of the equations appearing in a physics text are, physical systems (e.g., gas molecules), rather than, say, populations of bacteria.16 16

It may well be that van Fraassen’s appeal to language-in-use is meant to apply only to data models, so as to differentiate data models of bacteria populations from those of radioactive decay. In that case much of what follows does not apply. But then the subject-matter of the theory is fixed only at the point of contact with the data model, a deeply counterintuitive consequence

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So the objects picked out by the equations of a physical theory are physical systems, not abstract structures. To be sure, if the equations are understood as they would be in a mathematics text, we might concede for the sake of argument that they pick out classes of objects only sub specie formae. But if the context is that of a physics paper, the equations are accompanied and motivated by text (written, perhaps, in physics-Greek, physics-English, or physics-French), which is as much part of (the particular presentation of) the theory as are the equations themselves. The point is not merely that anything that can be said is said in a language, although that is true enough. Rather it is that the equations do not pick anything out non-trivially except in a richer context, and in the richer context under consideration here, the equations are being used — in conjunction with text — to make claims about the possible physical states of certain kinds of physical system. Hence structuralism lapses, for it is premised on a mistaken view of theoretical representation: even if the discipline of mathematics is interested in structure for its own sake, science is an activity that is directed outward to the world, and hence uses mathematical structure to represent things. We should not be tempted to reify structure as something attributed in our descriptions: to consider a thing under an abstract (or structural) description is neither to think of it as an abstract object, nor to think of it as something that bears a structural relation to one. Embedded in theories, mathematical equations can be used to make sophisticated and abstract claims about real physical systems; the representational cash value of mathematics, within science, must lie in the truth-conditions of the claims it can be used to make about them. There is no more reason to think that it can be used to convey only structural information than there is to think that twodimensional images can be used to convey only information about twodimensional objects. It may be objected here that, as noted above, van Fraassen’s appeal to the language in which the structural claim is made is driven by pragmatic rather than metaphysical considerations (see van Fraassen that we considered in Section 3. In any case, from the point of view of semantics van Fraassen has previously treated the observational and the theoretical symmetrically.

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1997, p. 525). But even if it were to be conceded that no metaphysical implications flow from the use of a language to describe the structural claims made by theories, it would still not save the argument for structuralism. Mixing structuralism with the thought that pragmatics determines choice of one structure among many yields no less explosive a brew than mixing it with the thought that one structure described in a preferred language offers the correct description of the world. In either case, pure structuralism must go, even though different metaphysical pictures are left in its wake. 17

6. The Interactive Approach It is time now to turn to our positive view of how the weak versions of the two grand approaches to theories can co-habit in what we call an “interactive approach.” Parts of our positive view have already emerged in previous sections. Our starting point is a well-known quote from Heinrich Hertz: To the question “What is Maxwell’s theory?” I know of no shorter or more definite answer than the following: Maxwell’s Theory is Maxwell’s system of equations. Every theory which leads to the same system of equations, and therefore comprises the same possible phenomena, I would consider as being a form or special case of Maxwell’s theory; every theory which leads to different equations, and therefore to different possible phenomena is a different theory. (1893, p. 21)

How far off the mark, if at all, was this claim? Leaving aside issues of historical interpretation, Hertz was concerned with the problem of individuating theories.18 Maxwell’s equations were important because, 17

This issue is discussed in more detail in Demopoulos and Friedman (1989), and Psillos (1999, chapter 3). 18 A careful reader might object that there is some unclarity in the Hertz quote about whether the notion of equation includes a physical interpretation of its terms. Could it not be the case that some non-electromagnetic domain could in principle be said to satisfy Maxwell’s equations? Is it clear that Hertz would not allow this? If Hertz allowed for this, then we would like to make clear that his position is modified: it is equations interpreted in the language of the theory that we are interested in. But it is not hard to see that for Hertz too the possible interpretations of Maxwell’s equations are doubly constrained. They

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by systematizing the most fundamental laws of behavior of the electromagnetic field, they put an order to what Hermann von Helmholtz (see Hertz 1955 [1894], p. 4) had called “the pathless wilderness” of the domain of electromagnetism. Hertz’s claim did not really miss the mark, because mathematical equations, which typically express laws of behavior, lie at the heart of any typical scientific theory, at least in mathematical physics. They are the core means by which a theory expresses its content and represents its domain. Now mathematical equations present a case in which two representational media work closely together: language and models of physical systems. Mathematical equations are bits of (a formal) language. (Giere is in agreement here: see his 1988, p. 86). They are written down on paper. They are translated into different, but equivalent, notation. They are interpretable, and are indeed interpreted and re-interpreted. Clearly an equation itself is not an extra-linguistic entity. It is a statement. It does say something about one or more extra-linguistic entities, but it is not one of them. So here we have linguistic representation at work at the heart of theory. Mathematical equations are surely part of what makes a theory what it is, and hence linguistic representational media are also part of makes a theory what it is. How, and exactly what, do mathematical equations represent? They describe the behavior of, and inter-connections among, physical magnitudes. These magnitudes, such as the strengths of electric and magnetic fields, are represented by mathematical entities, such as vectors. But we should not lose sight of the fact that it is physical magnitudes and not mathematical entities of any sort (e.g. abstract mathematical structures) that are being described. Take, for instance, the linear harmonic oscillator. This is a system which has a certain lawlike behavior described by a mathematical equation. This system is

are constrained from below: as he explicitly said in the quoted passage, the interpretation of Maxwell’s equations should be able to account for the same “possible phenomena.” But they are also constrained from above. Hertz’s embarkation on the problems of the foundations of mechanics (1955 [1894]) was motivated by his attempt to unify the mechanical picture of the world with the then emerging electromagnetic picture.

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physical (and not abstract-mathematical) precisely because it has physical properties (described in the language of physics), and if it exists, it is supposed to participate in causal interactions and processes. But a linear harmonic oscillator is an idealized physical system. It is idealized because some of the physical relationships holding within actual physical entities that can be modeled as linear harmonic oscillators (e.g. pendula and springs) have been eliminated, and because some of the parameters that influence (and determine) the behavior of such actual entities (e.g. pendula and springs) have been abstracted away.19 Exactly for this reason, a linear harmonic oscillator can be seen as an unactualized physical system.20 That is, strictly speaking, and as a matter of contingent fact about the world, it is uninstatiated. But this is if we talk strictly. For we have every reason to believe that a linear harmonic oscillator is inexactly instantiated in actual physical entities such as pendula and springs. Differently put, such physical systems are inexact counterparts of a linear harmonic oscillator. It is this fact of inexact instantiation that makes mathematical descriptions of linear harmonic oscillators so useful in describing and explaining the behavior of actual physical systems. From now on, we shall employ the expression ‘unactualized physical system’ (UPS) to refer to the systems studied by physical theories. This expression is meant to emphasize that the systems studied by physical theories are not the abstract mathematical entities of the semantic approach. If the entities described by physical theories were the abstract mathematical entities of the semantic approach, then in order to make them stand in any meaningful representational relation to actual physical systems (their actual counterparts), we would not only have to introduce theoretical hypotheses, but also interpret them physically. It follows from our argument in Section 5 that a linear harmonic oscillator qua mathematical entity could not meaningfully represent pendula and springs. (As a reminder: the relation of isomorphism is not enough for

19 For more on the relationship between idealization and abstraction, see Nowak and Nowakowa (2000, pp. 116-117). 20

Suppe (1989, p. 85) also relates idealized models to counterfactual situations.

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representation.) Qua unactualized physical system, a linear harmonic oscillator can be said to have actual, but inexact, counterparts, which explains why it can be used to represent their behavior. Our suggestion might create some unease. What, one might wonder, do theories represent? We think that this question admits of a canonical answer only if we take account of the contingent fact that the behavior of actual physical systems like springs, pendula and planetary systems is too complex to be studied directly, exactly and fully by physical theories we can devise. It is precisely because of this fact that there is need for “middle-men,” that is, for representational devices that are themselves the objects of direct, exact and full treatment, which can then be taken to represent indirectly, inexactly and partially (all these depending on the particular case) actual physical systems. So, the answer we offer to the foregoing question is the following. Theories study, via mathematical equations, the behavior of UPS (the middle-men), which, nonetheless, represent actual physical systems. Hence equations represent actual systems, if only indirectly, inexactly and partially. So, ultimately, the content of theories is the behavior of this-worldly physical systems, in particular those systems which (suitably prepared, perhaps in laboratories) closely resemble the UPS posited to represent them. Theories posit and study UPS in order to capture (and represent) the behavior of actual physical systems. UPS are suitable for theoretical investigation. And in so far as they have (inexact) counterparts, they guarantee that theories have empirical content. It is worth emphasizing two points. We should distinguish between the (clusters of) physical properties ascribed to unactualized physical systems in physical equations from the unactualized physical systems themselves. Only the latter can stand in relations of similarity to actual physical systems. Secondly there is the role of theoretical hypotheses. Where do we stand on this issue? We do admit that theoretical hypotheses sometimes have a role, as, for instance where exemplars are associated with a theory like quantum mechanics. In this case, there may be competing quantum-mechanical theories employing different exemplars to represent some class of physical systems. But we resist the view that theoretical hypotheses are indispensable. It seems a

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mistake to us to see theoretical hypotheses at work in Bohr’s 1913 model of the atom. That model was not set up as an application of a more general mechanical theory. It is part of its historical identity that it was about atomic structure. Nor are theoretical hypotheses needed to interpret the equations that describe the UPS. These are already interpreted, albeit at a general level (‘m’ stands for mass, ‘v’ stands for velocity and so on). Moreover, we have shown how theoretical hypotheses work, in so far as they do. Because the theoretical hypothesis links the UPS as described by the interpreted equation (rather than an abstract object) with actual systems, it is intelligible how the relation of similarity can apply. Do we consider theoretical hypotheses to be part of the theory when they are present? Not in the case of quantum mechanics, which was propounded, through its exemplars, prior to its model of the hydrogen atom. But quantum-mechanical equations still denote, via the standard interpretation of the terms that appear in the descriptions of its models. Yet they denote at such a general level that they can not be used to predict (a point often made by Nancy Cartwright, see her 1983). One might usefully call these UPS “theoretical models,” or as Hertz put it “dynamical models” (1955 [1894], p. 175). They are models in the sense that a UPS and what it is a model of are, again according to Hertz, “dynamically similar.” The qualifier ‘dynamical’ already takes care of the respect in which the model is similar to its actual but inexact counterparts. Actual physical systems, the subject-matter of scientific theories, are represented by dynamical models in virtue of the fact that their own dynamics can be subsumed under the dynamics of the model: if the theory is correct, then if they were exact instances of the kind of system represented by the model, the actual physical systems would behave exactly as the corresponding theoretical model does. This last point captures the central insight behind the weak version of the semantic view, as advanced by Giere (1988) and Suppes (1989), and corrects it by de-mathematizing it. The proposed correction of the view propounded by Giere and Suppe lies in our insistence that language, as a means of representation, is indispensable in our theorizing about the world: it does ineliminable representational work within

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theories. The process by which mathematical equations represent involves two representational media, neither of which can be left out without representational loss. The first step is the construction of an equation (a linguistic medium) which represents the behavior of a UPS. The second step is the comparison of the UPS (a non-linguistic medium) with what it is meant to represent: actual physical systems. In our two-step process of representation, the UPS is both the subject of (linguistic) representation, by an equation, and also a vehicle of (non-linguistic) representation, of actual physical systems: idealized, the latter are seen as inexact instances (or counterparts) of the UPS. (Hence our approach is “interactive.”) It should be stressed that these “steps” are merely notional, since one does not have to consider each separately, or in the suggested order, to interpret the model correctly. In any case we should certainly leave open the possibility that a theory directly describes actual physical systems in that the UPS it studies do have this-worldly exact counterparts. But it is much more typical that the theory’s UPS are not exactly instantiated in the world. Nothing of philosophical importance hangs on this issue. What is important is that if we leave one of the above media out of an account of theories, we leave out an essential part of the process by which theories represent their domain and have determinate empirical content. Not only should models not be considered in isolation from language (on pain of conflating physical models with abstract structures) but, more importantly, language in its own right is a central representational device for theories. It has been objected that the appeal to language as a representational device is inessential, since what really happens when the theory is applied to the world is the comparison of two objects, one abstract (the model) and one concrete (the worldly physical system) (see Giere 1988, p. 82). But care is needed here: to elaborate on a point made earlier, models should not be taken to be abstract objects, in the sense in which metaphysicians use that word. Take, for instance, a Newtonian model of the earth-moon system. To say that the earth-moon system has the structure of a two-body Newtonian system is to say that the latter is an abstraction of the former such that the two share structure. The description, in the language of mathematical physics, of

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a two-body Newtonian system is an abstraction in the sense that it subtracts such secondary features as the chemical constitution of the earth’s and moon’s masses. But from this it does not follow that a twobody Newtonian system is an abstract entity. Indeed it cannot be, if a two-body Newtonian system is to be comparable at all to the earthmoon system. For the latter inhabits ordinary physical space, it can enter into genuine causal relationships, its state changes over time. Of course, abstract and concrete systems can exhibit isomorphic structures, but as noted in section 5, mere isomorphism cannot do justice to representation; and if, as Giere, suggests, the required representational relation is similarity, it is not clear at all that it can obtain between abstract and concrete objects. In conclusion, the usual philosophical tools for individuating theories — models and statements — are separately unable to explain how theories fulfill their central task: representing the world. The linguistic approach (in both of its versions) has obscured the role of models (i.e. of UPS) in representing, while the non-linguistic approach has obscured the role of language (in particular, of mathematical equations). Theories are complex entities because both language and models are used — side by side — in order to represent. But theories are yet more complex than that: as argued in section 4, entities other than sentences and (semantic) models can play central roles in theoretical representation. That theories are consortia of representational media may be the most general and informative thing to say by way of characterizing their composite nature.

7. Unreconstructed Theories In pursuing their claims about particular scientific theories, philosophers and historians of science take as substrate the written, drawn and spoken products of scientific theorizing and distil the joint “content” of these products, using whatever formal tools are available to them. Of course the relationship between substrate and product in this process is not a simple one: the scientists’ claims may have to be rounded out to capture a theory’s commonly agreed implications,

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“filled in” with extra structure for completeness, or cleaned up in the interest of consistency. The nature and extent of this rational reconstruction will reflect the (philosophical or historical) purposes of the analysis. Ideally, it will aim to give an unambiguous answer to the question: What is Theory X ? (e.g., the Caloric Theory, or Newtonian Mechanics, or the General Theory of Relativity). Answering this question is supposed to give us a handle on the following question: what is the world like according to theory X ? Even more ideally, such reconstructions aim to provide the raw material for a more general attempt to theorize about what all these different theories have in common. This kind of “theory of theories” is what suffuses accounts of their relations to evidence, relations to other theories, and of the things they can be used to do, like predict and explain. Both standard views have been comrades in their attempts to rationally reconstruct scientific theories. Where they differ is in the tools they use. The received (linguistic) view went for axiomatization, and if first-order formalization predominated, this was a function of the availability and transparency of first-order methods. Proponents of the semantic (non-linguistic) view have not been so unanimous. Different approaches within the semantic conception utilize different tools and crave formalization in considerably different degrees: from the axiomatize-everything-in-set-theory approach of Sneed and the German structuralists, through van Fraassen’s early state-space approach and Beth-semantics, to Giere’s and Suppe’s more informal attempt to reconstruct theories as families of abstract entities (Suppe 1989, Chapter 1 provides a historical survey). Be that as it may, the standard views have alike aimed at rational reconstruction. We do not want to doubt the usefulness of (moderate) formalization and reconstruction. But we should not lose sight of the fact that they are reconstructions, or mistake their products for the theories themselves. The question “What is a scientific theory?” seems to have escaped an answer which states necessary and sufficient conditions, and for good reasons. If our analysis so far has been correct, the complexity of the ways scientific theories represent does not allow the answer to the foregoing question to be reduced to simple recipes. The “formal perspective” takes no account of the fact that theories are

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historical entities, and in the history of science there are no clean-cut versions of theories. We have argued that theories are complex and evolving entities which involve basic hypotheses (typically expressed as equations), linguistic fragments loaded with analogical associations, causal stories as to how phenomena are produced, auxiliary assumptions and “bridge principles,” abstract and concrete models, and diagrams. Holding everything together are the basic equations, which introduce relations among the constituent parts, and their subject-matter: an evolving domain of physical systems (evolving because, for instance, supposed sui generis optical phenomena turn out to be electromagnetic phenomena). Now it may be that what is said using any particular representational medium could have been said using another medium. We would acknowledge the contingency of particular historical manifestations of theories, and stress that any philosophical analysis of theories should take this into account. If this is right, there seems to be no more informative answer to the question of the “real nature” of scientific theories than that they are complex consortia of different representational media held together by family resemblances. What calls for philosophical analysis instead is the different ways they represent the world.

University of Durham Department of Philosophy 50 Old Elvet Durham DH1 3HN UK [email protected] University of Athens Department of Philosophy and History of Science, Panepistimioupolis Athens 157 71 Greece [email protected]

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REFERENCES Carnap, R. (1939). Foundations of Logic and Mathematics. Chicago: University of Chicago Press. Carnap, R. (1956). The Methodological Character of Theoretical Concepts. In: H. Feigl and M. Scriven (eds.), Minnesota Studies in the Philosophy of Science, vol. 1, pp. 38-76. Minneapolis: University of Minnesota Press. Carnap, R. (2000). Theoretical Concepts in Science. (Edited with an introduction by S. Psillos.) Studies in History and Philosophy of Science 31: 151172. Cartwright, N. (1983). How the Laws of Physics Lie. Oxford: Clarendon Press. da Costa, N. and S. French (1990). The Model Theoretic Approach in the Philosophy of Science. Philosophy of Science 57: 248-265. Demopoulos, W. and M. Friedman (1989). The Concept of Structure in The Analysis of Matter. In: C. Wade Savage and C. Anthony Anderson (eds.), Rereading Russell (Minnesota Studies in the Philosophy of Science, vol. 12), pp. 183-199. Minneapolis: University of Minnesota Press. Duhem, P. (1954 [1906]). The Aim and Structure of Physical Theory. Translated by P. P. Wiener, 1954. Princeton: Princeton University Press. Francoeur, E. (1998). The Forgotten Tool: The Design and Use of Molecular Models. Social Studies of Science 27: 7-40. French, S. and J. Ladyman (1998). Semantic Perspective on Idealization in Quantum Mechanics. In: N. Shanks (ed.), Idealization in Contemporary Physics (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 63), pp.51-73. Amsterdam: Rodopi. French, S. and J. Ladyman (1999). Reinflating the Semantic Approach. International Studies in the Philosophy of Science 13: 103-21. Giere, R.N. (1988). Explaining Science: A Cognitive Approach. Chicago: University of Chicago Press. Giere, R.N. (2000). Theories. In: W.H. Newton Smith (ed.), A Companion to the Philosophy of Science. Oxford: Blackwell. Goodman, N. (1968). Languages of Art. Indianapolis: Bobbs-Merrill. Hendry, R.F. (1999). Theories and Models: The Interactive View. In: R. Paton and I. Neilson (eds.), Visual Representations and Interpretations, pp. 121130. London: Springer-Verlag. Hendry, R.F. (2001). Mathematics, Representation and Molecular Structure. In: U. Klein (ed.), Tools and Modes of Representation in the Laboratory Sciences, pp. 221-236. Dordrecht: Kluwer. Hendry, R.F. (forthcoming). Wave Mechanics, Matrix Mechanics and Intertheoretic Equivalence. Unpublished manuscript.

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Hertz, H. (1893). Electric Waves. Translated by D.E. Jones. London: McMillan. Hertz, H. (1955 [1894]). The Principles of Mechanics Presented in a New Form. Translated by D. E. Jones and J. T. Walley, 1955. New York: Dover. Hesse, M.B. (1966). Models and Analogies in Science. Notre Dame: University of Notre Dame Press. Hughes, R.I.G. (1993). Theoretical Explanation. In: P. French, T. Uehling and H. Wettstein (eds.), Midwest Studies in Philosophy, vol. 18, pp. 132-153. Notre Dame: University of Notre Dame Press. Hughes, R.I.G. (1997). Models and Representation. Philosophy of Science 64 (Proceedings): S325-36. Knight, D.M. (1985). Scientific Theory and Visual Language. In: A. Ellenius (ed.), The Natural Sciences and the Arts: Aspects of Interaction from the Renaissance to the 20th Century, pp. 106-124. Stockholm: Almqvist and Wiksell International. Reprinted in: D. M. Knight, Science in the Romantic Era (Aldershot: Ashgate), pp.177-95. Knight, D.M. (1996). Illustrating Chemistry. In: B. S. Baigrie (ed.), Picturing Knowledge: Historical and Philosophical Problems Concerning the Use of Art in Science, pp. 135-163. Toronto: University of Toronto Press. Lakatos, I. (1970). Falsification and the Methodology of Scientific Research Programmes. In: I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge, pp.91-196. Cambridge: Cambridge University Press. Lloyd, E.A. (1988). The Structure and Confirmation of Evolutionary Theory. Westport: Greenwood Press. Müller, F. (1997). The Equivalence Myth of Quantum Mechanics: Parts I and II. Studies in History and Philosophy of Modern Physics 28B: 35-61 (I), 219247 (II). Newman, M. H. A. (1928). Mr. Russell’s ‘Causal Theory of Perception’. Mind 37: 137-148. Nowak, L. and I. Nowakowa (2000). Idealization X: The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam: Rodopi. Psillos, S. (1995). The Cognitive Interplay Between Theories and Models: The Case of 19th Century Optics. In: W. E. Herfel, W. Krajewski, I. Niiniluoto and R. Wójcicki (eds.), Theories and Models in Scientific Processes (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 44), pp. 105-133. Amsterdam: Rodopi. Psillos, S. (1999). Scientific Realism: How Science Tracks Truth. London: Routledge. Psillos, S. (2001). Is Structural Realism Possible? Philosophy of Science (Supplement) 68: S13-24.

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Schrödinger, E. (1928 [1926]). On the Relation between the Quantum Mechanics of Heisenberg, Born, and Jordan, and that of Schrödinger. In: Collected Papers on Wave Mechanics, pp. 45-61. London: Blackie, 1928. Originally published as: Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen, Annalen der Physik 79 (1926): 734-56. Suárez, M. (1999). Theories, Models and Representations. In: L. Magnani, N.J. Nersessian and P. Thagard (eds.), Model-Based Reasoning in Scientific Discovery. New York: Plenum. Suppe, F. (1977). The Search for Philosophic Understanding of Scientific Theories. In: F. Suppe (ed.), The Structure of Scientific Theories, pp. 1-241. Urbana: University of Illinois Press. Suppe, F. (1989). The Semantic Conception of Theories and Scientific Realism. Urbana: University of Illinois Press. Suppes, P. (1960). A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences. Synthese 12: 287-301. Suppes, P. (1967). Set-Theoretical Structures in Science. Mimeographed. Institute for Mathematical Studies in the Social Sciences. Stanford University, Stanford, California. Suppes, P. (1969). Models of Data. In: Studies in Methodology and Foundations of Science, pp. 24-35. Dordrecht: Reidel. Russell, B. (1927). The Analysis of Matter. London: Routledge and Kegan Paul. van Fraassen, B. C. (1980). The Scientific Image. Oxford: Clarendon Press. van Fraassen, B. C. (1989). Laws and Symmetry. Oxford: Clarendon Press. van Fraassen, B. C. (1995/1996). A Philosophical Approach to the Foundations of Science. Foundations of Science 1: 5-18. van Fraassen, B. C. (1997). Structure and Perspective: Philosophical Perplexity and Paradox. In: M.L. Dalla Chiara, K. Doets, D. Mundici, and J. van Benthem (eds.), Logic and Scientific Methods, pp. 511-530. Dordrecht: Kluwer. van Fraassen, B. C. and J. Sigman (1993). Interpretation in Science and the Arts. In: G. Levine (ed.), Realism and Representation: Essays on the Problem of Realism in Relation to Science, Literature and Culture, pp. 73-99. Madison: University of Wisconsin Press.

Izabella Nowakowa THE METHOD OF IDEAL TYPES VERSUS THE METHOD OF IDEALIZATION

I. The aim of the paper is to compare two traditions in the theory of idealization — the one stemming from Weber with the one stemming from Hegel. However, we will investigate the issue not on a historical but on a systematic plane. This will require us to consider the explications of both traditions. We will use the reconstruction proposed by C.G. Hempel and P. Oppenheim as an explication of the Weberian tradition and the reconstruction proposed by L. Nowak as an explication of the Hegelian tradition. It should be noted that the task has already been partially undertaken by Nowak (1980, ch. 5) who conducted a methodological analysis of the differences between the method of idealization/concretization and the method of ideal types. His main result was that while the method of idealization/concretization leads to the postulation of a special type of hypotheses, the method of ideal types leads to a special type of analytical statements. The task I set myself in this paper is to find conceptual differences between the traditions that generate so different methodologies.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 159-165. Amsterdam/New York, NY: Rodopi, 2007.

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II. In Weber’s tradition, the method is that of an instrumental construction of concepts of a certain kind. Such concepts serve to systematize real phenomena, where the “distance” between the real and the ideal type is the measure of the systematization (Pawáowski 1977, pp. 64 f ). In the Hegelian-Marxian tradition, on the other hand, the method is designed for the construction of statements of a certain type. One identifies idealizing conditions, under which a certain simple regularity holds, and then one waives those conditions and thus modifies the regularity. In this way, the original claim becomes more realistic or, in other words, concretized (Nowak 1971). These two methods are so different that one might wonder whether they are commensurable. In other words, it is unclear whether there is a consistent conceptual apparatus, which could serve to paraphrase the main ideas of both approaches to idealization, and which would then allow us to compare them.

III. Let us begin with a standard explication of Weber’s conception.1 Let R be a relation partially ordering the set of objects U. The relation of indistinguishability is defined as the product of the complements of relation R and its converse RĻ (I = non-R ∩ non-RĻ). On the additional assumption that I is transitive, it is an equivalence relation, which divides the set U into classes of abstraction. The family of those classes of abstraction turns out to be linearly ordered by relation W defined thus: XWY iff for every x ∈ X and for every y ∈ Y: xRy. The systematization of the set U is the set of classes of abstraction ordered by W. The extreme element of this systematization is called a “type”. If it is empty, it is called an “ideal type.” The concept whose denotation is the ideal type is called the “ideal-type concept.”

1

The idea of this explication derives from Hempel and Oppenheim (Hempel 1960). See also Pawáowski (1969; 1977, p. 108f ) and Kmita (1971).

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The construction just sketched manages to capture the central idea of the Weberian tradition but it does not capture the Hegelian way of understanding idealization. On the latter view, a crucial role is played by idealizing conditions, which eliminate the influence of certain factors on others. How can the role of such conditions be understood in terms of the systematization of a given set of objects? In any systematization ¢S0, S1, . . . , Sn, . . .², where S0 is the ideal type and S1, . . . , Sn, . . . are real types, all of its members are distinguished with the same respect ρ expressed in the original relation R. The difference between them is the difference of intensity. We can thus describe the difference by assigning different measures of intensity of ρ to the objects of the classes. The measure is at the lowest for the first, ideal, member of the systematization and it becomes the greater, the further away from the ideal a given member is: ρ(x) = m0, ρ(y) = m1, . . . , ρ(z) = mn, . . . where x, y, . . . , z, . . . are the elements of the members of the systematization S0, S1, . . . , Sn, . . ., and the measures assigned to them become ever greater: m0 < m1 < . . . < mn < . . . . This shows that the intuitions underlying the concept of an idealizing assumption cannot be introduced into Weber’s conception. After all, the point of introducing an idealizing assumption in the construction of a law is to abstract from a variety of factors. The point is to eliminate not the elements of some systematization but the whole systematization, which is considered inessential to a given one. Just as idealization consists in “disattaching” a systematization, so concretization consists in “reattaching” it. It should be emphasized that concretization cannot be understood as the “distance” between an ideal type and a given “real” member of a systematization. Any ideal type would then have an unlimited number of “concretizations” so conceived whereas an idealizational law has only one concretization with respect to a given secondary factor (see Kmita 1971). Both are operations on more than one systematization whereas the method of ideal types operates within one and the same systematization. This leads to the conclusion that a Hegelian-type of idealization cannot be reduced to a Weberian-type of idealization. Let’s consider whether the reverse reduction is possible.

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IV. Let a set Z of properties be given. Let a be an object characterized by a set G of properties, where G ⊂ Z.2 Each property from G pertains to object a with some intensity, whereas the remaining properties (Z – G) do not pertain to a at all — they are absent from a altogether or, as we shall also say, they are the property-lacks of a. Let a be a real object. This entails that a has a non-empty set of properties G and a nonempty set of property-lacks B (B = Z – G). A merely possible object with respect to a is an object aĻ such that aĻ has all the properties from G and all the property-lacks from B, however, at least one property from G pertains to aĻ to a different degree than it pertains to a. The set of what are called possible objects (possibilia) includes a and all the merely possible objects with respect to a. All the possible objects are equipped with the same properties (and property-lacks) as a. Possible objects differ, however, in the intensities with which the same properties pertain to them. The ideal (resp. mythical) type is a possible object with a minimal (resp. maximal) intensity of the properties. A reduct of an object a is such an object aĻ that lacks at least one property from the set G. A reduct of a is thus characterized by a smaller set of properties, and a greater set of property-lacks, than a.3 One can distinguish first-order reducts of a (which lack only one property from G), second-order reducts of a (which lack two properties from G), and so on. Finally, assuming that G has k properties, kth-order reducts are the so-called empty objects, characterized by no properties from Z. Whereas reducts of a have a smaller set of properties and a greater set of property-lacks than a, transcendentalia of a have a greater set of properties and a smaller set of property-lacks than a. First-order transcendentalia of a have one more property than a and one less property-

2

I’m following Nowak’s (1998, pp. 167f ) approach. The only change I’m making is that whereas Nowak uses a factualist language, I’m using a substantialist language. 3

The concept of a reduct captures the intuitions expressed by ZieliĔska (1981), who introduces the concept of an abstract to capture the same intuitions.

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lack than a, second-order transcendentalia have two more properties than a and two less property-lacks than a, and so on. In the limiting case, there are complete objects. A complete object is an object that has all the properties from Z. Given an object a, we can generate a set of its deformants, i.e. the set of all possibilia with respect to a (including the ideal and the mythical types), all reducts and transcendentalia of a, as well as possibilia with respect to the reducts (resp. transcendentalia) of a. Deformational procedures are counterfactual methods of recreating the table of deformants of a given object (Nowak 1990). 4 The procedure of potentialization of an object a consists in the postulation of a possible object aĻ such that aĻ differs from a in that a certain property ω pertains to aĻ to a different degree than it pertains to a. If the degree to which ω pertains to aĻ is greater than the degree to which ω pertains to a, we speak of a positive potentialization, otherwise we speak of a negative potentialization. Potentialization preserves the set of properties of the original object. The procedures of reduction and transcendentalization, on the other hand, change that set of properties. Reduction consists in the counterfactual postulation that an object a lacks some of its properties. Transcendentalization consists in counterfactually ascribing to a properties that it in fact lacks. Reduction decreases whereas transcendentalization increases the set of properties that an object has.

V. In terms of the conceptual apparatus just sketched, idealization can be identified with a joint procedure of reduction and negative potentialization. For example, to assume that the Moon is centrobaric is, first, to reduce all of its other geological, chemical, etc. properties (including those that have already been discovered as well as those that could still

4

I’m summarizing here the simplest approach to the matter. For possible alternative approaches, see Nowak (1992) and Paprzycka and Paprzycki (1993).

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be discovered) and, then, to submit some of the remaining mechanical properties to negative potentialization, assuming that the whole mass of the Moon is concentrated in one point. Let us consider how to capture the Weberian method of ideal types in this apparatus. It seems that it could be paraphrased as the extreme case of negative potentialization. It would consist in the counterfactual assignment of the minimal value to a certain property of an object. The limiting case of merely possible objects are ideal types, i.e. such possible objects “generated” by a that have at least one of the properties (shared by a) with minimal intensity. On the above conceptualization, idealization includes the method of ideal types as a component of its special case. Idealization may consist in, and in fact often does consist in, the fact that certain properties are subjected to reduction and other properties are minimized. Idealization then usually involves a combination of reduction and the method of ideal types.

VI. I would draw two conclusions. (1) It is impossible to reconstruct the method of idealization in terms of the conceptual apparatus of the method of ideal types. (2) It is, however, possible to reconstruct the method of ideal types in terms of the conceptual apparatus of the method of idealization; the method of ideal types turns out to be a component of a special case of idealization. In other words, Hegelian abstraction is idealization, while the Weberian method of ideal types is a certain kind of potentialization. 5

5

It should be added that the above conclusions have a purely conceptual character. They would have to be supplemented with a methodological analysis, which would indicate further differences between the two methods considered here (see also Nowak 1980, pp. 4 f ).

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Uniwersytet im. A. Mickiewicza Department of Philosophy ul. Szamarzewskiego 89c 60-568 PoznaĔ Poland REFERENCES Hempel, C.G. (1960). Fundamentals of Concept Formation in Empirical Sciences. Chicago: Chicago University Press. Kmita, J. (1971). Z metodologicznych problemów interpretacji humanistycznej [On the Methodological Problems of Humanistic Interpretation]. Warszawa: PWN. Lazari-Pawáowska, I. (1967). O pojĊciu typologicznym w humanistyce [On the Typological Concept in the Humanities]. In: T. Pawáowski (ed.), Logiczna teoria nauki, pp. 639-667. Warszawa: PWN. Nowak, L. (1971). U podstaw Marksowskiej metodologii nauk [On the Foundations of Marxian Methodology]. Warszawa: PWN. Nowak, L. (1980). The Structure of Idealization: Towards a Systematic Interpretation of the Marxian Idea of Science. Dordrecht: D. Reidel. Nowak, L. (1990). Abstracts are Not Our Constructs. The Mental Constructs are Abstracts. In: J. BrzeziĔski, F. Coniglione, T.A.F. Kuipers, L. Nowak (eds.), Idealization I (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 16), pp. 193-206. Amsterdam/Atlanta: Rodopi. Nowak, L. (1992). MyĞl o czymĞ jest tym wáaĞnie. Nie ma wiĊc teorii bytu i teorii poznania: jest metafizyka. [A Thought Is What It Is about: There Is Not a Theory of Being and a Theory of Knowledge – there is Metaphysics] In: J. BrzeziĔski, K. àastowski, T. Maruszewski (eds.), O związkach teoretycznych w filozofii nauki i psychologii (PoznaĔskie Studia z Filozofii Nauki 12), pp. 7-63. Warszawa-PoznaĔ: PWN. Paprzycka, K., M. Paprzycki (1993). Kilka uwag o istotnoĞci i procedurach deformacyjnych [Some Remarks on Essentiality and Deformational Procedures]. In: J. BrzeziĔski, K. àastowski (eds.), Kategorie filozoficzne a poznawczy status nauki (PoznaĔskie Studia z Filozofii Nauki 14), pp. 203-212. PoznaĔ: Wyd. UAM. Pawáowski, T. (1969). Metodologiczne zagadnienie humanistyki [The Methodological Problem of the Humanities]. Warszawa: PWN. Pawáowski, T. (1977). PojĊcie i metody wspóáczesnej humanistyki [The Concept and the Methods of Contemporary Humanities]. Wrocáaw: Ossolineum. ZieliĔska, R. (1981). Abstrakcja, idealizacja, generalizacja [Abstraction, Idealization, Generalization]. PoznaĔ: Wyd. UAM.

Igor Hanzel LESZEK NOWAK ON SCIENTIFIC LAWS AND SCIENTIFIC EXPLANATION

The publication of this festschrift allows me to express the indebtedness of Slovak philosophers1 to Professor Leszek Nowak’s lasting contribution to philosophy of science, and especially to the issue of scientific laws and scientific explanation. Because I regard this contribution as important and as profound as that of C. G. Hempel, viewed in the Anglo-Saxon world as the classic of scientific explanation, I will first give a summary of his view, and then show how it is superseded in all its aspects by L. Nowak’s approach to laws and explanation. Finally, I will present a further development of L. Nowak’s views on the latter.

1. The D-N Model and Empirical Laws According to Hempel, a potential explanation is a “potential answer to a question of the form ‘why it is the case that p?’, where the place of ‘p’

1

On the impact of L. Nowak’s philosophy of science in Slovakia see, e.g., ýerník (1977), Viceník (1988) and Hanzel (1999).

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 167-178. Amsterdam/New York, NY: Rodopi, 2007.

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is occupied by an empirical sentence detailing the facts to be explained” (1965a, p. 421). He then identifies a scientific explanation as a potential explanation with true premises. Hempel represents scientific explanation, later labeled by him as the D-N model, by the following schema (Hempel and Oppenheim 1965 [1948], p. 249):

Logical

C1, C2, . . . , Ck

Statements of antecedent conditions

L 1, L 2, . . . , L r

General Laws

Explanans

deduction

E

Description of the empirical phenomenon to be explained

Explanandum

But, Hempel suggests, the explanandum may have the nature of an empirical law (characterized by a general regularity). Thus the scientific laws from which the explanation derives are theoretical laws, theoretical principles, or empirical laws of a broader scope than the empirical law to be explained (Hempel and Oppenheim 1965 [1948], p. 247; Hempel 1965a, p. 343; Hempel 1966, p. 51). In both cases, scientific explanation should have the character of a deductive argument (Hempel 1965a, p. 336; Hempel 1966, p. 50), and the whole process of explanation should be a unity of two steps: the subsumption of the event or law to be explained under a certain set of laws and the former’s deduction from the latter together with certain singular conditions pertaining to the event to be explained. In Hempel’s writings, at first glance, scientific laws, which constitute the foundation of explanation, are subject to analysis. They are, according to him, empirical laws that express a “uniform connection between different empirical phenomena or different aspects of one and the same phenomenon” (1966, p. 54). Their structure amounts to “whenever and wherever conditions of a specified type F occur, then so will, always and without exception, certain conditions another type, G ” (1966, p. 54). So, the empirical type of scientific law can be expressed in this way: (1) (∀x) (F (x) → G(x))

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As an example of such a law Hempel offers the statement “Whenever the temperature of a gas increases while its pressure remains constant, its volume increases” (1966, p. 54). A similar structure, according to Hempel, can be found in the statement “whenever a body falls freely from rest in vacuum near the surface of the earth, the distance it covers in t seconds is 16t2 feet” (1966, p. 54). These scientific laws, occurring in D-N explanations, are referred to by Hempel as causal laws since: [they] are always presupposed by an explanatory statement to the effect that a particular event of a certain kind G (e.g., expansion of a gas under constant pressure; flow of current in a wire loop) was caused by an event of another kind F (e.g., heating of the gas; motion of the loop across a magnetic field). To see this, we need not enter into the complex ramifications of the notion of the cause; it is sufficient to note that the general maxim, “Same cause, same effect,” when applied to such explanatory statements, yields the implied claim that whenever an event of kind F occurs, it is accompanied by an event of kind G. (1966, p. 53)

2. The Limits of Hempel’s Approach Despite its widespread acceptance in the fifties and sixties of past century, Hempel’s approach to explanation was from the very beginning plagued by severe problems. Hempel has already encountered his first problem when attempting to provide a definition of a scientific explanation by means of simple model language in Part III of (Hempel and Oppenheim 1965 [1948]). While he insisted, in Part I, that the explanandum might also be a scientific law, the process of that definition brought him to a recognition of the problem which he articulated in footnote 33, a problem which forced him to restrict his reconstruction of scientific explanation to apply only to a case of explanation of an event (Hempel and Oppenheim 1965 [1948], p. 273): This is not a matter of free choice: The precise rational reconstruction of explanation as applied to general regularities presents peculiar problems for which we can offer no solution at present. The core of the difficulty can be indicated briefly by reference to an example: Kepler’s law, K, may be conjoined with Boyle’s law, B, to a stronger law, K.B; but derivation of K from the latter would not be considered as an explanation of the regularities stated in Kepler’s laws; rather, it would be viewed as representing, in effect, a pointless “explanation” of Kepler’s

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laws by themselves. The derivation of Kepler’s laws from Newton’s laws of motion and of gravitation, on the other hand, would be recognized as a genuine explanation in terms of more comprehensive regularities, or so-called higher-level laws. The problem therefore arises of setting up clear-cut criteria for the distinction of levels of explanation or for a comparison of generalized sentences as to their comprehensiveness. The establishment of adequate criteria for this purpose is as yet an open problem.

But, though Hempel would later (1965a; 1966) insist that the explanandum in a D-N explanation might be a scientific law, he never settled this problem. Thus, his contention has not been verified, and the question of how scientific laws are explained remains completely open within the D-N model. Hempel’s approach to scientific explanation is also beset by further problems; the following three have been selected for consideration here. H. E. Kyburg Jr. (1965) argues against Hempel’s view on scientific explanation as follows. Let ‘P ’ stands for the predicate ‘. . . is inserted into water’, ‘Q ’ stands for the predicate ‘. . . dissolves’ and ‘R ’ stands for the predicate ‘the magic spell ‘Abracadabra’ is pronounced over . . .’ . If we accept the view that scientific explanation has the character of a deductive argument then the following case of explanation (the range of the variable x is a set of entities, which are common salt; a is a constant denoting such an entity) (∀x) (P(x) → Q (x)) P (a) Q(a) cannot be distinguished from the following pseudo-explanation (∀x) (P(x) & R(x) → Q(x)) P (a) & R (a) Q(a) J. Woodward (1979) goes even further and claims that not even the first of the above given examples with the common salt expresses a genuine scientific explanation because it enables us to derive one and only one explanandum, namely that stated above. Thus it does not fulfill the so-called requirement of functional interdependence, which he states as follows:

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The law occurring in the explanans of a scientific explanation of some explanandum E must be stated in terms of variables or parameter variations in the value of which will permit the derivation of other explananda which are appropriately different from E. (1979, p. 46)

As an example of a scientific explanation which fulfills this requirement Woodward mentions the case of explanation of “Galileo’s law in terms of Newton’s laws of motion and the law of gravitation by assuming that the earth is a sphere and that the only force on a falling body is due to the earth’s attraction” (1979, p. 42), while for Newton’s laws hold also that “we could use them to derive an expression for the rate of fall of a body falling from a distance which is no longer negligible in comparison with the earth’s radius” (1979, p. 47). Finally, Hempel’s D-N model fails when dealing with problem of causal explanation. Hempel himself states the following problem regarding explanation based on the equation T = 2Ⱥ (l/g)½ for a simple pendulum (‘T ’ stands for the period of the pendulum, ‘l ’ for its length): The law for the simple pendulum makes it possible not only to infer the period of a pendulum from its length, but also conversely to infer its length from its period; in either case, the inference is of the form (D-N). Yet a sentence stating the length of a given pendulum, in conjunction with the law, will be much more readily regarded as explaining the pendulum’s period than a sentence stating the period, in conjunction with the law, would be considered as explaining the pendulum’s length. This distinction appears to reflect the idea that we might change the length of the pendulum at will and thus control its period as a “dependent variable,” whereas the reverse procedure does not seem possible. This conception is questionable, however; for we can also change the period of a given pendulum at will, namely, by changing its length. It cannot validly be argued that in the first case we have a change of length independently of a change of the period, for if the location of the pendulum remains fixed, then its length cannot be changed without also changing the period. (1965a, pp. 352-353)

Hempel’s approach to scientific laws leaves also much to be desired. What strikes one immediately is its superficiality. So, for example, he states the law “All gases expand when heated under constant pressure” (1965a, p. 338) but then, without exhausting the possibilities of the first-order predicate calculus, collapses its intricate “fine-structure” into the oversimplified formula (∀x) (F (x) → G (x)). He thus does not take into account neither that it pertains to entities of a certain kind

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(body, gas) nor that it holds only for certain idealizations (vacuum, constant pressure). If we summarize, we may say that Hempel’s approach to scientific explanation as expressed in his D-N model, fails in at least fourfold way: in respect to the reconstruction of explanation of a scientific law, in respect to the claim that scientific explanation should have the character of a deductive argument, in respect to its incapability to reconstruct the case of derivation of appropriately different explananda, and in respect to the place of causation in explanation.

3. Nowak’s Way Out Nowak’s (1972; 1980) innovation in philosophy of science is based on a path-breaking approach to the structure of scientific laws. It can be represented symbolically as follows: (2) (∀x) [G(x) & p1(x) = d1 & . . . & pk(x) = dk → F (k)(x) = fk(H(x))] ‘G ’ is a predicate letter denoting the class of objects for which the law is formulated (the universe of discourse), ‘p1’, . . . , ‘pk’, ‘H ’ and ‘F (k)’ are function terms denoting functions defined on the class, denoted as ‘G’, the universe of discourse, over which the individual variable x ranges. Here ‘F ’ denotes the phenomenon to be explained, ‘H ’ denotes the factor, which is the principal cause for the phenomenon understood as its effect; ‘p1’, . . . , ‘pk’ denote secondary factors (modifying conditions) that have a causal impact on the explained phenomenon (effect), they modify it; ‘d1’, . . . , ‘dk’ are names for certain numbers; ‘fk’ is a name for a function defined on the set of values of the function denoted by ‘H ’ and with values in the set of values of the function denoted by ‘F ’; ‘(k)’ as an upper index denotes the number of idealizing assumptions, where the latter, according to Nowak, can be symbolized as ‘pi (x) = di ’ (for i = 1, . . . , k), so that the numbers denoted by ‘di’ are the extreme elements of that set of numbers from which the function, denoted by ‘pi ’, takes its values. Nowak’s approach to scientific laws, as compared to Hempel’s, provides a deeper reconstruction of their internal structure. First, by an in-depth analysis of scientific laws, he shows that scientific laws are

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always stated for entities of a certain kind.2 Second, he reconstructs the fact that the law holds only if certain modifying conditions are not acting, thus, are equal to zero. Third, he reconstructs the causal context of scientific laws not as a regularity of events, but as the relation of a cause underlying and manifesting itself in, when certain modifying conditions are at work, a certain kind of phenomena. On the basis of Nowak’s reconstruction of the structure of scientific laws it is possible to solve Hempel’s problem with the pendulum stated above. The problem has its origin in the fact that Hempel misunderstood the very causal character of the law for the simple pendulum.3 It expresses the knowledge about the action of gravity — via the parameter g standing for the acceleration caused by the force of gravity — on a pendulum with the length l, while it is presupposed, via idealizations, that this length is not subject to change due to the impact of the force of gravity or of any other force. So, the force of gravity is the cause which, when certain modifying conditions are not at work, manifests itself on a pendulum with the length l with a period T of its swings. Hempel did not distinguish, from the point of view of causation, the equation T = 2Ⱥ(l/g)½ from the equation l = T2g/4Ⱥ2. While the former expresses the knowledge about the ontic relation of the cause to its manifestation, the latter expresses the epistemic approach of knowledge, via which one can find the determination of the pendulum given a certain effect (of a cause) on it. Nowak, after explicating his approach to the structure of scientific laws, proposes his model of scientific explanation. It is based on the idea that “the idealizational assumptions are removed one by one, this brings the law closer to facts, and appropriate corrections, resulting from the removal of those assumptions, are introduced into the consequent of the law” (1972, p. 537). This process of explanation, based on scientific laws with a structure similar to (2), and labelled scientific explanation by gradual concretization, can be symbolically represented as follows (1 ” j ” k+1): 2 3

L. Nowak provides an indepth analysis of many laws of physics in his (1977).

Hempel views that law not as a causal law (law of succession) but as a noncausal law (law of coexistence).

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(3) (∀x) [G(x) & pk(x)  dk & . . . & p1(x) = d1 → F (k-1)(x) = fk-1(H(x), pk(x))] (4) (∀x) [G(x) & pk(x)  dk & . . . & pk-j(x)  dk-j & . . . & & p(k-j-1)-1(x) = d(k-j-1)-1 → F(k-j-1)(x) = f(k-j-1)(H(x), pk(x), . . . ,pk-j(x))] where ‘pi (x)  di ’ means that an idealizing assumption has already been waived. Nowak’s approach conveys, in comparison with the D-N model a richer view of scientific explanation. According to Hempel’s D-N model it should have the character of a deductive subsumption: subsumption of the particular event we want to explain under a covering law plus deduction of this event from laws and singular conditions. According to Nowak, scientific explanation of a particular event contains not two but three moments. Subsumption of the particular event we want to explain under a law, where this particular event is not covered by this law as a whole, but only by the universe of discourse and the principal cause stated in it. Plus a move going in the opposite direction, the concretization of the law to the modifying conditions of the event to be explained, plus, only at the very end, the deduction of the event to be explained by the introduction of the singular conditions into the already concretized scientific law. In accordance with L. Nowak’s (1972, p. 538), let me introduce the sign ‘Z’ for gradual concretization, ‘L(k)’, ‘L(k-1)’, ‘L(k-j)’ as abbreviations for (2), (3) and (4), representing laws of the kth, (k-1)th and (k-j)th degree of idealization, respectively, while ‘Csing’ stands for singular conditions, ‘⊃’ for entailment and ‘E ’ for the event to be explained. Nowak’s approach to scientific explanation can then be symbolically represented as follows: (5) L(k) Z L(k-1) Z L(k-j) & Csing ⊃ E In this scheme, the move from L(k) to L(k-1), . . . , L(k-j) represents a reconstruction of the explanation of scientific laws from scientific laws. So, first, it is evident from (5) that, in contrast to Hempel’s D-N model, Nowak’s model of scientific explanation by gradual concretization reconstructs the case of explanation of scientific laws from scientific laws, and thus solves Hempel’s problem stated in footnote 33 quoted above.

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Second, Nowak’s approach to scientific explanation fulfils J. Woodward’s criterion of functional interdependence because it shows how, by waiving idealizing assumptions in different sequences, it is possible to derive different explananda. To make this point understandable, let us suppose that the explanans contains one law with the idealizations L(3). On its basis we can obtain, via gradual concretization, the following sequences of seven derived laws: L1(2), L2(2), L3(2); L12(1), L23(1), L13(1); L123(0). Here the lower indexes express which idealizing assumption — the first, or second, or the third — was already waived.4 Thus, the higher the number of idealizations contained in a law, which is part of the explanans, the larger the number of different laws that can be derived in the explanandum. Third, Nowak’s approach to scientific explanation solves Kyburg’s “common salt” problem. Explanation by gradual concretization does not have the character of a deductive argument, but that of a heuristic process creating new knowledge about the causal impact of the modifying conditions pk, pk-1, . . . , pk-j introduced in each subsequent concretization step, on the respective manifestations F(k), F(k-1), . . . , F(k-j).

4. On the Way to New Shores Yet another path-breaking aspect of Nowak’s approach to explanation was not as yet mentioned, namely, his approach to the notion of conditions. While Hempel explicitly deals in the D-N model only with singular conditions which are relevant for the individual event to be explained, Nowak, in addition to singular conditions, brings into his model of explanation modifying conditions, which are relevant for the manifestations of the underlying cause. Once this enlargement of the typology of conditions that appear in scientific explanations was accomplished, yet another enlargement of that typology suggested itself as plausible, namely, via the introduction of a type conditions upon which the very existence of the underlying cause would depend.

4

Here it is assumed that the laws Lij(m-n) and Lji(m-n) are identical.

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In (ýerník 1977),5 these conditions were labeled inherent (immanent, essential) conditions and are stated in the inherent type of scientific law, Li, its structure being expressed as follows: (6) (∀x) (C 1-jinh(x) `p] C (x) = f0(S(x))) Here ‘C 1-jinh’ stands for a conjunction of j inherent conditions; ‘C ’ expresses the cause, ‘S ’ the substance which exists in these conditions and in which C originates, while ‘q `p] r’ is an abbreviation for the sentential connective ‘If q then r is necessarily being produced from p’. What has to follow after the formulation of a scientific law with the structure of (6), is the formulation of yet another law, drawing upon a law of the type Li, which derives the phenomenon-effect E(k) from its cause C and its substance S. It can be labelled the inherent idealizational law, Li (k), and it has the following structure: (7) (∀x) [C 1-jinh(x) & p1-k(x) = d1-k `p] E (k)(x) = fk(C (x))] Because the knowledge of C in a law of type (7) draws upon the knowledge of its origin in S, where that knowledge is expressed in (6), instead of fk(C) we can write E(k) = gk(S), where gk(S) = fk (f0(S)). So (7) can be restated as follows: (7Ļ) (∀x) [C 1-jinh(x) & p1-k(x) = d1-k `p] E(k)(x) = gk(S (x))] From a law of type (7Ļ), one then can proceed by the method of gradual concretization, so that one obtains the various manifestations E(k-1), . . . , E(k-j). It is readily seen here that the various phenomena-effects are here derived as manifestations of the cause C ’s substance S. Yet another enlargement of the typology of idealizational laws was proposed in (Hanzel 1999). Based on the analysis of the second dynamic law of classical the following structure of scientific laws was reconstructed: (8) (∀x) [G(x) & p1(x) = d1 & . . . & pk(x) = dk ҏ→ f1(C(x)) = E(k)(x)] Here the idealized phenomenon E(k) is the point of departure for the discovery of the cause C underlying it. By comparing f1(C) = E(k) from (8) with E(k) = fk(C) from (7), it is possible to arrive at a conceptual distinction of two principal types of phenomena. First, there are

5

A further development of these views is given in (Hanzel 1999).

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phenomena-effects known before their causes are known, which are labelled appearances of the cause. Second, there are phenomenaeffects known after their causes are known and in fact inferred from the already known causes, which are labelled manifestations of the cause. So even if in (8) and (7) there appears one and the same symbol E(k), in the former it stands for an appearance in the kth degree of idealization while in the latter for a manifestation in the kth degree of idealization; their respective epistemic status in f1(C) = E(k) and in E(k) = fk(C) is different. One consequence of the reconstruction of such a structure of an idealizational law is a modification of the reconstruction of the process of explanation by gradual concretization. The corrections, taking into account the causal impact of the modifying conditions, have to be made in respect to the effect-phenomenon E(k) as appearance. The process of explanation by gradual concretization proceeding from a law of type L(k) with the structure of (8) leads to a law with the structure (∀x) [G(x) & pk(x)  dk & . . . & p1(x) = d1ҏ → → E (k-1)(x) = fk-1(E (k)(x), pk(x))] finally to arrive at (∀x) [G(x) & pk(x)  dk & . . . & pk-j(x)  dk & p(k-j-1)-1(x) = d(k-j-1)-1 → → E (k-j)(x) = fk-j (E (k)(x), pk(x), . . . , pk-j(x))]

Comenius University Philosophical Faculty Department of Philosophy of Science Gondova 2 818 01 Bratislava Slovak Republic e-mail: [email protected]

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REFERENCES ýerník, V. (1977). Pojem zákona v marxistickej metodológii vied [The Concept of Law in the Marxist Methodology of Science]. Bratislava: VydavateĐstvo Pravda. Hanzel, I. (1999). The Concept of Scientific Law in the Philosophy of Science and Epistemology. Dordrecht: Kluwer. Hempel, C. G. (1965a). Aspects of Scientific Explanation. In: Hempel (1965b), pp. 331-496. Hempel, C. G. (1965b). Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: The Free Press. Hempel, C. G. (1966). Philosophy of Natural Science. Englewood Cliffs, NJ: Prentice Hall. Hempel, C. G. and P. Oppenheim (1965 [1948]). Studies in the Logic of Explanation. In: Hempel (1965b), pp. 331-496. Kyburg, H. E., Jr. (1965). Discussion. Philosophy of Science 32: 147-151. Nowak, L. (1971). U podstaw Marksowskiej metodologii nauk [Foundations of Marx’s Methodology of Science]. Warszawa: PWN. Nowak, L. (1972). Laws of Science, Theory, Measurement. Philosophy of Science 39: 192-201. Nowak, L. (1977). U podstaw dialektyki Marksistowskiej [Foundations of Marxist Dialectics]. Warszawa: PWN. Nowak, L. (1980). The Structure of Idealization. Dordrecht: Reidel. Viceník, J. (1988). Spory o charakter metodológie vied [Conflicts about the Character of Methodology of Sciences]. Bratislava: VydavateĐstvo Pravda. Woodward, J. (1979). Scientific Explanation. The British Journal for the Philosophy of Science 30: 41-67.

Michael J. Shaffer IDEALIZATION, COUNTERFACTUALS, AND THE CORRESPONDENCE PRINCIPLE

1. Introduction In a recent revision (chapter 4 of Nowakowa and Nowak 2000) of an older article Leszek Nowak (1992) has attempted to rebut Niiniluoto’s 1990 critical suggestion that proponents of the PoznaĔ idealizational approach to the sciences have committed a rather elementary logical error in the formal machinery that they advocate for use in the analysis of scientific methodology.1 In this paper I criticize Nowak’s responses to Niiniluoto’s suggestion, and, subsequently, work out some of the consequences of that criticism for understanding the role that idealization plays in scientific methodology.

1.1. The PoznaĔ Theory of Idealization The defenders of the PoznaĔ approach to the philosophy of science wisely attribute great significance to the operation of idealization, and they are to be commended for this as more traditional methodological analyses of science almost completely ignored the role that idealization

1

Especially that methodology as worked out in Nowak’s classic (1980).

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 179-204. Amsterdam/New York, NY: Rodopi, 2007.

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plays in science. Moreover, those more traditional methodological approaches that did bother to mention the role that idealization plays in the sciences wholly failed to offer anything like an adequate formal analysis of the concept of idealization and the complex role it plays in science as a whole. This is not, however, true of the PoznaĔ school, and its methodology based on the following core insight: A scientific law is basically a deformation of phenomena being rather a caricature of facts than generalization of them. The deformation of fact is, however, deliberately planned. The thing is to eliminate inessential components of it. (Nowakowa and Nowak 2000, p. 110)

So the idea is that there are essential features that phenomena possess, and that science operates primarily by seeking to identify non-essential features of phenomena so that they can be explicitly ignored in formulating law statements. The result is that science seeks to discover idealized laws purged of inessential content; laws that reveal the hidden, essential, structure of the phenomena. What scientists are supposed to be doing is to identify the essential structures from among the complex observed phenomena that are cluttered with interfering contingencies. Subsequent to the identification of hypotheses concerning these essential features of phenomena we are supposed to add the interfering contingent factors back into more concrete versions of the law statement in question in order to bring the highly idealized essentialist hypothesis into rough congruence with the actual complexity of the phenomena. When we have achieved a sufficient degree of congruence between a concrete hypothesis and the phenomena we can empirically test the concrete hypothesis directly and the idealized hypothesis indirectly.2 Formally, the PoznaĔ methodology is rather simple and the fundamental concept employed by the PoznaĔ school is that of an idealizational statement, where such a statement is simply a conditional with an idealizing condition in the antecedent. Consider the candidate phenomena F. The structure of F is given as a sequence

2

Nowak notes that this methodological approach is ultimately Platonic in origin, but that its development is the result of combining Hegelian and Popperian insights (Nowakowa and Nowak 2000).

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of idealization statements, T: Tk, Tk-1, . . . , T1, T0. Each element of the set T is an idealization law of the following form: Tk: if (G(x) & p1(x) = 0 & p2(x) = 0 & . . . & pk-1(x) = 0), then F(x) = fk(H1(x), . . . , Hn(x)). Tk-1, . . . , T1, T0 are the concretizations of Tk such that: Tk-1: if (G(x) & p1(x) = 0 & p2(x) = 0 & . . . & pk-1(x) = 0 & pk(x) ≠ 0), then F(x) = fk-1(H1(x), . . . , Hn(x), pk(x)), ...................................................... Ti: if (G(x) & p1(x) = 0 & pi(x) = 0 & . . .& pi+1(x) = 0 & pk-1(x) ≠ 0 & pk(x) ≠ 0), then F(x) = fi(H1(x), . . ., Hn(x), pk(x), . . . , pi+1(x)), ...................................................... T1: if (G(x) & p1(x) = 0 & p2(x) ≠ 0 & . . .& pk-1(x) ≠ 0 & pk(x) ≠ 0), then F(x) = f1(H1(x), . . . , Hn(x), pk(x), . . . , p2(x)), T0: if (G(x) & p1(x) ≠ 0 & p2(x) ≠ 0 & . . .& pk-1(x) ≠ 0 & pk(x) ≠ 0), then F(x) = f0(H1(x), . . . , Hn(x), pk(x), . . . , p2(x), p1(x)). G(x) is supposed to be some realistic assumption (typically the specification of a type of system), pi(x) are idealizing assumptions, and the consequent F(x) = f0(H1(x), . . . , Hn(x), pk(x), . . . , p2(x), p1(x)) specifies the crucial features of phenomenon F(x) given the impact of the idealizing assumptions in place in that particular case. Each element of T is then ultimately a sub-theory derived from T0 on the basis of the correspondence principle, which typically is presented as follows: (CP) [Tk+1 & (p = 0)] ⊃ Tk This general schematic principle establishes a sort of asymptotic connection between two theories, Tk+1 and Tk, under the assumption that were some relevant factor in Tk+1 set to 0 we could derive Tk. In effect, the CP relates theories as precursor and successor.3 The iterated application of CP allows for the derivation of each element of T by

3

See Krajewski (1977) and Radder (1990) for an extended discussion of the interpretation of the correspondence principle.

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setting more such factors to 0.4 T0 is then a factual statement as all interfering contingencies have been added back in, while T is a complex statement that includes this factual statement as well as a series of non-factual statements generated by successively applying CP to T0. Strictly speaking, an idealizational law Tk for F is that statement that is most idealized in the sense that in such a statement all nonessential factors have been neglected. The crucial idea then is supposed to be that at least one of the concretizations of Tk will be such that it empirically testable, typically this will be true of at least T0, or one of the theoretical statements close to T0. The confirmational status of the various other theories in T is, due to the CP, supposed then to be logically parasitic on the concretization of Tk that is testable. So the confirmational status of the various other theories in T is wholly a matter of the formal relations that the non-testable elements of T bear to the testable concretization(s) in T, ideally the realistic theory T0.

2. Niiniluoto’s Critical Observation While I think that there are severe unresolved methodological problems with the account of the testability of such statements in the PoznaĔ approach and with the overt adherence to a form of essentialism on which that methodology is based, my immediate concern here is more basic and formal. When we examine the formulations of the elements of T: Tk, Tk-1, . . . , T1, T0 it is clear that Nowak intends the conditionals therein to be interpreted as ordinary material conditionals of the “if . . . , then . . .” sort (Nowakowa and Nowak 2000). Niiniluoto (1990) pointed out that the conditionals in Tk, Tk-1, . . . , T1 really ought to be interpreted as counterfactual conditionals of the form “if it were the case that . . . , then it would be the case that . . . ”. Thus, we would rewrite the whole sequence of idealizing claims as follows:

4

This principle plays a prominent role in Bohr’s and Poincaré’s philosophies, and it has received considerable philosophical attention in Krajewski (1976; 1977), in Post (1971), and in Zahar (1983; 2001).

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Nk: (G(x) & p1(x) = 0 & p2(x) = 0 & . . . & pk-1(x) = 0 & pk(x) = 0) Ÿ F(x) = fk(H(x)) k-1 N : (G(x) & p1(x) = 0 & p2(x) = 0 & . . . & pk-1(x) = 0) Ÿ F(x) = fk-1(H(x), pk(x)) ...................................................... N1: (G(x) & p1(x) = 0) Ÿ F(x) = f1(H(x), . . . , Hn(x), pk(x), . . . , p2(x)) N0: G(x) Ÿ F(x) = f0(H(x), pk(x), . . . , p2(x), p1(x)) where ‘Ÿ’ symbolizes the counterfactual conditional as opposed to the material conditional. Independent of Niiniluoto’s suggestion, I have advocated an approach to law statements that incorporate idealizing conditions in terms of counterfactuals, and so it should come as no surprise that I am sympathetic to Niiniluoto’s observation that the conditionals in T should be interpreted as counterfactuals.5 Recently, however, Nowak has critically responded to Niiniluoto’s suggestion, and he has argued that serious semantic and epistemological problems arise if we substitute counterfactuals for the material conditionals in the expressions T: Tk, Tk-1, . . . , T1, T0. Here I will address these responses, and, after doing so, I will suggest that interpreting the conditionals in T as material conditionals has some very real and very serious negative consequences for the PoznaĔ methodology. I will also argue that interpreting the conditionals in T as counterfactuals has several desirable consequences, not the least of which is that doing so yields a much more realistic view of how science actually operates.

3. Nowak’s Semantic Response Nowak’s first response to Niiniluoto’s suggestion about the interpretation of the conditionals in T concerns the semantic status of T as a whole; specifically it involves the claim that T is supposed to be, at least in some sense, a factual statement. T0 is clearly is intended to be a statement purged of idealization via the process of concretization, and so is intended to apply to the actual world. Take Gi to be the domain of 5

See Shaffer (2000; 2001) for an extended argument for this point.

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statements of the i-th degree of idealization where G is the universe of discourse as follows: x ∈ G0 iff x ∈ G & p1(x) ≠ 0 & p2(x) ≠ 0 & . . . & pk-1(x) ≠ 0 & pk(x) ≠ 0, x ∈ G1 iff x ∈ G & p1(x) = 0 & p2(x) ≠ 0 & . . . & pk-1(x) ≠ 0 & pk(x) ≠ 0, ...................................................... .. x ∈ Gk-1 iff x ∈ G & p1(x) = 0 & p2(x) ≠ 0 & . . . & pk-1(x) = 0 & pk(x) ≠ 0, x ∈ Gk iff x ∈ G & p1(x) = 0 & p2(x) = 0 & . . . & pk-1(x) = 0 & pk(x) =0. Gi is the domain that Ti strictly refers to, but N0 refers not only to G0, but also to G1, . . . , Gk-1, Gk, the ideal elements of the universe G, and so Nowak claims that N0 is a “supra-factual” statement; i.e. N0 appears to refer both to the factual domain G0 and to the non-factual domains G1, . . . , Gk-1, Gk. Nowak appears to hold that T0 is, however, supposed to be a factual statement referring only to G0. As a result, Niiniluoto’s revision would get the semantic status of T0 wrong. Implementing this suggestion would treat T0 as a sort of counterfactual statement and that, ipso facto, would be to treat T0 as non-factual in some problematic sense.

3.1. Counterfactuals, Idealization and Reference to the Facts To Nowak’s first criticism of Niiniluoto’s suggestion, there is an obvious and direct response that concerns the semantics of counterfactuals as typically understood in the sense of Lewis and Stalnaker, but, more specifically, as understood in Shaffer (2000). First, as counterfactuals are logically weaker than material conditionals, it is virtually trivial to treat T0 as an idealizing counterfactual with no idealizing conditions in the antecedent position, i.e. as N0. Thereby, all the conditionals in T can be treated as being logically of the same type, and it is not really a problem that N0 refers

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to the whole of G, but is true only in model G0. In possible worlds accounts of counterfactuals, such expressions have always been understood to refer to the set of worlds, and they indicate relations of similarity between those worlds/models. In Shaffer (2000), I offered a semantic account of counterfactuals concerning models ordered in terms of simplification that corresponds nicely to the relational structure of the elements of G. In brief, an idealizing counterfactual is true at some world just in case the consequent is true in close but simplified worlds where the idealizing conditions in question are met. As such, a factual claim is just an idealizing counterfactual that happens to hold in a complete world free of idealizing conditions. So, it is simply false that Niiniluoto’s suggested rendering of T is semantically incorrect in a way that cannot be easily dealt with; factual claims are just special cases of counterfactual claims. As it turns out, in point of fact, the semantics of the elements of T are much more peculiar on Nowak’s rendering. This is especially true when we consider the motivation behind the operation of idealization, viz. deliberate, but false, simplification. It seems difficult to interpret idealizing conditionals as anything other than counterfactuals when it is clear that the antecedents of such expressions are known to be false, but which are hypothetically entertained on the basis of the utility of simplification. Nevertheless, if we reject Niiniluoto’s proposal and, as Nowak does, we treat all the conditionals in T as material conditionals, then all of Tk, Tk-1, . . . , T1 turn out to be trivially true as every such element of T has a factually false antecedent relative to G0, and so accepting Nowak rendering of T would require either that we accept some revision to the model theoretic theory of truth such that statements cannot be considered in reference to various models, but only to the appropriate model that it mysteriously corresponds to, i.e. T0 is only interpretable in G0, T1 only in G1, etc., or that we can consider idealized theories in reference to various models but that all idealization statements are true at G0 as the antecedents of all the elements of any T except T0 are false at G0. It is hard to see how one could reasonably accept either option in light of the great success of model theory in general, especially its specific application to the semantics of counterfactuals

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and other expressions, and the sheer implausibility of committing ourselves to a view that all idealizational theories are true of the real, actual, world.6 It is neither especially problematic, nor implausible, to simply adopt Niiniluoto’s suggestion, and so there is much to recommend this revision to Nowak’s methodology. There is also good reason, however, to suspect that Nowak’s interpretation of the conditionals in T as material conditionals cannot be correct. Consider an idealizational statement of the form: Ti: if (G(x) & p1(x) = 0 & pi(x) = 0 & . . . & pi+1(x) = 0 & pk-1(x) ≠ 0 & pk(x) ≠ 0), then F(x) = fi(H1(x), . . . , Hn(x), pk(x), . . . , pi+1(x)). If the conditional in Ti really is a material conditional, then it must, as a matter of definition, both obey contraposition and satisfy strengthening of the antecedent. Material conditionals are such that obey both these closely related principles, but idealizational statements like Ti do not, in fact, satisfy these principles when scrutinized. As such, the conditionals in T, perhaps with the exception of T0, cannot be material conditionals. Let us consider the case of contraposition first. Nowak takes idealizational statements to have the following sort of form: (1) If (G(x) & p1(x) = 0 & pi(x) = 0 & . . . & pi+1(x) = 0 & pk-1(x) ≠ 0 & pk(x) ≠ 0), then F(x) = fi(H1(x), . . ., Hn(x), pk(x), . . . , pi+1(x)). If the conditional in this expression is a material conditional then this expression is logically equivalent to the claim: (2) If ¬[ F(x) = fi(H1(x), . . . , Hn(x), pk(x), . . . , pi+1(x))], then ¬[(G(x) & p1(x) = 0 & pi(x) = 0 & . . . & pi+1(x) = 0 & pk-1(x) ≠ 0 & pk(x) ≠ 0)]. However, it is not at all clear that statements like (2) are always true when statements like (1) are true. It may be true that F(x) does not exhibit the functional behavior described by fi(H1(x), . . . , Hn(x), pk(x),

6 There is some reason to believe that this is the kind of strategy Nowak has in mind as he introduces serious revisions to the theory of truth in the form of the concept of relative truth in his (1975) and later in Nowakowa and Nowak (2000, ch. 23), but this is, at best, an unreasonably heavy price to pay for maintaining that idealizing conditionals are material conditionals.

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. . . , pi+1(x)) and that ¬[(G(x) & p1(x) = 0 & pi(x) = 0 & . . . & pi+1(x) = 0 & pk-1(x) ≠ 0 & pk(x) ≠ 0) is true. This can be the case because F(x) = fi(H1(x), . . . , Hn(x), pk(x), . . . , pi+1(x)) may be false for some reason other than that ¬G(x) ∨ ¬(p1(x) = 0) ∨ ¬(p2(x) = 0) ∨ . . . ∨ ¬(pi+1(x) = 0) ∨ ¬(pk-1(x) = 0), say in the case that some other interfering cause prevents F(x) = fi(H1(x), . . . , Hn(x), pk(x), . . . , pi+1(x)) from being the case or that some requisite initial conditions are never met. Such cases are reminiscent of the sort of problems associated with conditionals like that in the much-discussed example, “If the match is struck, then it lights.” While this statement seems to be true, we are not, upon reflection, inclined to accept the contrapositive claim that “If it is not the case that the match lights, then it is not the case that it has been struck.” While the original uncontraposed statement seems intuitively to be true, we are not always so inclined to accept the truth of the contrapositive claim because it might well be the case that the match was, for example, wet. We might, of course, alter our assessment of that claim as well upon learning that the match was coated with paraffin. In any case, this behavior is a peculiar feature of the logic of causal conditionals. When inspected closely, theoretical claims like the idealization statements Nowak considers are also causal conditionals, although they are hypothetical in nature, and so we should expect that their behavior would be the same in this respect. Consider the following concrete example of an idealizing conditional that Nowak (1994) has employed: (I1) If x is a rolling ball which is perfectly round, projected along an ideally smooth and perfectly spherical unlimited plane and the resistance of the environment exerted upon x equals zero, then x moves along this plane with uniform perpetual motion. In this specific case it is clear that contraposition fails, as, if it did hold, we would be committed to the view that the following claim must, as a matter of logic, be true: (I2) If it is not the case that x moves along a plane with uniform perpetual motion, then it is not the case that x is a rolling ball which is perfectly round, projected along an ideally smooth and

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perfectly spherical unlimited plane and the resistance of the environment exerted upon x equals zero. However, while I1 seems true, I2 does not necessarily seem to be true; there are presumably any number of reasons why x might not move along a plane with a uniform perpetual motion other than that it is not the case that x is a rolling ball which is perfectly round, projected along an ideally smooth and perfectly spherical unlimited plane where the resistance of the environment exerted upon x equals zero. Specifically, I2 might be false because x is a hollow sphere filled with a liquid, thus producing an internal frictional force that makes x’s motion nonuniform. That conditionals of these sorts behave in this manner should obviously be the case as the consequent and antecedent of causal conditionals are not logically related in the sense of the material conditional, but rather are related in some other weaker manner. On an obviously related point, consider the relationship between the elements of T and the principle of strengthening of the antecedent. It should be obviously true that if T i is a claim incorporating the material conditional, then the subsequent introduction of any new idealizing condition or any other new information into the antecedent of T i in order to yield T i+1 should have no effect on the derivability of the consequent of T i. Conditionals that exhibit this feature are monotonic and are said to obey strengthening of the antecedent. However, even in Nowak’s own formal presentation of the method of idealization and concretization this is untrue as the consequent of some idealizational statement T i is not derivable from the antecedent of T i+1 that includes the introduction of information in the form of an additional idealizing assumption. In conjunction with the bare fact that idealization appears to be the operation of hypothetical simplification, both of these points suggest that the proper interpretation of the conditionals in T is that, pace Nowak, idealizing conditionals are counterfactuals. So, I suggest that we have good reasons to regard that Nowak’s semantic response to Niiniluoto’s proposal as unfounded and Niiniluoto’s suggestion that idealizing conditionals are counterfactuals as absolutely correct.

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4. Nowak’s Epistemological Response Nowak’s second response to Niiniluoto’s suggestion about the interpretation of the conditionals in T concerns the epistemological implications for the method of idealization in general that follow from the implementation of Niiniluoto’s suggestion. Nowak is concerned that if one were to interpret the conditionals in T as counterfactuals, then the whole motivation behind the PoznaĔ methodology will be undermined. More specifically, as N0 is a factual statement that is supposed to be justified in some ordinary, inductive, manner, there would be no need to really ever concern ourselves with Nk, Nk-1, . . . , N1, especially as if they are counterfactuals they have nothing to do with the actual world. With this kind of idea in mind Nowak claims that, “All that we need for explaining, predicting, and programming the empirical world is T0 [N0], allegedly a factual statement. Idealizations reduce to the role of counterfactual special cases of it, and concretization becomes superfluous . . .” (Nowakowa and Nowak 2002, p. 10; my notional alteration in brackets). So, Nowak claims, if we adopt Niiniluoto’s formal revision of T we make idealization and concretization cognitively irrelevant to scientific methodology.

4.1. The Cognitive Significance and Indispensability of Idealization With only a little bit of reflection we can see that Nowak’s second response to Niiniluoto’s suggestion is simply based on a misguided faith in our epistemic ability to understand, employ, or even formulate law statements purged of all idealizations. While it may be true that in a particular case knowledge of an N0-type law would vitiate the need to concern ourselves with Nk, Nk-1, . . . , N1-type laws, it is by no means the case that it is physically possible for us to come to know of or practically employ such laws. In point of fact, one of the primary motivations behind the operation of idealization is that of simplification in order to secure computational tractability, scientific understanding, etc. If this is true, then in spite of the fact that our knowledge of N0-type laws would vitiate the need to employ Nk, Nk-1,

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. . . , N1-type laws, the need for such knowledge is not in fact so vitiated as it is neither practical nor physically possible to do without in virtually all cases. As such, the motivation behind methodologies that acknowledge the significance of idealization in the sciences as they are actually practiced is in no way undermined by the mere fact that it is logically possible that N0-type laws exist. As an example of this sort of case consider the Euler equation for fluid flow: (E1) ǏDu/Dt = -∇p,7;8 where Ǐ is the fluid’s mass density, Du/Dt is the hydrodynamic derivative of the fluid velocity, that is Du/Dt = du/dt + u · ∇u, and ∇p is the pressure gradient. This equation is intended to hold true only of perfect, inviscid, fluids, even though it is often applied to real systems. That is to say that in the context of applying the Euler equation it is, falsely, assumed to be the case that there are no forces parallel to the surfaces of contact with the rest of the fluid, or there are no viscous forces that oppose the motion of the fluid along the direction of flow. So E1 really has the following form: (E1) If x is a fluid and there are no forces parallel to the surfaces of contact with the rest of the fluid, or there are no viscous forces that oppose the motion of the fluid along the direction of flow, then x’s behavior obeys ǏDu/Dt = -∇p. In order to incorporate the types of forces that have been idealized away in E1 into the description of the motion of a fluid one must turn to the Navier-Stokes equation: (E2) du/dt + u • ∇u = -1/Ǐ∇p + v∇2u,9 where once again du/dt + u • ∇u is the hydrodynamic derivative of the fluid velocity, v is the kinematic viscosity, ∇2u is the Laplacian of the fluid velocity, and the other terms are the same as in E1.

7

It is also being assumed that external forces are absent.

8

In what follows bold face will be used to indicate vector quantities.

9

Again, as in the case of the Euler equation, the absence of external forces is being assumed.

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E2, however, considerably more difficult to solve, it is a secondorder equation where the Euler equation is a first-order equation, and, in fact, is not even known whether the Navier-Stokes equation is solvable over long periods of time. So, Euler’s equation is computationally tractable in a way that the Navier-Stokes equation is not, and Euler’s equation holds true only in a model that is an intentional simplification of that in which the Navier-Stokes equation holds. However, in many cases the Euler equation provides us with results that are acceptable even though no real system satisfies this theory, but we must often employ such theories because we cannot, as a matter of computational complexity, use the more realistic theory at all.10 Nevertheless, E1 and E2 are intimately related in the sense that the models in which they hold are importantly similar. So idealization and concretization are important non-superfluous aspects of scientific practice and we do need to consider what occurs in other possible worlds even though there laws purged entirely of idealizing conditions may well exist. Moreover, if the points made in section 3 are taken into account, then we should be concerned with Nk, Nk-1, . . . , N1 and thereby Gk, Gk-1, . . . , G1 because they are necessary for us to fully understand the proper semantics of N0-type theories. Nowak’s epistemological concerns seem to derive from a devout faith in the correspondence principle as a logical method of discovery; i.e. as a method of generating new theories. For example, Nowak’s claims seem to suggest that unless we are given the CP and accept that the conditionals in T are material conditionals, there is no motivation for engaging in concretization. His point is that as a matter of historical fact scientists tend to produce theories that are simplified first and that they subsequently remove idealizing conditions in order to get closer to the real case in a way that allows us to logically derive the more idealized theory from the less idealized theory. There are many well-known, general, and serious objections to the existence of any such logic of discovery, but, more importantly, we shall see that the CP is itself at best dubious and that Nowak’s suggestion that 10

See Chorin and Marsden (1993) and Tritton (1977) for more detailed discussion of this case.

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interpreting the conditionals in T as material conditionals, rather than as counterfactuals, captures the methodological history of science better seems to be false.

5. The Correspondence Principle and the History of Scientific Progress The CP is a rather old principle and it is based on the idea that science progresses as a series of more sophisticated and realistic theories that logically capture their less refined predecessors by treating them as special cases of the newer theory. This allows for the retention of confirming instances in the face of theoretical progress and guides subsequent further progress by asserting that new theories ought to be the most conservative logical extensions of their predecessors that eliminate certain unrealistic (i.e. idealizing) assumptions. In the post-Kuhn, Feyerabend, and Hanson era of philosophy of science it is hardly worth mentioning that this is historically inaccurate, but the methodological force of the CP remains untouched by such observations. It is still possible to defend the CP as an a priori, normative, principle nevertheless. However, I suggest that the CP rests on a more basic assumption of methodological conservatism that is revealed to be wholly unwarranted when subjected to critical scrutiny.

5.1. The Progress of Science Nowak contends that treating the conditionals in T as material conditionals makes the operation of concretization coherent and captures the common practice of the sciences. These contentions are, however, simply false. First, let us consider what we would have to say about the actual methodological practice of scientists if we interpret the conditionals in T as material conditionals. If this were the case, then (1) the history of science would turn out to be constituted by a series of proposed theories that are trivially true, (2) which are presumably not known to be trivially true, and (3) which logically are implied by their successors. That such theories are trivially true on

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Nowak’s view is simply a function of the fact that the antecedents of the non-T0-type elements of every sequence T are false, and the CP appears to imply that scientific progress is merely an exercise in logic. However, concerning (1) and (2) respectively, the claim that past rejected theories were mere trivialities seems wildly implausible, and that the history of science is a sequence of such theories seems utterly unrealistic. Is it really plausible to believe that Galileo and Newton were really proposing trivially true theories of mechanics even though they were unaware of doing so? Consider the generic statement Tk: if (G(x) & p1(x) = 0 & p2(x) = 0 & . . . & pk-1(x) = 0), then F(x) = fk(H1(x), . . . , Hn(x)). Notice that in this theoretical claim the principle factors G(x) and F(x), and the contingent factors pi have been identified and taken account of. This is rarely the case in actual practice, and more often than not scientists have no idea exactly what contingent factors are at work in a particular case. Surely, for example, Galileo had only a vague idea about what confounding forces were at work in the mechanical cases he was concerned with, but, nevertheless, Galileo’s mechanical theories were not put forth as mere trivial truths even if he was not aware of all the factors omitted. This rendering of the status of theories in the history of science only makes sense on the assumption that Galilean mechanics is false and is a special case of a successor theory, and surely Galileo was not asserting that! Nowak’s methodology assumes that scientists are explicitly aware of idealizing factors and that science progresses by adding such factors back in by concretization under the aegis of the extreme version of the principle of conservatism about belief change; i.e. that we should never give up confirmed beliefs unless forced to do so, and, as we have already noted, this conception of scientific methodology would make the activity of progressive theory construction an exercise in trivial and monotonic logical development. However, concerning (3), none of this is plausibly true of the history or methodology of science. For example, Newton’s development of mechanics cannot plausibly and non-superficially be described as a mere mathematical extension of the theories of his predecessors, and Einstein’s theory of mechanics cannot plausibly and non-superficially be described as a mere mathe-

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matical extension of classical mechanics.11 The semantics of such theories that are related as precursor and successor are often massively different, and to consider only the formal relations between the equations of two theories as the CP suggests, even if there are such formal similarities between successor and predecessor theories, overlooks the differences in the meanings of those theories. Scientific theories are not merely formal systems, the development of which requires only formal syntactic operations. If science were that easy then the development of science would be no more than a trivial exercise in deductive explanation, but, sadly, this is not the case.

5.2. The Correspondence Principle and Conservative Belief Change Historical inaccuracies of Nowak’s views aside, one might still be tempted to argue that treating the conditionals in T as material conditionals is methodologically correct and that the CP provides justification for this. In other words, the CP is a methodological norm that ought to be obeyed in the construction of theories. Recall that the CP is typically stated formally as follows: (CP) [Tk+1 & (p = 0)] ⊃ Tk. When read as a methodological imperative, CP tells us that successor theories like Tk+1 ought to logically entail their simpler, more idealized, predecessors like Tk. But what exactly is the motivation for accepting that we ought to obey this imperative in progressive theory development/construction? Unless we accept the CP on the basis of mere intuition, we ought to be able to offer some justification in support of the principle, especially in light of its manifest historical inaccuracy.12 Typical discussions of the CP say little or nothing about its justification other than alluding to the insight that we ought to try to retain as much of a previously confirmed theory as is possible when we

11

See Friedman (2000; 2001) for a defense of this point.

12

See Laudan (1981) for a host of historical examples that violate the CP.

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propose a more sophisticated successor.13 What this amounts to is a less than explicit appeal to version of the principle of epistemological conservatism as it applies to belief change, and the CP is, in fact, based on an ultra-conservative and wholly implausible version of the principle of epistemological conservatism as it applies to belief dynamics. I shall attempt to show that this is so in what might appear to be a rather roundabout way, and I will begin by introducing what is currently the most influential theory of belief change, the theory defended by Carlos Alchourrón, Peter Gärdenfors, and David Makinson (AGM).14

5.3. The AGM Theory of Belief Dynamics The purpose of the AGM theory is to provide us with a theory of the rationality of belief change, and this sort of theory stands in sharp contrast to traditional theories of epistemic rationality that almost universally deal with belief support or justification; with the rationality of belief as such. So the AGM theory of belief revision ought to be viewed as a theory of the dynamics of belief states, as opposed to a theory of the static features of belief states. The essential idea behind this epistemological theory is that there are normative rules that govern how one ought to change one’s beliefs in light either of acquiring new beliefs or revising beliefs that one already holds. The AGM theory is fundamentally based on the concept of a belief state, belief set or a corpus of beliefs, K, satisfying the following minimal conditions where it is assumed that belief states are given a representation in some language L and where a, b, c, . . . are sentences of L: (Df BS) A set of sentences, K, is a belief state if and only if (i) ¬(K f ⊥), and (ii) if K f b, then b ∈ K. 13

See, for example, Post (1971) for an explicit defense of this sort of ultraconservatism. 14 Hansson (1999) offers an extensive, and considerably more detailed, introduction. (Gärdenfors 1988) is the canonical presentation of the theory, however. In what follows, I will remain faithful to both, but will also make use of elements of (Gärdenfors and Makinson 1984), (Olsson 1997), (Hansson and Olsson 1999), and (Rott 2000).

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Here ‘f’ is a standard definition of logical consequence for L, and so (Df BS) requires that K is logically consistent and is closed under logical consequence. We can then define the content of a belief state as the set of logical consequences of K, so {b: K f b} =df Cn(K). Given this basic form of epistemic representation, the AGM theory is intended to be a normative theory about how a given belief state Ki which satisfies (Df BS) is related to other belief states Kn satisfying (Df BS) relative to: (1) the addition of a new belief b to Ki, or (2) the retraction of b from Ki, where b ∈ Ki. Belief changes of the latter kind are termed contractions (÷), but belief changes of the former kind must be further subdivided into those that require giving up some elements of Ki and those that do not. Additions of beliefs that do not require giving up previously held beliefs are termed expansions (+), and those that do are termed revisions (∗).15 As such, the dynamics of beliefs will then simply be the epistemically normative rules that govern rational cases of contraction, revision and expansion of belief states. Expansion of Ki by a sentence b is defined using the notion of the content of a belief state as follows: (Df +) K + b = Cn(K ∩ { b }) Moreover, revision can be defined in terms of expansion and contraction in accord with the Levi identity as follows: (Levi identity) K ∗ b = (K ÷ ¬ b) + b Combining the simple concept of belief state expansion defined above with some principled concept of belief state contraction then yields a complete specification of the possible dynamic belief changes relative to belief states. Contraction obviously then turns out to be the central concept of the AGM theory. The fundamental insight behind the AGM theory is that belief changes that are contractions should be fundamentally conservative in nature; in other words, in belief changes one ought to make the minimal alterations necessary to incorporate new information and

15

In point of fact, the AGM theory really only holds that there are two dynamical operations on belief states, as revision is defined in terms of expansion and contraction.

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maintain or restore logical consistency. This fundamental assumption in the AGM theory is supposed to be justified in virtue of a principle of informational economy that holds that information is valuable and so we should retain it at all costs unless we are forced to do otherwise. Gärdenfors (1992) presents the informal version of this intuition, which he calls the principle of conservation (POC), as follows: (POC) When changing beliefs in response to new evidence, you should continue to believe as many of the old beliefs as possible. (p. 381) After having considered and rejected several interpretations of this basic intuition in (Alchourrón, Gärdenfors and Makinson 1985) and (Gärdenfors 1988), the POC was given formal explication in terms of the concept of partial meet contraction (PMC). Partial meet contraction is defined as follows: (PMC) K ÷ b = ∪γ (K ⊥ b) K ⊥ b is inclusion-maximal set of subsets of K that do not imply b, γ is a selection function such that γ (K ⊥ b) is a non-empty subset of K ⊥ b, unless b is empty. Where b is empty γ (K ⊥ b) is just K. The so-called AGM postulates explicitly tell us what rules govern such changes, and they are as follows: (P1-Closure) (P2-Inclusion) (P3-Vacuity) (P4-Success) (P5-Extensionality) (P6-Recovery)

Cn(K ÷ b) = K ÷ b, K ÷ b ⊆ K, If b ∉ K, then K ÷ b = K, If b ∉ Cn(∅), then b ∉ K ÷ b, If b ↔ c ∈ Cn(∅), then K ÷ b = K ÷ c, K ⊆ (K ÷ b) + b.16

Various representation theorems show that ÷ on K is a PMC operation if and only if ÷ satisfies P1-P6. In addition to the presentation of AGM belief dynamics based on PMC, Gärdenfors (1984, 1988), and Gärdenfors and Makinson (1984) showed that AGM belief dynamics could be interpreted in terms of the 16

This presentation of the AGM contraction postulates follows Gärdenfors (1988) and Hansson and Olsson (2000) most closely with only minor notational variations to yield consistency of formalism.

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concept of epistemic entrenchment, or epistemic importance, that also provides an intuitively satisfying explication of contraction in terms of the POC. The basic intuition behind this interpretation of belief change is that we ought to give up those beliefs that are least entrenched. Gärdenfors and Makinson (1988) explain, The epistemic entrenchment of a fact represents how important it is for problem solving or planning on the basis of the knowledge system and in this way determines the database priority of the fact. (p. 84)

In addition, using the older term epistemic importance, Gärdenfors (1984) explains that, My main thesis is then that when we have to give up some of our beliefs we retain those with greatest epistemic importance. (p. 137)

This concept of epistemic entrenchment is given a more formal presentation as follows. Given that a and b are sentences, ‘a ” b’ signifies that b is at least as entrenched as a, and ‘a < b’ signifies that b is more entrenched than a where a < b = a ” b & ¬b ” a. Epistemic entrenchment is governed by the following postulates: (E1-Transitivity) If a ” b and b ” c, then a ” c. (E2-Dominance) If a f b, then a ” b. (E3-Conjunctiveness) For any a and b, a ” (a & b) or b ” (a & b). (E4-Minimality) If K is consistent, then a ∉ K if and only if a ” b for all b. (E5-Maximality) If b ” a for all b, then f a. These postulates yield a comparative ordering on K of all sentences a, b, c, . . . of K in L, and representation theorems show that ” on K is an EEC (epistemic entrenchment contraction) if and only if ” satisfies E1-E5. Perhaps more interestingly, Gärdenfors (1988) proved the following central theorem of the AGM theory: (AGMT) A contraction function ÷ satisfies P1-P6 if and only if ” satisfies E1-E5, where b ” a if and only if b ∉ K ÷ (a & b) for all a and b in L.17 17

Rott (1991) also includes a related proof that the concepts of epistemic entrenchment contraction and partial meet contraction are strictly equivalent

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So, it should be obvious that the AGM concept of a contraction can be interpreted either in terms of the basic concept of minimal belief change (PMC) that satisfies P1-P6 or in terms of the basic concept of epistemic entrenchment (EEC) that satisfies E1-E5. In defense of the core conservative assumption of AGM, Gärdenfors essentially argues that information is an intrinsically valuable epistemic resource that should not be ceded lightly even in the face of undermining evidence.18 Gärdenfors explicitly tells us that, When we change our beliefs, we want to retain as much as possible of our old beliefs; information is in general not gratuitous, and unnecessary losses of information are therefore to be avoided. (1992, p. 381)

Retention of information from theory to successor theory, then, in spite of evidential undermining, is a fundamental epistemic virtue for Gärdenfors. However, the AGM theory does allow for the loss of information in such belief changes in the cases of contraction and revision. So, while the AGM theory is conservative, it is not ultraconservative in the sense that no information losses are allowed. Let us now return to our examination of the CP in light of our brief excursion into the theory of belief dynamics. What exactly does the PoznaĔ/ Nowak methodology, which is based on the CP, advise us to do when we find that a particular we theory we have entertained does not accord with the data? Presumably, by the CP, we are supposed to propose a new theory that deductively implies the old theory when some parameter p is set equal to 0, even though we know that p ≠ 0. We are always, at least in the case of mature sciences,19 supposed to retain all of the precursor theory as a special case of the successor theory. In essence we are advised not to give up Tk, but rather to retain all of Tk because of its instrumental utility and its confirmational status. But, it is hard to see how this makes any sense on the PoznaĔ/Nowak methodology. The correspondence principle makes it a normative matter that it should be

18 19

Harman (1986) makes essentially the same point.

See Krajewski (1977) for discussion of the relevance of the mature/immature science distinction in this context.

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the case that [Tk+1 & (p = 0)] ⊃ Tk for any two theories related as precursor and successor. However, the conditional in CP cannot then itself be a material conditional without rendering CP vacuously true as explicitly acknowledged by Krajewski (1976, p. 383) because, as a matter of fact, in applications of CP p ≠ 0 in Tk+1. Given the AGM theory, however, it is clear what the significance of the CP really is. The CP is a normative claim concerning the dynamic relation between successor and precursor theories, and it is manifestly ultra-conservative in a way that even the AGM theory is not. In AGM terms Tk is the revision of Tk+1, Tk+1 * p = 0, which is equivalent to the contracting of Tk+1 by removing p ≠ 0, Tk+1 ÷ p ≠ 0, followed by the expansion of the resulting theory by p = 0. So by the Levi identity we see that if the CP is not utterly trivial it must really assert that: (CPĻ) Tk = (Tk+1 ∗ (p = 0)) = (Tk+1 ÷ (p ≠ 0)) + (p = 0).20 However, if this is true, then it may well turn out, even given the AGM version of the principle of epistemological conservatism, that Tk is not a special case of Tk+1, as the process of AGM revision may require significant mutilation of Tk in order to arrive at Tk+1. The PoznaĔ/Nowak methodology appears to be even more conservative than the AGM theorist’s conservatism in legislating that Tk should be a special case of Tk+1, and defenders of the CP are thus faced with an undesirable dilemma: either they must accept that the CP, and not the CPĻ, is the correct rendering of their methodological principle and that the CP is vacuous, or they must offer some justification for the ultra-conservative, normative, restriction of the operation of belief revision to cases where Tk is a special case of Tk+1. The first horn of this dilemma is obviously not acceptable and so Nowak and the other defenders of the PoznaĔ methodology must seemingly opt for the second horn. But is it plausible to believe that a principle stronger than the AGM POC, as formalized in PMC and EEC, ought to be imposed on changes of belief? Consider the POC again: 20

Equivalently, the CP can be understood as claiming that Tk+1 is the revision of Tk by p ≠ 0, which involves the contraction of Tk by p = 0 followed by expansion with p ≠ 0.

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(POC) When changing beliefs in response to new evidence, you should continue to believe as many of the old beliefs as possible. (Gärdenfors 1992, p. 381) This principle is itself unjustified in the AGM framework and taken only to be an intuitively plausible assumption by the AGM theorists. Moreover, the force of the intuition grounding this assumption is based on the rather imprecise principle of informational economy noted above. Nevertheless, it is no more than an assumption and if the weak version of the POC has no serious justification, then, a forteriori, neither does the principle defended by the PoznaĔ school that asserts that we ought always to retain all old theoretical beliefs as special cases of our new theoretical beliefs. This is not to say, of course, that it is impossible to find such a justification. However, given that the history of science is characterized by belief revisions that utterly fail to even remotely conform to the POC, let alone any stronger principle, we ought to be at least a little suspicious that any such justification are forthcoming. The sheer implausibility of the conservatism of the principle defended by Nowak and the PoznaĔ school seems obvious when one notes that, in entrenchment terms, they are asserting that all information is of precisely the same maximal value so, other things equal, no information should be lost in theory change. This seems simply to be false, as much information seems to be of little or no value whatsoever. Gärdenfors is acutely aware of this epistemic fact and he explains that, Not all sentences that are believed to be true are of equal value for planning or problem-solving purposes, but certain pieces of knowledge about the world are more important than others when planning future actions, conducting science, or reasoning in general. (1992, p. 387)

While this seems true, Gärdenfors is also candid in that he tells us that there is no accepted, or even well understood, account of the relative informational value of beliefs (1988, pp. 91-94). As a result, there is no real justification available for the AGM versions of epistemological conservatism, let alone for the ultra-conservative version defended by Nowak and the PoznaĔ school, as there is nothing like a coherent understanding of the principle of informational economy on

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which it is supposed to be based to warrant our accepting this principle.

6. Conclusion So what can we conclude from this examination of the views on idealization defended by Nowak and the PoznaĔ school? The lessons are, I think, twofold. First, analytic philosophy of science owes a great debt to Leszek Nowak for taking the concept of idealization seriously and for offering up one of the most thorough and technical analyses of that concept. Second, that there are formidable logical problems with that methodology concerning the nature and semantics of conditionals it employs, with the correspondence principle on which that methodology is based, and with the accuracy of that methodology as a coherent reconstruction of the history of science. Nevertheless, as the topic of idealization in the sciences is one of supreme importance these problems should be viewed as opportunities for deeper investigation.

St. Cloud State University Department of Philosophy 720 4th Avenue South St. Cloud, MN 56301 E-mail: [email protected]

REFERENCES Alchourrón, C., P. Gärdenfors and D. Makinson (1985). On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. The Journal of Symbolic Logic 50: 510-530. Chorin, A. and J. Marsden (1990). A Mathematical Introduction to Fluid Dynamics. Third edition. New York: Springer-Verlag. Friedman, M. (2000). Transcendental Philosophy and A Priori Knowledge: A Neo-Kantian Perspective. In: P. Boghossian and C. Peacocke (eds.), New Essays on the A Priori, pp. 367-383. Oxford: Clarendon Press.

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Friedman, M. (2001). The Dynamics of Reason. Stanford, CA: CSLI Publications. Gärdenfors, P. (1984). Epistemic Importance and Minimal Changes of Belief. Australasian Journal of Philosophy 62: 136-157. Gärdenfors, P. (1988). Knowledge in Flux. Cambridge, MA: The MIT Press. Gärdenfors, P. (1992). The Dynamics of Belief Systems: Foundations versus Coherence Theories. In: C. Bicchieri and M. L. Dalla Chiara (eds.), Knowledge, Belief and Strategic Interaction, pp. 377-396. Cambridge: Cambridge University Press. Gärdenfors, P. and D. Makinson (1984). Revisions of Knowledge Systems Using Epistemic Entrenchment. In: M. Vardi (ed.), Proceedings of the Second Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 84-95. San Francisco: Morgan Kaufmann Publishers. Hansson, S. O. (1999). A Textbook of Belief Dynamics. Dordrecht: Kluwer. Hansson, S.O. and E. Olsson (1999). Providing Foundations for Coherentism. Erkenntnis 51: 243-265. Harman, G. (1986). Change In View. Cambridge: The MIT Press. Krajewski, W. (1976). Correspondence Principle and Idealization. In: J. PrzeáĊcki, K. Szaniawski and R. Wójcicki (eds.), Formal Methods in the Methodology of the Empirical Sciences, pp. 380-386. Dordrecht: D. Reidel. Krajewski, W. (1977). Correspondence Principle and the Growth of Knowledge. Dordrecht: D. Reidel. Laudan, L. (1981). A Confutation of Convergent Realism. Philosophy of Science 48: 19-49. Niiniluoto, I. (1990). Theories, Approximations and Idealizations. In: J. BrzeziĔski, F. Coniglione, T.A.F. Kuipers, and L. Nowak (eds.), Idealization I: General Problems (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 16), pp. 9-57. Amsterdam: Rodopi. Nowak, L. (1975). Relative Truth, the Correspondence Principle, and Absolute Truth. The Philosophy of Science 42: 187-202. Nowak, L. (1980). The Structure of Idealization. Dordrecht: D. Reidel. Nowak, L. (1992). The Idealizational Approach to Science: A Survey. In: BrzeziĔski and Nowak (eds.), Idealization III: Approximation and Truth (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 25), pp. 9-63. Amsterdam: Rodopi. Nowak, L. (1994). Remarks on the Nature of Galileo’s Methodological Revolution. In: Kuokkanen, M. (ed.) Idealization VII: Structuralism, Idealization and Approximation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 42). Amsterdam: Rodopi.

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Nowakowa, I. and L. Nowak (2000). Idealization X: The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam: Rodopi. Olsson, E. (1997). Coherence. Ph.D. Dissertation: University of Uppsala. Post, H. (1971). Correspondence, Invariance and Heuristics: In Praise of Conservative Induction. Studies in the History and Philosophy of Science 2: 213-255. Radder, H. (1990). Heuristics and the Generalized Correspondence Principle. British Journal for the Philosophy of Science 42: 195-226. Rott, H. (1991). Two Methods of Constructing Contractions and Revisions of Knowledge Systems. Journal of Philosophical Logic 20: 149-173. Rott, H. (2000). Two Dogmas of Belief Revision. The Journal of Philosophy 97: 503-522. Shaffer, M. (2000). Idealization and Empirical Testing. Ph.D. dissertation. Miami: University of Miami. Shaffer, M. (2001). Bayesian Confirmation of Theories that Incorporate Idealizations. Philosophy of Science 68: 36-52. Tritton, D. J. (1977). Physical Fluid Dynamics. New York: Van Nordstrom Reinhold. Zahar, E. (1983). Logic of Discovery or Psychology of Invention? British Journal for the Philosophy of Science 34: 243-261. Zahar, E. (2000). Poincaré’s Philosophy. Chicago: Open Court.

Krzysztof àastowski SYNTHETIC AND NEUTRALISTIC THEORY OF EVOLUTION: THE ISSUE OF METHODOLOGICAL CORRELATIONS

The issue of the article has already been discussed in the Polish literature. It was covered, in an exquisite manner, by Prof. Jerzy Szweykowski (1987). The article can be characterized as a model of the analytical view of applying the neutralistic theory to the explication of the processes of molecular evolution Szweykowski’s source materials and account were also used by W. Makaáowski (1991) when he reconstructed the main theorems of Kimura’s theory and sought to show the scope of its application to the empirical research. I point to the works selected, as I harbor no doubts that the biological aspects of the issue presented in my article have been dealt with in a model manner from the theoretical point of view. The task of the present article is to confront the two theories and to show the methodological and theoretical consequences of such a comparison. One may ask what kind of approach that is. I believe that if one keeps certain independence of the reigning assertions (which can be achieved by means of certain simplifications without which science cannot function), then one is capable of presenting such aspects of the

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 205-218. Amsterdam/New York, NY: Rodopi, 2007.

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issue that cast light on the methodological status of the theory in a given scientific branch. In other words, one can then observe such components and features of a theory that otherwise are very difficult to observe, if one confines oneself to their mere empirical interpretations. I have in mind here such issues as, for example, the mutual correlation of the two theories and the scope of their mutual exclusion. Such questions suffice to analyze the prospects for the development of these theoretical conceptions and to make the attempts of new experimental references. I shall begin with the classical view, i.e. I shall briefly present the theory of natural selection and the synthetic theory of evolution. I shall then proceed to characterize the variants of the neutralistic theory. In this characterization, I shall confine myself to using the crucial elements (and their order) that are taken into account in the views analyzed.

1. Reconstruction of the Classical view I shall present the structures that are essential to the two theories [TNS] and [STE] by specifying the main factor and the secondary factors.1 The classical version of the theory of natural selection [TNS] can be most easily characterized by three essential elements: the natural selection (NS), the hybridization in the process of heredity (h) and the environmental conditions (e). It has the following order of the essentiality of the factors: [TNS] NS NS, h NS, h, e 1 I use here the conceptual apparatus of the Idealization Theory of Science [ITS], as the apparatus makes it possible to analyze the characteristics of scientific theories and their correlations in a simple manner [Nowak 1974, 1977, 1980, 1996]. I use only some elements of the apparatus, such as the main factor of the essential structure, etc.

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The synthetic theory of evolution [STE], which was created in the last thirty years of the twentieth century, refers to the same main factor that was given in Darwin’s theory, i.e. in the theory of natural selection [TNS] (àastowski and Nowak 1982; àastowski 1987; Nowak and Nowakowa 2000; Nowak 2004). However, among the secondary factors essential to this view, one quotes not the hybridization in the process of heredity (h) but, in the course of the historical transformations of concepts, its more detailed characterizations: one introduces in the structure of this theory of evolution recombination (rec) and mutation (mut), which are derivative of the concept of hybridization. Thus, the expanded version of the theory of natural selection [STE] has the following order of the essentiality of the factors: [STE] NS+ NS+, rec NS+, rec, mut NS+, rec, mut, e where NS+ is the mechanism of natural selection understood in accordance with the synthesis of the twentieth century (i.e. the synthetic theory of evolution); the symbol ‘+’ denotes the description of the dependence which contains the law of natural selection; in [STE], it is valid with the modified presuppositions (in comparison with [TNS]): recombination (rec) mutation (mut), e — the environmental conditions (àastowski 1987). It is worth emphasizing that in the more extended view of [STE], i.e. in Szmalhauzen’s theory (the theory of stabilizing selection), one explicates more thoroughly one of the factors, viz. mutation (Szmalhauzen 1975). The author gives variants of mutation and distinguishes positive and negative mutation. He states, however, that they do not always occur (àastowski 1987). I shall not explicate this case further. Both views [TNS] and [STE] share the main factor: natural selection NS and NS+, respectively. They differ with regard to the secondary factors. From the methodological point of view, such a situation (with certain necessary conceptual simplifications) is called “dialectical correspondence,” since the main factor (and the main dependence:

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natural selection) is the very same mechanism and the differences consist in its cooperation with the secondary factors.

2. Darwin’s and Kimura’s Problem A very interesting epistemological (theoretical and methodological) issue is the search for the correlations between two great theories: Darwin’s and Kimura’s. It is the question of the type of correspondence or of a lack of such (Nowakowa 1982; 1991). Many answers have been given here. Szweykowski (1987), for instance, in his reconstruction gives “a point where the two theories meet” (this being a metaphor, as otherwise it would be difficult to express what the point is). It is the problem of the ‘cost’ of selection that every population bears when generating the substitutions of mutation. In my opinion another answer is worth considering. I think that the issue can be shown with a very simple pattern which illustrates Darwin’s reasoning and, at the same time, renders it possible to formulate Kimura’s dilemma. I shall, therefore present graphically the patterns which present Darwin’s reasoning [STE] (Fig. 1) and Kimura’s [NTE] (Fig. 2). The former shows the effects of the natural selection in such a manner that on the left side of the point which is shown by the arrow and the “zero” individuals (populations) subject to selection are given, i.e. the negative effect of the evolutionary test (death). On the right, the populations which succeed in adapting — surviving (the positive effect the test). It is possible to show which survive and which die, because the natural selection tests their adaptability with regard to the conditions in which these live. From the contemporary point of view, the crucial element of the pattern is the “zero” point, where the natural selection is incapable of testing the adaptability. In other words, the adaptability (and the entire theory of Kimura pivots on it) is neutral with regard to the environmental conditions. Thus, it is somewhat powerless with such individuals, populations or — and that is Kimura’s apt qualification — genes. Consequently, Kimura’s dilemma could be articulated in the form of the following question: what evolutionary regularities populations,

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genes, genotypes are subject to when their adaptability is neutral (i.e. is “zero”). As we can see on the pattern enclosed, Darwin cannot answer the question. Furthermore, it is by no means clear whether Darwin saw the theoretical problem at all. Thus, it was Kimura who first interpreted the issue in such a manner and made an attempt to systematize it.

0

Fig. 1. Patterns of Darwin’s selection and of Kimura’s paraphrased question. The mechanism of natural selection in the view [STE]. The “zero” symbol denotes the area which in this model is not subject to the test of natural selection.

The second pattern shows the situation in which the “zero” point was characterized as: (i) on the one hand not subject to the mechanism of selection and adaptation and (ii) on the other as subject to a particular control of the genetic drift which (at least in Kimura’s theory) is the only mechanism that determines the preservation or elimination of the genetic features in a given population. What happens with the genes on “the verge of adaptability” is solely dependent on the nature and frequency of substitutions of mutations. If these substitutions are positive or negative (i.e. neutral), they are subject to the natural selection, if, however, they are neutral, then they are determined by the genetic drift in such a manner that they either

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spread or disappear. Fig. 2 shows a more complicated form of the dependence on the genetic drift, as quasi-neutral mutations are here taken into consideration (they are situated in the range from –½ Ne to ½ Ne).

– ½ Ne

½ Ne

Fig. 2. The pattern shows the range of influence of the selection and genetic drift in the view of the synthetic theory of molecular evolution [STME] (cf. Makaáowski 1991). The scope of evolutionary mechanisms is characterized by two types of influence: (i) negative selection (the left side) or positive selection (the right side), and (ii) the genetic drift (marked with the range from –½ Ne to ½ Ne).

The solution to Kimura’s dilemma can be presented in the following manner. The question: which evolutionary mechanism determines the survival of (genetic) features of populations when no natural selection tests them is answered in the following way: it is determined by the genetic drift and the increase or decrease of the given genetic features depends on the effective number of the population, i.e. Ne.2 2

‘Ne’ denotes the number of individuals of a population that effectively interbreed, i.e. participate in the process of reproduction (cf. e.g. Kimura 1983).

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Therefore, it is clear why we do not find the answer to the question about the evolutionary mechanism (in the point ‘zero’) in Darwin’s theory. It was only the full and proper conceptualization of the concept of mutation (with the idea of neutral mutations and their substitutions) that made it possible to include the issue to the considerations of evolution (the molecular evolution in particular). Thus, Kimura was the first to show the theoretical importance of Darwin’s problem and the possible solution to the problem.

3. Reconstruction of the Molecular View In Kimura’s view the main factor in the molecular evolution is the genetic drift. The genetic drift are the accidental changes of the frequency of a gene in a population caused by the random distribution of gametes in the process of reproduction (Kimura 1983). Yet, apart from the factor, mutations are also of great importance. Neutral mutation is a particularly significant variant of mutation in the description of changes in the frequency of the genes in the process of molecular evolution. The neutral mutation (mneu) is such a change of the structure of a gene (more precisely: the parts of the structure) that it does not cause any functional effects in the way the mutated gene behaves. Kimura is, however, aware that the changeability of the genetic material includes also the variants of these mutations that have been recognized earlier, i.e. the positive mutations (mpos) and negative (mneg). Nevertheless, as the theory [NTE] presupposes that the intensity of the selection (positive and negative) is “zero,” the theory describes only the molecular process of the evolution which occurs solely with the neutral mutations, for then the conditions for the random and quasi-random distribution of genes in a population are met. For the reasons mentioned above in the description of the essential structures that are assumed in the research of the molecular evolution, two types must be distinguished:

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1) molecular with the drift as the main factor — Kimura’s classical [NTE]: [NTE] GD GD, m GD, mneu, e where GD is the genetic drift and the rest as above. 2) molecular with the selection as the main factor; from Kimura’s perspective, a nonclassical view that could be called a selectionist theory of molecular evolution [SelTME]: [SelTME] I NS/S/ NS/S/, mpoz NS/S/, mpoz, mneg NS/S/, mpoz, mneg, e

where: NS/S/ is the natural selectionI(reduced to the mechanism of molecular selection) and the rest as above. Thus, if Kimura, apart from the nonclassical version [NTE], allows to use the nonclassical version [SelTME] when explaining the molecular evolution, then one could assume that he might accept the third view of the essential structure which will be called the synthetic theory of molecular evolution [STME]3: 3) the expanded neutralistic theory — the “synthetic” version [STME]: [STME] GD, DN/S/ GD, DN/S/, mneu GD, DN/S/, mneu, mpoz GD, DN/S/, mneu, mpoz, mneg GD, DN/S/, mneu, mpoz, mneg, e where GD is the genetic drift, mneu — the neutral mutation, mpos — the positive mutation, mneg — the negative mutation, e — the environment. 3

W. Makaáowski (1991) was the first to propose this.

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As we can observe, it admits as equally important two (main) factors: the genetic drift and the selection (as the molecular variant of the natural selection). Their impact on the process of molecular evolution is different. Which secondary factors will concur with the main factor depends on the nature of the genetic “material.” In such a situation, the question arises: how can we establish which mechanism will take place in a given evolutionary situation. It seems that the answer is the following: which mechanism appears in the evolution depends on the factor e, i.e. on the environmental conditions. Nonetheless, we believe that it cannot be treated as the main factor, for its peculiar effect consists in this that as long as the genetic features (the emerging mutations) are tested by it, the selection favors the better (the more advantageous) over the worse (the more disadvantageous). But if the mutations are small, neutral (i.e. nonfunctional), then they are insignificant for the selection, since the e factor (i.e. the environmental conditions molecularly understood) does not test such mutations. In other words, the occurrence of neutral mutations precludes the influence of the factor e. It goes without saying that the “ability” to evade the influence of this factor depends on the frequency with which the neutral mutations occur and the intensity of the mutation, i.e. how far does the mutation change the structure of the gene. The correlation mentioned above was accepted by Kimura in the consequence of the critique of the early version of [NTE]. He, therefore, modified his theory taking into consideration the fact that on the molecular level mutations rarely have “strictly” neutral nature. After a series of experiments, it transpired that quasi-neutral mutations are most frequent. These are changes whose quasi-neutrality depends on the effective number of the population Ne, i.e. the number of the individuals that participate in the reproduction (Kimura 1983). Thus, the greater the population, the more frequent the neutral and the quasi-neutral mutations and the more complicated it is for the factor e to take part in the process. This fact can be explained as a type of escape of subtle genes (the carriers of neutral changes) from the environmental conditions in which they happen to exist. If they evade the test, i.e. being tested by the factor e, they will be affected by the

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genetic drift, the mechanism that does not “chose,” but at random determines which neutral mutations will (in the course of the complex process of heredity) spread and which will not. The factor e which generates the selective evaluation of the quality of the genetic features operates in such a manner that when the genetic drift operates in a haphazard way, it determines at random which substitutions of mutations will survive and which will disappear. The mechanism of the process of the molecular evolution is twofold, but at the same time alternative: when the majority of the genetic features is advantageous, in a standard evolution many individuals survive and mechanisms of “comfort choices” dominate; it is easy to reject the worse features in order to guarantee the survival of the better. When, however, in relatively less numerous populations (whose number due to the great intensity of the selection decreased dramatically) the genetic drift appears (the “invisible player”), then the chance of survival becomes random. Thus, in the course of the molecular evolution both mechanisms operate. This fact should be noted in the concepts that are applied here. Therefore, in the description of a relatively full course of the molecular evolution, the following set of factors should be assumed: 4) The expanded version of the neutralistic theory (the “synthetic” version [STME] — the superpositional view): [STME] GD || DN/S/ GD || DN/S/, mneu GD || DN/S/, mneu, mpoz GD || DN/S/, mneu, mpoz, mneg GD || DN/S/, mneu, mpoz, mneg, e where ‘||’ should be read as ‘the effect GD precludes NS/S/’ and respectively: ‘the effect NS/S/ precludes GD’ — or briefly: ‘GD and NS/S/ operate alternatively’; the rest as above. The synthetic theory of the molecular evolution [STME] reduces the understanding of the mechanism [NS] to the factor of selection (which was denoted as [NS/S/]). As we can see, it is quite easy to pass from this structure to the two presented above, since it is enough to assume that for the first case:

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NS/S/ = 0 or NS/S/ § 0; and for the other that NS/S/ >> 0. For the former the [NTE] is valid, and for the latter the [SelTME]. In the terms of the classical view of the Idealization Theory of Science, such a situation is characterized as idealization (concretization) superpositional (Nowak 1974). Thus, at the molecular level of evolution, there are basically two mutually exclusive mechanisms: the selection and the genetic drift. The theory [SelTME] explains the former, the [NTE] — the latter. One can, therefore, ask what is the methodological relation between them? Such an issue is very frequently posed in the methodological research. An example of this is M. Bunge’s observation, who quoting Kimura’s theory writes: If two theories are regarded as competitive, then it is due to the fact that they share the meanings and allow posing some common problems. For instance, the theory that some mutations are neutral concurs with the standard genetics according to which every mutation is either advantageous or — most frequently — disadvantageous. (Bunge 1984, p. 52)

According to M. Bunge, the methodological hypothesis is: the theory [STME] refutes directly the theory [SelTME] and indirectly the theory [STE].4 It is possible that the relation of refutation goes even further, i.e. it reaches the [TNS], but such an extension of the hypothesis can only be drawn when one has investigated the theoretical consequences which would appear, if one considered the valid (and, of course, invalid) assumptions that are made in the research of biological and molecular evolution, i.e. the assumptions that aggregate this theoretical view (àastowski 1987). For the time being, the justification of the answer given is the following: the theory [STME] refutes the [SelTME] because: (1) it is richer in contents, since it describes a new factor, i.e. the genetic drift, when the [SelTME] shows only the factor of selection; (2) the theory

4 For lack of space, I cannot discuss thoroughly the issue of the refutation of a theory in the ITS. The account of the problem in the ITS is to be fund in K. Paprzycka (1990). Undoubtedly, the polemics between the proponents of Darwin and Kimura concerns the refutation of Darwin’s theory by Kimura’s theory.

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[STME] is more extensive, as it includes not only the process of molecular evolution with the positive and negative mutations, but first and foremost: the neutral mutations.

4. Summary The main conclusions that have been reached after the theoretical and methodological analysis of the selected views of the evolution and their correlations. 1. M. Kimura’s original version of the neutralistic theory displayed only the significance of the neutral mutation and the genetic drift (the version [NTE]). The later version, extended by the inclusion of selection, enabled a reconstruction of Kimura’s view in the version of [SelTME]. The theoretical reasons for their superpositional view justify the synthetic view, i.e. the [STME]. 2. The synthetic view of the molecular evolution [STME] allows two main mutually exclusive factors (mechanisms): the natural selection reduced to the effects of the selection [NS/S/] and the genetic drift [GD]. 3. The methodological view of the main factors in the evolution shows that the natural selection and the genetic drift operate alternatively, i.e. when a given theory describes the effects of one of them (e.g., the natural selection), then the other gains the intensity “zero” (its impact on the mutation is neutral) or close to “zero” (its impact on the mutation is quasi-neutral). In other words, the evolutionary effect of the former precludes the influence of the latter and vice versa. 4. There is a formal analogy between the level of population (morphological) and the level of genetics (molecular): while the, so called, phenomenon of recombination determines (increases or decreases) the morphological diversity, characterized in the terms of the frequency of features and their intensity, the neutral mutations (and their random frequency) determine the range of the genetic (molecular) diversity.

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However, the question whether the neutral mutations affect the frequency of features in a population or the intensity of features in an individual remains open. 5. For the time being, it has been established that there are methodological relations between selected theories of evolution, such as the dialectical correspondence and refutation. This conclusion justifies the opinion that M. Kimura’s neutralistic theory of the molecular evolution is not anti-Darwinian — as some of its opponents purported — but rather non-Darwinian. It is non-Darwinian, since it refutes the theory [STE] which is a “synthetic” view and a transformation of Darwin’s idea expressed in the classical theory of natural selection [TNS].

Uniwersytet im. A. Mickiewicza Department of Philosophy ul. Szamarzewskiego 89c 60-569 PoznaĔ Poland E-mail: [email protected]

REFERENCES Bunge, M. (1984). Zmiana w nauce: stopniowa czy katastroficzna? Studia Filozoficzne 9. Kimura, M. (1983). The Neutral Theory of Molecular Evolution. Cambridge: Cambridge University Press. àastowski, K. (1987). Rozwój teorii ewolucji: Studium metodologiczne. PoznaĔ: Wydawnictwo Naukowe UAM. àastowski, K. and L. Nowak (1982). Galileusz nauk biologicznych. Kosmos 3-4: 195-210. Makaáowski, W. (1991). Mechanizmy ewolucji molekularnej w Ğwietle syntetycznej i neutralistycznej teorii ewolucji: Ewolucja genów tRNA jako kryterium powiązaĔ teoretycznych i stosowalnoĞci empirycznej obu teorii. Ph.D. Dissertation: Uniwersytet im. A. Mickiewicza. Nowak, L. (1974). Zasady marksistowskiej filozofii nauki: Próba systematycznej rekonstrukcji. Warszawa: PWN. Nowak, L. (1977). WstĊp do idealizacyjnej teorii nauki. Warszawa: PWN.

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Nowak, L. (1980). The Structure of Idealization. Dordrecht: Reidel. Nowak, L. (1996). Idealizacyjna koncepcja nauki: Przegląd zastosowaĔ i rozwiniĊü. In: R. Egiert, A. Klawiter, P. Przybysz (eds.), Oblicza idealizacji (PoznaĔskie Studia z Filozofii Humanistyki 2[15]), pp. 11-74. PoznaĔ: Wydawnictwo Naukowe UAM. Nowak, L. (2004). Metodologia Karola Darwina. W: K. àastowski (red.). Teoria i metoda w biologii ewolucyjnej (PoznaĔskie Studia z Filozofii Humanistyki 20), pp. 13-56. PoznaĔ: Wydawnictwo Zysk i S-ka. Nowak, L. and I. Nowakowa (2000). The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam: Rodopi. Nowakowa, I. (1975). Dialektyczna korespondencja a rozwój nauki. Warszawa — PoznaĔ: PWN. Nowakowa, I. (1982). Dialectical Correspondence and Essential Truth. In: W. Krajewski (ed.), Polish Essays in the Philosophy of the Natural Sciences (Boston Studies in the Philosophy of Science, vol. 68), pp. 135-146. Dordrecht: Reidel. Nowakowa, I. (1991). ZmiennoĞü i staáoĞü w rozwoju nauki. PoznaĔ: Nakom. Paprzycka, K. (1990). Reduction and Correspondence in the Idealizational Approach to Science. In: J. BrzeziĔski, F. Coniglione, T.A.F. Kuipers, and L. Nowak (eds.), Idealization I: General Problems (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 16), pp. 277-286. Amsterdam: Rodopi. Szmalhauzen, I.I. (1975). Czynniki ewolucji. Teoria doboru stabilizującego. Warszawa: PWN. Szweykowski, J. (1987). Ewolucyjna teoria obojĊtnych mutacji (neutralistyczna) profesora Motoo Kimury. Kosmos 3: 375-394.

Adolfo García de la Sienra IDEALIZATION IN THE LABOR THEORY OF VALUE∗

Introduction My aim in the present paper is to assess the current status of the foundations of the Labor Theory of Value from the point of view of Leszek Nowak’s doctrine of idealization, but it seems to me that Nowak’s theory is better understood and appreciated if it is reconsidered within the conceptual framework introduced by Uskali Mäki for the analysis of idealization in economics. Accordingly, the first section is devoted to discuss the nature of idealization taking into account Mäki’s detailed and careful distinctions. In the second section Nowak’s doctrine is presented from the vantage point of these distinctions. In the third and last part, I propose an updated perspective on the foundations of the Labor Theory of Value.

1. Idealization as Isolation There are basically two positions within philosophy regarding the question “What is there?’.” The first one attaches primordial worth to

∗

This paper was written with support of CONACYT Project 28630-H.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 219-233. Amsterdam/New York, NY: Rodopi, 2007.

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ordinary, pre-theoretical experience, and sees the different sciences merely as ways of deepening this experience; the second attaches primordial worth to some science (usually physics), sees ordinary experience as a sort of naive theory, and sets up the methodological task of substituting a systematic theoretical body (“scientific experience”) for “naive” experience. Thus, according to the first position, which for lack of a better term may be dubbed ‘experiential holism’, there are indeed flowers, beautiful women, sunrises, friends, smiling children and the things with their properties and relations as we experience them in our daily, very human lives. According to the second position (known as scientism), all such things are an illusion that will melt down before the shining rays of theoretical physics (or any other discipline deemed as the “true” or “hard” science). But the question regarding which of these two positions is the true one is not a theoretical one because each is grounded in a respective hidden presupposition about what is truly real and has self-existence. This is not, however, the place to show how and why this is so.1 I will just put my cards on the table presupposing (and also making plausible) that ordinary experience is not a theory that can be refuted as, say, Aristotelian Dynamics. I claim that at least some aspects of ordinary experience must be distinguished from the interpretation humans make of them, always within the framework of a (religiously oriented) worldview. I take as evident that all men, in all times, no matter their religion and culture, are aware not of sense-data in the empiricist sense, but of real properties of real things with which, moreover, they interact in order to survive. For instance, could you imagine a tribe in which no individual has some idea of which herbs and animals are edible and which are not? Or a clan at war that cannot tell stones from sticks? Clearly, no such human group could survive. But this is an evolutionary argument to the effect that a certain fashionable universal skepticism (or cultural relativism), of the sort advocated by many philosophers nowadays, is far-fetched: All human groups share a certain set of universal concepts 1

For a complete treatment of this issue, see Clouser (2005). See also Walsh and Middleton (1994), Part 1.

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that allow them to survive in an environment (nature) that (you can rest assured) is not tailored by their wishes or previously concocted concepts. The universality of these concepts also makes possible communication among cultures that are distant in space, time and content. Some relativist philosophers have suggested that what a thing is is relative to the conceptual frame within which it is conceived. A typical example is that of the American natives who thought that the Spanish riders were centaurs. Cultural relativism claims that nobody (especially not the Westerners) is entitled to “impose” his view upon that of the natives, by saying that “actually” there were two entities (the rider and the horse) and not one. This is, of course, politically correct but also stupid, and the warriors who suffered that confusion turned out to be dead wrong, as history shows. Things and their properties are not abstract entities and are experienced in their full integrity not mainly in contemplation, but above all in the production process, in the interaction between man and its means of labor. If this fact is not accepted, it is impossible to make sense of the different types of abstraction, nay, of the very notion of abstraction. Talking about abstraction presupposes that there is something to be abstracted and also an object out of which this something is abstracted. A first approach to abstraction makes a distinction between low and high abstraction. Low abstraction is basically the focusing of our attention on some parts or aspects of a situation. Imagine some hunters looking for sharp stones to cut meat. They will mentally single out stones from other types of things around, and also thin edges from other configurations exhibited by stones. Of course, focusing upon certain stones is not the same as piling them up in a heap. One thing is to focus upon the stones (i.e. view them as the only relevant type of thing in a material system for a given human purpose) and quite another to separate them from their original environment. Experimentation not only separates things from their original environment, but also places them under controlled situations, isolating them from certain causal factors that are deemed relevant for the phenomenon under study. The first type of operation, which somehow “isolates” the stones or some of their properties by not

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paying attention to their environment, is called ‘theoretical isolation’ by Mäki.2 The second operation is called ‘material isolation’ by the same author. Yet, I find the term ‘theoretical’ a little bit excessive for low abstraction. It sounds funny to say that primitive (or any) hunters are engaged in theoretical activity when looking for stones to kill a bear! Thus, I propose as the first, fundamental distinction, that between material isolation and intellectual isolation. Material isolation is the operation of putting a material system (a rock, a plant, a virus, a chemical substance) beyond certain causes acting upon it. Intellectual isolation is entirely a mental operation that focuses upon certain things, properties or relations, without thereby materially isolating such things, properties or relations. An intellectual isolation that focuses upon the nature, property or relation of a thing, but keeps seeing the nature, the property or the relation as the nature, property or relation of the thing, I will call “low” abstraction. If it “detaches” the nature, property or relation from this particular thing in order to consider the nature, property or relation in itself, as capable of being instantiated in different things, it will be called “high” or “theoretical” abstraction. Thus, theoretical isolation is only one type of intellectual isolation. It is possible to move from low to high abstraction, and vice versa. If I jump from considering my knife to consider the universal knife then I am moving to another level of abstraction, a theoretical (high) one. This type of abstraction is called ‘vertical abstraction’. To this operation there corresponds a sort of inverse one called ‘vertical deisolation’: that of moving from high to low abstraction, as when you move from the universal knife to this particular knife. But there is also a type of isolation and corresponding inverse within the same level of abstraction. Suppose that, in a first intellectual operation, the knife as being in my pocket is isolated, so that I focus my attention upon the-knife-in-the-pocket. And suppose, further, that in a second operation I disregard my pocket and consider only the 2

Mäki (1994, p. 150). The following discussion is based upon the distinctions introduced in this and subsequent pages.

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knife. Clearly, the result of this second operation is at the same level of abstraction as that of the first (both are low). If, as a result of this type of horizontal isolation, I formulate an accurate sentence about the knife itself, the result is a true assertion that fails to mention many other things about the knife (for instance, that it is in my pocket), and so it “violates” the “whole truth” which is to say that it does not contain or imply all true assertions about the knife: it omits them. Nevertheless, since what it claims is not a distortion of reality, it is said that it does not violate “nothing-but-the-truth.” The operation of taking those omitted items into account again is called ‘horizontal deisolation’. This suggests that a twofold distinction is inescapable, namely between horizontal and vertical isolation. Horizontal isolation takes place when both the starting and the finishing point of the intellectual operation are within the same level of abstraction (both high or both low). Vertical isolation takes place when we move from low to high abstraction. Vertical and horizontal de-isolation are, respectively, the inverse operations. But horizontal isolation can be performed also by means of idealizing assumptions, which is more interesting from a metatheoretical point of view. For there are two types of horizontal isolation. The one of the example, based upon mere omissions, is a very common one. A second one operates upon high abstractions and consists of isolating the universal by means of explicitly formulated idealizing assumptions. The verbal expression of this isolation ends up producing counterfactual conditionals that stipulate what would happen if the powers of the isolated universal were operating in different sets of conditions. For instance, in a first operation the nature of motion is abstracted and then particular cases of unimpeded motion are observed. Now, it is possible to experience particular cases of unimpeded motion but never a case of a body not at all subjected to forces preventing it from moving in an entirely free way (inertially). To say that a body not subjected to any forces will move in a certain way (e.g. in a rectilinear and uniform manner) is a (putatively) true statement about inertial motion, even though perhaps never in the

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history of mankind will there be someone in a position enabling him to directly verify it. Newton’s First Law is an example of such a statement. Mäki distinguishes among two types of idealizing assumptions: nullifying idealizations and stabilizing idealizations. Nullifying assumptions express that a certain factor, which is usually present affecting the powers of the isolated universal, is missing. If p(x) is the degree in which factor x is present, a nullifying assumption can be expressed in the form p(x) = 0. A stabilizing assumption states that the rate of change of factor p at x is nullified, and is expressed as pĻ(x) = 0.

2. Nowak’s Doctrine of Idealization In order to present his doctrine of idealization, Nowak discusses the Labor Theory of Value (LTV) beginning with the introduction of a universe of discourse U defined by a domain assumption, that is a formula G(x), in such a way that x ∈ U ↔ G(x). ‘G(x)’ means ‘x is a commodity (within a certain economic system)’, so that U must be understood as a universe of commodities. Nowak (1980, p. 28) sees this formula as a realistic assumption that actually refers to real commodities in a certain market. He also claims that U is the universe of discourse of LTV. An idealizing condition for Nowak is precisely what was called above an idealizing assumption. A formula p(x) = 0 is an idealizing condition iff “0 symbolizes the minimum value of the magnitude p and, for each actual object a: p(a) ≠ 0” (Nowak 1980, p. 28). Since all the elements of the universe of discourse U are actual commodities, I take this as implying that p(x) ≠ 0 for every x in any imaginable set U of commodities. This means that it is impossible to observe a situation in which p(x) ≠ 0 actually holds. Another type of idealizing condition has the form p(x) = f Ļ(x) = 0

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with the same provisos made for the first type. Notice that these two types are precisely what Mäki called nullifying and stabilizing assumptions, respectively. An idealizational statement is a statement of the form (T k) ∀x [if G(x) and p1(x) = 0 and . . . and pk(x) = 0, then F(x) = fk(H1(x), . . . , Hn(x))] where G(x) is a realistic condition, p1(x) = 0, . . . , pk(x) = 0 are idealizing assumptions horizontally isolating universal F, H1, . . . , Hn are magnitudes, and fk specifies the way in which these magnitudes relate to F given the idealizing assumptions p1(x) = 0, . . . , pk(x) = 0. These assumptions are not negligibility assumptions, since they are not introduced with the intention of neglecting a factor that is in fact irrelevant for F. But they can be seen as heuristic assumptions3 since they are made for the sake of theory-building, in order to consider first the operation of F in a simpler case, before starting a process of horizontal de-isolation (which Nowak calls “concretization”) considering the operation of F under more complex situations. Following a suggestion due to Mäki (1994, p. 158), (T k) should be seen as the metalevel promise that the first-step assumptions p1(x) = 0, . . . , pk(x) = 0 will be relaxed afterwards in order to consider the operation of F under situations in which p1(x) = 0, . . . , pk(x) = 0 are no longer supposed to hold. The process of horizontal de-isolation (“concretization”) in this case proceeds by modifying assumptions p1(x) = 0, . . . , pk(x) = 0. Thus, if condition pk(x) = 0 is changed, we get the first de-isolation of (T k): (T k-1) ∀x [if G(x) and p1(x) = 0 and . . . and pk-1(x) = 0 and pk(x) ≠ 0, then F(x) = fk-1(H1(x), . . . , Hn(x), pk(x))] As the remaining idealizing assumptions are eliminated, we get a sequence of sentences of the form (T k-j) ∀x [if G(x) and p1(x) = 0 and . . . and pj (x) = 0 and pj+1(x) ≠ 0 and . . . and pk(x) ≠ 0, then F(x) = fk-j (H1(x), . . . , Hn(x), pj+1(x), . . . , pk(x))] 3

For a discussion on the meaning of these assumptions, see García de la Sienra (1994).

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until we reach in the limit, when the meta-level promise is completely fulfilled, the perfect de-isolation of F: (T 0) ∀x [if G(x) and p1(x) ≠ 0 and . . . and pk(x) ≠ 0, then F(x) = f0(H1(x), . . . , Hn(x), p1(x), . . . , pk(x))] Nowak calls (T 0) a “factual statement” (Nowak 1980, p. 30), a way of speaking that suggests that statements (T 1)-(T k) are not factual. But it is obvious that nothing in Nowak’s view prevents treating (T 1)-(T k) as true statements regarding the behavior of F under certain circumstances, even if these circumstances are never observed in experience. The following question arises here: How do you know that if conditions p1(x) = 0, . . . , pk(x) = 0 hold then equation F(x) = fk(H1(x), . . . , Hn(x)) holds as well? After all, such conditions are never given in experience! In a certain sense, sentences of the form (T k) are reached by experience, by observing the way in which the operation of factors p1, . . . , pk does affect F. For instance, Newton observed that a body in seemingly rectilinear uniform motion suffered a change of speed or direction when a new force was applied to it. He then concluded that a body not subjected to any force should move in a rectilinear and uniform way. Unfortunately, it is harder to have that kind of observation in the social sciences. Hence, instead of relying on observation or mere conjectures, economic theorizing proceeds to choose conditions p1(x) = 0, . . . , pk(x) = 0 in such a way that they are jointly sufficient to prove equation F(x) = fk(H1(x), . . . , Hn(x)) as a theorem. This is, for instance, what Morishima does in order to prove that labor values “are the equilibrium prices prevailing in a society with simple commodity production where people behave in the Walrasian manner” (Morishima 1973, p. 45), or that the profits and surplus values are proportional throughout the economy if and only if all industries have the same composition of capital (Morishima 1973, p. 74). One important lesson of Newton’s application of the method of idealization is, however, that a general form of law must be sought, a

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form that logically implies all the previous idealizational statements reached by horizontal isolation. This is brilliantly exemplified by the derivability of the First Law out of the Second.

3. The Labor Theory of Value Revisited Both Nowak and Bert Hamminga have made logico-historical analyses of Marx’s application of the method of idealization in Das Kapital (Hamminga 1990; Nowak 1980). In this last section I would like to take advantage of the previous discussion in order to propose an updated perspective on the foundations of the Labor Theory of Value. It seems to me that the work on the foundations of LTV has been unable to distinguish two entangled problems. The first problem is that of vertically isolating the universal labor-value providing a completely general definition of labor-value (even if implicitly, by means of axioms). The second one is to horizontally de-isolate a particular definition of labor-value in order to obtain less idealized versions of the Law of Value. Solving the second does not necessarily solve the first one and I suspect that this is the reason why the formulation of the Law of Value, that Marx provided as outcome of the sequence of “concretizations” so aptly described by Nowak and Hamminga, is really a mess. The most idealized formulation of the Law of Value is the following: (LV1) The price of a unit of good m, in an economy with μ types of goods (1 ” m ” μ) is equal to the labor value of m, namely the amount of socially necessary labor time directly and indirectly needed to produce that unit. Compare this with the (Hamminga 1990, p. 106):

following,

less

idealized

formulation

(LV2) p(x) = cost(x) + (cost(x) + rfix(x) + cmer(x))⋅RAPRO where: cost(x) = dep(x) + cir(x) + var(x) and dep(x) is the depreciation of the fixed capital required to produce good x, cir(x) is the circulating capital, var(x) is the variable capital,

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rfix(x) is the remaining fixed capital (after depreciation), cmer(x) is the merchant capital. § cost (k, m ) · SUR − ¨¨ − cost (k ) ¸¸ − abs(k ) share ( k , m ) © ¹ RAPRO = § ctot (k, m) · CTOT + ¨¨ − ctot (k ) ¸¸ © share(k, m) ¹

SUR is the total surplus value in the whole country (there are k spheres of production); cost(k, m) is the cost of producing agricultural goods applying capital m; share(k, m) is the percentage of agricultural produce that has resulted from applying capital m in agriculture; abs(k) is the absolute rent; ctot(k,m) is the total capital m applied in agriculture; CTOT is total capital in the economy. After this metamorphosis, it is really impossible to figure out what is exactly the meaning of the Law of Value. Is it a law of priceformation? A mere worm or a butterfly? Marx actually said that prices are “lawlike modifications of value” (“durch allgemeine Gesetze bestimmte Modifikationen”).4 But one wonders whether a baroque a construction as (LV2) can be seriously taken as the fundamental law of LTV. I think that it cannot. In the first place, formulation (LV1) of the Law of Value requires a particular definition of value that cannot be given unless a fair amount of idealizing assumptions is made.5 What this means is that (LV1) is based upon a not sufficiently general understanding of the universal labor-value. Notice, in the second place, that (LV2) does not even address this problem and stays within the very same definition of labor-value presupposed by (LV1). What is required, though, is the use of a general concept of labor-value out of which a general statement of the Law of Value can be formulated.6 I

4

Quoted by Hamminga (1990), p. 92.

5

For instance, that there is no problem of choice of techniques, no joint production problem, no problem of heterogeneous concrete labors, etc. Morishima (1973, pp. 12, 22) enlists no less than eight assumptions just in order to define the concept of labor-value. Additional assumptions are required to horizontally isolate it and establish (LV 1). 6

Finding the most general concept of labor-value, rather than a general statement of the Law of Value, was my main goal in García de la Sienra (1992).

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suspect that such general concept of labor-value should entitle us to provide also a general formulation of the Law of Value itself, and that the difficulties leading to (LV2) (which is itself more a problem than a solution) spring from a wrong understanding of the essence of laborvalue. Thus, I suggest that perhaps we should try first to vertically isolate the universal labor-value, providing a fully general definition of the concept, and then set upon ourselves the task of providing a general formulation of the Law of Value. As a matter of fact, I think that Marx’s error was precisely to keep a limited definition of labor-value, meaningful only under certain very idealized conditions, when he started a de-isolation process intended to provide versions of the Law of Value under less idealized conditions. The problem is that he never saw that he was still working within the idealized conditions that allowed him to introduce the limited definition of labor-value in the first place, and that perhaps these conditions no longer held in the models he was obtaining by way of concretization. Hence the complexity of (LV2).7 I think that the root of the error is this: the conception of laborvalue under the analogy of a physical substance that is somehow “transferred” to the final products in the economy. Against this error — which might be called the ‘fetishism of Labor’ — I propose a very different understanding of labor-value, namely as the costs in terms of shadow wages of the commodities efficiently produced. This is not the place to get into the details, but the idea is roughly the following. Suppose that there are η branches, each one with a production possibility set Yh, a closed convex cone (not necessarily polyhedrical) in the linear space Bv+μ, where v is the number of heterogeneous labors and μ that of commodities. It was proven in (García de la Sienra 2002) that if it is possible to activate an aggregated production process

In other words, in that book I was mainly concerned with vertically isolating the universal labor-value. 7

Thus, if the universal is not vertically isolated to an appropriate degree, you cannot concretize by jeans of horizontal de-isolation. This is what I meant when I said (García de la Sienra 1992, p. 128) that “contrary to what Mäki (1992) suggests, it is not the same to concretize than to de-isolate determinations.”

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~ y ∈Y =

¦

μ h =1

Yh

with positive net outputs, and labor is both indispensable and productive, then there is a finite number of activities y͂h , one in each branch, such that every nonnegative linear combination of these activities is efficient. On the other hand, it was proven in (García de la Sienra 1996) that for every convex polyhedral cone Y * of efficient processes there is a pair (w, p) of hourly wages and prices such that ˆ of the net output of any process y ∈ Y *, in terms of the the worth py price system p, is equal to the worth wy of the labor power of the same process, in terms of the “wage” system w (García de la Sienra 1996, Theorem 2, p. 73): ˆ = wy py

Moreover, even though there may be many pairs (w, p) that satisfy the equation, for any such system p of prices there is a unique system of y ∈ Y * and vice versa wages w that satisfies the equation for every ~ (García de la Sienra 1996, Theorem 1, pp. 71-72). In García de la Sienra (1992, p. 140), I defined a valid price system ˆ ≥ ( > ) py ˆ ′ whenever y • (>) yĻ. for Y* as a price system p such that py That is to say, a valid price system is a system of prices that assigns a greater monetary value to those net inputs that require more labor in order to be produced. I defined then (García de la Sienra 1992, p. 141) abstract labor as a binary relation V defined over the set

{ [ ]

ˆ ∈Y * L = y y, y

}

of labor input vectors induced by a valid price system p in the sense that ˆ ≥ py ˆ′ y V yĻ iff py

On the other hand in (García de la Sienra 1996, p. 72), I defined analogously a valid reduction for Y * as a system of wages w such that ˆ ≥ ( >) y ˆ ′ . In other words, a reduction is a wy • (>) wyĻ whenever y system of wages that assigns a greater salary to the workers in those processes that yield a larger net output. Relative value can then be defined as a binary relation  over the set N of net outputs, by the condition

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ˆ>y ˆ ′ iff wy • wyĻ y ˆ can In terms of the previous concepts, the labor-value of net output y be defined as the number wy. The system of shadow wages w is called ‘reduction’ because it reduces the heterogeneous labors to a common measure. The meaning of this reduction is interesting. It amounts to socially weighing the different types of labor, attributing to each a certain worth in the production process. This is a way of understanding Aristotle’s claim (Nichomachean Ethics, 1132b30) that reciprocity in exchange must be made in accordance to a proportion and not on the basis of equality. The idealizing assumption that labor is homogeneous presupposes that all labors are deemed as equal, and so they are reduced by means of a reduction of the form w = (1, . . . , 1) consisting of pure ones. Vectors of labor inputs x are indeed measured in terms of socially necessary labor-time: Entry xn of x expresses the socially necessary amount of labor-time of trade n efficiently employed in process ~ x . But value is not a physical magnitude: it is a social relationship. A “social planner” could decide (according to some criterion) which system of weights w is “fair” and then determine the corresponding system of shadow prices p corresponding to this system of weights (such a p does exist, and is unique, if w is valid). Or, if p is a system of valid market prices, then “the market” (represented by this system of prices) actually imposes a particular system of weights w that does not have to be fair according to any criterion. What is the “true” labor-value of the goods in the market? The only answer to this question that makes sense to me is that it is the one determined by a “fair” weighing of the different trades. Thus, the concept of labor-value is an ethico-economic concept and not a technological one. That is perhaps why Marx was so puzzled with it. In his Contribution to a Critique of Political Economy (p. 45), he wrote: a new difficulty arises: on the one hand commodities must enter the exchange process as materialised universal labour-time, on the other hand, the labour-time of individuals becomes materialized universal labor-time only as the result of the exchange process.

Which of these two (incompatible) alternatives is true? We have seen that the first one is that of the “social planner”; the second one that of

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“the market.” Since there is no such a thing as a social planner in a capitalist economy (at least of the type Marx was analyzing), it follows that Marx was forced to define labor-value in terms of market-reduced (abstract) labor. Yet this is precisely what he did not do, sticking all the way to the notion of homogenous labor! What is, then, the form and meaning of the Law of Value? I would like to leave this question here as an open problem, although important steps to connect pairs of shadow wages-prices (w, p) with systems of market prices and wages have been given by Ulrich Krause (1979; 1980; 1981; 1982). I think that the agenda must be pursued in this direction, in order to reach a reasonable formulation of the empirical claim of LTV. There is no doubt the Nowak’s seminal work on the method of idealization will be important in this endeavor.

Universidad Veracruzana Facultad de Economía Av. Xalapa y Manuel Ávila Camacho 91020 Xalapa, Veracruz Mexico E-mail: [email protected]

REFERENCES Aristotle (1984). Nichomachean Ethics. In: The Complete Works of Aristotle, edited by Jonathan Barnes, vol. II, pp. 1729-1867. Princeton: Princeton University Press. BrzeziĔski, J., F. Coniglione, T.A.F. Kuipers and L. Nowak, eds. (1990). Idealization I: General Problems. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 16. Amsterdam: Rodopi. Clouser, R. A. (2005). The Myth of Religious Neutrality. Notre Dame: University of Notre Dame Press. Dilworth, C., ed. (1992). Idealization VI: Intelligibility in Science. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 26. Amsterdam: Rodopi. García de la Sienra, A. (1992). The Logical Foundations of the Marxian Theory of Value. Dordrecht: Kluwer.

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García de la Sienra, A. (1994). Idealization and Empirical Adequacy in Economic Theory. In: Hamminga et al. (1994), pp. 117-133. García de la Sienra, A. (1996). La medición del trabajo abstracto. Economía Mexicana 5(1): 63-75. García de la Sienra, A. (2002). A Non-Substitution Theorem with Heterogeneous Labor. Revista Mexicana de Economía y Finanzas 1: 3-13. Hamminga, B. (1990). The Structure of Six Transformations in Marx’s Capital. In: BrzeziĔski et al. (1990), pp. 89-111. Hamminga, B. and N. B. de Marchi, eds. (1994). Idealization VI: Idealization in Economics. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 38. Amsterdam: Rodopi. Krause, U. (1979). Geld und abstrakte Arbeit. Frankfurt: Campus Verlag. Krause, U. (1980). Abstract Labor in General Joint Systems. Metroeconomica 32: 115-135. Krause, U. (1981). Abstract Labour and the Fundamental Marxian Theorem. Review of Economic Studies 48: 173-178. Krause, U. (1982). Money and Abstract Labour. London: Verso. Mäki, U. (1992). On the Method of Idealization in Economics. In: Dilworth (1992), pp. 317-351. Mäki, U. (1994). Isolation, Idealization Hamminga et al. (1994), pp. 147-168.

and

Truth

in

Economics.

In:

Marx, K. (1970). Contribution to a Critique of Political Economy. New York: International Publishers. Morishima, M. (1973). Marx’s Economics. A Dual Theory of Value and Growth. Cambridge: Cambridge University Press. Nowak, L. (1980). The Structure of Idealization. Dordrecht: Reidel. Walsh, B. J. and J. Richard Middleton (1984). The Transforming Vision. Downers Grove: Intervarsity Press.

Krzysztof Brzechczyn ON THE APPLICATION OF NON-MARXIAN HISTORICAL MATERIALISM TO DEVELOPMENT OF NON-EUROPEAN SOCIETIES

1. Introduction Non-Marxian historical materialism created in the late 1970s by Leszek Nowak (1983; 1991) is, on the one hand, a modification of Karl Marx’s historical materialism and, on the other hand, its extension. It can be seen to be a modification because Nowak in the “economic part” of his theory tries to explicate the relationship between two internal developmental mechanisms of historical materialism, namely, the mechanism of contradiction between the owners and direct producers with the mechanism of dependency of relations of production on the productive forces. The “political” and “cultural” parts of Nowak’s theory are, however, his original contributions to the philosophy of history which can not be read or interpreted in Karl Marx’s writings. The belief that class divisions spontaneously emerged in the other spheres of human activity, e.g. in politics and culture is one beyond Marx’s historical materialism. In Nowak’s view of social reality, the conflicts between the rulers and the citizens or the priests and the indoctrinated occur according to its own internal logic and hence, they are irreducible to economic contradictions.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 235-254. Amsterdam/New York, NY: Rodopi, 2007.

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The vision of historical development presented in non-Marxian historical materialism includes the history of class societies in the course of two and half thousands years from the societies of ancient Greece and Rome to the modern capitalist societies of Western and “real-soc” societies of Eastern Europe. However, the range of the application of Nowak’s theory is limited to the history of European societies. Hitherto, the problem of historical development of nonEuropean societies was not analyzed in this respect. It would appear that only one paper has been devoted to the problem of colonization, decolonization and development of Third World societies. Its authors, Katarzyna Paprzycka and Leszek Nowak (1989) consider the development of two types of societies: class societies (capitalist) belonging to European civilization and supra-class societies, on the lower level of technological development — which belong to nonEuropean civilizations. In their considerations, the authors (1989, p. 302) try to answer the following questions: (i) when did capitalist society became aggressive? (ii) what are social consequences of colonization for the capitalist metropolis and the subordinated society? (iii) when the conquered society is able to gain independence? (iv) how does colonization influence the social structure of the independent, post-colonial society? The base of the authors’ analysis is the model of capitalist society (Nowak 1989) and model I of the theory of (political) supra-class society (Nowak 1987, see also his 1991). In the model of capitalist society there are two sources of aggressiveness. The first comes from the relation of power, the second — from the relation of property. The social relations between the class of rulers and the class citizens in a given society are described by the bell-curve. This means that in the case of weak (state of class peace) as well as very intensive control (state of declassation) of the rulers over the citizens, political resistance is weak. When the political control reaches moderate level (state of revolution), civil resistance becomes revolutionary. Therefore, from the political side, the tendency of aggressiveness begins when power regulation goes beyond the threshold of class peace. Beyond this

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point, the further maximization of power by the class of rulers intensifies civil resistance. Then, the maximization of power regulation at the cost of external societies becomes more profitable for the class of rulers. Likewise, the social relations between the class of owners and the class of direct producers can be also described by the bell-curve. Therefore, in the case of weak (state of class peace) as well as very intensive exploitation (state of declassation) of direct producers by the owners, economic resistance is weak. When exploitation reaches moderate level (state of revolution), the resistance of the direct producers becomes revolutionary. Therefore from the economic side, the tendency of aggressiveness begins when the level of exploitation passes the threshold of class peace threatening the outbreak of the revolution. The resistance of direct producers impedes the appropriation of the surplus value by the owners in the society under analysis. External aggressiveness creates the possibility of extramaximization of profits coming from the conquest of others societies (in the form of raw materials, markets, and access to cheap labor). Thus, answer to question (i) is following. The capitalist metropolis becomes aggressive when the level of exploitation and political control passes the threshold of class peace, but does not reach yet the interval of revolutionary perturbations. In the model of capitalist society this state of social affairs refers to the phase of cyclical development. K. Paprzycka and L. Nowak also consider the social consequences of conquest for a capitalist metropolis and colonial country (answer to question ii). Generally speaking, efficient colonization prolongs the state of class peace in the economic and political sphere. Due to this: • in the phase of cyclical development the periods of class peace become extended; the size of this modification depends on the number of aggressions and size of economic and political profits coming from successful conquest; • the intensity of class conflict is reduced, diminishing the chances for a civil loop in the metropolis and consequently — the chances for capitalist society to become totalitarian; • the phase of cyclical development is shortened, accelerating the phase of class peace.

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As a result of the technological development in the phase of class peace, the aggressiveness of the capitalist metropolis diminishes the prospect of achieving the level of colonial désintéressement. The conditions of economic development cause backward colonial provinces to become the unequal partners of more advanced capitalist metropolis because the economic cooperation requires the existence of a highly developed infrastructure. Moreover, in the conditions of class peace, neither the ruling class, nor the people’s class has an interest in possessing colonies. Furthermore, K. Paprzycka and L. Nowak analyze the consequences of colonialism for colonial societies. In the political dimension, all the inhabitants of a colony enslaved by metropolitan authorities are second rank citizens of the empire. The relations between the metropolitan power and citizens of the colony fall under the scheme of the model of purely political society composed of the phases of declassation, totalization and gradual revalorization of autonomous social relations leading to cyclical civil revolutions with a wider social base. This, it may be argued, answers the above question (iii). The colony initiates the fight for independence against the metropolis when the citizen movement becomes mass social phenomenon to threaten colonial rule. Simultaneously, in the colony there occurs a process of socialeconomic development. The indicator of its advancement is the formation of private property. As a consequence of economic competition there is initially formed at first a petty (handicraft, peasantry), middle and grand bourgeoisie. Thus, the liberation of the colony, according to the authors, is a coincidence of two processes: • the attainment colonial désintéressement by the metropolis; • formation of enough momentum for a civil movement. What happens after gaining political independence depends on the economic level of the colony’s development. In this respect the above authors distinguish three developmental variants what is answer to question (iv): (i) The variant of the national liberating loop. If a colony gains political independence in the pre-capitalist phase of develop-

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ment, the new revolutionary authorities seize the means of capitalist production possessed by foreign capital. Thus, subordinating the whole economy, they became the double class of rulers-owners. (ii) The variant of premature liberation. When the gaining of independence occurs in the petty-capitalistic stage of development in a colonial society, a system develops which is neither class, nor totalitarian in nature. The state nationalizes the means of production, which was in the hands of foreign capital but it does not exclusively control the economy because a native bourgeoisie emerges. The authors characterize this mixed social system in the following way: The natural ally, the ruler-owner, is the petty-bourgeoisie.IDue to the alliance directed against the grand bourgeoisie, both the further economic growth of capitalism is being stopped (petty-ownership is supported by the state) and the limitation of the stratum of large owners normally imposed on the political power is weakened. Therefore, the latter develops to a great extent according to regularities of its own, as if it were a pure political system. Thus an increase of the control over the masses leads to incessant revolutions; in the case of victory a civil loop takes place, but it remains a civil one, i.e. it does not lead to totalitarianism whereas in the case of the defeat of the masses, their declassing does not occur as it is at variance with the interest of both grand and pettybourgeoisie. The system closes thus both the possibility of totalitarisation “from below” and “from above,” simply reproducing itself. As long as such a system remains in the petty-capitalist stage of development, totalitarianism does not pose a danger. (Paprzycka and Nowak 1989, p. 307)

In this social system therefore,Itotalitarianism occurs when it transforms in a fully capitalist society. (iii) The variant of capitalization. If gaining independence occurs in the capitalist stage of development, colonial society enters the path of standard capitalist development with separate classes of rulers, owners and the people class. These groups of liberating after the

three developmental variants can be referred to certain countries in the Third World. The variant of the nationalloop approximates the development of black Africa, where collapse of colonial regimes, revolutionary power seized

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control over the means of production. Thus the variant of capitalization would approximate the development of the Far East. The variant of premature liberation characterizes the countries of Latin America. These variants are, however, only local ramifications of the one universal line of development characterized for European societies: The inclusion of these considerations into a more general framework of non-Marxian historical materialism reveals that the three variants of the development of the Third World are different roads to totalitarization and then to socialism. If in a given colony there occurs a civilnational loop (variant i), it immediately reaches totalitarianism (or fascism). When a given country is liberated too early (variant ii), then the process of the totalitarization of the country is delayed until the capitalization of the country appears which, in the normal way, leads from the final stage of capitalism to totalitarianism. Finally, when a country builds capitalism before political liberation, then totalitarianism comes in the normal way (variant iii). (Paprzycka and Nowak 1989, p. 310)

In non-Marxian historical materialism in the present configuration, the developmental mechanisms of societies being a part of European civilization gain universal status. Thus, colonization is seen as “a process of the transformation of supra-class societies in class societies” (Paprzycka and Nowak 1989, p. 309). Let us repeat, according to the developmental mechanism described in Nowak’s theory, these societies will be transformed into totalitarian systems and those in turn into socialist ones. However, against this conceptualization of colonization, one can raise some serious objections.

2. An Attempt at Critical Analysis In this part of this paper I would like to test the presented model of colonization against the history of Latin America, and being more precise — the history of Mexico (more on this: Brzechczyn 2004b, abridged version: Brzechczyn 2004a). First and foremost, the Paprzycka and Nowak (1989) approach is not a good conceptualization of the so-called early colonial expansiveness initiated by the discovery of America and executed by the states of the Iberian Peninsula: Spain and Portugal. At the turn of the 16th century, Spain was not yet a capitalist

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society.1 Latin America, liberated from the rule of Spain prior to this country, became capitalist (e.g. Vilar 1991, p. 57), and then prior to the Spanish metropolis, was able to enter into the phase of colonial désintéressement.2 Furthermore, the conceptualization of conquered societies and their transformation during and after colonization is highly unconvincing. In the pre-Columbian Aztec society conquered by Spaniards there indeed occurred an accumulation of property and power in the hands of the one class but the emerging social system was totalitarian in economic, not in political version, as Paprzycka and Nowak presuppose. The class of owners-rulers dominated in the Aztec society, and this fact determined the nature of Aztec hegemony imposed all over Mezoamerica. This expansion was effected in the interest of the double class of owners-rulers, which maximized the surplus in the form of tribute, free labor and the seizure of land. The social interest satisfied at the time of expansion determined the formula of Aztec domination in Mezoamerica. The construction of a loose hegemony which preserved the native political structures instead of those imposed by the empire (like Incas in South America), in which native rule would have been abolished.  However, totalitarian structures (of the economic type) outlived the conquest. The class of encomenderos, originating from the first generation of conquistadors, was the source of a new class of ownersrulers. Conquistadors, possessing military power, assured their economic rule over the Indian peasant class in the Mexico Valley. The encomienda distributed among the first conquerors of Mexico was the institutional expression of an E-totalitarian system where political rule became the basis on which tribute was collected from Indian communities and their workforce administered. The E-totalitarian 1

This is emphasized by Kieniewicz (1986, pp. 79-84) writing about the precolonial feudal character of Iberian expansiveness, based on traditions of struggle with Arabs on American ground. 2

àepkowski (1991, pp. 182-183) objects to the conceptualization of Latin American liberation in terms of decolonization processes (to be more precise their first phase), maintaining that it is an actualization from political reasons of these events.

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system in the Spanish version led to devastating social results causing a drastic fall of the Indian population, experiencing economic exploitation and political subjugation. Upsetting the balance of population facilitated the interference of political authority from the Spanish metropolis with economic life, which as a result lessened the social impact of the encomenderos class competing with the Spanish Crown. Initially, the authorities curbed the rights of owners-rulers to supervise the workforce from Indian communities, and later, it completely deprived them of the right to administer Indian labor. Since the mid 17th century, the political authorities within the confines of repartimiento de trabajo became the exclusive administrator of the Indian workforce. The Encomenderos were transformed into a single class of owners, which used only the Indian tribute, paid first in kind and later in cash.  Still this does not mean that the E-totalitarian social system vanished. Simultaneously in the second half of the 16th century in Mexico, the hacienda came into existence — a huge latifundium breeding animals and producing food sold on the local market in Mexico City and in mining centers. The owners descending from the Creole people, who fulfilled the role of administrators in a bureaucratic pyramid of the Vice kingdom of New Spain, made the Indian peasant class settle in haciendas dependent on them. The main, but not the only, source of creating non-economic dependency was peonage — service for payment of a debt, which if not paid off, made people stay in a landed estate. The social system generated by the hacienda was based on the alliance between the class of owners and rulers. 3  At the same time in Mexico a different supra-class structure, combining spiritual with economic rule, took shape. The spiritual rule of the Catholic Church was feasible thanks to the support of political authority and guaranteed in the encomienda system — since each encomendero was obliged to build a church, pay the priest for his

3

Kieniewicz (1986, p. 168) questions the thesis defended by adherents of the modern world capitalist system, which contend that capitalism in Latin America was introduced during the Spanish reign.

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services and ensure that the Indian people participate in religious ceremonies. On the other hand, the Inquisition, whose decisions were carried out by political authority, provided the most visible prop for the political system of the Church, The supra-class alliance between the class of rulers and priests-owners took the shape of an accumulation of class divisions: 10 vice kings of New Spain were priests; also the clergy fulfilled functions at lower administrative tiers, for instance at the level of the audience. Because the alliance between political and spiritual power was the base of social order, the social might of the class of priests-owners was untouched throughout whole colonial periods. The history of Mexican society in the first period after gaining independence also did not fall under the developmental variant (i), (ii) or (iii). There was no classical national-liberating loop in which power seized control over the means of coercion and production. There was also no rise of a mature capitalist society with the emergence of a grand bourgeoisie as a main social class. The social development of Mexico did not fall under variant (ii) because: • the rulers did not seize “the main means of production,” • the class of great owners in the first period of Mexican independence additionally transformed into the disposers of means of coercion which, among other factors, led to the anarchization of the political system in this country; • the double class of priests-owners still exerted a great impact on the social life of the country; • the main axis of social conflict in the first half of the XIXth century took place between the class of rulers and the class of priests-owners. Therefore, in order to conceptualize the history of Mexican society it is not enough to make precise the model of colonialism but there is also the need to elaborate a theory of a new type of society initiating a new line of development.

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3. An Outline of Scientific Research Programme Now, I would like to consider how many separate types of societies initiating the separate lines of development are possible to distinguish in non-Marxian historical materialism. This typology will be based on the following criteria: • what type of class interest dominates in a given society; • what is the level of cumulation of class divisions, namely, whether the dominating class is single, double or triple; • what is the relation between the dominated classes of social potentates. Let us introduce these criteria in more detail. In the case of class (triple-moment) and supraclass societies (double- and single-moment) the application of the criterion (i) leads to distinguishing the dominant class of disposers of the material means of society. It can be a class of rulers maximizing power regulation or a class of owners maximizing profit or a class of priests, which maximizes spiritual domination. In the case of societies in which the one social class controlling the means of coercion, production and indoctrination is able to maximize these three class interests, this criterion leads to distinguishing the priority class interest of that class. The domination of class A over class B means that in the case of conflict between them, in the long-run, the interest of class A is maximized. A social class, which dominates over the rest of society this way, is called the main class. The priority of the class interest of type A over the class interest of type B means that in the situation in which the maximization of interest of B excludes the maximization of class interest of A, in the long-run the interest of A is maximized. In other words, the class interest of B is instrumentally subordinated to the maximization of interest of A. The main class interest in a given society realized by the triple class of disposers will be this class interest which has such understood priority over the remaining class interests. Depending on whether the class interest is maximization of power, profit or spiritual domination as an understood priority in a given society, one may

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distinguish respectively a political, economic or hierocratical type of developmental line. The one and the same class of social potentates can merge the disposition over the social means of two (e.g. means of production and means of coercion), or three (e.g. means of production, means of coercion and means of indoctrination) kinds of material means. In this respect it is possible to distinguish single (e.g. rulers), double (e.g. rulers-owners) and triple (e.g. rulers-owners-priests) social classes. This is the second criterion of the constructed typology. Depending on the level of the accumulation of class divisions, one can distinguish single-, double- and triple-moment variant of each type of the developmental line. For example, the political type of a developmental line can be in triple-moment variant (the class of rulers is a single class), in double-moment variant (class of rulers seizes disposition of the means of production or mass communication) or single-moment variant (the class of rulers seizes disposition of means of production and mass communication). The application of criterion (iii) with regards to class societies leads to the characterization of the relation between subordinated social classes dominated by the main class, with regard to single-moment societies — relations between derivative class interests realized by the triple class, with regards to double-moment societies — the relation between the maximization of the derivative class interest of the double class and maximization of class interest of the single class of potentates. In case of class societies the domination of class B over class C means that in the long-run, the conflict between them will see the interest of class B maximized. However, the main class of this society still subordinates both these social classes. In single-moment societies, the priority of the class interest of B over the class interest of C means that in case of conflict between them, the interest of B is maximized in the long-run. In other words, the class interest of C is instrumentally subordinated to the maximization of the class interest of B — and these two are instrumentally subordinated to the main interest of the triple class.

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In case of double-moment societies, the priority of the derivative class interest of the double class over the social interest of the single class means that in the case of conflict between them, in the long-run, the perspective of the derivative interest of the double class is maximized in a given society. Depending on the relationship between the subordinated classes (or class interests), one can distinguish different versions (political, hierocratical, economic) of each variant of each type of developmental lines. For example, the name of the version of a hierocratical triplemoment society characterizes the relations between the subordinated classes of rulers and owners. In the case of a political version of such a society, the rulers dominate the owners whereas in the case of a economic version — the owners dominate the rulers. It is worth reminding that both social classes are subordinated to the class of priests. In summing up, depending on the class interest, the maximization of power regulation, surplus value or spiritual domination has priority in realization by each class of social potentates, one can respectively distinguish: political, economic and hierocratical types of a developmental line. Depending on the level of accumulation of class divisions, each type of developmental line can occur in a triple, double and one moment variant. Depending on the relationship between derivative class interests (or subordinated classes), one can distinguish different versions: political, economic and hierocratical of each variant of a given type of a developmental line. Crossing these criteria, one can distinguish 18 types of societies, which initiate separate lines of development. Let us briefly characterize them. 1.1.1. Hierocratical triple-moment society in a political version (priests + rulers + owners). This type of developmental line is constituted by a society where the class of priests has priority over the other classes of social potentates. This variant of society consists of four social classes: of priests, rulers, owners and the people. In its political version the class of rulers dominates the class of owners.

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1.1.2. Hierocratical triple-moment society in an economic version (priests + owners + rulers). In this type of society, the class of priests has priority over the other classes of social potentates. In this version of society a different relationship occurs between the subordinated classes because in this case the owners dominate the class of rulers. 1.2.1. Hierocratical double-moment society in a political version (priests-rulers + owners). This society consists of three classes: of priests-rulers, owners and the people. In this social system the class of priests having additionally control over the means of coercion, dominates the single class of owners. 1.2.2. Hierocratical double-moment society in an economic version (priests-owners + rulers). In this version of society, the class of priests having control over the means of production has still class priority in society. In this example of a social system the maximization of surplus value is subordinated to the maximization of spiritual domination. 1.3.1. Hierocratical single-moment society in a political version (priests-rulers-owners). This society consists of two classes: the triple class of the priests-rulers-owners and the people’s class. The main interest of the triple class is the maximization of spiritual domination. Furthermore, the maximization of the surplus value is subordinated to the maximization of the power regulation and both these derivative interests are subordinated to the enlargement of the spiritual domination over society. 1.3.2. Hierocratical single-moment society in an economic version (priests-owners-rulers). This version of a society still consists of two classes: the triple class of priests-owners-rulers and the people’s class. In this instance, a different relationship occurs between derivative class interests because the maximization of power regulation is instrumentally subordinated to the maximization of surplus value. 2.1.1. Economic triple-moment society in a political version (owners + rulers + priests). This type of developmental line is constituted by a society where the class of owners has priority over the other classes of social potentates. This variant of society consists of

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four classes: owners, rulers, priests and the people. In its political version the rulers dominate the priests. 2.1.2. Economic triple-moment society in a hierocratical version (owners + priests + rulers). The main class of social potentates is the same as in the previous version of society. In this case, however, another relationship occurs between the subordinated classes because the priests dominate the rulers. 2.2.1. Economic double-moment society in a political version (ownersrulers + priests). This society consists of three classes: the double class of owners-rulers, the class of priests and the people class. In this version of a social system, the maximization of power regulation is instrumentally subordinated to the maximization of surplus value by the class of owners-rulers. This class dominates the single class of priests. 2.2.2. Economic double-moment society in a hierocratical version (owners-priests + rulers). This version of a double-moment society, the class of owners having control over the means of indoctrination dominates the single class of rulers. The enlargement of spiritual domination is instrumentally subordinated to the maximization of the surplus value by the owners-priests. 2.3.1. Economic single-moment society in a hierocratical version (owners-priests-rulers). This society consists of two classes: the triple class having control over the means of production, coercion, indoctrination and the people’s class. For the triple class, the maximization of the surplus value has priority over the maximization of other class interests: spiritual domination and political power. In this version of a society, maximization of power regulation is instrumentally subordinated to the maximization of spiritual domination. 2.3.2. Economic single-moment society in a political version (ownersrulers-priests). In this version of a single moment society, the maximization of surplus value still has priority over the other class interests but the enlargement of spiritual domination is instrumentally subordinated to the deepening of political power.

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3.1.1. Political triple-moment society in an economic version (rulers + owners + priests). This type of developmental line is constituted by a society where the class of rulers has priority over the other classes of social potentates. This variant of society consists of four classes: rulers, owners, priests and the people. In the economic version of this society, the class of owner dominates over the class of priests. 3.1.2. Political triple-moment society in a hierocratical version (rulers + priests + owners). In comparison with the previous version of society there is a reverse relation between the subordinated social classes because in this case the class of priests dominates the class of owners. 3.2.1. Political double-moment society in an economic version (rulersowners + priests). This society consists of three classes: the double class of rulers-owners, the class of priests and people; in this social system the maximization of value surplus is instrumentally subordinated to the maximization of power regulation by the class of rulers-owners. 3.2.2. Political double-moment society in a hierocratical version (rulers-priests + owners). In this version of society the maximization of spiritual domination is instrumentally subordinated to the maximization of power regulation by the class of rulerspriests. This class, it is worth reminding, dominates the class of owners. 3.3.1. Political single-moment society in an economic version (rulersowners-priests). This society consists of two classes: the class of rulers-owners-priests and the people’s class. The priority interest for the triple class is the maximization of power regulation. In the economic version of this society the maximization of the spiritual domination is subordinated to the maximization of surplus value. 3.3.2. Political single-moment society in a hierocratical version (rulerspriests-owners). In this version of a political single-moment society there is a reverse relationship between derivative class interests. The maximization of surplus value is instrumentally subordinated to the deepening of the spiritual power and this

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class interest, to repeat, is subordinated to the maximization of power regulation by the class of rulers-priests-owners. Societies belonging to different types of lines of development evolve according to different mechanisms. Societies therefore belonging to the political type of developmental line evolve according to the regularities of the political moment and those of the economic type, according to the regularities of the economic moment. Societies belonged to the hierocratical type of developmental line thus evolve according to the regularities of the spiritual moment of society. These regularities are essentially changed in the case of each variant of society. In the singlemoment societies a given class of the social potentates disposes also the other material means useful in the maximization of the main for this class, interest. In this variant of society, the main tendency of social development is the mechanism of people resistance. This is changed in the case of double-moment societies. The existence of single classes of social potentates, apart from the double class, brings about the rise of a new social tendency in social development — the mechanism of supra-class competition and supra-class alliance. This tendency becomes more important in triple-moment societies. In this kind of social system, the main barrier in the maximization of class interest by the dominating class is not only the people’s resistance but also the objections of other classes of social potentates. In certain developmental phases of this kind of societies, at least, the supra-class competition and supra-class alliance became the main developmental mechanism. So much is possible to be said on each developmental line at this level of concretization of non-Marxian historical materialism. One can gain fuller characteristics therefore, when one can elaborate the theories of the development of each type of society. I would like to suggest that the developmental diversity of nonEuropean civilizations could be interpreted with the aid of the above constructed typology of societies. The characteristic feature of societies belonged to European civilization was separation of class divisions. The accumulation of class division based on European civilization, when it took place, proved to be unstable (Brzechczyn 1993). In turn, different configurations of cumulated class divisions — which in the

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conceptual framework of non-Marxian historical materialism is their distinctive feature — appeared in the history of other civilizations. It is also worth recognizing that this typology is not exhaustive — it ignores, e.g. the existence of primitive societies, in which the class structure did not form. Moreover, some elements of this typology are not present because certain types of societies did not emerge from the primitive stage of history. Furthermore, some lines of development can lead up the “blind street” of the historical process, meaning that they will not transform further. This is exemplified in the philosophy of history where according to Francis Fukuyama (1992), modern capitalism leads to the end of social evolution. In addition, the constitution of 18 separate lines of developments in the historical process depends on the compliance of many, implicitly accepted, conditions. I will consider one of them in more detail, namely, the condition of stability. In order to form a separate line of development, a given configuration of class domination has to be socially stable. This means that in subsequent periods of time, this same configuration of class domination is able to reproduce itself. In line with this intuitive definition it is worth recognizing that one of the conditions of social stability thus understood, it is growth or at least, maintaining this same population, which depends among other factors on the preservation of the ecological equilibrium in the relations between society and nature. The social consequences of upsetting the ecological equilibrium are described by Jean Dorst (1987, pp. 58-62). The Yucatan peninsula inhabited by the Mayas during the classical period had lime soil with a fragile hydrological equilibrium. During the rain season its plains were covered by water but during the drought season, it changed into a region of cracked salt. The Mayas at that time cultivated maize as a basic foodstuff. However, this plant was harmful for the soil because the root system of maize and the means of cultivation exposed the soil to erosion. During the classical period the Maya population increased reaching the number of three million. Therefore, the Mayas were forced to enlarge the cultivation area from fertile plains to the mountainsides. Grubbing up slope forests, which protected soil, accelerated the erosion of the land and gradually clogged the system of

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lakes and rivers. The soils lost their fertility according to a typical process: on the hills the naked rocks remained but on the plains infertile layers covered the soil. The fertility of soil was so low, that it could not provide food for the growing population. Furthermore, a bad water economy deteriorated the river communication and caused a lack of water. The disturbance of the ecological equilibrium contributed to the decline of this civilization in the 9th —10th century — one which this civilization never recovered from.

4. The Perspectives of Non-Marxian Historical Materialism: A Summary The above constructed typology of developmental lines serves as a “road map” of non-Marxian historical materialism. In the present shape this theory is a set of the following models: • pure hierocratical society which can be the point of departure in the building of the theory of societies belonged to the hierocratical type of the developmental line; • pure economic society and its further concretizations which can be the point of departure in building the theory of societies belonged to the economic type of the developmental line; • pure political society and its further concretizations which can be the point of departure in building the theory of societies belonged to the political type of the developmental line; • economic triple-moment society (2.1.1) transformed into a political triple-moment society (3.1.1.); however, this model is not complete because the influence of the class of priests is still ignored. Non-Marxian historical materialism still lacks: • a complete theory of hierocratical (1.3.1; 1.3.2), economic (2.3.1; 2.3.2) and political (3.3.1; 3.3.2.) society in single-moment versions; in the theory of this last type of society the control of the economy by the rulers was partially analyzed (Nowak 1991; Siegel 1997);

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• a theory of hierocratical (1.2.1; 1.2.2.), economic (2.2.1; 2.2.2) and political (3.2.1. 3.2.2) society in the double-moment variant; • a theory of hierocratical triple-moment society in a political (1.1.1) and economic version (1.1.2) and hierocratical versions of economic (2.1.2) and political (3.1.2) triple-moment societies; • a complete theory of economic triple-moment society in a political version (2.1.1.) and political triple-moment society in an economic version (3.1.1). In summing up, the above mentioned theoretical gaps form the developmental perspectives of non-Marxian historical materialism as a scientific research program. As one can see, a great deal of research is yet to be done. After fulfilling these theoretical gaps, non-Marxian historical materialism can become a theory of historical process in regard to the chronological and geographical range comparable to the historiosophy elaborated by Arnold Toynbee (1947/1957) or, let us mention a Polish example of this kind of the humanities, Feliks Koneczny (1962).

Uniwersytet im. A. Mickiewicza Department of Philosophy ul. Szamarzewskiego 89c 60-569 PoznaĔ Poland E-mail: [email protected]

REFERENCES Brzechczyn, K. (1993). The State of Teutonic Order as a Socialist Society. In: L. Nowak and M. Paprzycki (eds.), Social System, Rationality and Revolution (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 33), pp. 397-417. Amsterdam, Atlanta, GA: Rodopi. Brzechczyn, K. (2004a). The Collapse of Real Socialism in Eastern Europe versus the Overthrow of the Spanish Colonial Empire in Latin America: An Attempt at Comparative Analysis. Journal of Interdisciplinary Studies in History and Archaeology 1(2): 105-133.

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Brzechczyn, K. (2004b). O wieloĞci linii rozwojowych w procesie historycznym. Próba interpretacji ewolucji spoáeczeĔstwa meksykaĔskiego [On the Multitude of Developmental Lines in Historical Process. An Attempt at Interpretation of Evolution of Mexican Society]. PoznaĔ: Wydawnictwo Naukowe UAM. Dorst, J. (1987). Siáa Īycia (La Force do Vivant). Warszawa: PIW. Fukuyama, F. (1992). The End of History and the Last Man. New York: Free Press. Kieniewicz, J. (1986). Od ekspansji do dominacji. Próba teorii kolonializmu [From Expansion to Domination. An Attempt of Theory of Colonialism]. Warszawa: Czytelnik. Koneczny, F. (1962). On the Plurality of Civilizations. With preface by A. Toynbee. London. Polonica Publications. àepkowski, T. (1991). Ameryka àaciĔska: rewolucje niepodlegáoĞciowe i początki nowych paĔstwowoĞci [Latin America: Independence Revolutions and the Beginnings of the New States]. In: W. Zajewski (ed.), Europa i Ğwiat w epoce restauracji, romantyzmu i rewolucji 1815-1849 [Europe and World in Epoch of Restauration, Romanticism and Revolution], pp. 175-220. Warszawa: Wiedza Powszechna. Nowak, L. (1983). Property and Power: Towards a non-Marxian Historical Materialism. Dordrecht: Reidel. Nowak, L. (1987). A Model of Socialist Society. Studies in Soviet Thought 34: 1-55. Nowak, L. (1989). An Idealizational Model of Capitalist Society. In: L. Nowak (ed.), Dimensions of the Historical Process (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 13), pp. 217-259. Amsterdam: Rodopi. Nowak, L. (1991). Power. Towards a Dynamic Theory of Real Socialism. New York/London: Greenwood Press. Paprzycka, K. and L. Nowak (1989). On the Social Nature of Colonization. In: L. Nowak (ed.) Dimensions of the Historical Process (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 13), pp. 299-312. Amsterdam: Rodopi. Siegel, A. (1997). Entdifferenzierung, Desintegration, Re-differenzierung. Zur Modellierung des politisch-okonomischen Krisenzyklus in der Volksrepublik Polen. In: K-S. Rehberg (ed.), Differenz und Integration. Die Zukunft moderner Gesellschaften. Verhandlungen des 28. kongresses der Deutschen Gesellschaft für Soziologie im Oktober 1996 in Dresden, Vol. II: Sektionen, Arbeitsgruppen, Foren, Fedor-Stepun-Tagung. Wiesbaden: Westdeutscher. Toynbee, A. (1947/1957). A Study of History. Vol. I-II (Abridgement of Vol. IX by D.C. Somervell). New York/London: Oxford University Press. Vilar, P. (1991). Historia Hiszpanii [History of Spain]. Warszawa: PWN.

SCIENCE AND ONTOLOGY

C. Ulises Moulines MODEL CONSTRUCTION, IDEALIZATION, AND SCIENTIFIC ONTOLOGY

Professor Nowak has made lasting contributions to the analysis of the notion of idealization and has convincingly argued for the great significance this notion (unduly neglected by most epistemological approaches before him) has for understanding the essence of modern scientific knowledge. He sees in Galileo’s systematic introduction of (mathematically oriented) idealizations the single most important turning point in the development of methodology, which distinguishes modern from Aristotelian science (see Nowak 1980, pp. 34ff ). The notion of idealization as something significant for dealing with empirical knowledge has, of course, a tradition much older than Galileo’s, but it was only he who elevated it to the essential mark of truly scientific research. It is Galilean idealization which characterizes modern science (see also McMullin 1985 and Haase 1995). And the challenge for the present-day epistemologist is exactly to explicate the nature of this primordial element of empirical science, which is being continuously applied, in a more or less intuitive, unreflected way by scientists of all disciplines in their everyday practice. Prof. Nowak has devoted a great part of his intellectual work to respond to this challenge.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 257-271. Amsterdam/New York, NY: Rodopi, 2007.

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While I fully agree with Nowak’s emphasis put on the significance of idealization for understanding the true nature of modern scientific thought and find many of his analyses quite illuminating, there are some (perhaps not crucial but nevertheless important) points where I think I find myself in disagreement with his interpretation of idealization and with the ontological presuppositions he seems to feel compelled to adopt when dealing with the matter. The first source of disagreement is a general methodological one. Nowak adopts a thoroughly syntacticist perspective to analyze idealization: lawlike statements are the kinds of entities primarily set as subjects of idealization according to him. Being a convinced supporter of a semanticist perspective (in a very general sense of «semanticism») in philosophy of science, I would rather favor taking models or structures as the primary items in this context. To my view, idealization has primarily to do with model construction and with model comparison, and only derivatively with the comparison of lawlike statements. Secondly, Nowak’s approach seems to be, at least in part, dependent on an essentialist metaphysics, where a distinction between “real” and “ideal” objects is assumed. Now, whatever metaphysical grounds for espousing any kind of essentialism one may have, I don’t think there are any cogent methodological or metatheoretical reasons for endorsing it if our task is to explicate the idealization practice in empirical science. Moreover, well-known immanent difficulties immediately appear when endorsing essentialism as a general theory of science.1 Finally, though Nowak recognizes that approximation does play a role in the process of matching theory with experience, he seems to reduce it to the secondary role of “epsilontics” for the comparison of the values of the parameters appearing in the different laws. At any rate, his approach doesn’t consider approximation on its own, independently of idealization. From my own point of view, I consider approximation at least as fundamental for empirical science as 1

For a thorough criticism of Nowak’s essentialism with respect to the idealization issue, see Haase (1995), § 2.1.4.

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idealization, and moreover I think that the two notions, though interrelated, have to be conceptually distinguished; they are in need of different explications – both from a logical and a methodological point of view. Very roughly speaking, idealization is rather connected with model construction, whereas approximation is a relationship between already constructed models.2 It is not my purpose here to argue in detail for these points, nor to underscore my divergences with Nowak’s approach. Rather, I propose to consider the issue of idealization within an ontological setting. As will appear more clearly below, here, as in so many other cases, the epistemological issue of idealization is most fruitfully discussed as an onto-epistemological one. (I suspect Nowak himself would agree with this general point of view.) I’ll design a model, i.e. a “meta-model,” of the way the (imperfect) match between theory and experience works; I assume this is what idealization is all about in the last analysis. Then, the reader may judge by himself what the (implicit) reasons may be for a convergence or a divergence between Nowak’s approach and the one proposed here. In the traditional wording, ontology is the discipline of Being in general. In a less bombastic, but eventually equivalent way of speaking, Quine (1953) has characterized it as the discipline of what there is. And all what there is, also following Quine, are the values of bound variables. Though Quine’s slogan is in need of some minor qualifications and revisions, I still think it is a good starting point for doing ontology.3 The question, however, is to determine where these bound variables are to be found. My answer (which I think also follows the spirit though perhaps not the letter of Quine’s slogan) is that they are to be found in scientific texts, or more precisely, in the formulations of

2 In previous writings, I have devoted much work to the analysis of approximation both in an intra- and an inter-theoretical setting; my explication of the approximation concept reaches much further than mere “epsilontics” and encompasses also what may be called “qualitative approximation”; see Moulines (1976; 1981); Balzer, Moulines and Sneed (1987); Moulines and Straub (1994); Moulines (1996). 3

For an assessment of a somewhat modified Quinean perspective on ontological matters, see Moulines (1994; 1998).

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scientific theories in standard scientific texts. I feel no inhibition in pleading for a “scientistic” ontology: If you want to find out what there is in the world around you, ask science! I won’t argue at length in favor of this kind of “scientism”; I may just point out that it responds to an “economic” strategy founded on historical induction: Whenever there has been a dissent on what there is between science on the one hand and common sense, metaphysics, religion, or whatever on the other, in the long run it has always been science who has won the battle.4 Though I think there are very good reasons why this is so, I cannot dwell upon this point here. Therefore, having taken this “scientistic” decision in matters ontological, our next task is to investigate the way scientists take their “ontological commitments” (to employ another of Quine’s famous phrases) within the theoretical frame of their respective disciplines. Now, the first thing we notice is that the starting point for any scientific investigation is a more or less loosely determined piece of (ultimately sensorial) experience.5 Nonetheless, unless we are hardnosed ontological phenomenalists (which I’m not), we won’t assume that the elements of a particular piece of experience is actually what there is. Let’s rather say that scientific research starts with a particular experiential situation (ES) and the final goal is to find out what there is behind ES — to find out the “Hidden Being Behind Appearances.” Scientists (or whoever) may describe ES by means of particular expressions of ordinary language, like ‘wet’, ‘hot’, ‘sweet’, ‘brown’, and so on. But a “scientific ontology” will not be one where it is assumed that these predicates apply to what really is. Our starting point is necessarily an ES we describe in ordinary language but our goal is to get “behind” ES and describe it within the conceptual frame of a scientific theory. 4

By ‘science’, I mean the collection of well-established, institutionally anchored scientific disciplines. 5

In this discussion, I leave aside the realm of pure mathematics, not because I think that the ontological questions related to mathematics are uninteresting, quite the contrary, but rather because dealing with them would go far beyond the scope of this article. In the present context of discussion, mathematics will be considered in its purely instrumental value for empirical science.

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A first obstacle to attain this goal, however, comes from the fact that the identity criteria for any ES considered are too fuzzy and uncertain for our purposes. The conceptual demarcations of experiential objects characteristic of ordinary life have to be further refined and modified for scientific purposes. To do this, scientists perform a series of actions and interactions, mainly consisting in the linguistic communication with their peers, the systematic observation and/or the manipulation of medium-sized objects. This leads, in a first step, to the constitution of what we may call an “operational base,” OB, for ES ; in this way, the original ES gets transformed and codified in an intersubjectively controlled experiential situation (ICES). The same or another OB may serve to determine other ICESs. It is important to be aware of the fact that a successful codification process leading from an original ES into an ICES (indeed, a first form of “idealization”) never is the outcome of the heroic action of a single individual but rather of intersubjective communication. Or, to put it more cautiously, the only ICES that science takes seriously for ontological purposes are those intersubjectively constructed. Whether or not Wittgenstein’s arguments against the possibility of a private language are totally convincing (I tend to believe they are not), at any rate, it surely is the case that the starting point for the ontological commitments of science (and these are the only ones that interest us here) is an intersubjectively controlled language. The construction of ICESs always takes place within a collective entity, a “group of partners” (GP) standing in regular interaction. At least since Thomas Kuhn, we know that these entities are the real subjects of science. In this sense, scientific ontology depends on pragmatics. Of course, this is only the first step in the direction of a full-fledged scientific ontology. What comes next? To discuss this question, I propose to lay out a couple of schematic examples instead of a general argument.

First Example While lying on his terrace, Johnny (or his ancestor Nebuchadnezzar) faces an experiential situation, let’s call it ‘ESp’, which intrigues him

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and which may be described (without any ontological commitment) as follows: “Experience of the sky on a clear night; slowly moving sparkling points on various positions.” In order to interpret ESp correctly, Johnny-Nebuchadnezzar meets a group of partners, GP°, all of them equally intrigued by the nightly sky, and they agree to proceed in the following way. First, they agree to undertake systematic observations on many following nights. Second, they agree to determine lapses of time by means of a device (a medium-sized object) called ‘a clock’. (We need not imagine here a quite sophisticated, i.e. “theoretized” apparatus; it would be enough to have a sandglass, on which GP° makes some marks: The time elapsed is determined by the number of marks covered by the falling sand.) Third, on a long series of following nights, always beginning at the same time (i.e. from the same mark on the sandglass on) and after equal lapses (i.e. after the same number of covered marks), GP° focuses its special attention on those sparkling points which move irregularly. Fourth, after some hesitations, GP° decides to devote itself only to the irregularly moving points and to give them a generic name: ‘planets’. They give also proper names to the individual points: ‘Mercury’, ‘Venus’, etc. At this point, we can say that GP° has transformed the original ESp into a clearly demarcated ICESp. We go on now to the next phase of the scientific enterprise. GP notices that, for a thorough investigation of the issue about the nightly sky, there is more required than mere observations and denominations. One has to “fix them on paper.” GP° decides to represent ICESp in the following way. They take squared paper, agree on marking on the paper a “center of coordinates” representing a particular sparkling point (e.g. the so-called “North star”) and they determine the relative positions of the planets with respect to the North star by means of successive marks on the paper within regular lapses of time. On a great number of sheets they obtain in this manner a great number of marked points.

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This representation we may call an “ICESp-corresponding data model,” or just DMp. The representation has been established according to a set of conventions or “axioms”: (A1) Point p1 on the paper, when the sand covers mark m, represents Mercury. (A2) Point p2 on the paper, when the sand covers mark m, represents Venus. . . . (Am) Point pm on the paper, when the sand covers mark mĻ, represents Mercury. . . . (An) The distance from p1 to the center, when the sand covers mark m, is r1. (An+1) The distance from p2 to the center, when the sand covers mark m, is r2. . . . After some quarrels and reconciliations within GP° (what sociologists of science call ‘negotiations’), GP° agrees to accept “axioms” (A1), (A2), . . . , (Am), . . . , (An), (An+1), . . . . This process of acceptance is followed partly by convention (e.g. for (A1), (A2), . . . ) and partly through procedures normalized and admitted by GP° (related, for example, to the way the number of boxes on the squared paper separating each pi from the center of coordinates for establishing (An), (An+1), . . . , is to be counted). As soon as the process of acceptance comes to an end, GP° declares the statements (A1), (A2), . . . , (An+1), . . . to be true. Consider now the following structure: DMp =: ¢{p1, . . . , p5}, { . . . , mi, . . .}, d ² where d is a diadic function consisting of the triples ¢pi, mi, ri ², with ri ∈Q

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which are the values of those parameters correlated in each statement (An+j), with j ≥ 0. The construction process just illustrated leads to the conclusion that DMp is a kind of structure that is a “model” of the axioms (A1), . . . , (An), . . . in a sense similar, though not identical, to the standard Tarskian notion of “model of a formalized theory.” It is similar to the standard model notion in the sense that the triples ¢pi, mi, ri² satisfy (in the strong Tarskian sense of “satisfying”) the formulae (An+j) for j ≥ 0. However, it is not quite a Tarskian model since we cannot really speak of “satisfaction” with respect to the formulae (Ak) for k < n: What we have here are rather operational presuppositions to settle the “universe of discourse” of DMp. Taking into account both aspects (the analogy as well as the non-identity with the formal model notion), it seems to be justified to apply to the structure DMp the special denomination “data model.” Up to this point, we still haven’t talked about ontology. We still haven’t said what there is. Neither the sparkling points on the nightly sky, nor the marks on the sandglass, nor the marked points on the squared paper, none of these elements of GP°’s experiential space are what really is — at least from the point of view of a scientific ontology. For, up to this point, GP° has not taken any serious ontological commitment. According to the “scientism” in matters ontological we have adopted from the beginning, in order to come to such a commitment, GP° has got to work within the frame of at least one wellestablished scientific theory. So, we arrive at a qualitatively new phase in our enterprise. Let’s assume somebody (GP° itself or some other group of partners) has elaborated a specific theory, call it ‘Tp’, for the time being only as a purely mathematical formalism. According to the general semanticist standpoint adopted here, the identity criterion for it is its proper model class, M[Tp]. Let’s suppose the elements of this class have the form: x ∈ M[Tp] → x = ¢D, I, IR, R1, . . . , Rm, f1, . . . , fn² so that the components of any x are characterized as follows: (*1) D is a finite, non-empty set (whose elements Tp’s inventor just calls ‘dots’).

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(*2) I is isomorphic to an interval of IR (whose elements are called ‘instants’). (*3) Ri and fj are relations and functions defined over D and/or I and/or IR. Further, any x ∈ M[Tp] satisfies some “proper axioms” or “laws,” i.e. formulae relating D, I, Ri and fj with each other. (For the purposes of illustration, we can imagine they are the formulae known as ‘the laws of Kepler’ or ‘the laws of Newton’, or something of the sort.) Up to this point, we are still outside ontology. All this is pure mathematics (and I’ve already said that we just make the simplifying assumption that mathematics has nothing to do with what there really is). For the time being, to be a “dot” just means being an element of any set D that is, in turn, the first component of a given structure x that is, again in turn, an element of the class M[Tp] characterized in purely formal terms. The same goes for the term ‘instant’. Now, suppose GP° is able to prove mathematically the following claim: There is at least a concrete u° ∈ M[Tp] such that: DMp is a substructure of u° (abbreviated as: DMp § u°). The concept of substructure relevant here may be explicated in following terms. Let u° = ¢D°, I°, IR, R°1, . . . ,R°m, . . . , f °1, . . . , f °n² where, for some f °i, we change this symbol into s° and characterize it as follows: s°: D° × I° → IR2 Then, formula ‘DMp § u° ’ means that following conditions are fulfilled: (1) {p1, . . . , p5} ⊆ D°; (2) {. . ., mi, . . .} ⊆ I°; (3) s°/ {p1, . . . , p5} × {. . . , mi, . . . } × IR2 = d. From the claim ‘DMp § u° ’ (which has been mathematically proven) GP° concludes now: The experiential situation ICESp can be subsumed under theory Tp. Clearly, this conclusion is not a logically valid inference; it rather corresponds to what GP° understands under “subsumption of

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experience under a theory” or, to put it more crudely, to pointing out that theory Tp “works well” with respect to ICESp. At this point, finally, GP° (as well as we ourselves, as philosophers of science analyzing scientific behavior) are allowed for the first time to engage into ontological commitments and to declare: Planets are really dots. Or, to put it somewhat differently “What there is in the nightly sky are dots”; or still, in the traditional jargon: “The Being hidden behind the nightly appearances consists of dots.” My claim is that this schematic and admittedly oversimplified example is in principle paradigmatic for the way ontological issues are solved from a scientific point of view. I say “in principle” because following complication may arise.

Second Example Let’s suppose we are confronted with another intersubjectively controlled, experiential situation ICES of the following kind. GP° observes a number of more or less round, medium-sized rigid bodies, which any member of GP° can see and touch (and smell if he/she wishes). GP agrees thoroughly to polish these bodies (according to some standardized procedures), to put them on an equally well polished table, and to push the spheres so that they move on straight lines, rotate and collide with each other. GP° systematically observes the changes of direction and rotation of the spheres, and represents all this in a way analogous to, though not identical with, the case of the planets. (For example, now the objects are not represented by points but by volumes, and the representation of the motion is not two- but three-dimensional, etc.) Suppose that GP° comes in this way to the construction of another “data model” DMr. Suppose, further, that somebody invents another theory, call it ‘Tr’ essentially different from Tp and whose models have the structure x = ¢C, I, IR, . . . ², thereby satisfying laws different from those of Tp (say, the principles of the conservation of kinetic energy and of angular momentum). C ’s elements are now called ‘chunks’.

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Assume, further, that, by going through a formal argument analogous to the case of the planets with respect to the theory Tp of dots, GP° now comes to the inference that, for a given v° ∈ M[Tr], the claim is valid: DMr § v° and that, therefore, the conclusion is warranted ICESr can be subsumed under Tr. In this case, we may go on to the ontological way of speaking and declare that chunks really exist, or that «the hidden Being behind the rotating and colliding round bodies on the table consists of chunks». Since it is not the case that ICESr = ICESp, nor that DMr = DMp, and since the laws of Tp and Tr are different, non-equivalent formulae, there is no reason to assume that chunks have anything to do with dots. Even if we would assume that our experiential situations are restricted to ICESp and ICESr, we would be obliged bitterly to acknowledge that there is no unified ontological constitution of reality, since Being is sometimes being a dot and sometimes being a chunk. Suppose, however, that GP notices the following fact: For any model v of Tr that is ontologically relevant, i.e. for any v ∈ M[Tr] really subsuming a given ICESr, one can proceed according to the following steps: (a) One reinterprets v’s basic domain as being not a simple set, but rather a set of sets. Instead of having C = {c1, . . . , cn}, we would have C = {{d1, . . . , dk}, {dĻ1, . . . , dĻl}, . . . , {dĻĻ1, . . . , dĻĻm}, . . . }. (b) One takes the great union D = UC = {d1, . . . , dk, dĻ1, . . . , dĻl, dĻĻ1, . . . , dĻĻm} as the basic domain of a structure u which comes out as a model of Tp, i.e. u ∈ M[Tp] . (c) It is possible to prove mathematically that, if you add some special conditions to Tp’s proper axioms, i.e. if you presuppose that u ∈ Mi [Tp], where Mi [Tp] is an axiomatizable proper subset of M[Tp], then u also satisfies some formulae which are equivalent to Tr’s proper axioms. In this situation, we can say that Tr (at least in the area of relevant experiential situations) is reducible to Tp and, in particular, that, for any (ontologically relevant) v ∈ M[Tr] with D1(v) = C, there is a

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corresponding u ∈ M[Tp] with D1(u) = D, such that C ⊆ ℘(D). Therefore, it seems plausible to admit that, in spite of the difference between the theories applicable to different experiential situations, the ontological unity has been restored: Chunks are “in fact” sets of dots, and consequently, the Being “hidden behind the phenomena” still only consists in dots. There are several directions in which this possible situation may be generalized in order to speak of a reestablished unity of Being in spite of having different, non-equivalent theories that are applicable to different experiential situations. (I) One possible direction is this. The set-theoretical relationship between C and D may come out as being more complex than the simple formula C ⊆ ℘(D) suggests. It could be the case that the experiential situations require several distinct basic domains D1, . . . , Dn instead of a single D but nevertheless allow for a reconstruction of C as a complex configuration of a relational kind over the Di ; an example for this might be illustrated by the formula: C ⊆ ℘(B1 × ℘(B2) × B3) Any construction of a given set out of the successive application of the set-theoretical operations of a Cartesian product and power-set building on some previously given sets is known in the mathematical literature since Bourbaki as the construction of an echelon set (out of the given sets). In this case too, it is plausible to say that, what “really exists,” is not constituted by the elements of C but rather by the basic elements of those Bi that settle the base for the echelon set C. (II) Secondly, it will usually be the case that the derivation of the laws satisfied by v from the laws and additional special conditions satisfied by v’s counterpart u (as illustrated in point (c) above) doesn’t work exactly but only approximately. To deal with this case in a serious way, a serious (i.e. a precise and plausible) notion of approximation as a kind of intertheoretical relation is needed. Intertheoretical approximation should not at all be confused with idealization. It is a very different kind of notion. But its formal explication poses no particular problem (at least not as a matter of principle): The structuralist approach in philosophy of science has provided such an explication

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(and its illustration by means of real-life examples) some time ago; it is essentially based on the technical notions of a uniform structure and a blur (as a kind of “model-theoretical fuzzy-set”). For the details, see Moulines (1980; 1981), as well as Balzer, Moulines and Sneed (1987, Ch. 7). At any rate, what interests the ontologist here is that, even if there is no exact derivation of the laws of one theory from those of the other, and therefore there is no exact relationship between their corresponding models, the notion of intertheoretical approximation makes it possible to recover the ontological unity. (III) Thirdly, there is some hope for an ontological unification even in those cases where the laws of one theory cannot be derived either exactly or approximately from the laws and special conditions of the other. Imagine the following situation. There is a theory T with a model v ∈ M [T] and a basic domain C, so that GP “suspects” that, for another theory T °, the model v with its domain C has “something to do” with T °. However, even by adding special conditions to T °, GP is not able to find a v-corresponding model in T °, u ∈ Mi[T °], allowing for an exact or approximate derivation of T ’s laws from the laws and special conditions of T °. Still, GP should not necessarily despair. One might be able to establish the following intertheoretical relationship (expressed in exclusively model-theoretical terms) between T and T°: v can be connected with a particular u° ∈ Mi [T °] with a basic domain D and subsuming the same experiential situation as before (or a similar one); this connection may consist, for example, in the identification ‘C ⊆ ℘(D)’ without thereby hindering v’s ability to subsume the corresponding experiential situation. In this case, we could conclude that, even though the nomological reduction between both theories is not possible anymore, we may speak of an ontological reduction, and we (or GP) may claim that the elements of C of T are “nothing but” sets (or structures) of elements of D of T°. Let’s summarize the results of our considerations. Let’s suppose we have a theory T with some models subsuming — through idealization — some experiential situations that interest us; in these models, the basic domains D1, . . . , Dn appear. Let’s further assume we find (or invent) another theory T ° having models subsuming the same, or similar, and

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possibly other interesting experiential situations and having basic domains D°1, . . . , D°m. And let’s finally suppose that, for any relevant model v of T, and for all its basic domains Di, we can find a relevant model u° of T ° with one or several domains D°j, such that v and u° are linked together through at least one of the configurations depicted in situations (I) to (III) above. In such a case, we may claim that T is ontologically reducible to T ° and that the only ontologically relevant commitments we have taken are those corresponding to T °. The only Real Being is being according to T °. A final word on matters ontological. Imagine for a moment we would have a single BIG THEORY T ° to which all other scientific theories Ti would have the kind of relationship we have just called “ontological reducibility.” In this situation, I think we would be warranted in claiming that we have a unified ontological picture of THE WORLD. Is present-day science in this situation? Certainly not! Some scientists, especially physicists, are trying very hard to make it come about; some other scientists, mainly non-physicists, are doing their best to hinder it; and most other scientists just don’t care. We, as philosophers of science, cannot decide the issue; but, at least, we know in quite precise terms what it would be like to have either a positive or a negative answer to the question.

University of Munich Institute for Philosophy, Logic, and Theory of Science Ludwig Str. 31 80539 Münich, Germany E-mail: [email protected]

REFERENCES Balzer, W., C.U. Moulines and J.D. Sneed (1987). An Architectonic for Science. Dordrecht: Reidel. Haase, M. (1995). Galileische Idealisierung. Berlin/New York: De Gruyter. McMullin, E. (1985). Galilean Idealization. Studies in History and Philosophy of Science 16: 247-273.

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Moulines, C.U. (1976). Approximate Application of Empirical Theories. A General Explication. Erkenntnis 10: 201-227. Moulines, C.U. (1980). Intertheoretic Case. Synthese 45: 387-412.

Approximation:

The

Kepler-Newton

Moulines, C.U. (1981). A General Scheme for Intertheoretic Approximation. In: A. Hartkämper, H.J. Schmidt (eds.), Structure and Approximation in Physical Theories, pp. 123-146. New York: Plenum. Moulines, C.U. (1994). Wer bestimmt, was es gibt? Zum Verhältnis zwischen Ontologie und Wissenschaftstheorie. Zeitschrift für philosophische Forschung 48(2): 175-191. Moulines, C.U. (1996). Structuralist Models, Idealization and Approximation. In: R. Hegselmann, U. Müller and K.G. Troitzsch (eds.), Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View, pp. 157-167. Dordrecht: Kluwer. Moulines, C.U. (1998). What Classes of Things Are There? In: C. Martinez, U. Rivas, L. Villegas (eds.), Truth in Perspective. Recent Issues in Logic, Representation and Ontology, pp. 317-330. Hants: Ashgate. Moulines, C.U. and R. Straub (1994). Approximation and Idealization from the Structuralist Point of View. In: M. Kuokkanen (ed.), Idealization VII: Structuralism, Idealization and Approximation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 42), pp. 25-48. Amsterdam: Rodopi. Nowak, L. (1980). The Structure of Idealization. Towards a Systematic Interpretation of the Marxian Idea of Science. Dordrecht: Reidel. Quine, W.V.O. (1953). From a Logical Point of View. New York: Harper and Row.

Thomas Mormann REPRESENTATIONS, POSSIBLE WORLDS, AND THE IDEALIZATIONAL APPROACH TO SCIENCE

In this paper I’d like to show that there are interesting relations between the Idealizational Approach to Science (IAS) inaugurated by Leszek Nowak, and the combinatorial account of possible worlds favored by David Armstrong and other analytic philosophers of the Anglo-Saxon scene. As I want to show, the two philosophical currents share common ground in that both may be characterized as representational accounts in the sense that for IAS as well as for Armstrong’s combinatorialism the concept of representational constructions plays a crucial role. The elucidation of the role of representation turns out to be a useful tool to shed some new light on the metaphysical foundations of IAS, in particular on the problem whether Nowak’s modal suprarealism provides a satisfying metaphysical framework for IAS or not.

1. Introduction Theories of science do not hold in the actual world, rather, they are valid in some ideal(ized) world. This, in a nutshell, may be considered as the core thesis of the Idealizational Approach to Science (IAS

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 273-302. Amsterdam/New York, NY: Rodopi, 2007.

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henceforth) inaugurated by Leszek Nowak and elaborated by him and many collaborators during the last twenty-five years (cf. Nowak 1980, Nowakowa and Nowak 2000).1 At first glance, it might look as if the “ideal worlds” of IAS could be taken as “possible worlds” in the sense of possible worlds semantics. According to David Lewis, possible worlds may be characterized as “ways things might have been” (Lewis 1973, p. 84). As has been pointed out by Nowak, this account of possible worlds does not fit the needs of IAS. The ideal worlds of IAS, however, are not “ways things might have been” — they are impossible worlds. To recall one of Nowak’s pet examples: there is no way the earth might have been a mass point of dimension 0. Hence, Lewis’s possible worlds are rather useless for the purposes of the idealizational approach to science. Thus, IAS has to look elsewhere for a working metaphysics of ideal worlds. In some sense, Nowak’s modal “supra-realism” (SR) can be seen as an attempt to take charge of the task of formulating an adequate possibilist or idealist(?) metaphysics for IAS. For some reasons to be dealt with in detail later, I think, however, that SR is a less than optimal solution for the needs of IAS. Somewhat surprisingly, David Lewis has been the only contemporary metaphysician of possibilia ever mentioned by Nowak and the Poznan school.2 The main aim of this paper is to argue that there are other metaphysical theories of the possible which better fit the demands of IAS than modal realism. In a preliminary fashion, these other accounts of modality may be characterized as combinatorial or representational theories of modality.3 The best-known representative

1

Other labels for IAS are ‘The PoznaĔ School’ or ‘The Polish Idealizational Model’. I prefer a non-geographic label since maybe not all philosophers from PoznaĔ (to say nothing about all of Poland) may subscribe to IAS, while there may be non-Polish philosophers who endorse it.

2

At least, this holds for Nowakowa and Nowak’s (2000) The Richness of Idealization (RI henceforth), which I take to be a preliminary summa of IAS. 3

The combinatorial approach to possible worlds may be traced back to Wittgenstein’s Tractatus, its most ardent contemporary defender is David Armstrong (cf. Armstrong 1989, 1997). Ignoring some more fine-grained

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of a combinatorial account of possibilia is David Armstrong, who defended it in many publications, in particular in (Armstrong 1989 and 1997).4 At first glance, the combinatorial account may seem rather unattractive for IAS. In order to be applicable for the idealizational approach it has to be reformulated in such a way that its representational features are made explicit. Thereby it can be ensured that the ideal worlds IAS needs become available in a combinatorial framework. An particular advantage of the combinatorial-representational account of possibility, as it may be dubbed, is that it naturally derives from the most original piece of IAS, to wit, its theory of deformational procedures as the driving force of all scientific cognizing. According to IAS, the aim of science is not to give an accurate, “copying” representation of the world, rather science attempts to get an understanding of the world by applying appropriate deformational procedures to the facts of the actual world which leads to various idealized worlds. I propose to interpret these idealized worlds as idealizing representations of the actual world. Thereby a close connection between the conceptual deformational procedures of IAS and the theory of scientific representations is established. This has the useful side-effect that the insights of IAS may be used to counter some still wide-spread miscomprehensions of what is the role of representation in science: often, representation in science is understood in the sense that scientific representations should give us an accurate “mirroring picture” of how the world really looks like. I think it is still necessary to point out that this conception of “mirror representation” has not much to do with the role representation plays in the real practice of science. It is one of the strong points of (IAS) to have shown that representation in science means idealizing representation, based on certain deformational procedures. Idealizing representations have nothing to do whatsoever with the kind of mirror representation Rorty

differences, in the following I will identify combinatorialism with Armstrong’s approach. 4

The combinatorial approach to possibilia can be traced back to Wittgenstein’s Tractatus (cf. Bradley 1992; Skyrms 1986).

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has been attacking in his anti-representationalist crusade (cf. Rorty 1991). As is suggested by IAS, philosophy of science could be conceived of as a pragmatic theory of scientific representations: how they are constructed, how they are changed, combined, and what are the various ways in which they are connected. This amounts to a sort of a combinatorial theory of scientific representations, or, in the original jargon of IAS, to a combinatorial theory of ideal worlds generated by the various deformational procedures. It is one of the great achievements of IAS to have developed such a combinatorial theory of deformational procedures in great detail. IAS provides a useful framework for investigating the variety of idealizing procedures employed in the sciences. Many authors have contributed to this task offering detailed case studies dealing with the multi-facetted kinds of idealizations and their interrelations as they occur in various sciences (cf. RI, in particular Part II, Chapters 4 and 9). My aim in this paper is not to add a further detailed study to this impressive corpus. Rather, I’d like to make explicit the relations between deformational procedures in the sense of IAS, and what may be called representational and combinatorial accounts of possible worlds and scientific theories (cf. Ibarra and Mormann 1997). More precisely I want to show that the concept of representation may be considered as common source of concepts of deformation and combination as generating procedures of ideal worlds and scientific theories. The outline of this paper is as follows: in the next section Idealization as Representation I first recall the basic ingredients of Nowak’s account of idealization and then I intend to elucidate the concept of idealization in a representational framework. I want to show that conceptual deformation in the sense of IAS and scientific representation are essentially one and the same thing. Or, to put it differently, representation in science amounts to conceptual deformation, in particular, to idealization. Taking into account this close relation of idealization and scientific representation helps bar some still current miscomprehensions about the role of representation in scientific theorizing. In section 3 Recombination as Representation it is argued that IAS and combinatorial theories of possibility share es-

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sential features, to wit, what David Armstrong has aptly called actual world chauvinism: according both to IAS and the combinatorial account ideal and possible worlds depend on the actual world. The ideal worlds of IAS are idealized worlds of the actual world analogously as the possible worlds of the combinatorial account are recombinations of building blocks taken from the actual world. This feature starkly contrasts with all kinds of modal realisms according to which other possible worlds have the same ontological status as the actual one. They do not depend on the actual one. The aim of section 4 Representation, Recombination and IAS is to show that IAS offers a useful contribution for the role representation and recombination play in scientific theorizing. Section 5 IAS and Supra-Realism deals with Nowak’s most recent proposal for a metaphysics of possibilia adapted to the needs of IAS, dubbed by him ‘supra-realism’ (SR). I argue that there are certain tensions between SR and IAS since SR subscribes to a radical modal realism that seems hardly compatible with the constructivist actual world chauvinism of traditional IAS. We close with some general remarks on the role of mathematics plays for matters idealizational in science.

2. Idealization as Representation Let us start by recalling the basics of Nowak’s account of idealization. Since I do not aim at a full presentation I don’t want to delve into the technical details of the various kinds of idealizations and its relatives5 that have been developed by IAS over the years. Hence, I ignore many of the more subtle technicalities. Cut down to its bare bones, Nowak’s account of idealization may be formally described as follows: Let d be a (possible or actual) object to be studied by science, and assume U and U* to be universes of properties the object d may or may not have. The state of affairs that d has the property u ∈ U may be denoted by (d, u, U).

5

For instance, one now finds distinctions between idealizations sensu stricto, quasi-idealizations, proto-idealizations etc. etc.

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(2.1) Definition. A counterfactual deformation of the state of affairs6 (d, u, U) is a state of affair (d, u*, U*), u* ∈ U*. The state of affairs (d, u*, U*) is called a soft deformation of (d, u, U) if and only if U = U*, and it is a hard deformation if and only if U  U*. In the generality as stated, the definition of a counterfactual deformation is not very useful. One has to become more specific in order to obtain some non-trivial results. A crucial task of a theory of counterfactual deformations is to distinguish between “good” or “useful” deformations and those that are not. This distinction is, of course, a pragmatic matter. It depends on the practical and theoretical contexts in which counterfactual deformations occur, whether they are useful or not. In order that a deformation (d, u*, U*) of (d, u, U) may be possibly useful at all, the universes U and U* have to be structurally related in some way or other. An important case is the following: assume U = U1 × U2. In this case we may simplify our denotation writing (d, u1, u2, U1, U2) instead of (d, (u1, u2), U1 x U2). Now we can define the two most important kinds of hard counterfactual deformations (IAS) is dealing with: reduction and transcendentalization: (2.2) Definition. Let U = U1 x U2 be a universe of properties and (d, u1, u2, U1, U2) be a state of affairs. Then the states of affairs (d, u1, U1) and (d, u2, U2) are called reductions of (d, u1, u2, U1, U2). Reversely, (d, u1, u2, U1, U2) is called a transcendentalization of the states of affairs (d, u1, U1) and (d, u2, U2). The authors related to IAS have gathered sufficient motivations and many examples to render plausible the contention that these (and other) deformational procedures indeed capture some essential aspects of science. Detailed treatments of the complementary moves of reduction and transcendentalization can be found in (RI) and other

6

Beware: calling (d, u, U) a state of affairs is not meant to imply that (d, u, U) obtains in the actual world. States of affairs that obtain in the actual world are called facts.

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accounts of IAS. Hence, there is no need to rehearse them here. In order to present a reasonable completed sketch of IAS, we need, however, the following further example. It deals with a universe of properties U for which a certain extreme element u0 ∈ U has been singled out. Intuitively, this extreme element is to be interpreted as a limiting value a system may reach only under “ideal circumstances.” Often u0 may be rendered to assume the numerical values 0 or ∞. (2.3) Definition. An ideation of the state of affairs (d, u, U) is defined as the counterfactual deformation (d, u0, U). There may be other kinds of basic counterfactual deformations besides reduction, transcendentalization and ideation. But here I do not aim at a complete description and classification of these procedures. Rather, I’d like to emphasize the following point: according to IAS the various kinds of counterfactual deformations can be combined in various ways yielding a huge variety of complex deformations.7 That is to say, a given initial state of affairs (d, u, U) may be submitted to various sorts of deformations, thereby finally yielding a state of affairs (d, ϕ (u, d), ϕ (U)). The components ϕ (u) and ϕ (U) of this state depend on the original state (d, u, U) in a more or less complicated way. In particular, we have the species of idealization defined as the combination of reduction and ideation as defined above. 8 Then, according to IAS, science can be described as a complex practice engaged in dealing with the construction, combination, and alteration of various deformational procedures, in particular with idealizations of various kinds. Taking into account that the states of affairs obtained by the various idealizational procedures of science, usually are not facts, i.e., states of affairs of the actual world, one observes that science, as concerned with idealized states of affairs of type (d, ϕ (u, d), ϕ (U)), is primarily

7

A tiny piece of this variety of idealizations in form of a lattice has been discussed in some detail in (Ibarra and Mormann 1994).

8

A nice example of the variety of possible idealizational deformations a physical system may be submitted to is the textbook case of the simple pendulum where the deformational procedures can be shown to form a lattice in the sense of mathematics (cf. Ibarra and Mormann 1994).

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concerned with ideal worlds and not with the actual world (at least not directly). Here, of course, an ideal world is meant to be a suitable collection of ideal states of affairs (d, ϕ (u, d), ϕ (U)). This succinct recapitulation of the basic claims of IAS may suffice to make sense of its core thesis according to which science is dealing with ideal worlds, and not with the actual one. Now we are ready to tackle the promised representational re-interpretation of IAS. Its basic claim may be formulated as follows: Thesis 1 Ideal worlds are representations of the actual world. At least implicitly, this statement can be found in many contributions to IAS. But I think it is worth to be stated explicitly. More precisely I contend that states of affairs such as (d, u1, U), (d, u1, u2, U1, U2), etc. are representations of the object d in disguise. I hasten to add that this assertion is not to be interpreted as the confession that I subscribe to a naive realism according to which the object d is something “given,” whilst the other components of (d, u, U) are just fictions. Rather, the object d is to be considered as our contingent starting point. It may well be the case that in later stages of the scientific process states of affairs (d, u1, U1) take over the role of d. That is to say, I contend that the transcendentalization (d, u1, u2, U1, U2) of (d, u1, U1) may also be understood as a representation of (d, u1, U1) as well as an ideation (d, u0, U) may be considered as a representation of (d, u, U). Already at this early formal stage one can see that a representation in this general sense need not yield a faithful “pictorial” image of the state of affairs it represents. Information may well get lost, or, complementarily, new features may be added. Representation has a double face as a means for reducing as well as for introducing complexity. In terms of IAS, idealizational procedures comprise reductions as well as transcendentalizations. The argument that idealization is representation is based on an elementary formal observation: assume that in the framework of IAS we consider some state of affairs (d, u, U). Then, at least formally, this state of affairs corresponds to a representation d —r→ u by which the object d is represented by u ∈ U. The complete representation of d by u may be denoted by (d, u, U) or, in a more telling manner, rendering

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explicit the representational direction, by d ——→ u, with the universe of properties U being understood. In the most abstract interpretation, u may be interpreted as a property characterizing d, or, more realistically, u may be interpreted as a state-space vector characterizing the system u. Obviously, formally it does not matter whether one uses the “state-of-affairs” notation (d, u, U) or the “functional” or “representational” notation d —r→ u: one may be translated without rest into the other, and vice versa. As it stands, this is not more than a trivial change of denotation. I hope to make clear, however, that it is more, namely, a useful change of perspective that helps shed new light on what IAS really amounts to. First let us note that the representational notation suggests a more global understanding of idealization: usually one does not submit just one object d to a conceptual deformation, rather one will have some class D of objects that is deformed simultaneously in such a way that to each d ∈ D there corresponds a unique u(d ) ∈ U. In set theoretical notation this could be denoted by {u(d ); d ∈ D} but the standard functional notation D —r→ U is certainly more natural and suggestive. Summarizing the previous considerations and taking into account that all kinds of idealizational procedures may be conceived of as representations as indicated above, we may assert the following more general thesis: Thesis 2 Ideal worlds are representations of ideal worlds (or the actual world). More precisely, the states of affairs of one ideal world represent states of affairs of another ideal world. Before we go on, it may be expedient to unpack this rather opaque thesis a little bit: (i) the representational character of ideal worlds ensures that ideal world do not exist an und für sich, rather, they exist for the sake of some other world, so to speak, be this other world the actual or an ideal world. Hence, the universe of worlds should not be conceived as a set of isolated “lonely” worlds but rather as a net of representationally interrelated worlds. The network of worlds is centered in the sense that ultimately every ideal world is (how ever indirectly) representationally related to the actual world, since otherwise it had to be considered as an idle free-floating idealization good for nothing; (ii) the representational network constituted by a

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complex texture of ideal worlds is not simply there, rather it is the result of the collective efforts of the members of the scientific community who are engaged in rebuilding, extending and applying it in manifold ways. In the rest of this section I’d like to elaborate this broad picture of the representational web of science by relating it to what may be called the representational approach to science. In (Ibarra and Mormann 1998), we proposed as the general format of empirical theories the following: If D is a realm of data and C a the realm of symbolic constructs, then an empirical theory is a representation r: D ——→ C mapping an empirical datum d to its theoretical conceptualization r(d ) ∈ C. The mapping r may be said to provide a theoretical representation of the data D by the symbolic constructs C. As has been explained in detail there, in this way an empirical theory may be seen as a representation. Of course, not any map D ——→ C will do. Rather, the representation r has to satisfy certain structural requirements whose details need not interest us here (see Ibarra and Mormann 1997). For the purposes of the present paper, the internal details of these mappings D ——→ C are less important than the fact that theoretical representations of this kind never live in isolation, rather, they form a representational network. This may be explained as follows: the domains D and C are not to be conceived of as belonging to totally different and separated categories, the empirical and the theoretical, say. Rather the following holds: one and the same domain D may be represented by several different entities C, E, or F, and a representing domain C itself may be represented by further idealizing representations C ——→ E, C ——→ E. Often, it may be useful to stick together representations. Thereby, from A —r→ B and B —s→ C one obtains a combined representation A —s•r→ C etc. etc. Summarizing one may say that any theory of representations should comprise a combinatorial part describing the various possibilities of combinations and iterations of representations. As we shall see in the next section, IAS may be said to have provided exactly this — a combinatorial theory of idealizing representations. A plausible requirement the combinations or concatenations of representations may have to satisfy that it is associative. That is to say, representations f, g, and h which “match” should satisfy the

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law of associativity: f • (g • h) = (f • g) • h. These combinations of representations are of utmost importance for the practice of science. For instance, in the standard representational theory of measurement the numerical measurement of an empirical domain D is conceptualized as a representation r: D ——→ R of D into the real numbers R. This is a rather idealized description. Actually, by a closer inspection the representation D —r→ R should be regarded as a more or less extended chain of representations (2.4)

D ——→ E ——→ F ——→ . . . ——→ R

In most cases, numerical or, more generally, mathematical representations of empirical data cannot be “read off ” directly, usually they have to considered as constructs which have been built by a more or less complicated constructional processes. The long way from data to theory shows that the standard dichotomy is a very simplified picture at best. A closer look, quite in line with IAS, would reveal the long road between data and theoretical constructs and describe this way in a more detailed manner (cf. Ibarra and Mormann 1997). Even if strictly speaking scientific knowledge has to be described as a chain of representations it may sometimes be convenient to squeeze together the ends of the representational chain, putting them into a black box, so to speak. Thereby one obtains the short representational sequence D ——→ C which corresponds to the standard two-level model D ——→ T of data D and theoretical constructs T. Thereby we end up with the traditional conception of two different conceptual and methodological levels in scientific knowledge: the empirical and the theoretical level. This distinction is found not only in the account of scientific theories favored by the Logical Empiricists of the Vienna Circle, but also in Nagel’s The Structure of Science (1961). It is still present in the various versions of the post-positivist or post-empiricist versions of the semantic conception of theories. It can be considered, however, only as a first approximation. It is one of the real assets of IAS as a theory of idealizational representations that it overcomes this oversimplified picture of science To state it once more quite explicitly: taking the actual world as the starting point of our constructions of ideal worlds should not be understood as the naive realistic stance according to which the actual

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world is just there, waiting for conceptual deformations, while the ideal worlds are mere fictions. This would correspond to the primitive instrumentalist stance according to which the data are the only “really” existing entities and the idealized constructs are “really” non-existing symbols invented only for the sake of prediction. Hence, acknowledging the role of representations for ontology does not mean that all entities have to have the same ontological status: it may well be expedient to distinguish between highly theoretical entities such as electrons and positrons and, say, the philosopher’s notorious apple tree. Rather, we should define the world as the totality of all representational entities that occurs in some way or other in scientific representations. Depending on where an entity appears in the various representational chains one may attribute to it a different ontological status. But these more fine-grained questions will not concern us in the following. Let us pause for a moment and take stock what we have achieved so far: I hope to have rendered plausible the thesis that the various deformational, in particular idealizational procedures considered by IAS as the essential ingredients of scientific reasoning, may be conceived of as representations. More precisely, according to Thesis 1 and Thesis 2 ideal worlds may be conceived of as representations. In the next section I want to argue that also Armstrong’s recombinatorial theory of possible worlds has a representational base. This means, against first evidence, IAS and the recombinatorial account of possible world share a common ground. In the following sections this common representational ground is exploited to sketch a metaphysics of ideal worlds adapted to the needs of IAS.

3. Recombination as Representation At first glance, Armstrong’s combinatorial account of possible worlds is not very attractive from the point of view of IAS: a strict combinatorial account is known to suffer badly from a shortage of worlds. Alien individuals and alien properties, i.e. individuals and properties that do not occur in the actual world, are not admitted as citizens of other

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possible worlds (cf. Armstrong 1989, 1997). For instance, if there are n electrons in the actual world, strictly speaking, a world with (n+1) electrons would come out as an impossible one — let us assume that the number of electrons is constant in some sense. Clearly, this is a serious drawback from the perspective of IAS. Hence, if not even Lewis’s rich universe of possible worlds can deliver the many worlds IAS is in need for, the austere combinatorial accounts score much worse, or so it seems. Before it will be shown how these shortcomings may be overcome by re-interpreting the combinatorial account in a representational framework, let us mention the features of the recombinatorialism that make it particularly appealing to IAS (cf. Armstrong 1989): (3.1) Basic Assumptions of the Recombinatorial Account of Possible Worlds. (i) The combinatorial approach subscribes to an unmitigated “actual world chauvinism” (Armstrong’s expression) giving the actual world a distinguished position in the universe of worlds. In other words, Armstrong’s universe is a centered universe. (ii) The combinatorial approach is thoroughly constructive in that its worlds are dependent on the actual world as being constructed from building blocks that arise from the actual world in a sense to be specified. Before we go on let us notice that the analogues of (3.1)(i) and (3.2)(ii) also hold for the ideal worlds of IAS, at least to some extent. The worlds of IAS are idealized worlds. This means, they are worlds constructed from the actual world with the aid of idealizing procedures. Hence IAS subscribes to a constructive attitude similar to the combinatorial account. By contrast, Lewis’s universe of possible worlds is structured quite differently: according to his modal realism, being actual is an indexical matter, and there is no distinguished place for the actual world that happens to be actual just for us. This implies in particular that other possible Lewisian worlds cannot be thought of as constructed from the actual world: all possible worlds are on an equal footing. Hence, contrary to the appearances, IAS has not much to expect from any kind of modal realism. This, of course, does not render Armstrong’s austere combinatorial account automatically more

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appealing to the follower of IAS. In the rest of this section, I want to show that the shortcomings of the traditional combinatorial accounts may be overcome in a representational framework in such a way that its principal advantages, to wit, actual world chauvinism and the constructive character of the worlds, are preserved. Thereby the “representationally” reformed combinatorialism may be considered as a promising candidate for the office of a possibilist metaphysics for IAS. The standard story of combinatorialism reads like this: there is the one actual world, and all possible worlds are recombinations of the basic building blocks of the actual world. In its simplest form these blocks are states of affairs. All other entities, in particular individuals and properties are abstractions of, or are constituted from states of affairs. Thus, neither individuals nor universals (properties) exist in the actual world. Rather, they are abstractions from its basic components, to wit, the facts or states of affairs. Hence, for a combinatorialist speaking of the world’s properties or individuals is a mere façon de parler. Strictly speaking, there are only states of affairs. States of affairs and nothing else are the basic building blocks of the actual world W. For simplifying the technical problems let us assume that all atomic states of affairs are monadic states of affairs that can be described by statements of the form Fa, Gb, etc. to be read as “a is an F,” or “G is instantiated by b.” Taking seriously the thesis that states of affairs are the basic building blocks of the actual world, we have to explain how individuals a, b, . . . and properties F, G, . . . are constituted from the underlying basic states of affairs. According to Armstrong, this constitution is not be understood as a “tinker-toy picture,” rather: . . . [t]he constituents are essentially aspects of, abstractions from, the states of affairs. . . . We may think of an individual, such as a, as no more than an abstraction from all those states of affairs in which a figures, F as an abstraction from all those states of affairs in which F figures, and similar for relation R. (Armstrong 1989, p. 43)

If we concentrate on individuals and a monadic predicates a good first approximation to this “abstraction” would be to consider individuals and monadic properties as equivalence classes of states of affairs

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with respect to certain equivalence relations. Under the simplifying assumption that all atomic states of affairs are monadic this is not too difficult: assume that on the actual world W two equivalence relations ~1 (“compresence”) and ~2 (“similiarity”) are defined. Then, an individual a may be conceived of as an equivalence class of states of affairs with respect to ~1, i.e., a = [s]1 for some s. Seen from the individual’s side this means that an individual is identified with the class of states of affairs in which it occurs. The individual “Socrates” is identified with the class of states of affairs in which it occur. Analogously, a property F is an equivalence class [t]2 for some state of affairs t. Looked at from the property’s perspective this means, a property is identified with its extension, i.e. all the individuals that instantiate it. Thereby, for instance, the property “wise” is identified with the class of states of affairs in which it occurs. Assuming further that these equivalence relations are orthogonal in the sense that for any two atomic states of affairs s and t one has (3.2) For all states of affairs s, t: If s ~1t and s ~2 t then s = t Denoting the set of equivalence classes of states of affairs with respect to ~1 and ~2 by [W]1 and [W]2, respectively we may identify the set of equivalence classes [W]1 with the class I of individuals and [W]2 with the class U of universals or properties of W. It does not matter if one identifies I and U with the world’s individuals and universals or, more cautiously, one only claims that I and U represent individuals and universals in a unique way. In any case, the relations ~1 and ~2 do the job of distilling individuals and properties out of the more fundamental states of affairs (cf. Bacon 1995). Thus the actual world may be described as a structure (W, ~1, ~2) where W is the class of state of affairs and the relations ~1 and ~2 are equivalence relations W orthogonal to each other. Then we can summarize the explication of the world’s structure obtained so far by the representation of the following kind (3.3) W —r→ [W]1 × [W]2 , r(s) := ([s]1, [s]2) Here r is the natural map by which a state of affairs s is represented by ([s]1, [s]2). The orthogonality of the equivalence relations ~1 and ~2 ensures that r is 1-1, i.e. to every state of affairs s of W there

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corresponds exactly one ordered pair ([s]1, [s]2).9 Although the actual world W is uniquely characterized by the set (3.4) r (W) := {([s]1,[s]2); s is a state of affairs of W} one should note that r (W) is not identical with W, rather r(W) is a set theoretical substitute of the actual world W, more precisely a subset of [W]1 × [W]2. This means r (W) as a substitute of W is a formal object construed by some representational means from the actual world. This is important since other combinatorial worlds are obtained by the stipulation that a world V is just a subset of [W]1 × [W]2. Hence, according to the combinatorial account a possible world V is a set theoretical construction based on the set theoretical representation W —r→ [W]1 × [W]2. Quite literally it may be understood as a deformation of the representation r, since V may be considered as a deformation of r (W). It is expedient to dwell upon this point a little bit further: the present reconstruction of the combinatorial account shows that combinatorialism is soaked with representational ingredients, even if these often remain implicit. The existence of these representational elements suggests a plausible liberalization of the orthodox representational approach as I want to show now. If a set-theoretical representation such as r: W ——→ [W]1 × [W]2 is admissible and, strictly speaking, even indispensable for combinatorialism, it is hard to see why other mathematical representations had to be considered as inadmissible. For instance, if one considers a world in which the earth is represented as a perfect sphere in the sense of mathematics, one may doubt if this world can be considered as a way things might have been. If one allows, however, that the earth’s form deviates, say, 1% or 2% from an ideal sphere, most people would assent that such a world is indeed a possible world. Mathematically, these representations are on a par with the radically idealizing representation that treats the earth as a mass-point. This means that from the perspective of a representational approach the categorical difference between mathematical substitutes of possible worlds and the ideal worlds of IAS becomes

9

The reverse does of course not hold, provided W is not a “full world” in the sense of RI.

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blurred.10 It appears to be hardly possible drawing a neat line between the representations corresponding to possible worlds understood as ways things might have been and those representations that lead to ideal worlds in the sense of IAS. In other words, if we rely on mathematics as the principal organon for generating possible or ideal ersatz worlds this distinction become pointless. This will be spelt out in more detail in the next section. Before we come to this let us note that already at this stage some constructions of IAS can be recovered in the combinatorial framework: a combinatorial world W * having the same individuals as the actual one may be characterized as a soft deformation and one with less individuals can be considered as a reduct of the actual world. The point I want to make should now be evident. It may be formulated in the following thesis: Thesis 3 The ideal worlds of IAS and the possible worlds of combinatorialism are representational constructions. They are built up from ingredients to be found in the actual world that are submitted to certain procedures. In IAS they are called “conceptual deformations” or “idealizations,” in the combinatorial account they are used to be called “recombinations.” Formally, both may be characterized as representational constructs. It should be noted that the possible worlds of combinatorialism need not be possible worlds in the sense of “ways things might have been.” There is no reason to assume that combinatorial worlds can be obtained from the actual world by a sequence of possible causal transformation. Rather, as Armstrong has repeatedly emphasized, a genuine combinatorial account subscribes to the Humean thesis that there are no causal relations at all between the combinatorially possible states of affairs. In other words, all mathematically possible combinations represent combinatorially possible worlds, regardless of any causal considerations. This attitude is in line with that of IAS since 10

Lewis always insisted that his possible worlds are not mathematical constructions, and moreover that his other worlds are not constructs of any kind.

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for this approach the construction of idealized or otherwise conceptually deformed states of affairs (d, φ (u, d), φ (U)) as described in section 2, does not take into account any causal constraints. Combinatorialism as well as IAS subscribe to the thesis that the construction of worlds is not limited by causal constraints. Rather, it is carried out by following the constitutional rules of some kind of metaphysical combinatorics. The difference between the two approaches is that the IAS constructions through idealizational deformations are not subjected to any restrictions at all (except, of course, limitations of logical consistency), while Armstrong’s deformations are recombinations in a strict sense. Without arguing for it in detail I will assume in the following that there is no reason to stick to the restrictions of Armstrong’s austere combinatorialism, in particular, since there is no principled mathematical reason to contend that only certain mathematical constructions lead to admissible worlds but others not. Hence, I think it is of secondary importance if these representational constructions are called idealizations, recombinations, conceptual deformations or whatsoever. The important fact is that both combinatorialism and IAS are thoroughly constructive approaches, according to which “possible” or “ideal” worlds are constructed entities. As distinguished from IAS, the deformational procedures admitted by Armstrong’s combinatorialism are extremely restricted: given the facts, i.e. the states of affairs of the actual world, the only possible worlds admitted are those obtained by recombining particulars and properties of the actual world. Armstrong’s reasons for this austerity need not concern us here. If one does not share the premises of his empiricist naturalism there is no reason to restrict the spectrum of possible constructional methods as severely as he does. Thereby, a natural liberalization of the combinatorial account of possible worlds comes in sight. This representationally reformulated combinatorialism preserves its virtuous features as stated in (3.1), but avoids its shortcomings. Moreover, it fits the needs of IAS. In the rest of this section I intend to characterize this representational recombinatorial account succinctly. The starting point is a representation W —r→ S (W) where S (W) is some mathematical structure, which according to science expresses something like the essential structure of the actual world. Or, more

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modestly, it represents some aspects of the structure of the actual world that are considered essential by science. It is a matter of science, not of philosophy, to provide such a representation. Hence, from a philosophical point of view there is not much to say about it. Modern science suggests that S (W) will be a highly sophisticated mathematical structure. Certainly, a states-of-affairs representation in the sense of Armstrong is a very stark simplification. Modern mathematized science hardly gives us reasons to believe that the structure of the actual world is really thus simple as is supposed by the factual metaphysics on which Armstrong’s account is based. This is not to say that it is to be considered as false or useless, the only claim I make is that S (W) need not have the simple form Armstrong’s combinatorialism assumes it to have. In principle, any structure in line with science would do. From this basic representation, which encapsulates a model of the actual world, other ideal worlds are obtained by submitting this model to appropriate mathematical variations. These mathematical variations may comprise conceptual deformations and recombinations in the sense of IAS as special cases. Probably, however, the variations based on S (W) comprise other procedures as well. Generally we may say that elementary combinatorialism should be replaced by some kind of structural variation account whose details will depend on the actual mathematical models contemporary science provides. Such a structural variation approach may be considered as a general framework for the generation of possible and/or ideal worlds. It may be characterized as an scientifically informed approach since it takes into account all conceptual tools of modern science, in particular the mathematical ones. It explicitly refrains from getting involved in the hopeless endeavor to distinguish by philosophical means between admissible and non-admissible scientific methods for building worlds. Thereby the structural variation approach is more versatile and flexible than the restricted combinatorial account of Armstrong and the sometimes clumsy set-theoretical deformational procedures of IAS. On the other hand, it preserves the virtues of these accounts by maintaining a strong actual world chauvinism and a highly constructive attitude. Thereby the structure of the actual world determines the modal sphere of

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worlds that has to be taken into consideration if we want to deal successfully with matters modal. It seems not to be far fetched to contend that the basic assumption of the structural variation approach is the basic thesis of Galilean or Marxian science according to which one has to find an abstract representation of the actual world in order to determine the sphere of possible worlds. In contrast to traditional combinatorialism, the structural variation account does not assume that all possible worlds are construed by elementary recombinations of elements of the actual world. Rather, possible worlds are obtained from the actual one as variations of its essential representation. Recombinations and idealizational constructions may be understood as instances of structural variations. Hence, IAS and the structural variation share many features, in particular a strong constructional flavor. Both consider worlds as conceptual entities to be constructed from a conceptual base that ultimately points back to the actual world and our knowledge of it. Nevertheless, there is an important difference between IAS and the structural variation account. According to the latter, (possible or ideal) worlds are mathematical constructions. Even more, the role of mathematics in science is seen to provide the means for constructing ideal “Galilean” worlds susceptible to mathematical argumentation. As far as I can see, the role of mathematics in scientific idealization is underestimated and only implicitly dealt with in IAS.11 Although IAS convincingly argues for the important role of idealization in science, it hardly mentions the fact that at least in the natural sciences the raison d’être of the various idealizing procedures is to build up a domain of worlds that is directly susceptible to mathematical arguments. This feature strictly separates ideal worlds from the actual world which is not of the kind of entities for that mathematical considerations directly apply. I think that this feature of ideal worlds, to wit, that they are domains to which mathematical arguments directly apply is somewhat underestimated by IAS. Although ideal worlds are characterized as the stage where idealized laws hold, it is rarely stated explicitly that these ideal laws are mathematical laws. IAS takes the mathematical 11

In RI, the role of mathematics in science is not treated at all.

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character of most idealizations as a contingent fact without further philosophical significance. This is misleading. It may well be the case that mathematics is the proper organon for generating ideal worlds.

4. Representations, Recombinations, and IAS Maintaining that only IAS would benefit from a closer contact with representational considerations would be a serious distortion of the facts. Quite the contrary: also representational accounts may benefit from tapping the sources of IAS and learning something about how representation in science really works. All too often, in epistemology and philosophy of science the concept of representation is seriously misunderstood by taking representing as some sort of mirroring (cf. Rorty 1991). IAS may help overcome this simplistic and objectivist conception of representation. An essential step in this endeavor is to recognize the active role the representing subject plays. Main-stream philosophy of science has been liable to neglect the role of the theorizing subject. Telling examples are the various positivist and postpositivist philosophies of science which are at pains to elucidate the notion of a scientific theory without ever saying a word about the subject which is, after all the agent that invents, modifies and uses the theories in question. The representational account sketched in this paper so far, may be judged guilty of the very same neglect as well. Till now we have talked about representations ignoring for whom these representations are made and who has invented them. Here, IAS comes to the rescue. The idealizational approach to science offers detailed and elaborated arguments that show that representation in science has nothing to do with idle mirroring representation. Evidently, the representations of science, i.e. the ideal worlds of IAS, are our worlds in which the idealized laws of our theories hold while the actual world is one that always escapes our theoretical and practical efforts, at least partially. In order words, the ideal worlds of science clearly show that the representations encapsulated in them, are our representations. Therefore, they should not be understood as giving us direct access to the world “as it really is like.” Rather, as IAS shows that

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it is a long and difficult road from the idealized worlds back to the actual one. It is one of the main assets of IAS not to have been content with the bald contention that ideal worlds (or representations) are constructions. Rather, this current of philosophy of science has produced detailed investigations of the various kinds of idealizations as that occur in the sciences. It goes without saying that this is not the place to give a detailed account of these investigations. Just let me mention the following ones which indicate that IAS takes seriously the multitude of idealizational procedures and their combinations. According to RI one can distinguish at least the following five types of idealization: (4.1) (i) (ii) (iii) (iv) (v)

Deformational Procedures according to IAS12 (RI, p. 163) Idealization sensu stricto (I) Stabilization (S) Semi-idealization (s) Quasi-Idealization (Q) Aggregation (A)

Generalizing the considerations of section 2 all these deformational procedures may be considered as operators that can be applied to some system x, x being a system of the actual world, or, more generally, of an appropriate ideal world. To be specific, let us denote the system we get from x after the application of I or S by I (x) or S (x), and analogously for the other operators. Even if one makes the simplifying assumption (cf. Ibarra and Mormann 1994) that the order in which the deformation operators are applied to x plays no role, i.e. even if one assumes A(B (x)) = B (A(x)) for all A, B ∈{I, S, s, Q, A} we obtain not less than 25 — 1 = 31 possibly distinct conceptual deformations of the system x.13 12

This list is not intended to be complete. In the framework of IAS other deformational procedures have been proposed, e.g. proto-idealization (cf. RI). In general, there is no reason to expect that philosophy of science will ever be able to present a complete list of idealizational procedures used in science. Probably it is an interesting problem to investigate which kinds of idealizational procedures are used by which sciences. 13

One should say “possibly different” since it may happen that for some systems not all operators apply and/or yield different results. According to RI,

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Painted with a broad brush the picture emerging from this sketch is the following one: philosophy of science, understood as a pragmatic theory of scientific theorizing, may be conceived as a combinatorial theory of scientific representations, i.e. a theory that takes into account the pragmatic virtues and deficiencies science is working with. The ideal worlds of IAS are not simply “out there” representing the actual world as it objectively is. Rather, its worlds are our constructions, made by us for our purposes and designed according to our rules. Thereby, IAS is fully in line with Peirce’s pragmatic theory of representation according to which the concept of representation cannot be fully understood in terms of the dyad of the represented and the representing alone.14 Representation essentially requires the participation of an representing and interpreting subject, it is always somebody’s representation. In a similar vein, an ideal world in the sense of IAS is always somebody’s world. From the point of view of IAS it does not make much sense to contend that an ideal worlds are objective being totally detached from a subject that has created them. Hence, to paraphrase a famous dictum of Peirce, idealizations are always idealizations of something and for somebody. There are no idealizations an sich, they always refer to some non-idealized world. Representations are not simply there, rather they are constructed by somebody for certain purposes. In contrast to the efforts of neopragmatism to trivialize the concept of representation in order to discard it from the philosophical discourse altogether, IAS convincingly argues that representation is a complex concept in need of a theory. As has been shown by the detailed studies carried out in the framework of IAS scientific representations do not live in isolation. Rather, they may be iterated and combined in various ways. Hence, at least to some extent philosophy of science as a theory of scientific representation make be characterized as a combinatorial theory of scientific representations. up to now only twelve of the less complicated combinations of these deformations have been studied in some more detail. 14

It should be noted that Peirce’s high esteem for representation contrasts starkly with the rejection of this concept in modern currents of “neopragmatism” such as Rorty’s (cf. Rorty 1991, pp. 154f ).

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An important medium for scientific representations is mathematics. On the other hand, various types of material representations play an essential role for scientific representations. A general theory of scientific representations should be able to deal with all kinds of representations occurring in science. Representations do not “speak for themselves.” Rather, they are in need of interpretation. Hence, a large part of scientific practice consists in interpreting and reinterpreting scientific representations. In this way, representation becomes a reflexive concept, i.e. there are representations of representations, representations of representations of representations etc. A theory of scientific representations has to deal with this fact. The idealizational approach to science may be conceived as an attempt to realize such a reflexive combinatorial theory of scientific representation.

5. The Idealizational Approach to Science and Supra-Realism Now let us come to a discussion of Nowak’s modal supra-realism (SR) which may be considered as metaphysics of the possible (or the ideal) especially tailored for the purposes of IAS. Nowak himself considers SR as a radicalization of Lewis’s modal realism. In this section I want to argue that this interpretation may be somewhat misleading and tends to obscure some essential points of the metaphysics of idealization as understood in the idealizational account. The main objection Nowak launches against the modal realism of Lewis is that this account does not yield sufficiently many possible worlds for IAS. Hence, he is convinced that Lewis’s doctrine of modal possibilism requires a significant strengthening in order to admit the existence of ideal worlds. To understand why Nowak considers Lewis’s universe of worlds as insufficient and what kind of strengthening he has in mind, consider the following quotation in which he states his conception of a Lewisian possible world: Let us consider a single object a and the universe U of (elementary) properties. Let a subset S of U be composed of these properties which per-

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tain to a in definite degrees; the space of properties will be thus the set of facts of the type P(a) = n, where P belongs to S, and n belongs to the set of values of property P. Now, within this extremely simplified framework the Lewis’ notion of the possible world as a “way the object(s) a could have been” might be identified simply with every set of states of affairs of the type P(a) = m where m may, but needs not, be different than n and, moreover, for some P from S, P(a) = m  n. Every set of such states of affairs would thus constitute a (one-object) merelypossible world. (RI, p. 275)

Nowak rightly remarks that this kind of worlds does not suffice to satisfy the demands of IAS. Rather, we need more worlds, and, more precisely, different kinds of worlds: (5.1) Kinds of Worlds According to Supra-Realism (SR). According to SR there are the following three categories of worlds: Worlds of category I: Worlds built over the actual world. Worlds of category II: Worlds built over reducts of the actual world. They may be characterized as contractions of the actual world. Worlds of category III: Worlds built over transcendentalia of the actual world are called extensions of the actual world. According to Nowak, worlds of category I may be identified with Lewisian possible worlds, to wit, as “ways things might have been.” On the other hand, for worlds of category II and III there is no place in Lewis’s universe of possible worlds, they genuinely belong to the metaphysical doctrine dubbed “supra-realism” and conceived by Nowak “as significant strengthening [of Lewis’s realism] admit[ting] the existence of ideal worlds . . . ” (RI, p. 449). I think that this characterization of supra-realism as a strengthening of modal realism is misleading since it ignores two essentials of Lewis’s account, to wit, its indexicality and its non-constructive character. Lewisian worlds do not depend on the actual world, they may be similar to it but this does not mean that they can be considered as variations of the actual world, and the actual world does not play a distinguished role in the Lewisian universe of possible worlds. In this respect, all kinds of modal realisms on the one hand, and all kinds of combinatorialisms are opposed to each other. The former accounts may be said to subscribe the thesis of a homogeneous, centerless universe of worlds while the latter favor an

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inhomogeneous, centered universe of worlds in which the actual world plays a distinctive role. As has been argued in the preceding sections, IAS, at least in its traditional version, goes well together with a constructive approach based on an non-homogeneous, centered universe of worlds. In his most recent writings, however, the essential features of IAS, to wit, the non-homogeneity and the centeredness of the universe of ideal worlds and their constructional character are openly retracted in favor of the strong plurality-of-worlds thesis which may be considered as the core of SR. In the following I want to argue that (SR) is an uneasy compromise between a full-fledged modal realism à la Lewis, and a constructivist ersatz account, as Lewis would have called it. According to Lewis, possible worlds are what they are. They cannot be reduced to anything else. In particular, their existence does not depend on us. Other possible worlds exist in the same way as ours. Period. In some way, Nowak’s SR wants to have it both, the advantages of Lewis’s relentless realism and the advantages of some more economic ersatz account. Let us first gather some evidence that SR indeed recants the constructive character of ideal worlds when he asserts: In a word, all our idealizational “constructs” are not constructs but true descriptions of some existing, ideal worlds. . . . As it were, we are unable to theoretically invent something which would not hold nowhere, in no world. (RI, p. 459)

Consequently, “Our thoughts” are “objective states of affairs” . . . We, people, possess an ability to coordinate some of our states with situations in possible worlds [of category I — T.M.] but also in contractions and expansions of possible worlds (i.e., in possible worlds of categories II and III, respectively). (RI, p. 460)

Indeed, as Nowak rightly remarks, “the nature of this ability is really surprising.” For scientific knowledge it has the following consequence: Idealizational laws are exact descriptions of what is going on in simple, e.g. two-factors worlds inhabited by ideas, that is, worlds being contractions of that of ours.

Some people will certainly qualify this as a monstrous metaphysics. Be that as it may. I do not want to follow them. Rather, I want to emphasize a feature of SR that renders it a strange mixture of realism and

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neural constructivism as one may call it. On the one hand, possible worlds are simply out there independent of our constructive efforts. This is the realist face of SR. Without doubt, SR is a much more radical version of modal realism than Lewis’s, because SR admits much more worlds. On the other hand, SR has a thoroughly conceptual component since the worlds “out there” depend on our neural equipment. More precisely, we have a surprisingly direct contact with them: it suffices to put our neurons in a consistent constellation and we are there — at some possible world whose states of affairs are completely described by the neuronal constellation in which we happen to be. One may doubt, of course, whether it makes sense to speak of a neural constellation as being states that can be described as consistent or not. If this is denied, SR has to fall back to our linguistic and conceptual abilities which happen to determine the sphere of possible worlds. Of course, it is not plausible to assume that there is one privileged language or one privileged conceptual scheme which determines the domain of possible worlds. Rather, Nowak would have to admit that all languages have equal rights in access to the ideals worlds of SR, i.e., just any consistent assertion in any conceivable language would yield a state of affairs obtaining in some possible worlds. Next, there is the problem of a possible plurality of logical frameworks: is it admissible, one may ask, to use a paraconsistent logic in order to obtain even more possible worlds, or do we have to stick to classical logic? All these are problems that Nowak’s sketch of SR leaves unsolved up to now. Maybe an elaborated version of SR can cope with these problems. But even then two problems remain: first, one may object that SR is unnecessarily liberal: if every consistent statement uttered by us uniquely corresponds to one state of affairs of a possible world and vice versa, why not conceptualize SR as a sort of linguistic or conceptual ersatzism according to which possible worlds are suitable consistent classes of statements or propositions? Why do we really need this miraculous ability that our thoughts are directly correlated (by some sort of Leibnizian pre-stabilized harmony?) with the states of affairs of ideal worlds? Secondly, one may object that SR is in danger of losing contact to science. After all, the ideal worlds of science have to be consistent but consistency is certainly not sufficient to characterize them. Most

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possible states of affairs in this sense, i.e., most consistent states of affairs are scientifically completely uninteresting. Hence, as a metaphysical underpinning of IAS as philosophy of science, SR does not deliver, at least not in its present embryonic state. In this respect, it seems to me, some kind of a less extravagant representational combinatorialism scores at least as well.

6. Concluding Remarks As a kind of resume, I’d like to restate the basic thesis of this paper as follows: starting from the basic insight of IAS according to which scientific theories do not directly refer to the blooming buzzing chaos of the actual world but rather to appropriately chosen ideal world, I propose to subsume the various idealizing and deformational procedures, in particular representation and recombination by which the ideal worlds are constructed, under the common heading of structural variation. In this way, mathematics becomes the organon for generating the ken of scientifically relevant ideal worlds as the domain of possibilities. To put it bluntly, the ideal worlds science is dealing with, turn out to be mathematical worlds in a broad sense. This does not mean that they are quantitative worlds in some old-fashioned sense of the word. Quite the contrary, modern mathematics can hardly be characterized as the science of the quantitative, and one may well doubt that this characterization has ever made sense. In any case, today there is no justification to subscribe to such an impoverished conception of mathematics. In this way, the burden to come to grips with modality, is shifted to mathematics as the principal organon of idealization. This move does not solve the problem of idealization, of course. A skeptic may well ask for a more detailed and elaborate story of how mathematics succeeds to fulfill the modal demands of the sciences. This is a deep problem for philosophy of mathematics. It may be related to Wigner’s notorious “unreasonable effectiveness of mathematics in the natural sciences.” Regrettably, in contemporary philosophy of science and mathematics, the problem of the applicability of mathematics in science is rarely addressed (cf. Steiner 1989). Never-

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theless, I think, it could be fruitful to re-conceptualize the metaphysical problems concerning the role of idealization by bringing this problem in contact with philosophy of mathematics. This may be done for the mutual benefit of both parties.

The University of the Basque Country UPV/EHU Department of Logic and Philosophy of Science P.O. Box 1249 20.080 Donostia-San Sebastian Spain E-mail: [email protected]

REFERENCES Armstrong, D. M. (1989). A Combinatorial Theory of Possibility. Cambridge: Cambridge University Press. Armstrong, D.M. (1997). A World of States of Affairs. Cambridge: Cambridge University Press. Bacon, J. (1995). Universals and Property Instances: The Alphabet of Being. Oxford: Basil Blackwell. Bradley, R. (1992). The Nature of all Being: A Study of Wittgenstein's Modal Atomism. New York: Oxford University Press. Haase, M. (1995). Galileische Idealisierung. Berlin: de Gruyter. Ibarra, A. and T. Mormann (1994). Counterfactual Deformation and in a Structuralist Framework. In: M. Kuokkanen (ed.), Idealization VII: Structuralism, Idealization and Approximation (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 42), pp. 81-94. Atlanta, GA, Amsterdam: Rodopi. Ibarra, A. and T. Mormann (1997). Theories as Representations. In: A. Ibarra and T. Mormann (eds.), Representations of Scientific Rationality (PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 61), pp. 59-87. Atlanta, GA, Amsterdam: Rodopi. Lewis, D. (1973). Counterfactuals. Oxford: Blackwell Publishers. Lewis, D. (1986). On The Plurality of Worlds. Oxford: Blackwell Publishers. Nagel, E. (1961). The Structure of Science. New York: Harcourt, Brace and World. Nowak, L. (1980). The Structure of Idealization. Towards a Systematic Interpretation of the Marxian Idea of Science. Dordrecht: Reidel.

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Nowak, L. (1989). On the (Idealizational) Structure of Economic Theories, Erkenntnis 30: 225-246. Nowakowa, I., and L. Nowak (2000). The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam: Rodopi. Rorty, R. (1991). The Mirror of Nature. Princeton: Princeton University Press. Skyrms, B. (1986). Tractarian Nominalism. Philosophical Studies 40: 199-206. Steiner, M. (1989). The Application of Mathematics to Natural Science. The Journal of Philosophy of Science 86: 449-480. Wittgenstein, L. (1961). Tractatus Logico-Philosophicus. Translated by D.R. Pears and B.F. McGuiness. London: Routledge and Kegan Paul.

Evandro Agazzi IDEALIZATION, INTELLECTUAL INTUITION, INTERPRETATION, AND ONTOLOGY IN SCIENCE

Leszek Nowak’s most notable and original contribution to the philosophy of science is certainly his elaboration of a fully fledged theory of idealization. Though he maintains that his theory is a formal presentation of Marx’s basic epistemological approaches, and though he also recognizes the merits of authors such as Max Weber in the appreciation of the role of idealization in science, it remains indisputable that the Marxian ideas are only a loose indication of the main features of this methodological procedure, and Weber’s theory is only partially in keeping with Nowak’s proposals. My aim in this contribution is that of underlining certain fundamental aspects of Nowak’s theory that I consider especially significant because they express a view of science that has a general purport and, in particular, has several points of contact with the epistemology of science I have developed myself. Of course, the fact of being in agreement with my ideas is not in itself a special merit but it shows that certain important points can be attained through quite different intellectual pathways, and this can be an indication that they are intrinsically sound.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 303-314. Amsterdam/New York, NY: Rodopi, 2007.

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1. What Is a Scientific Object? In the general theory of scientific objectivity I have been elaborating for more than forty years I introduce a distinction between a “thing” and an “object” (in particular a scientific object) by maintaining that a thing becomes the “object” of a particular investigation when it is considered from a specific “point of view,” that is, when only certain particular attributes of it are taken into consideration, whereas all the other attributes are disregarded. These attributes are intellectually expressed through certain concepts and linguistically formulated by means of certain predicates. An object, however, is not just a bundle or set of attributes, but a structured set of attributes, and this implies that also certain functional relations between the attributes must be captured or introduced, that must also be expressed at an intellectual and linguistic level. When, instead of a single thing, we consider the investigation of reality as a whole, we can determine the characteristics of a particular science: this is an investigation of reality from a specific point of view, that is, an investigation restricted to the consideration of a finite set of attributes and of certain functional relations holding among them, that are represented by certain concepts and linguistically expressed by certain predicates. In the case of the empirical sciences, it is mandatory that at least a few predicates be linked with certain standardized operational procedures that enable one to test whether a sentence including exclusively such predicates (which I call “basic predicates”) is immediately true or false. I call such operational procedures “criteria of protocolarity” or “criteria of referentiality,” for reasons that will be clear in the sequel. Within this approach scientific objects are abstract entities in the sense that they are not concrete entities, though they are proposed and studied with the purpose of investigating concrete reality. As a consequence, I distinguish the domain of objects and the domain of referents of a science: the domain of objects is totally and unambiguously determined by the finite set of attributes selected by the science in question, and these objects are only “abstract,” while the domain of referents is not determined a priori since it is “open” to include whatever concrete “thing” to which the abstract attributes apply within

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the margins of approximation permitted by the operational procedures of referentiality. In other words, the scientific object is an intellectual entity that, as such, has an intentional reality (that is, it is “real” only as an entity belonging to the realm of what we can construct by means of our “intentionality” in the precise philosophical sense of this notion), and is totally determined as the structured set of attributes that it encodes. Any concrete object, on the contrary, is largely undetermined since it can exemplify several abstract objects to the extent that its attributes concretely satisfy the structure of some abstract object, but at the same time it also exemplifies several other attributes such that, in its complexity, it can never precisely exemplify the structure of an abstract object (the potential infinity of its attributes precludes such a perfect exemplification, due to the overlapping of these attributes that usually allows only for a partial satisfaction of each of them). The aim of any empirical science is, admittedly, that of describing, understanding and explaining the behaviour of concrete events considered from a certain “point of view” and this, as we have seen, implies the selection of certain relevant attributes as the specific object of the inquiry. This first step is sufficient for the ascertainment of certain “regularities” in the occurrence of the events (the so-called empirical generalizations) but is not sufficient for providing an interpretation and an explanation of them. In order to fulfil this task a hermeneutic step is needed, that consists in the proposal of an abstract framework or Gestalt in which certain abstract objects are postulated whose mutual relationships and interactions are thought to causally account for the observed concrete regularities. I call this abstract framework a model of the empirical domain of investigation and a scientific theory can be understood as the explicitation and linguistic formulation of the content of this model. This notion of model is different from the one adopted in the semantic of formal systems, in which the model is defined as a non empty domain of generic entities on which the formal expressions of the language can be “interpreted.” According to this meaning, the model is something that is found after the construction of the formal system and is due to “satisfy” the formal system itself. According to my different meaning, the model is prior to

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the construction of the theory, let alone to the formal presentation of it, and the theory is, in the last analysis, a theory of the abstract model. According to this approach, the traditional “sentential view” of theories is not totally discarded, but its purport is limited: a theory can be seen as a system of sentences, but only because this is necessary in order to make explicit the content of the original Gestalt or model and put it to test. This is why the sentences of a theory have usually the form of laws of a different level of generality, depending on the fact that they express more fundamental or more detailed features of the model. To test a theory we need to determine at least one referential sentence, that is, a sentence that is entailed by its laws and contains only predicates that can be operationally connected with concrete entities, such that we can see whether the state of affairs referred to by the sentence actually obtains (that is, exemplifies the conclusion derived from the theory) or not. If the result of the test is negative, we cannot conclude (as it was maintained in the “received view”) that the theory is false, but only that it is more or less “inadequate,” and a closer scrutiny can bring us sometimes to see which laws of the theory should be reformulated in order to better express the intuitive content of the original Gestalt without clashing with the empirical results, sometimes to introduce certain modifications, additional details, or refinements in this Gestalt in order to cope with the “intended domain of referents” that should exemplify it. Only in certain extreme situations could we be led to the conclusion that the whole Gestalt must be abandoned, and this not for simply logical reasons, but for much more complex hermeneutic reasons.

2. Abstraction and Idealization In the above sketchy discourse I have often used the term ‘abstract’ but not the term ‘ideal’ and this may appear as a significant difference with respect to Nowak’s theory, in which abstraction and idealization are distinguished. The difference, however, is more terminological than substantial and mainly depends on the sense according to which we use the notion of abstraction. Nowak himself notes that abstraction is

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understood by many authors as a methodological move consisting in “leaving out of consideration” certain features or aspects of concrete entities (this is a widespread use of this notion, both in philosophy and in common language where abstraction often means “separation” and “to make abstraction from” something means to disregard this something), without recognizing to the result of this operation the status of an ideal model. For this reason he prefers to speak of idealization in order to stress explicitly this specific feature. I prefer to understand abstraction in a more traditional philosophical sense, according to which abstraction is a typical intellectual operation consisting in the formation of concepts that are universal and distinct from the individual representations offered by sense perception. In other words, I recognize a legitimate and specific role of the intellectual intuition and equate this essentially (but not exclusively) with abstraction. The products of this intellectual operation are qualified as “abstract entities.” This way of conceiving the products of abstraction, as Nowak notes, was also that of Marx and this is why he maintains that Marxian abstraction is in fact idealization. Therefore, in trying to rigorously formalize this notion, Nowak introduces an additional condition, that should serve to stress the difference between a purely “selective” abstraction and genuine idealization, namely that the entities defined by abstraction do not have concrete existence and in this sense be ideal. I agree with this remark but simply because the results of an abstraction (in the traditional sense that I share) are precisely concepts or intellectual constructions that are endowed with an intentional reality and not with a concrete reality. They encode properties or attributes but do not possess these attributes, that are exemplified in concrete things. For example, the concept of dog encodes several properties, such as that of barking, but it does not bark, whereas those animals that exemplify this concept do bark. After this clarifications it is easy to see that a complete agreement exists between Nowak’s position and mine: the role of his “abstraction” is equivalent to the procedure of “selection” of particular specific attributes that is the precondition for the determination of scientific objects according to my approach. This is only the first step or starting point. The second step consists in the conceptualization of these

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selected attributes which, in Nowak’s terminology, leads to “ideal” objects and laws, and in my terminology to “abstract” objects and laws. I would have no difficulty in calling them “ideal” (and occasionally I have done this in my papers) but for reasons that are slightly different from those of Nowak. If I understand correctly his position, he calls them ideal because they do not correspond to any “really existing” entity and, in this sense, they are false if applied to concrete reality (for this reason he requires that certain “idealizing conditions” explicitly indicating this fact be expressed). According to my view, these objects are ideal simply because they belong to a different ontological level with respect to concrete reality: they are intentionally real, they belong to the domain of concepts and sense and this entails ipso facto that they do not have the different ontological status of concrete things, independently of any special condition that should be formulated in order to stress this fact.

3. Encoding and Exemplifying. Sense and Reference There is, however, a difference between our positions that deserves some comments. In my position the ideal statements are in themselves neither true nor false because they belong to the domain of sense, while truth and falsity require that the additional procedure of reference be performed. To use a distinction already mentioned, ideal entities encode properties and relations that may or may not be exemplified in “concrete reality.” The notion of concrete reality, however, must be made precise and this may seem rather easy at first: for any scientific discourse we may consider as concrete reality its intended domain of referents. This solution, however, is still insufficient because we cannot rest on the vague intuitive apprehension of the “domain of things” we intended to study (for example, physical bodies, social events, economic phenomena, literary productions and so on) because even such large fields are investigated only “from a certain point of view,” that is, only regarding certain selected attributes. Therefore, we need to avail ourselves of certain referential procedures that link these selected attributes with the

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corresponding basics predicates of our theory. As indicated above, these are the operational procedures that play the role of criteria of referentiality and, for this reason, enable us, first, to exemplify the ideal concepts and, then, to test whether or not the empirical sentences containing them are also exemplified or not (that is, whether they are true or false). Therefore, the actually intended domain of referents is determined by the adopted criteria of referentiality, and its ontological status is also determined by them. In other words, “concrete reality” is not only the realm of physical things: according to the different sciences their concrete object of study can be the domain of mental phenomena, the dynamic of social events, the consistency of a philosophical work, the complex personality of a character in a novel. They are “real” but belong to different “kinds of reality” to which we have access through different criteria of referentiality. These remarks allow us to get rid of certain claims that are expressed in order to support an anti-realist view of science. Some people say, for example: scientific laws and theories lie because material points with no extension, rigid bodies, perfect gases, frictionless motions, elastic recoil, and so on do not exist and the laws and theories describing their properties and behaviour do not obtain in the real world. Such statements rest on the ignorance of the difference between encoding and exemplifying: the mentioned entities are ideal objects encoding certain attributes and as such belong to the ontological level of conceptual reality and not to the level of concrete reality; they express a sense and their reference can be established only by means of opportune criteria of referentiality that will enable us to see how and within what limits of accuracy they can also be exemplified within a specific “concrete” domain of reference. Only at this stage can we see whether the laws or theories lie or not. I think that Nowak would largely agree with these considerations though I find in his theory certain points that could bring to misunderstandings. More precisely, when he defines the notion of “idealizing assumption,” he requires that, on the ground of a given body of available knowledge, a propositional function p(x)=d is introduced and it is known that no object in the domain of discourse G concerned has the property p in the degree d. This is tantamount to

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saying that this propositional function is always false in G (similar conditions are posited in the definition of “quasi-idealizing assumption”). This definition enters also in the definition of an “idealizational law” and is also reinforced by the requirement that the equation F (x) = H (x) (which expresses the specific nomological content of the law as a consequence of the idealizing conditions) is not always satisfied by the objects of G. This way of characterizing idealizations could justify prima facie the claims of those who maintain that, to the extent that, as Nowak (correctly) says, “in advanced empirical sciences the formulation of idealizational laws is necessary,” these advanced sciences do not tell the truth about their intended domain of investigation. For this reason I would suggest that such requirements of non-satisfiability be dropped from the characterization of idealization since, in my view, they are already contained in the fact that idealizations simply encode a restricted and selected number of attributes and relations and, as such, could be referentially applied only to concrete objects totally and exclusively characterized by such attributes but this, as we have already seen, is never the case. Therefore, these requirements of non-satisfiability are only intuitively plausible, but cannot play a rigorous formal role because they cannot rely upon a precise condition of referentiality which, on the contrary, is manageable for those who Nowak calls “realistic assumptions” and “factual laws.”

4. Gradual Concretization The problem of linking idealizations with concrete reality, however, is not overlooked by Nowak, who has devoted to it an elaborated theory of “concretization.” Leaving aside a detailed presentation of this theory, we simply note that its spirit consists in remaining within the idealizational approach and producing a sequence of idealizations that are progressively more “concrete” in the sense of weakening the original idealizing assumptions, that is, by introducing the consideration of parameters that had been initially disregarded but whose significance becomes patent in order to understand and explain the facts of the

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investigated domain. Since the highest order of the ideal type entails the lowest degree of resemblance with the real objects, a weakening of the idealizing assumptions produces a decrease of the order of the ideal type and an increase of the resemblance with the real objects. Therefore, the performance of successive concretizations — be they strict concretization (direct or indirect), or approximate concretizations — corresponds to the proposal of introducing modifications or corrections in the original idealizational law without discarding it, that is, by rendering it in a way more complex (since additional parameters are introduced) and in another way less complex (since the number of its idealizing conditions is reduced). The preservation of the consistency between the different orders of idealization is secured by an appropriate “coordination principle” whose role is that of indicating what kind of “correction” is implied by the introduction of the new parameter with respect to the principal factor considered in the higher idealizational law. Needless to say, the different levels of law attained in the process of concretization still concern ideal objects belonging to different domains and these laws can be said to be “semantically true” in their models, without being “factually true” in the “real” model. This is an interesting feature since it indicates in Nowak’s perspective an independence of sense and reference: contrary to the logical-empiricist tenet, sense does not “come up” from observational evidence to theoretical constructions, but is already present in all the steps of the abstract or ideal hierarchy and offers the stuff for constructing ideal objects to which a particular notion of semantic truth is applicable. The contact with the “real world” occurs as a kind of last step in the process of concretization, namely when the sequence of the idealizational laws connected by the relation of strict concretization terminates with a factual statement, which is qualified as the final concretization of the original idealizational law. This development of Nowak’s theory is, again, fully in keeping with the “hermeneutic” approach to science and scientific theories I have outlined above and developed in some of my works. More precisely, I consider it as a notable formal explicitation of those views that I have only intuitively expressed by speaking of the original Gestalt that

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presides over the elaboration of scientific theories and that can undergo modifications and corrections of different degree of importance in the effort of coping with factual evidence coming from the study of the intended domain of referents. Nowak has convincingly stated how the “selected attributes” entering as constituents of this Gestalt can be made explicit through idealizing assumptions and connected by means of idealizational laws, and at the same time has offered a suitable formal framework for mastering the process of integration of new attributes in the Gestalt for making it more and more empirically adequate. Nevertheless, neither Nowak nor myself intend this fact in an instrumentalistic sense: we share the conviction that science aims at a true understanding and explanation of reality and that this is possible only by means of an intellectual penetration overstepping pure and simple empirical observation. Both of us are aware that explanation can only take place within a hermeneutic framework, that is, that interpretation is a prerequisite for explanation. He does not express himself precisely in these terms, but his making explanation a kind of natural outcome of subsequent concretizations (that produce subsequent idealizations, i.e., subsequent hermeneutic frameworks) has essentially this sense.

5. A Few Open Questions Still certain differences remain. One concerns the role of intellectual intuition that, in my view, is the source of abstraction and idealization. If one wants to overcome strict empiricism (as Nowak too certainly wants), one has to explain how we can select, among the numberless features of reality that empirical perception shows us, those that are salient and pregnant or, to put it differently, how we can adopt a particular “point of view” on reality that is certainly not comparable with a perceptual vantage point but corresponds to the capability of focusing on certain attributes of a general character that are estimated to be particularly significant. Nowak, as far as I could see, does not consider the importance of this intellectual intuition that is relevant not only to account for the genesis of idealizations (in this case it could

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be ignored with only minor disadvantages) but also for understanding the nature of idealizations, that is, the particular ontological status they possess. They are too important not to be considered “real,” especially if one maintains that science takes them as its specific objects, but what kind of reality is their? The answer that seems satisfactory is that they are intellectual entities, endowed with the specific ontological status of intentional reality. This makes them susceptible of objective investigation, of a discourse that can make claims of truth, without the condition that they must in turn be true of the concrete world. This ontological status, however, could bring to an idealistic or antirealistic conception of science (something that also Nowak does not want), unless a significant relation is established between this ontological region and the ontology of “concrete objects.” This is why I consider essential to understand that ideal objects encode a structured set of attributes that can be exemplified by concrete objects and I think that this relation is captured by the distinction between sense and reference. The ideal objects are structures of sense, but they are constructed with the aim of speaking of the concrete world, that is, they must be susceptible of a reference to the concrete world such that the concrete objects could be seen as acceptable exemplifications of the ideal objects. Such a reference is not immediate, and Nowak’s theory of concretization indicates how it can gradually be attained, but he does not avail himself of the notion of referentiality, and this leaves its treatment of the issue incomplete. In fact, even if an idealizational law receives a “final concretization” consisting in a “factual statement,” it remains unclear how we could qualify a statement factual. From the point of view of the sense, there is no distinction between a factual and an idealizational statement. The point of discrimination is that a factual statement is, in addition to having a sense, also directly referential. This condition, however, can be satisfied only if we have at our disposal certain non-linguistic and non-mental tools or criteria of referentiality that are linked with the attributes occurring in the factual statement. This is precisely the reason for which I have insisted on referentiality and operational criteria of referentiality in my approach, and I believe that this could be a useful integration to Nowak’s theory

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of idealization that could better substantiate his realist view of science without falling into the shortcomings of radical empiricism. By saying this I do not simply express a wish. In presenting his theory as a formal explicitation of the Marxian epistemology, Nowak summarizes the fundamental lines of this epistemology in two theses: (I) conceptual knowledge is acquired through abstraction and gradual concretization; (II) praxis constitutes the criterion of validity for conceptual knowledge. He declares that his goal is that of studying in detail point (I). The second point, however, is of not less capital importance not only for scholars who have taken inspiration from Marx, but in itself. In particular, I have not taken inspiration from Marx but one of the most fundamental of my claims is that operational standardized procedures are indispensable for granting the objectivity of scientific knowledge (both in the sense of allowing for intersubjective agreement among scientists, and of determining the reference of any science to its specific objects) and that they are those criteria of referentiality that serve to put hypotheses and theories to test (that is, to “validate” them, to use Marx’s expression). This is tantamount to saying that also in my view praxis is the means for validating knowledge, not according to an impoverished instrumentalistic sense, but in the deeper sense that thinking and observing are not sufficient for producing that “encounter” with concrete reality that could legitimate calling true (though only partially and relatively) a determined piece of knowledge. Therefore, my way of conceiving the role of operationality, strictly bound to theory, abstraction and idealization not less than to factual reality, can be considered as a good instantiation of what Marx understands as praxis, and this is an additional reason for thinking that Nowak and myself could find here additional ground of agreement.

University of Genoa Department of Philosophy Via Balbi, 4 16126 Genova Italy E-mail: [email protected]

Piotr Przybysz WHAT DOES TO BE MEAN IN LESZEK NOWAK’S CONCEPTION OF UNITARIAN METAPHYSICS?

The main ideas and concepts presented by Leszek Nowak in his work Being and Thought (1998) are the building blocks of his metaphysical system. The number of issues raised by this work is very vast indeed, including metaphysical reflections on being, some paraphrases of key propositions of classical metaphysics and polemics with their authors. This presentation cannot pretend to being comprehensive. After a general introduction, I will present an overview of being as one of the key categories in this metaphysics. My aim is a critique of the extreme negativist understanding of being presented by Nowak.

1. Metaphysical Positivism as a Common-Sense View about Being and Existence The metaphysical ideas presented by Leszek Nowak in Being and Thought (1998) are a critical reaction to the predominant trend in metaphysics, referred to as metaphysical positivism. This term is not used for a specific school in philosophy; nor does it denote the metaphysics as inspired by the views of A. Comte or R. Carnap. According to L. Nowak (1998, pp. 111-112ff ), metaphysical positivism is

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 315-324. Amsterdam/New York, NY: Rodopi, 2007.

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the most widespread thinking pattern in today's metaphysical discussion and rests on the following dogmas: (a) (b) (c) (d) (e) (f)

the dogma of a single world; the dogma of substantialism; the dogma of positivity of existence; the dogma of the positive character of all natural regularities; the dogma of multiple positive elements of the world; and the dogma of subjectivity of consciousness.

According to the proponents of metaphysical positivism, (a) there is just one world, viz. the one we live in. The world understood in this way, is (b) composed of things or derivatives of things: e.g. relations, attributes or facts. (c) Whatever exists is always positive; there are no negative facts. Thus, there can be nothing in the world that would not have a positive aspect. (d) Some positive aspects of the world trigger other positive aspects: if something exists and brings about something else then this other thing is also positive. (e) What exists positively, exists in multiplicity: the world consists of multiple things and facts superimposed over them. (f) We create images of fragments of the world understood in this way — they are mental representations, which can nevertheless be creative sometimes. Humans are thus capable of creating images of what need not necessarily exist, but of what is viable, desired or abhorred, that can form comprehensive visions projected in literature, painting or philosophy. L. Nowak’s aim is to provide a critique of such an approach and to supply a metaphysical alternative to it. According to Nowak, the mission of philosophy is to reject common-sense intuitions. The result of rejecting these dogmas is supposed to be a very radical metaphysical system, which is best called negativist metaphysics and which has been presented in depth in Being and Thought.

2. Basic Ideas of Unitarian Metaphysics The conception outlined in Being and Thought (Nowak 1998) stems from three basic ideas: attributivism, negativism and multi-worldliness.

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The Intuition of Attributivism. According to metaphysical positivism, the main metaphysical question “What is the fundamental ontological category?” has a straightforward answer: the category of an object. A philosophical justification for this point of view can be found as early as Aristotle’s Categories. In refutation of this standpoint, Nowak recalls the fact that there is no direct access to the object itself (what is directly available for perception are not so much objects, as impressions correlated with the attributes of objects). He pinpoints the difficulties of denoting objects by way of using verbal expressions: language does not venture beyond attributes. In itself it only indicates that a network of attributes exists — and nothing apart from that. (p. 123)

For this reason, Nowak accepts the view that the basic ontological category is that of an attribute. Unitarian metaphysics is thus an attributivist rather than a substantialist view. The Intuition of Negativism. Another crucial metaphysical question is whether everything that exists is positive. Metaphysical positivism provides a confirmatory answer. In light of what has been said, whenever we state something negative (“my eyes are not blue,” “I have no money”), what is negative stems from specific attributes of the language and reasoning. Especially language users may use empty names, false sentences and wander in their thinking away from judging facts to judging capabilities or possibilities. In other words, the source of negatives is not the objective reality but rather the subjectively and specifically human language and the meanders of thinking. Unitarian metaphysics adamantly rejects the ascription of negatives merely to language and thought. On this view, negativity is a part of reality itself, in which it plays a vital role. In a broader sense, negativity is part of being. According to unitarian metaphysics, being can be said to break down into a positive and negative component. The dichotomy of positive and negative is inherent to being itself, and prior to language or thinking. The intuition of that reality has negative components can be directly transposed onto the assumption of attributivism mentioned

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above. This results in the following hypothesis about attributes as the main components of reality: (i) each attribute has a positive and negative aspect; (ii) a positive occurrence of an attribute is matched by its opposite, i.e. its negative occurrence (“lack”); thus the opposite of a positive occurrence of an attribute is a negative occurrence and vice versa. (iii) the opposite of an occurrence of an attribute is not the same as logical negation (p. 127). The intuition of negativity acquires a technical meaning from other of Nowak’s concepts: opposition, complement and negation. Possible Worlds Hypothesis. One of the fundamental claims of metaphysical positivism is, according to Nowak, the belief that there is only one world namely the world we live in. Unitarian metaphysics, on the other hand, advocates the pluralism of worlds. It postulates that numerous worlds function alongside one another. Each of them contains objects of various categories, i.e. physical objects, material points, etc.

3. What does to Be Mean in Unitarian Metaphysics? The basic intuition can be expressed thus: (U) to be is to contain a certain lack, that is: to be is to contain a negative feature (pp. 249-250). This claim rejects one of the dogmas of metaphysical positivism, what Nowak calls Parmenides’ dogma. Indeed, both in common-sense thinking and in standard metaphysics, being is associated with positive occurrences, whereas lack or negatives (no money, not going to the theatre, etc.) is associated with the non-occurrence or the lack of being. Nowak replaces this positivist conception of being with his own negativist approach. I believe that, on the one hand, (U) contains a grain of truth about existence that coincides with our intuitions but that, on the other hand, if carried to its extreme, it implies an interesting though

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controversial philosophical standpoint, which contradicts commonsense intuitions. Nowak defines his technical concept of being through the concept of essentiality, which is grounded in certain relations among attributes. In general terms, an attribute A is essential to an attribute B if the fact that A adopts a certain value e x c l u d e s the fact that B adopts certain values (p. 250). Defining essentiality through the concept of exclusion is one of the most important, and at the same time the most characteristic, feature of the conception in question. The network of essentiality relations understood in this way forms the essential structure of an attribute (object, fact, world): its essentiality for other attributes consists in what it excludes in them, what it does not allow. It is assumed that an attribute can adopt positive, neutral or negative values. It is further assumed that if A is essential for B, A must adopt either a negative or a positive value. The measure of essentiality of A for B is the size of the area of exclusion for the occurrence of a positive value in B. This means that if an attribute adopts a positive or a negative value, another attribute cannot adopt a positive value any more. And due to the relation of opposition between negatives and positives in a given attribute, when B cannot adopt a certain positive value, it must adopt a certain negative value. In summary, when A is essential for B then: (1) A adopts a positive or a negative value; (2) the fact that A adopts a positive or a negative value precludes B from adopting a certain positive value; (3) since B is precluded from adopting a certain positive value, it is forced to adopt a certain negative value. The characteristic feature of L. Nowak’s view is that what influences reality is the adoption by an attribute of either a positive or a negative value. In other words, not only positives but also negatives have an effect on the world. In what way can this concept of essentiality be helpful in defining being? Unless I am wrong, the justification for (U) can be broken down into several argumentation stages, all of which are separate claims of unitarian metaphysics: (1) to be is to possess essence; (2) to possess essence is to possess a non-empty essential structure;

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(3) to possess a non-empty essential structure is to be in a relation with something else that exerts influence; (4) exerting influence is done by way of exclusion; (5) exclusion consists in the fact that a positive or a negative occurrence of an attribute precludes a positive occurrence of another attribute and forces a negative occurrence thereof. The adoption of the foregoing claims steers us clearly toward the conclusion (U). The first three premises in this argument are hardly controversial. However, premise (4), and especially (5), can raise doubts. It is exactly these claims, which underscore the special and original character of the concept of being advocated by unitarian metaphysics.

4. Can Standard Metaphysics Accept the Negativist Conception of Being? We might wonder whether there is really no place for the negativist concept of being in standard metaphysics. Not quite, I believe. For the negativist concept of being can be interpreted as a conceptualization of an idea that has always been present in the history of metaphysics, i.e. the idea that there are negative components in existence. If put this way, ontological positivism can connect with metaphysical positivism, that is with the belief that being is “tainted” by nature and only that exists which contains seeds of destruction. This old, pre-Socratean idea is the key to metaphysical negativism. If only what is complex exists in a natural way then nothing that is complex is eternal, and thus sooner or later it will disintegrate and pass away. It is thus that composition itself as well as its components are already the source . . . of decomposition and destruction. A deeper negativity may, of course, stem from negative features of some elements . . . , or from opposing features of elements from different groups . . . Ontological positivism is thus not incompatible with either metaphysical or ontological negativism. (Perzanowski 2002, pp. 479-480)

Regardless of how convincing the general intuitive claim about the mutual compatibility of positivism and metaphysical negativism may

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be (and the above formulation does seem credible and convincing), the issue that remains open is whether it is possible to reconcile particular claims of metaphysical negativism in their unitarian version with the positivist claims. A criterion for such reconciliation could be, for example, the degree to which claims (1)-(5), which are premises for the negativist thesis about existence (U), can be incorporated into metaphysical positivism. I believe that, on an intuitive level, Nowak’s concept of being need not be viewed as incompatible with metaphysical positivism. After all, Nowak’s view explains a phenomenon well known to and also partially conceptualized by the positivists (see, for example, Wittgenstein’s concept of “negative facts”). However, on the level of deep assumptions, the two views will be difficult to reconcile. It is clear that premises (1)-(3) could easily refer to a universe composed of positives. It might even be possible for a metaphysical positivist to accept claim (4) about exclusion as a mechanism through which essential relations between positive attributes are realized, which might in turn lead him to revise his own doctrine so as to present exclusion in positive terms, though admitting that it is “negative” in some sense. There is, however, no chance of incorporating claim (5) into positivism since, for one, this doctrine does not accept negatives as components of being and, moreover, it would not accept that negatives may actively participate in creating reality (that negative occurrences in a certain attribute might cause a lack of a positive occurrence in another attribute). The negativist conception of being also touches quite obviously on a certain old metaphysical issue. It is quite easy to see this account as a theoretical justification for the idea, known to Eastern philosophy and religion, that nothingness exists. It is also not difficult to see how challenging this view is for attempts at defining the Absolute exclusively in positive terms. In any case, instead of understanding nothingness in terms of a lack of being, as is usual, Nowak puts forward the opposite formula — that the existing being is the presence of nothingness. Nevertheless, I suppose, we could try to use at least a portion of Nowak’s ideas in standard metaphysics.

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5. The Moderate and the Extreme Versions of the Negativist Conception of Being The theoretical conflict between the two standpoints, the positivist and the negativist, is in addition aggravated by Nowak’s adoption of the extremely controversial claim on the gradation of existence (pp. 260262). It can be stated as follows: (6) Being admits of degrees: the more negatives in relation to the total number of situations there are, to the greater extent something exists. For example, a certain world can be described as “being in the k-th degree,” where k is the ratio of negatives that are present in this particular world to the total of its situations (Nowak 2003). And thus, according to Nowak, there are neither “complete worlds,” which would consist of positive situations only, nor “positive-neutral worlds,” which would consist of positive and neutral situations only, nor “neutral worlds,” which would consist solely of neutral situations, i.e. worlds in which nothing is excluded. These worlds cannot exist in negativist unitarian metaphysics. Only those worlds can exist that contain some negative situations, i.e. situations in which there is some exclusion and in which some attribute is forced to adopt a negative value. if a world exists, it means that it contains a certain essentiality structure. If, however, one attribute is essential for another in a certain world then, in this world, certain positive situations do not happen, viz. those from the exclusion area; ontic holes appear in place of all such excluded situations . . . This means that only those worlds exist that have some negative sphere . . . (Nowak 1998, p. 261).

Nowak claims further that there is a hierarchy, within which some worlds exist in a greater degree than others. In unitarian metaphysics, it is the so-called “non-worlds,” i.e. worlds that consist only of negative situations, that exist most fully. Worlds that are structurally closer to non-worlds exist to a greater extent than worlds that are structurally further removed from non-worlds. Undoubtedly, to propose this hierarchy of being is a fairly risky manoeuvre. It leads directly to the view, endorsed by Nowak (p. 293), that our world exists to a lesser extent than nothingness.

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The question we should ask at this point is whether the claims (U) and (6) are inextricably related or not. In other words, does the negativist hypothesis about being imply the idea of the gradation of being? I do not think so, and I believe that although the idea of the gradation of being is a striking and extreme addition to the original negativist conception of being, the latter does not imply the former. What the negativist conception of being does imply is the claim that only worlds that contain at least one negative situation exist. There is, however, nothing in this view that would force the claim that existence admits of degrees. We can thus distinguish two versions of the negativist conception of being: the moderate (though still radical in virtue of its acceptance of (5)) and the extreme version. The moderate negativist conception of being would be made up of claims (1)-(5), while and the extreme version would in addition accept claim (6). What is the point of making this distinction? Drawing the line between the extreme version of the negativist conception of being and the positivist metaphysics is worthwhile in itself, but it is also meant to pave an alternative path of the development of thought. However, it is also important for a given metaphysical conception what other proposals can take over from it and use for their own theoretical purposes. The quite original conceptualization of the intuition on the negativist sources of being proposed in unitarian metaphysics is worth studying even, or perhaps mainly, by positivist metaphysicians. Perhaps, it is they who will have to revise their own doctrine so as to take into account the negativist conception of being i n s o m e w a y . No metaphysical positivist could accept the claim that our world exists less than nothingness, while there may be who would accept the claim about the relevance of negative elements to being. It is to them that the moderate version of metaphysical negativism can be particularly appealing for they could easily, I believe, accept the majority of its claims. The same cannot be said of the extreme version. Whether this will happen remains to be seen but the opportunity for exchanging thoughts and intuitions between metaphysical positivism and negativism in itself is worthwhile.

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Uniwersytet im. A. Mickiewicza Department of Philosophy ul. Szamarzewskiego 89c 60-569 PoznaĔ Poland E-mail: [email protected]

REFERENCES CzeĪowski, T. (1948). O metafizyce jej kierunkach i zagadnieniach [On Metaphysics, Its Orientations and Problems]. ToruĔ: KsiĊgarnia Naukowa T. SzczĊsny i S-ka. Nowak, L. (1989). Some Remarks on the Place of Logical Empiricism in 20th Century. In: K. Szaniawski (ed.), The Vienna Circle and the Lvov-Warsaw School, pp. 375-390. Dordrecht: Kluwer. Nowak, L. (1998). Byt i myĞl. Tom 1 : NicoĞü i istnienie [Being and Thought. Vol. 1: Being and Existence]. PoznaĔ: Zysk i s-ka. Perzanowski, J. (2002). Pozytywizm i negatywizm metafizyczny [Metaphysical positivism and negativism]. In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, P. Przybysz (et al.), Odwaga filozofowania. Leszkowi Nowakowi w darze, pp. 477-495. PoznaĔ: Wydawnictwo Naukowe Humaniora.

Roberto Poli FORMAL AND ONTOLOGICAL ROUNDABOUTS

1. Introduction Nowak’s intellectual creativity and ability to develop his ideas systematically are among the strongest of his talents, as evidenced by his renowned theory of idealization. One wishes him the same success in his new scientific enterprise, that of unitarian metaphysics. In this paper I shall only consider a few formal and ontological (that is rational or categorical) aspects of metaphysics (Hartmann 1935; 1952). To date, my exposure to unitarian metaphysics has been rather limited. I may therefore have missed something essential to it. Further discussion will help clarify any missing ideas or misunderstandings. The history of Western science (inclusive of ontology, as one of the sciences) shows that the passage from any local theoretical framework (i.e. from the theory of some kind of phenomenon – physical, chemical, economic, legal or whatever), or from general methodological theories (as for the idealizational understanding of science) to metaphysical (ontological) ones, is beset by difficulties. In fact, metaphysics magnifies any possible categorical weakness present in the source theories. Insofar as unitarian metaphysics is (also) a generalization of the idealizational understanding of science, it proves that the latter suffers from a number of deficiencies. Unfortunately, however, unitarian metaphysics seems to have problems of its own.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 59-115. Amsterdam/New York, NY: Rodopi, 2007.

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2. A Few Basic Data Let me summarize the basic steps of unitarian metaphysics. Let X be an object, and P a set of attributes (properties); P is subsequently divided into two subsets, S and ¯ S . S is the space of attributes of X: each point of S represents an attribute possessed in some degree by X. ¯ S is the set of attributes not possessed by X. Basically, ¯ S is the complement of S with respect to P. ¯ S may therefore be represented as P – S. Attributes pertaining to the set S are termed positive, and attributes pertaining to P – S are termed negative (cf. Nowak 1997). We shall shortly see that a serious problem lurks in this apparently unproblematic setting (see section 4 below). Objects and attributes are not on a par. The latter, in fact, play a deeper and more substantial role than the former. Attributes are the basic building blocks of unitarian metaphysics, whereas objects are subsequent and derived from attributes. In short, objects are collections of attributes. So far, the theory’s general framework is classical enough. Its underlying formal model is basically set theoretic, with points understood as attributes. An object is a bundle (set) of attributes. Basic attributes (“points”) are simples, by which is meant that they are not composed of other attributes. The only serious departure from other set-theoretic understandings of metaphysics is the further requisite that points (basic attributes) should vary in intensity. Different objects are therefore distinguished not only by different attributes but by the intensity (degree) of their attributes as well. Objects with the same attributes but different degrees of intensity are different objects. The point is relevant because intensity is the crucial aspect of Nowak’s understanding of modalities. Possible objects, in fact, are given by variations of intensity. More precisely, an object XĻ is (merely) possible relative to X if (1) both X and XĻ share the same set P of attributes, and (2) XĻ possesses at least one attribute to a different extent from X. Possible worlds are collections of objects grounded on the same set of attributes and distinguished by the latter’s different intensities. A clear understanding of the idea of intensity is therefore mandatory for precise development of the modal part of the theory.

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3. Intensities Given Nowak’s otherwise classical formal framework, I confess I am bewildered by the above idea of simples that can vary. I do not see how Nowak can harmonize this aspect of his theory with his formal framework. According to the latter, all the variability one may think of requires and depends on some structure, i.e., it requires and depends on some complex. I am not against the idea of thick atoms, which is the idea of basic elements (“simples”) endowed with a rich structure. Recent formal developments, as in the case of synthetic differential geometry, provide substance for the claim. Among the many outcomes of synthetic differential geometry, it will be recalled that a new, original and highly interesting theory of the continuum derives therefrom. There is nevertheless a price to be paid (providing it is a price), namely the failure of the principle of the excluded third.1 A different and much easier way out is to consider intensities as atoms, and attributes as types (sets or classes). Thus, attributes become collections of intensities, and the difference between attributes and objects is that the latter are collections constituted of atoms, so that every atom belongs to a different class of intensities (each is the representative of its equivalence class). This picture is thoroughly set theoretic. On the other hand, Nowak’s explicit claim that attributes are simples seems to rule out this interpretation. As a matter of fact, one discerns an underlying indecision between the two interpretations that I have put forward. In the rest of the paper, I shall no longer consider the problem of the intensity of being. Henceforth, attributes will be interpreted as basic items, with no internal variation.

1 Bell (1998) is a philosophically oriented elementary introduction to synthetic differential geometry. Schuster, Berger and Osswald (2001) explores new formal theories of the continuum. The thin-thick terminology is due to Albertazzi (2002). The ontological and formal problem of thick points and its link with process semantics are discussed by Poli (2004).

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4. Negatives Returning to the other main points of the theory, I am also perplexed by the concept of a “negative attribute.” Providing that my understanding is correct, the concept of a “negative attribute” appears to be interpreted in two different ways. According to the first interpretation, a negative attribute is an attribute which an object does not possess. According to the second interpretation, a negative attribute is the complement of a positive attribute. The two interpretations are patently different. The former claims that an object lacks an attribute, the latter that an object possesses an attribute, which is the complement of another attribute. The understanding of “negative” seems to waver continuously between the two readings. Further analysis of the second of the just mentioned interpretations might be helpful. In short, the “complement” interpretation claims that the difference between positive and negative attributes is the same as the difference between concave and convex, or between a temperature of say 15° above or below zero. Both cases (the so-called positive and the so-called negative) are perfectly determinate and are termed positive or negative only (well, mainly) by convention. The distinction between conventionally positive and conventionally negative attributes can be traced back at least to Kant (1763) and does not raise any major ontological problem. In fact, the above separation between a positive and a negative side of attributes is simply not well-grounded from an ontological viewpoint: in both cases one is dealing with one and the same attribute, seen from different viewpoints or considered in respect to a conventionally established point-zero. The conclusion is therefore that in such cases there is one and only one attribute (call it temperature or curvature or whatever). Unitarian metaphysics does not admit more than one actual object with the same attributes. We are therefore forced to conclude that two objects composed of the same set of attributes can be distinguished only if the degree (intensity) of at least one attribute is different (thus distinguishing actual from possible objects) or if at least one attribute is positively possessed by one object and negatively possessed by the other.

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From what we have just seen, it is clear that this interpretation of attributes views them as types (or classes) whose elements may be divided into two subclasses, termed positive and negative. I have already pointed out that unitarian metaphysics does not seem willing to accept the idea of attribute as class. We have nevertheless found different paths in that direction. The troubles encountered by the interpretation of a negative attribute as complement of a positive one suggest reverting to the other interpretation, i.e. to the idea of negative attribute as lacking attribute. The idea of considering objects not only from the point of view of the attributes that they have, but also from the point of view of those they lack seems promising. Let us explore the following hypothesis: Thesis of Maximality Objects are maximal entities. Given the set P of the world’s attributes, any object is composed of all attributes, either in positive or in negative. Let us consider the following trivial example. Let P be {a, b}. The world grounded on P may contain four non-equivalent objects: ab, ab ¯, ¯ ab and ¯ a¯ b . ab is the top, what Nowak calls “transcendental object.” It is positively composed of all the world’s attributes. ¯ a¯ b is the bottom, the null object, the maximum reduct, the object negatively composed of all the world’s attributes. ab ¯ and ¯ ab are, let’s say, normal objects, that is, objects composed by both positive and negative attributes. A few comments are in order. If the above interpretation is correct, negative attributes do not play any role whatever. Inclusion, as customary, is governed by positive attributes alone. The only exception is bottom, understood as an element of everything. It is well known that accepting the bottom simplifies calculation and helps generalization. If its metaphysical legitimacy is nevertheless questioned, other choices are available, as for mereology. Trivial though it may be, the example is valuable in that it provides needed evidence in favor of a conclusion that is not apparent in Nowak’s writings: the formal structure underlying unitarian metaphysics is lattice theory.

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5. Holes and Other Vagaries From the above conclusion, it follows that the extensive talks about ontic holes (Paprzycka 2000) lose much of their interest, as it should be. In fact, there is nothing negative in P – S. It is a set like any other. Moreover, bundles do not have holes. The latter arise only if more complex structures are considered. A little Aristotle may be of help here. The idea of ontic holes, or lacks, may require what Aristotle called “by nature.” An object may only lack something that by nature it should possess and for some reason it actually does not have. Humans do not lack the attribute of being iron-made because being iron-made is not part of their nature. However difficult it may be to set out the concept of “by nature” precisely, it nevertheless provides a hint as to where the problem lies. All the problems discussed thus far converge on the question as to which formal framework is best suited to ontological analyses.

6. Dynamics The problem addressed by the previous section calls for a theory of both wholes and of levels of reality. The “by nature” requisite, in fact, requires a given structure (whole) at a certain level of complexity and energy. Aristotle discussed the “by nature” requisite in his theory of wholes. The questions concerning the theories of wholes and their parts and of the levels of reality are highly intricate and I cannot deal with them in any detail here (but see Poli 2001ab). I restrict myself to making the following point. A level of reality may comprise different kinds of dynamics. One may subsequently distinguish between (a) dynamics relative to the unfolding of reality, i.e. those relative to processes internal to a stratum of reality which lead to realization of its possibilities, and (b) dynamics relative to the potentiation of the level, i.e. those relative to processes among strata of reality by which a higher level emerges from a lower one. The terminology is very close to that adopted by Nowak himself. Prima facie, I do not regard this as a mere lexical coincidence. On the other hand, a few scattered notes by Nowak

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seem to imply that he has trouble with the theories of both wholes and of levels of reality and prefers to follow a different route. Not having enough information, I am forced to leave the situation unresolved.

7. Codimension We saw earlier that elementary algebra provides the basic formal structure of unitarian metaphysics. For my part, I simply do not believe that lattices are basically everything that metaphysics has in store. As soon as the general framework is made more flexible, new possibilities emerge. Let us seriously maintain that P is a space of attributes. The latter may therefore be considered the dimensions of P. In every space – let us say of dimension n – sub-spaces of smaller dimension are discernible. For instance, a three-dimensional space comprises not only three-dimensional objects but also twodimensional objects (planes), one-dimensional objects (lines), and zero-dimensional objects (points). This much is obvious. Let us now relativize to a base the concept of dimension. One may therefore say that a plane is a 2 dimensional base in a 3 (or more) dimensional space. We define as the codimension of a base the difference between the dimension of the environment space and the dimension of the base. In Nowak’s terms, positive attributes form the base’s (the object’s) dimension and negative ones form its codimension. If the base consists of a plane in a three-dimensional environment space, its codimension is 3 – 2 = 1. If instead the base is a line in a threedimensional environment space, its codimension is 3 – 1 = 2. The important point is that there are situations in which the codimension of a base yields fundamental information, more important than the information provided by its dimensions. The following elementary example may be helpful. Consider a geographical map (i.e. a two-dimensional model) and assume that we wish to cross a boundary on it. In geographical maps, boundaries are drawn as lines – that is, they are one-dimensional objects. In this case, the codimension of the event “crossing a

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boundary” is given by 2 – 1 = 1. The same situation can be modeled in more concrete terms. Let the environment space now be a threedimensional physical region so that crossing a boundary is like passing through a door – that is, a two-dimensional surface. In this case too – and this is the interesting point – the codimension of the phenomenon “crossing a boundary” is the same, because we have 3 – 2 = 1. If we then add a temporal dimension, the environmental space becomes four-dimensional, while the boundary becomes three-dimensional (the two dimensions of the door plus time). And once again the crossing is one-dimensional: 4 – 3 = 1. This radical and rather crude example (from which many technical details have been omitted, for example exact specification of what a base is) shows that what characterizes a considered phenomenon is not the dimension of the environment space, nor that of the relevant sub-space, but the difference between their dimensions. Given that what remains constant in the multiplicity of constructable models is the codimension of the phenomenon, we may ignore the specificity of models and concentrate on the codimension of the phenomena under scrutiny. From an ontological point of view, this finding strikes me as of considerable importance. It tells us that the phenomena being modeled display symmetries (or, if one prefers, invariants) which are independent from many positive details of its models. Negative information may be deeper than any positive information (but note how seriously misleading the terms ‘positive’ and ‘negative’ are!). At bottom, the above example tells us that objects have an intrinsic hardness and are therefore not the fruit of our projections.

8. Adjoints “Reductions” and “transcendentalizations” are straightforward procedures: minus one or plus one attribute, and iterations thereof. Apart from terminological infelicities, the idea behind them is clear enough. I think it is a basically correct idea. Unfortunately, Nowak’s reliance on elementary algebra has the effect of trivializing the idea. To make its yield apparent we are compelled to adopt a richer environment.

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The mathematical theory of categories may provide a way out. Let me consider only the simplest example, namely the connection between the category of topological spaces (T) and the category of sets (S). These two categories may be linked by a functor, going from spaces to sets, F: T → S. The functor F is called a forgetful functor, because it “forgets” structure. Given any topological space T*, the forgetful functor applied to T* gives its underlying set, that is, the collection of its points deprived of their opens. Rewriting what I have just said in Nowak’s own terminology, any application of a forgetful functor provides the reduct of a structured collection of items. The question now becomes: what about transcendentalization? From a mathematical viewpoints, Nowak’s transcendentalizations are cases of lifting functors, i.e. of functors adding structure. It is easy to realize that the problem now becomes: which structures should be added? The great advantage of category theory is that it studies connections between functors. To cut a long story short, forgetting and lifting functors are connected by special relations (called ‘adjoints’). More precisely, as far as our example is concerned, the forgetful functor between T and S has both a left and a right adjoint: the former assigns to each set its discrete space, the latter its co-discrete space. In other words, the former assigns to a set S its most disconnected space, the latter its most connected space. This proves that there may be different lifts (transcendentalizations, in Nowak’s terms) from a set to the spaces based on it. Adjunctions are everywhere in mathematics. To provide a couple of logically oriented examples, quantifiers and modalities can both be seen as cases of adjunction. The situation may sometimes be iterated, adding more and more structure to initial items or forgetting more and more structure from complex items. Further details require rather heavy technicalities, because compatibility conditions (called coherence conditions) among the various operations should be properly specified. Technicalities aside, what really matters is that category theory provides the formal environment for studying the relationships between reductions and transcendentalizations.

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Contemporary mathematics provides the tools for exploring the characteristics of the far from trivial operations of passing from simple to complex structures, and vice versa. Unitarian metaphysics (and, for that matter, the methodology of idealization as well) is still mainly based on trivial mathematics. The problem is not that elementary algebra is wrong. Obviously, it is not. The point is that elementary algebra is too poor and too rigid a tool for ontological analysis. In fact, I see no reason for holding that the basic structures of reality rely on or instantiate the simplest aspects of elementary algebra. Full-fledged ontology requires more powerful and more flexible conceptual and formal environments.

University of Trento and Mitteleuropa Foundation 41 Venice square 38100 Trento Italy E-mail: [email protected]

REFERENCES Albertazzi, L. (2002). Continua. In: L. Albertazzi (ed.), Unfolding Perceptual Continua. Amsterdam: Benjamins. Bell, J. (1998). A Primer of Infinitesimal Analysis. Cambridge: Cambridge University Press. Hartmann, N. (1935). Zur Grundlegung der Ontologie. Berlin: W. de Gruyter. Hartmann, N. (1952). The New Ways of Ontology. Chicago. Kant, I. (1763). Versuch den Begriff der negativen Grössen in die Weltweisheit einzuführen. In: Werke, vol. 2, pp. 779-819. Wissenschaftliche Buchgesellschaft: Darmstadt, 1968. Nowak, L. (1997). On the Concept of Nothingness. Axiomathes 8 (1-3): 381-394. Paprzycka, K. (2000). Idealization in Unitarian Metaphysics. Axiomathes 11 (1-3): 7-19. Poli, R. (2001a). The Basic Problem of the Theory of Levels of Reality. Axiomathes 12: 3-4. Poli, R. (2001b). Alwis. Ontology for Knowledge Engineers. Ph.D. Thesis: Utrecht.

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Poli, R. (2004). Process Semantics. In: M. Weber (ed.), After Whitehead: Rescher on Process Metaphysics, pp. 267-288. Frankfurt: Ontos Verlag. Schuster, P., U. Berger and H. Osswald (2001). Reuniting the Antipodes – Constructive and Nonstandard Views of the Continuum. Dordrecht: Kluwer.

Jan WoleĔski METALOGIC AND ONTOLOGY

This paper discusses some ideas from Nowak’s book Being and Thought (1998). The main concern of this massive philosophical treatise is to curb the “anti-metaphysical aggression” coming from the side of postmodernism. He argues for a radical philosophy in the fight against the excesses of contemporary anti-metaphysical attitudes. Generally speaking, the radical philosopher has nothing against the rejection of natural intuitions, provided that these are not fulfilling the philosophical needs that stem from philosophical experience. Nowak also considers philosophy as thematically prior to any other intellectual activity, including science. His unitary metaphysics is a reflection of this attitude as applied to philosophy and its tasks. Furthermore, he contrasts unitary metaphysics with standard metaphysics, which takes a more traditional point of view. I agree with several Nowak’s metaphilosophical views such as a belief in the power of analytical methods and in denying that metaphysical ideas that are commonplace are, therefore, automatically true. However, there are also important differences between us. I do not believe in the priority of philosophy over other intellectual performances, I see no reason to maintain that there is a particular philosophical experience and I have a more epistemological standpoint in philosophy. The negation of the priority of philosophy is particularly important when considering its

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 337-351. Amsterdam/New York, NY: Rodopi, 2007.

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relation to logic. Nowak writes that “philosophy is needed for interpreting logic, but not inversely” (p. 76). I do not claim that logic is necessary for philosophical interpretation, because this postulate would be clearly unwise and at odds with many philosophical enterprises. My view is more careful and runs like this: logic is (at least, sometimes) useful in the clarification of philosophical problems, including those that come from natural intuitions. My task in this paper is to make few remarks on unitary metaphysics and standard metaphysics from a logical point of view. Since, in my view, metalogic plays a prominent role in contemporary philosophical applications of logic, I will employ some metalogical concepts and results. Using a simplified scheme of phenomenology, I differentiate between metaphysics and ontology. Roughly speaking, the latter considers pure possibilities, but the former investigates their realizations. If one says that the world consists of individuals, he or she proposes an ontological thesis. On the other hand, a statement that individuals are material bodies or spiritual souls is metaphysical in character. Nowak’s opus magnum contains ontological as well metaphysical theses. Since logic and metalogic rather than metaphysics motivate ontology (hence, the former can be qualified as formal), my further remarks concern the ontological content of Nowak’s theory or, more modestly, some elements of negativistic unitary metaphysics. Anticipating the outcome, I will try to show that the theory of logical models supports standard metaphysics more than unitary one. Nowak (p. 111, p. 439) characterizes standard metaphysics through the following theses (the author labels them as “dogmas”): (A) The thesis about uniqueness of the world: the world is one and everything that exists, belongs to it; (B) The thesis about substantiality of the world: the world consists of things; all properties and relations are defined on the set of things; (C) The thesis that existence is positive: everything what exists is somehow determinate;

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(D) The thesis about the positive character of regularities: some phenomena (that is, things having some qualities) influence other phenomena; (E) The thesis about plurality: there are many things located in time or space; (F) The thesis that consciousness is subjective: people are suitable qualified to make representations of the world. The theses (D) and (E) are not subjected to ontological analysis; they are metaphysical claims. In order to consider (F) in an ontological scheme related to metalogic, we should reformulate this thesis. We can do that by interpreting representations as sets of accepted sentences. Assuming that these sets are consistent or can be modified in order to avoid inconsistencies, the objects of representations become models in the logical sense, because every consistent set of sentences has a model (the Gödel-Malcev completeness theorem). Consequently, inconsistent sets of sentences do not represent anything or they are defective representations. This view immediately leads to the important question of how logical models as set-theoretical structures are related to the world, but I will not consider this problem, except a few remarks in the last part of the present paper. Let L be a formalized language of the first-order. That L is firstorder (elementary) offers the simplest assumption and, moreover, enables us to apply the best-defined and clearest metalogical properties. The alphabet (AL) of L consists of following categories of expressions: (a) possibly denumerably infinite set of individual variables x1, x2, x3, . . . ; (b) a countable (denumerably infinite, finite or empty set) of individual constants a1, a2, a3, . . . ; (c) a countable (denumerably infinite, finite or empty) set of function letters f1, f2, f3, . . . ; (d) a possibly denumerably infinite set of predicate letters P1, P2, P3, . . . ; (e) logical constants: propositional connectives and quantifiers. Since a closer syntactic description of L (in particular, the definition of L-formulas), is not relevant for my further remarks, it will be skipped. The only important thing to note is that L is a set of sentences. L is considered as formalized, but interpreted in a referential way. This means that semantical relations express the relationships between language and the world. The word ‘world’ should be understood cum

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grano salis here (see above). In fact, we are thinking about a domain of objects, the properties of objects and the relationships between objects (these properties are defined over the domain). Our first task consists in defining the concept of interpretation of L. This will be done in two stages. First, we show how to interpret the alphabet AL and, then, we pass to L as a set of sentences. We also assume that the logical behavior of logical constants is already established. Hence, it remains to work with individual variables, individual constants, function-letters and predicates. We think about variables as representing objects, about individual constants as names of concrete objects (individual), functions-letters as names of functions, unary predicates as referring to properties, n-ary predicates (n • 2) as referring to n-relations and quantifiers as functions of a kind. An interpretation of L is determined by a structure (a relational system) ℜ = ¢U, a1, a2, . . . , f1(1), f1(2), . . . , fi(j), P1(1), P1(2), . . . , Pi(j), . . . ² where (a) U is a non-empty (no other condition is imposed on cardinality, that is, U can be finite, denumerably infinite or uncountable) set of objects (the carrier of interpretation, the universe of discourse); (b) for every i (i = 1, 2, . . . ), ai ∈ U (we say that ai is a distinguished element of U); (c) for every i, j (i, j = 1, 2, . . . ), fi: U × . . . (i-times) × U ⎯⎯⎯→ U, that is, fi is a function which maps the Cartesian product of U taken i-times into U; and (d) for every i (i = 1, 2, . . .) Pi ⊆ U × . . . (i-times) × U. Intuitively, any object of the type Pi(j) is an i-ary relation defined on U; according to earlier explanations concerning ALFOL, the sets defined in (a) and (b) can be empty, contrary to the set {P1, P2, P3, . . . } of predicates. If i = 1, Pi ⊆ U and can be called a property (more strictly: a property extensionally interpreted). Although U is not empty, we should not exclude the empty property to be identified with the empty set ∅. Since ∅ is a subset of any set, every universe allows the empty property. Incidentally, this case is a good illustration of the difference between extensional and intensional interpretation of properties, because the predicates ‘ . . . is a round square’ and ‘ . . . is the greatest standard natural number’ have different meanings (intensions), but actually refer to the same set, namely the empty set. Hence, we have many

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intensional properties corresponding to one extensional. Thus, these properties, which are co-extensive are not distinguishable from the extensional point of view. Hence, ∅ is termed as ‘the empty property’, not ‘an empty property’. The structure ℜ is suitable for an interpretation of L, if both are similar, that is, their signatures are coherent (this is an informal label; technically, signatures are similar or not, but I do not enter into details and present some rudiments only). We know in advance something about L, for example, that it distinguishes (or not) some individual constants or has predicates of such and such number of arguments (the number is called ‘the arity’); if a predicate has n-arguments, we say that it is n-ary (note that the index i in explanations of denotations of function letters and predicate letters concerns arities; this is confusing and, therefore, the exact characterization of function (predicate) letters as well as their denotations requires two indexes: one referring to the place in the suitable sequence and second referring to their arities). The interpretative structure ℜ must be coherent with the alphabet in the sense that if L distinguishes some constants and has predicates of a kind, ℜ should contain corresponding entities, for example distinguished individuals and n-ary relations. Details are provided by the content of the sets {a1, a2, a, . . . } and {P1, P2, P3, . . . }. Technically speaking, this decides the signature of language L (I sketch here only some rudiments). Assume that we have two individual constants a1 and a2, one unary predicate Pi and one binary predicate Pj. This language has the signature ¢0, 0; 1; 2² (it is customary to designate constants by 0 and predicates by numerals expressing their arities). If we are told that this sequence is a signature of a language, we know that this language has two constants, one unary predicate and one binary predicate, although we do not know anything concrete about related constants and predicates. However, we also know that a proper structure for our language must have at least signature ¢0*; 1*; 2*² (asterisked numbers indicate signatures of interpretations), that is, contain at least one distinguished constant, one unary predicate and one binary predicate. Why “at least” and not “the same”? The answer it that we do not exclude the situation that two (or more) constants name the same objects and two (or more) predicates refer to the same

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property or relations. Perhaps an example will make these explanations more transparent. Let L has {‘Socrates’, ‘Plato’, ‘Aristotle’} as the set of constants and {‘is a philosopher’, and ‘is the teacher of ’} as the set predicates. Assume that we do not know anything about denotations of particular expressions. We know only that the signature of L is ¢0, 0, 0; 1; 2². Looking for interpretation of L we can consider structures with signatures ¢0*, 0*, 0*; 1*; 2*², ¢0*, 0*; 1*; 2*², and ¢0*; 1*; 2*². If our interpretation is to be historically faithful, the structure should have the signature ¢0*, 0*; 1*; 2*², because the constants ‘Aristotle’ and ‘Plato’ refer to the same person. Now, if the interpretative structure had no binary relation, the sentence ‘Socrates is a teacher of Plato’ could not be interpreted by it. The above considerations suggest that three different parameters are involved in every interpretation, namely AL, ℜ and a correlation between them. The last element is displayed by a valuation function V, which ascribes semantical values taken from the structure ℜ to expressions taken from AL. Since the structure ℜ is a fairly complicated set, it is convenient to convert it into a family of sets: ℘AL-ℜ = {U, { a1, a2, . . . }, {f1, f2, f3(, . . . }, {P1, P2, P3, . . . }} The notation ℘AL-ℜ indicates that the set in question is related to the alphabet AL (of L) and the structure ℜ; we can assume that ℘AL-ℜ has the same signature as ℜ. Formally speaking, an interpretation ℑ is the triple ¢L, ℘AL-ℜ, V², where V: AL ⎯⎯⎯→ ℘AL-ℜℜ. More specifically, we have: (Val) (a) VVAR: VAR ⎯⎯⎯→ U; (b) VCO: CO ⎯⎯⎯→ {a1, a2, a3, . . . }; (c) VFUN: FUN ⎯⎯⎯→ {f1, f2, f3, . . . }; (d) VPRE: PRE ⎯⎯⎯→ {P1, P2, P3}. Thus, variables are mapped into U, individual constants into the set of distinguished elements, function-letters into functions, and predicates into suitable (according to the number of members) properties and relations. If AL has no constants or functions, the mappings defined in (Valb-c) above are empty. The function V is neither injective nor surjective. That V is not injective provides a formal reason why signatures of AL and ℜ can be different.

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Now, we are prepared to define the context V([. . .], ℑ) (to be read “the value of an expression [. . .] according to the interpretation ℑ”). It is done by: (DfV[. . .]) (a) V(vi, ℑ) = ui, where ui ∈ U; (b) V(ai, ℑ) = ai; (c) V(fj, ℑ) = fi; (d) V(Pi(j), ℑ) = Pi. The interpretation of AL does not determine the truth-values of sentences (and the semantical interpretation of open formulas), although it is an essentially contribution to this issue. Thus, we need to have the concept of truth at our disposal. Since we assume classical logic, we have that for any A ∈ L, V(A, ℑ) = 1 (truth) or V(A, ℑ) = 0 (falsehood). We now arrive at the point which requires the concept of a model is to be introduced, because truth is always relativized to a model. Intuitively, a model of a language is a structure in which sentences of a given L have logical values, that is, they are true or false. Another way of speaking about models consists in regarding them as structures in which some subsets of L are true. Language as the whole cannot entirely consist of true sentences, because if it contains negation and satisfies the principle of bivalence, it must at least have true sentences as well as false sentences. Hence, if model of a set X of sentences is defined as a structure in which all elements belonging to this set are true, languages in their integrity could not have models. The definition is as follow: (M) A model of X is structure Ÿ = ¢U, a1, a2, a3, . . . , P1(1), P1(2), . . . , P2(1), P2(2), . . . , Pi(j)² such that for every A ∈ X, Ÿş A (means: ‘A is true in Ÿ’). Now we should define the concept of truth. I will not do that in the most abstract manner. Let us restrict ourselves to so-called canonical models, that is, structures in which every object has its own individual name (this enables us to avoid an appeal to the concept of satisfaction). The standard model of arithmetic of natural numbers is an example here, because every numeral is a name of a suitable number. If the

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model ƻ is canonical, we do not need to consider open formulas, because for any formula of the type P (x1, . . . , xi), we have a corresponding sentence P (a1, . . . , ai) in which no term is a variable. For simplicity, I limit the task to unary predicates and ignore the function letters. The definition is as follows: Ÿşℑ P(a) if and only if a ∈ P; Ÿşℑ ¬A if and only if Ÿ not-şℑ A; Ÿşℑ A ∧ B if and only if Ÿşℑ A and Ÿşℑ B; Ÿşℑ A ∨ B if and only if Ÿşℑ A or Ÿşℑ B; Ÿşℑ A Ÿ B if and only if Ÿ not-şℑ A or Ÿşℑ B; Ÿşℑ A ⇔ B if and only if Ÿşℑ A and Ÿşℑ B or Ÿ not-şℑ A and Ÿ not-şℑ A; (g) Ÿşℑ ∀xA(x) if and only if Ÿşℑ A(x), for any every formula A(x/a); (h) Ÿşℑ ∃xA(x) if and only if Ÿşℑ A(a), for some formula A(x/a).

(T) (a) (b) (c) (d) (e) (f)

These points state that: (a) a formula of the type P (a) is true, provided that the objects named by the constant a belongs to the set P; (b) negation of a sentence A is true, provided that A is not true; (c), (d), (e) and (f) repeat semantical rules of propositional calculus for disjunction, implication and equivalence; (g) the universal sentence is true, provided that the formula A(x) becomes true under all substitutions of the variable x by individual constants; (i) the existential sentence is true, provided that the formula A(x) becomes true under some (at least one) substitutions of the variable x by individual constants. (T) as well as the full Tarskian definition via the concept of satisfaction show that truth is independent of valuations of free variables. This means that truth (relative to an interpretation) is dependent of how matters look in the domain taken as the basis for ℑ. Accordingly, we can say that if Ω is a model of A, then V(A) = Ω. This means that truth of a sentence is the mapping of this sentence into its model. What are sources of interpretations of L? According to the above description, we only know that the signatures of L and ℜ should be coherent, and that the carriers of relational systems must be nonempty. Of course, if AL contains a binary predicate P, but ℜ has no

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binary relation, this structure does not generate an interpretation of this predicate. In fact, no other general constraints are imposed on interpretations. In particular, the denotations can be freely ascribed to expressions of L. However, one should see that there is a difference between valuations of variables and valuations of other expressions. Different valuations of variables do not exceed the same language and its interpretations. Other expressions function as individual constants or parameters (function letter and predicate letters), not variables. Suppose that we consider a unary predicate P. We can ascribe an arbitrary subset, let say U1, of U as its denotation in one act of interpretation, but another set, let say U2, can serve as the value of P under another interpretation. Now, if languages as conceived as the pairs consisting of expressions and their interpretations, two different interpretations provide different languages. For instance, if our language contains the predicate ‘is blue’ one interpretation consists in ascribing the set of blue objects, but another can take the set of green objects as its denotation. Both cases generate different languages, because they appeal to different interpretations. These remarks show that we should clearly distinguish between formal languages, that is, languages without any interpretation and formalized languages, that is, languages with arbitrary but established interpretation. We can now return to theses (A)-(F) as characteristic for standard metaphysics. The only important assumption concerning the cardinality of U points out its non-emptiness; eventually, we can work with free logic as our formal basis, but I will not exploit this possibility. The characterization of ℑ does not determines links between objects defined on U, in particular, properties and relations. If we look at, for example, two subsets, let say, U1 and U2, it is not known whether inclusion, identity or exclusion hold between them. Hence, we cannot deduce whether certain properties determine others or not. Perhaps it is a weakness of the ontological scheme derived from metalogic, but it is not suitable for (D) and (E). On the other hand, the theses (B) and (C) have a straightforward interpretation in the assumed analytic vocabulary. Essentially, every individual belongs to a set. This means that it is determined or qualified in some way. This justifies (C). In order to support (B), it is enough to observe that all properties and

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relations are defined on U, that is, on the set of things (objects) constituting the carrier of interpretations. Finally, as far as the matter concerns (F), we see that any representation of any model assumes that L is interpreted, because non-interpreted languages are not representations in any reasonable sense. There remains the thesis (A). Its understanding in the framework of metalogic cannot be direct. We need to assume that a logical model of the set X regarded as our knowledge is the world. However, we do not know in advance which model and which interpretation should be treated in such a way. Everything that is granted from the purely logical point of view reduces itself to the consistency of X; according to the second Gödel incompleteness theorem, this statement is more an assumption than something effectively provable. Moreover, if X is a set of first-order sentences, it has, according to the Löwenheim-Skolem theorem, models of different cardinalities. This directly leads to the consequence that these models enable us to define very different properties. Passing to higher-order logic improves the situation to some extent, but this advantage comes at the price of inaccuracies consisting in the lack of complete formalization. Furthermore, if X suffices for elementary arithmetic, it has extensions, which are (by assumptions) internally consistent but mutually incoherent. How we should depict the proper (standard, intentional) model? I see no other possibility than to admit that our received natural interpretation must be the starting point. We can further modify it relatively to the development of knowledge, but the basic can should be considered as given in advance. The causal theory of perception and cognition provides some support for this view. Assuming that the natural meaning of expressions appeared as a result of causal influences things on us, we can say that although language does not necessarily guarantee the truth of sentences itself, it does constitute a suitable linguistic device to speak about the world truly or falsely. The whole issue is, then, reduced to truth-criteria, but not to truth-definition. Assume now that we have a certain initial stock of truths at our disposal. Accordingly, we can define the world W as the model of maximally consistent set of sentences. Such a model exists by the Lindenbaum maximalization theorem (every consistent set of sen-

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tences has a maximally consistent extension) and it is unique, relatively to properties of truth, not only consistency. Of course, we can consider alternative worlds, but the real world is unique, even if we do not know of its properties. Nowak developed the foundations of an alternative metaphysicalontological scheme in Being and Thought. His ideas are based on six main principles (see p. 439), but I skip two theses about the essential nature of negativity and the negative essence of causality, because both are mostly metaphysical. I will concentrate on the remaining four principles that are given in a simplified form below: (I) The thesis about plurality of worlds: there is (subsists) a hierarchy of worlds from the empty to the complete; (II) The thesis about outer-world-beingness: every world is a maximally consistent set of situations, but there also subsists its outer part which is made up of inconsistent situations; (III) The thesis of atributivism: elementary situations are positive, negative (ideal objects) or neutral (fictive objects) realizations of properties (attributes); (IV) The thesis about negativity of existence: something exists if and only if it contains a negative. The theses (I) and (II) are seen as alternatives to (A), the thesis (III) is contrary to (B), and the thesis (J) goes against (C). It is not possible to give deeper analysis of negative unitary metaphysics. I only show some differences holding between it and standard ontology; of course, I am restricted to points that are expressible in my language. Standard ontology excludes the empty world. It only allows for empty intensional properties or the empty extensional property. One can eventually introduce the degenerate structure ¢∅². However, it is not particularly interesting, because, due to the emptiness of its carrier, all properties and relations definable in it are also empty. In fact, since empty properties and empty relations are distinguishable by intensions only, the empty world ¢∅² contains the only property and the empty relation. Moreover, not all logical laws hold in the empty structure. In particular, the formula ∀xA(x) Ÿ ∃xA(x) is not valid in ¢∅², because its antecedent is true, but its consequent is false. There is no middle world between ¢∅² and W

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understood as the maximal set of true sentences; it is maximally consistent by definition. However, if the initial set X of truths is incomplete, it is extendible to various maximally consistent sets. For example, we can consider the set of truths about the past and a contingent sentence A about the future. The sets X ∪ {A} and X ∪ {¬A} are both consistent, but their maximally consistent extensions MAX(X ∪ {A}) and MAX(X ∪ {¬A}) are different. The same concerns models of these sets. We can say that models of MAX(X ∪ {A}) and MAX(X ∪ {¬A}) are possible worlds and one of them is the real world. In a sense, the reducts the real world to models of subsets of the all truths represent fragments of the world as the whole. Due to the axiom of choice, we can introduce an ordering of the set of worlds. This gives a hierarchy with ¢∅² and W as limit cases, and fragments of the latter as middle points. The same holds for arbitrary possible worlds. In particular, although the real world is unique and because it is the model of the maximal set of truths and therefore it had the property of maximality, the inconsistent situation, that is, the empty set, does occur in it. I am not certain whether this analysis satisfies all intuitions expressed in (I). On the other hand, standard ontology is not as weak as it seems at first sight. Perhaps the differences between the standard account and negativistic unitary ontology are not vital with respect to the points (A) on the one hand and the points (I) and (II) on the other hand. However, this is not the case with respect to the theses (B) and (III). The latter thesis means that only attributes actually exist, while things are nothing more than bundles of properties. This view is at odds with (II). Independently of how individuals are interpreted in the framework of standard set theory, they cannot be reduced to a bundle of attributes. Otherwise speaking, individuals cannot be represented by products of a number of sets. Nowak maintains (see pp. 135-136) that the dualism of sets and individuals weakens standard (that is, based on set theory) ontology, because it cannot explain the concept of being an individual object. I do not think that this objection is very convincing. Although the concept of set belongs to primitive ideas of our theoretical vocabulary, exactly the same holds for the predicate ‘to be a member’. Perhaps the sentence ‘An individual is an object belonging to

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a set, but it is not a set’ is not entirely trivial. The standard ontology considers all entities as set-theoretical concepts superimposed on U, that is, the set of individuals. The thesis of attributivism is fairly nonstandard in this respect. The thesis (IV) is similarly non-standard. According to the standard ontology, every individual belongs to some set. This means that every individual possesses a property. Assume that u does not belongs to Ui, where Ui ⊆ U. Then, u belongs to U – Ui (the difference of sets U and Ui). We can express this fact by saying that u is not Ui. Nothing more can be said about negative properties. In particular, this language does not provide devices enabling us to distinguish privations (lack of something) from contradictory negations. There is nothing surprising in that. That an individual object that is green and is simultaneously non-red, is justified by means of optics, which can explain co-existence and exclusion in the world of color. However, ontology is not entitled to consider existence in this way. If we conceive it as a formal discipline (a formal theory of objects), it should not distinguish any object and any property. If we are looking at the properties of properties, formal ontology has the means to distinguish empty and non-empty properties (including the maximal property, that is, U), and positive and negative properties; perhaps cases of molecular attributes (defined by ‘or’, ‘and’, etc.) are to be also included here. All these cases are clearly definable in standard ontology. I suspect that the difference between the standard ontological view and Nowak’s account is not very deep in this respect. On the other hand, both views are radically different about Parmenides’ thesis ‘It is not truth, that something is a non-being’, which is rejected by standard ontology, but is accepted by negativistic the unitary one. Negativistic unitary ontology, as it is outline in Being and Thought, is a mixture of metaphysics and ontology (in my interpretation of these concepts). The border between these two is vague. In pointing out this feature of Nowak’s theory, I must mention that I assume a metaontological position on which every ontological theory is an interpretation of a system of formal logic, comprising first-order logic (or something equivalent to it, for example, the LeĞniewski ontology) at least. If one accepts the priority of philosophical experience over any

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other, the situation becomes different. The whole system must be constructed according to intuitions, which are taken as fundamental. Of course, this is not impossible, but I have serious doubts concerning the source of intuitions and, what is perhaps more important, the instruments controlling their correctness. In spite of some misgivings concerning standard ontology (I do not say that everything is satisfactory and clear in it, for example, the problem whether logical models are good conceptualizations and categorizations of the world), the fact that it formalizes certain natural intuitions lends support to it as a theory. I repeat once more that if we accept the causal theory of cognition, there is no reason to reject formal semantics in its settheoretical dressing as an abstract expression of natural intuitions. Negativistic unitary metaphysics does not have an adequate logical base (Nowak admits this, see p. 459, p. 465). In Being and Thought we find many logical analyses, sometimes classical, sometimes modal, sometimes fairly non-classical. This last qualification concerns, for example, various kinds of negation and a logical basis for the Parmenides thesis (see above). It is a fundamental question, because, at least in Nowak’s account, the matter does not concerns the degenerate structure ¢∅² but something much more essential. I suspect that any metaphysical consideration must appeal to intensional logic, which is a fairly complicated issue. Finally, I would like to touch the relation between ontology and metaphysics, and epistemology. Negativistic unitary metaphysics sees metaphysics (ontology) as absolutely prior to epistemology. My view, related to Ajdukiewicz’s standpoint, is different. According to Ajdukiewicz, metaphysical solutions consist in deriving consequences from epistemological theses. I do not go this far but I do maintain that every (or almost every) metaphysical (ontological) problem has an epistemological dimension. Inversely, every epistemological problem hast a metaphysical (ontological) dimension. In the formal scheme used in this paper, that dualism has its expression in the necessity of taking into account the triple ¢language, its interpretation, an interpretative structure². In my opinion, speaking about languages without an interpretation, that is, without an objectual reference as well as speaking about worlds without their conceptualizations, leads to a philosophical

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dead-end (I do not direct this remark against Nowak). However, these underpin standard philosophy. In contrast, Nowak’s radical account rejects these assumptions. Perhaps this is what determines that Being and Thought is a genuine metaphysical treatise, brave and adventurous.

Uniwersytet JagielloĔski Department of Philosophy ul. Grodzka 52 31-044 Kraków Poland E-mail: [email protected]

REFERENCES Nowak, L. (1998). Byt i myĞl [Being and Thought]. Vol. 1. PoznaĔ: Zysk i S-ka.

SCIENCE, PHILOSOPHY AND VALUES

Max Urchs ON THE STRUCTURE OF DECEPTIVE SPEECH ACTS: LYING AS AN ELEMENT OF COMMUNICATION

Your normal reaction to the title of this paper may range from sheer amazement to irritation: Deceiving by means of oral information means lying. Writing about the structure of speech acts is synonymous with providing its logical analysis. So this text claims to contribute to a logic of lying. But, what has logic got to do with lying? That suspicious question seems legitimate on all counts. ‘The logic of lying’ sounds a bit odd indeed. Of course, ‘logic of lying’ means the formal structure behind these specific (speech) acts. We do not use the term as synonymous with ‘ideology’ or ‘mechanism’ or ‘causal net’ as it appears to be used in ‘The Logic of war in Sudan’ or ‘The Logic of Debt Relief for the Poorest Countries’. And yet, to some extent, your reservation will be confirmed in the course of this paper. However, the topic seems to contain some logical aspects after all. I will do my best to make them explicit. Lying is an ubiquitous element of communication. This is not to say that lying is just normal talk. If lying would be the normal way in which we speak to each other, then it would certainly in a Kantian manner undermine the conditions for its own possibility: expecting a lie by default, prevents me from being lied to. ‘Ubiquitous’ means that lies

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 355-374. Amsterdam/New York, NY: Rodopi, 2007.

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appear in all forms of communicative context and that they are much more frequent than one is usually inclined to assume. There is little doubt that deceptive speech acts in general are a “hot topic” in current philosophical debate as well as in cognitive psychology and linguistics. Only within the last few months Polish scientific publishers came up with three important volumes (Antas 2000; Chudy 2003; Witkowski 2002). Nevertheless, in this paper we will concentrate exclusively at the logical structure of deceptive speech acts and at some problems concerning an adequate formalization of lies.

1. Lying as an Element of Communication The first assumption I need to state is this: In many types of communication, lying is an important element. 1 Experiments conducted in cognitive psychology yield that lies are much more common in every day talk than the speaker realizes. To find this out the experimenters together with the speaker have to investigate carefully the protocol of the given talk. Than they find an amazing number of lies. However, up to my knowledge, a second aspect of this result went unmentioned so far: the test person who listened to the talk did not catch the lies neither. Being lied to is always a shock. The listener would certainly remember that. Some of the lies he did not catch. But some others he just didn’t register consciously. So one might interpret this finding that way: at the one hand, we do not remember all lies we tell, and at the other hand we do not register all lies we are told. Nevertheless we certainly make our speech sufficiently clear and we understand it reasonably well. That is, often enough we cope with lies quite good without even noticing them.

1

This is meant purely descriptive, not normatively. Although, the anthropological aspects of lying shall well deserve a much more throughout treatment than they normally receive (see e.g. Sommer 1992).

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Deceptive speech acts have some characteristic internal structure. Moreover, in order to be efficient they must respect certain requirements of rationality. Perhaps, all kinds of human intellectual activity should respect some internal rational structure. Otherwise they will normally fail. In particular this holds for communication. Even a highly emotional outcry must fit into the given circumstances in order to carry the intended message. Any such kind of rational rule following falls into the traditional realm of logic. And at least in that respect the phenomenon of lying is subject to logical investigation, too. This, I admit, is an extremely weak connection. In that sense almost anything composes into a very large and very complex structure of “logic, lie and libido.” Yet there should be a much more essential connection between the two topics. Ethnology pretends that lying, conscious deception etc. are deeply rooted in the evolution of human intellect. Under the conditions given on Earth, they seem to be unavoidable preconditions for sheer survival of the higher species, and the more so for the rise of social life, enforcing intellectual progress and bringing about sophisticated forms of communication. So, far from being just a sign of moral defectiveness, lying seems to be a central element of any intellectual activity from its very beginning. Modeling results of intellectual activity, however, is the very centre court of logic.

2. A Lie as a Subject of Logic Given that lying plays in particular an important role in human communication, logic should care for it. Amazingly enough, it does not! The topic was almost completely ignored by traditional logic.

2.1. The Liar Sometimes, lies are an explicit subject of logic. The most prominent example here is, doubtless, the Liar. The so-called antinomy of the Liar, or Eubulides’ antinomy, is an ancient and respectable topic in

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logic. The problem is very old, indeed. In its oldest formulation, perhaps, it takes the following shape: A nasty crocodile took away a child playing at the bank of the Nil. Its mother demanded the return of the little one. They agreed upon the following procedure: the woman makes claim. If and only if this statement is true, the crocodile will return the child. So she states: “You won’t give back my child!” “Well then” — explains the crocodile — “if this is true, it means you won’t get your child. If it is a lie, then, according to our agreement, you lost it.” Obviously, the woman objects: “Not so! If I spoke the truth, you have to return my child. That’s what we agreed. But in case I lied, then contrary to what I said, you will give my child back to me!” The quarrel could last quite a while. And in fact it did. Countless variants are known from the philosophical literature. One of them even made its way into the Holy Bible. You all remember the story: St. Paul intended to calm Titus, who went out to Crete in order to convert the locals and bitterly complained about his hard job. St. Paul expressed his sympathy in an Epistle to him: For there are many unruly men, vain talkers and deceivers, specially they of the circumscription, whose mouths must be stopped; men who overthrow whole houses teaching things which they ought not, for filthy lurce’s sake. One of themselves, a prophet of their own, said. Cretans are always liars, evil beasts, idle gluttons. (Titus 1, 12)

Actually, that was not yet an antinomy, unless we assume that this prophet was the only inhabitant of the island. But the prominent source boosted the discussion, which was around at all times. There is only one reported case (see Ajdukiewicz 1931) of an ancient philosopher, Philetas of Kos, who committed suicide in great despair, since he was unable to solve the puzzle. Usually, the Liar paradox was treated merely as a funny, but not really important logical riddle. Things changed considerably only much later, when Bertrand Russell found a way to rise the liar in the realm of (naive) set theory. The set of all set which are not an element of its own damaged Gottlob Frege’s project of foundations of arithmetic. But at the same time it gave rise to a hitherto unprecedented boom in fundamental research in mathematics. In some sense, that marked the birth of modern mathematical logic as foundations of mathematics. The most powerful

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project in this evolution was a program, initiated by David Hilbert to prove the consistency of mathematics once and forever: all branches of modern mathematics were to be transformed into axiomatic theories and all these theories were to be proven free of contradictions. Unfortunately, it was again the liar, i.e. the obstruction that brought out Hilbert’s Program in a sense, which made an end to it, at least — again — in a sense. The reason was Kurt Gödel’s so-called second theorem: Gödel’s second incompleteness theorem proves that formal systems T satisfying certain conditions “cannot prove their own consistency,” in the sense that a suitable formalization in the language of T of the statement “T is consistent” cannot be proved in T. Of course, T has to be in fact consistent, since otherwise everything is provable in T. The second incompleteness theorem applies in particular to those formal systems that can be used to develop all of the ordinary mathematics that one finds in textbooks. The decisive point is that such a system has to be rich enough to include formal arithmetic. Then, by using an ingenious technique, so-called Gödelization, the system is able to “speak about its own sentences.” Now, Gödel’s idea was to investigate a sentence which said “I have no proof.” This, however, is nothing but the arithmetical reincarnation of our old friend. If it has a proof, then we have a problem. If not, then what it says is true, and it should have a proof after all. (Since all true mathematical sentences should be provable.) That is hard stuff and until now whole newly generated branches of mathematical logic are investigating the scope of this result and try to tame its consequences. Yet it is not our business to become absorbed in these tendencies, which reach out far into philosophy and theoretical linguistics, for one simple reason: “The Liar” doesn’t lie. It needs a very peculiar understanding of lying to subsume the statement “Hoc est falsum” under our theme. So we need not care for it.

2.2. Formal Accounts So far for the most prominent example. In classical logic, “to lie” usually just means to contradict the truth. This doesn’t simply mean

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“falsehood,” since falsehood may come in various degrees. Already such a simple understanding may result, as we saw, in interesting logical problems. E.g., Raymond Smullyan wrote a very entertaining and instructive book about liars and logic-knights, that leads the reader as far as to Gödel’s theorems. That kind of consideration found practical application as well. Stanisáaw Uáam and John von Neumann started investigations of equation systems with a given number of false equations. The question is: are there algorithms for solving them in spite of this obstruction? Of course, such algorithms shall possibly turn out to be extremely useful for reasoning in databases with partially defective information. However, the notion of lie assumed in these approaches, is far from any intuitive understanding of this concept. Besides of this, there are few attempts to be found in the literature that investigate in greater detail the formal structure of lies or of deceptive utterances. The problem is to construct a metamathematical counterpart of the concept of lying. What formal means to this end are available in modern logic? I found the following examples in the literature2. Meinong’s monograph “On suppositions” (1977) is an early attempt to give an explication of lie which meets the standards suitable for logical formalization. Meinong himself did not seek for the final logical form of his considerations. This was done only recently by Urszula ĩegleĔ (1996). Let me quote her relevant definitions: SxyĮ =df Wx ByĮ LxyĮ =df Wx ByĮ ∧ ¬BxĮ where SxyĮ reads “x wants y to believe Į,” whereas LxyĮ stands for “x lies to y that Į,” i.e. “x wants y to believe Į although x does not believe in Į.” In a next step she proposes an implicit, i.e. axiomatic characterization of the predicates involved. Oversimplified as this may seem, it is already sufficient to prove some modest theorems, for instance: 2

Certainly, there are many more of them. E.g., Marek Tokarz’s recent contributions to communication theory or Gabriel Falkenbergs non-standard account to lying are highly relevant. I did include, however, only those proposals that cope with deceptive speech acts in a fully formal framework.

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Lxyp Æ WxByBxp ĩegleĔ ends with a suggestion that the well developed means of epistemic logic might be used to refine Meinong’s approach to lying. In fact, epistemic logic is a very promising framework for this purpose.

2.2.1. Epistemic Logic Werner Stelzner (1984) makes use of the means of epistemic logic to approach the problem. He assumes the following notion of lie: “Usually, a statement is called a lie, if the speaker internally rejects the sentence which he publicly affirms.” In his notation, Stelzner arrives at the following formula: L(x,p,t,y) =df O(x,p,t) ∧ A∗α(x,p,t,y) where O(x,p,t) =df ∃q ∃r (Ai(x,q,t) ∧ V(x,q,t,r) ∧ V(x,p,t, ¬r)). The predicates A∗α and Ai stand for external and internal acceptance, respectively, whereas V(x,p,t,q) stands for “x understands p as q at t.” In the above formulas, t is the time interval when x claims p to y. Therefore O(x,p,t) means that x rejects p at t. Hence, x lies to y about p at t, iff he explicitly states x, though simultaneously he rejects p. Contrary to this, Klaus Wuttich (1991) assumes a stronger definition of what he calls a “promising lie”: Le(x,p,t,y) =df K(x,¬p,t) ∧ A∗α(x,p,t,y) where K(x,p,t) means: x knows p at t. This is because he claims that in order to deceive successfully, one has to know the truth — you just cannot intentionally show somebody the wrong way without knowing the right one. Of course, from now on all hinges on the (axiomatic) characterization of the predicators involved. Subsequently, a completely internal logical debate sets on, discussing the formal details of the proposed explication, drawing inferences from it, considering variants and improvements — in a word, there starts the happy business of construction of formal calculi. Though the connections with contextual aspects of lying are fading away rapidly.

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2.2.2. Theory of Communication One may hope to may a better strike in speech act theory. This branch is more closely connected with pragmatic aspects of communication and shall pay better attention to the subtleties of deceptive utterances. Let me take Georg Meggle’s work as an example of this kind of research. Meggle’s aim is not exactly to build a calculus of lies, but a very similar one: a calculus of deception (although his logical standards are rather low). As usual, lies turn out to be special forms of deception: a lie is an overt deceptive utterance — overt with respect to the intended result of deception, not with respect to the very act of deception, to be sure. Meggles motivation is perfectly honorable: to improve our capacities of discovering deception by using logical methods of analysis and reasoning. To get started, he assumes some rather harsh idealizations: a world populated by two persons x and y, who have exactly one of two intentional states: believing and intending, represented by B and W, respectively. At a first level, there are only a handful of elementary states in such a world: from B(x,p); B(y,p) to ¬B(x,¬p); ¬B(y, ¬p), and for W accordingly. Trouble begins with iteration: if x believes something concerning the beliefs of somebody, then the number of possible cases grows rapidly. This, on the other side, yields a lot of raw material to define more sophisticated concepts. For instance, the intention to deceive is explicated by the following wild predication (BĻ means “later than B”): W(x,BĻ(y,p)) ∧ B(x,¬p) But despite of such technical doubts, there remains a hollow feeling while scrutinizing more and more subtle cases of lie and deception: it is not even the rapidly rising number of cases hard to re-translate into natural language. After all, exaggerated diversification is quite typical also in philosophical analysis of lying, which all too often comes as unworldly casuistry. Rather the problem lies in the technically poor means Meggle decided to work with. Why should a world that abstracted as Meggles two person community — moreover persons with pretty poor mental life — show something interesting about our real world and the lies within our real world communication? I cannot

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help to think about a glass beard game here, entertaining, sophisticated and nice but — with no clear connection to real life.

2.3. Why there Is No Logic of Lie so far Compared with the results of logical investigations of “normal,” i.e. true utterances, that doesn’t look impressive. What is the reason for such a state of affairs? First of all, we saw that any adequate formalization of the concept of lie needs quite powerful logical tools. However, the more powerful a formal language is, i.e. the more details from natural language it can express, the more demanding is usually the metamathematical apparatus required to control reasoning in the given formal language. Here we have a trade off which is well-known from research in Artificial Intelligence: I mean the trade-off between a comfortable and precise (and therefore usually very sophisticated) language of formalization on the one hand and limited as well as expensive resources for processing the formalized material on the other hand. Sometimes it may pay off to work with a modest but less complicated language which needs little memory and low calculating capacities. It goes without saying that there was no need for such a decision in former times: there was no appropriate formalism available at all. But then we face another problem. An utterance is a lie only if it brings about a conflict between the verbal representation of some state of affairs and the speakers mental representation of this very state of affairs. Of course, this is not yet a definition (since there is no if-part) and it seems not very clear. What kind of conflict it talks about? Does it mean that the verbal representation inadequate because it is too narrow — did we say too little? Or is it too broad? You all know the notorious problem with telling the truth, but precisely the truth: all truth and nothing beyond. Or is the inadequacy at the other side: at the side of the mental representation? All of these cases may happen. That means, if understood in a standard setting, a lie contradicts the truth. If we perform our formalization in a very simple formal language this may lead to inconsistencies. Nowadays, we have much

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better technical means available. As a result we have the freedom to choose an appropriate formalization, i.e. one in which no such inconsistencies occur. However, as indicated above, there may be reason to choose a plain and simple formal language after all and to accept the inconsistencies. But, the question is: how could we possibly do this? We all know that traditional logic is almost helpless when coping with inconsistencies. The reason is a fundamental principle of logic, called the Law of Excluded Contradiction. Should we be afraid of contradictions? Yes, we certainly should! Actually, the ex contradictione quodlibet principle is considered to be the very keystone of rationality in our cultural tradition. You better don’t rattle the keystones, since the whole beautiful vault may collapse. But it is not only a matter of Western cultural tradition — contradictions indeed indicate a deviation from normality, from the usual standards of rationality. Therefore it seems perfectly in order to assume the ex contradictione quodlibet sequitur principle. This principle leads to explosion of the system whenever one single contradiction occurs. The horror contradictionis is endemic between rational thinkers. Aristotle holds: This principle is our only weapon against error and falsehood. (àukasiewicz 1987, p. 138) and we may add “and against lies”. He concludes: The principle that two contradictory statements are not both true is the most certain of all. (Aristotle, Metaphysics Γ6, 1011b13-14) As a result, in philosophy (and in logic) the motive of lie was widely neglected. Was Aristotle right to damn contradictions? Yes and no! The notion of contradiction is of iridescent paronymy. Not every inconsistency means that from now on any rational inferences are impossible. Otherwise e.g. jurisdiction would break down immediately. In court hearings, it is quite usual to present extremely inconsistent opinions: at least the accused party may lie as much as it pleases. And yet the judge makes his more or less consistent conclusions from what he is told. Anyhow, Aristotle’s opinion was extremely influential ever since.

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And yet there was another tradition — suppressed but never fully extinct. This tradition leads from the early Greek philosophers, Parmenides and Heraclitus in particular, through the sophists to Fichte, Hegel, Marx and, nowadays, to post-structural and postmodern approaches. There is a current research hypothesis stating that the sophists were in possession of an alternative formal system which, in contrast to Aristotle’s syllogistics, was able to deal with inconsistent talk. However, sources are rare and corrupted and thus any reliable reconstruction of that sophist logic seems very hard to achieve. Be that as it may, 2.500 years later formal logic has arrived at various calculi which fit to handle reasoning with inconsistent sets of premises in a controlled way.

2.3.1. The Law of Contradiction Revisited One possible way to achieve this leads trough a closer inspection of Aristotle’s law. Imagine that you have to take down a dispute, e.g. in court. Suddenly, somebody claims A and some other participant opposes claiming A is not true, or non-A for short. She may err or lie, no matter what. On your sheet of paper you wrote down scrupulous A and non-A. And now you observe a remarkable fact: The discussion goes on and may become quite exiting — but no one of the participants panics! None of them feels constrained to accept any claim as true. Both claiming a thesis and then attacking it by claiming its negation are quite popular events in any course of a discussion. This does not cause the discussion to break down because of so-called overcompleteness. It is impossible that both A and non-A are true. In the realm of twovalued logic one of them must be false. So (at least) one thesis on your sheet of paper is false. Nevertheless, this fact seems to be not dangerous at all. Let us now assume, as a second case, that some of the participants claims both A and non-A at the same time. This causes a quite different situation! What is the difference? One can precisely describe the conditions under which inconsistent claims may occur in the minutes. Assume that the quarrel goes about A. Some of the participants have

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reason to claim that A is true while the other ones disagree: according to them A is not true. And there is no possibility to persuade one of those groups by logical reasons only to give up their position. As far as there is no new empirical evidence accepted by all participants each of them has a generally used defense: “We are right and the others are wrong!” But now assume that one and the same speaker claims that A is true and at the same time he disagrees and claims that A is not true. Then there are purely logical reasons which should persuade him to change his mind. One can remind him of the common use of the words et and non from which follows that his claim makes no sense. Obviously, the above defense strategy should not be used in this case. Otherwise the speaker would characterize himself as intellectually somewhat embarrassed. That means, if there occurs a contradictory claim in the minutes (not merely claims which are inconsistent with each other) then the person who claimed it either does not use the common language of all of the other participants (and is therefore not a rational speaker) or he is mentally puzzled (whence, not a rational speaker). In any case it seems the best to exclude him from a rational discussion. The reason is, that at least I would expect just everything from somebody who claims obvious contradictions like A et non-A. In this sense, it seems quite reasonable to assume that anything follows from A et non-A — a rational discussion becomes overcomplete by a contradictory claim. The principle ex contradictione quodlibet is therefore in keep with discursive logic: From A et non-A follows anything. On the other hand, we had observed that from a false claim made in discussion do not follow everything. That means, in the logical framework appropriate for formalizing the discussion the following ex falso quodlibet is not a permissible rule: From A follows anything or from non-A follows anything; in other words From A and non-A follows anything. Therefore it seems reasonable to dismiss the ex falso quodlibet principle and at the same time to keep the ex contradictione quodlibet principle.

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2.3.2. Inconsistency-Tolerant Reasoning as a Promising Tool There are various ways to incorporate this view in logical calculi. As a result, inconsistencies in sets of premises are tamed and reasoning from such sets can be handled in a controlled manner. These inconsistency-tolerant calculi are special cases of so-called paraconsistent systems. I admit, the name is unfortunate, but the issue is a hot research topic in modern logic. In any case, the framework nicely fits the formal analysis of lying.

3. How to Formalize? 3.1. The Crazy Tailor Until now, we’ve left out something very important. The missing item hinges on the common sense idea of the duty of logic. What is the role logic has to perform in philosophy and in the sciences? Perhaps, the standard answer goes like this: Logic has to distinguish the correct forms of reasoning from unreliable or false patterns of inference. Thereby, logic figures out the logical truth — it establishes a set of tautological formulae. That, however, is not the whole truth. Normally, even the most sophisticated forms of reasoning can be controlled by common sense alone. It is a myth that modern logic is necessary to tell apart the correct conclusion from the incorrect ones. With the possible exception of very few examples from formal ontology (e.g., some proofs of the existence of God), all scientific reasoning can be performed perfectly well without the huge apparatus of modern logic. Controlling inferences is simply not the main task logic has to perform. The main task rather consists, instead, in conceptual analysis and construction. Logic is largely the art of definition. It provides and sharpens the raw material for subsequent construction of logical calculi. In other words: it explicates the basic concepts from the realm under consideration. Let us look again at the material collected in the literature and evaluate it from this point of view. The resulting impression is even more frustrating then it was the first time. All the approaches proposed

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so far are far removed from the subtlety and sophistification of the linguistic material they set out to investigate. In order to perform logical analysis of any linguistic or philosophical entity, it shall be given a precise form. Yet, needless to say, this precise concept should stay as close as possible to the naturallanguage concept that we intend to analyze. There is absolutely no point in gambling with artificial formal constructs that share nothing but the name with its natural-language originals. This, however, is what the working logician does all too often. And this is what makes Stanisáaw Lem call him a “crazy tailor.”3

3.2. The Role of Background Knowledge Whether a statement is a lie or not depends on your background knowledge. To be more precise: a statement is a lie or not with respect to some knowledge basis. I agree with Stelzner that a lie is a multiplace relation. But I think a quadruple (as he supposes) is insufficient to characterize it — we need a pentuple: a speaker, a listener, a statement, a knowledge basis and a temporal variable. Perhaps one could merge the last two positions into an updated knowledge basis. What explicitly include a knowledge basis? It may be the poverty of your knowledge that make you fall victim to liars. For example, it is very easy to lie to young children. They just don’t know enough about the world — their realm of possibility is not easily crossed. I remember 3

In his witty essay “SzaleĔstwo z metodą,” Stanisáaw Lem narrates about a tailor. This tailor does not know anything about people, animals, or the world. He does not care about these things — he makes clothes. They look quite unusual: small or large, elastic or stiff, having no holes at all or any number of tubes, which he calls “sleeves” and “pants,” consisting of various pieces. If he finishes a dress, he takes it into a large storehouse. Already there are suits that might fit a man or a horse or a tree, clothes for dinosaurs, unicorns, mermaids or beings unknown to anybody on earth. Everyone must confess, Lem claims, that the work of this tailor is sheer madness. — One might well have a more charitable attitude towards the work of a mathematician or a logician than the one revealed by Lem. In any case, the “crazy tailor” makes logical entities we can immediately work with. His obvious disadvantage, however, is that it is impossible to find out the proper formalization by logical means alone. (See Lem 1974, pp. 145 ff.)

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a quarrel with my three-years-old son about bedtime. He wanted me to check my watch to see whether it was already time for him to be asleep. Unfortunately, I didn’t have my watch with me. That made him curious about where the watch might be. Carelessly, I joked to him that the watch was very busy that day and it hadn’t made its way back to my wrist. That was of course a perfect occasion to divert my attention and the immediate follow-up question was: “Tell me what the watch was doing all day!” I told him a bunch of wild falsehoods about what it was doing: It watched TV, then it went to the storehouse for a new wristband and right now it’s sitting in the bathtub brushing its teeth. But now he caught me: “That’s not true! It won’t do that in the bathtub.” The story touched a part of reality he was informed about. Every evening he had to leave the bathtub before brushing his teeth and he never saw anybody doing otherwise. So this relatively mild lie was the one he recognized against the background of his specific world-view: it contradicted other information stored in his knowledge basis. But as a matter of fact, he did not realize the preceding falsehoods, because there wasn’t enough relevant information available. Often enough, it happens to be the other way around. You may take a true statement for a lie because of your insufficient knowledge. To give an example, you may remember one scene from the famous movie “Chinatown.” The detective asked a suspicious lady about a young girl he had seen in her company and she answered: “That was my sister!” He didn’t believe her. So she told him: “She is my daughter.” He took that for a lie, too. So she kept explaining: “She’s my sister, my daughter, my sister, my daughter, . . . ” making him really upset. But, contrary to his conviction, it wasn’t a lie. He simply didn’t understand the message. The woman had been raped by her father and gave birth to a daughter who consequently was her younger sister. The detective’s knowledge basis (or: the available part of his knowledge basis) wasn’t broad enough to let him grasp this fact. Therefore he mistook the true answer for a lie.

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3.3. Flic-Flac Lies Sometimes the matter is even more complicated. It may switch back and forth between truth and falsehood, according to an expanding knowledge basis. Imagine a mathematician telling you that yesterday, after great effort, he succeeded in squaring a circle by ruler and a pair of compasses alone. Now, if you have very poor understanding of mathematics, then it will probably seem to you that the guy is just kidding: how could he possibly square a circle? After all, a circle is round and a square has edges. There is no such thing as a round square. So one thing is sure: you can’t square a circle. But, knowing a little bit more about mathematics you understand the real content of what was going on: he was telling you that he solved the problem of squaring the circle, i.e. he succeeded in constructing a square with the same area as a given circle using ruler and compasses alone. Now your reaction is quite different: you are not longer annoyed by this apparently silly lie, but you congratulate him! For all you know, this is a great result. The Greeks were seeking a solution for it and so did all the mathematicians for the next two-thousand years. So it is a big thing — and he finally did it! Yet perhaps you may have an even larger knowledge of mathematics. Namely, you may know about Carl Louis Ferdinand von Lindemann’s 1882 result saying that Π is transcendental (that is, Π is not the root of any algebraic equation with rational coefficients), from which it follows that the ancient problem of circle squaring is unsolvable. And since the fellow is a mathematician, he must know this. So what he did was shamelessly lie to you. Therefore we have a silly lie switching into a very distinguished mathematical statement and back to a shameless lie again. It all depends on you mathematical education. What is the upshot of these examples? It seems that an adequate formal counterpart of the concept of lie shall include, among other things, the notion of a knowledge basis. There are many results available from a branch of logic called knowledge revision. Nevertheless, all sorts of background information, world-knowledge and so on are subject to very serious formal and philosophical obstacles. The

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best known is perhaps the notorious frame-problem. That’s hard stuff for logical formalization.

3.4. A Lie Is What Really Hurts Me A lie must be told on purpose. On some purpose. I don’t want to go deeper here, since there might be very different intentions behind a lie, indeed. Usually we assume some aim the liar wants to achieve, either personally or because of some group interest. But there is plenty of other motives: perhaps on enjoys the feeling derived from successfully deceiving others, takes an extreme misanthropic stance, is conducting field research or has taken a vow to never tell the truth again. These all are good reasons to lie. Yet even if we eliminate this difficulty, our troubles do not end. Things are even worse. Somewhere I found the aphorism “What counts as a lie is decided by the victim.” That seems very reasonable, too. For an utterance to be a lie it shall be credited the potential to hurt. This is certainly less then a rigid criterion, again. Kant and Augustine, on the one hand, will feel offended by any utterance they recognize as intended falsehood. A loving mother, on the other hand, will hardly find any lie at all in the tales of her dear child. And in between there is a plethora of nuances. Anyway, if there is no emotional reaction whatever to some falsehood we are told, then I would hesitate to call it a lie. A message that did not cause the even mildest reaction, the slightest change in my attention, could not have been a lie. In other words, for an utterance to be a lie there must be a reasonable chance for having some negative effects. That means, we have one more hidden indexical and of course a further kind of vagueness of the concept follows therefrom: even under fixed conditions, a given utterance may be classified as a lie by one person and not classified as such by her neighbor. Furthermore, it may simply depend on my expectations whether or not something will really hurt me. But if this is true, then any explication of this concept requires quite a few facts about causal dependencies and subjective expectation in order to qualify statements under given circumstances as lies. These topics, however, are very

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inconvenient objects of logical formalization again. Closely connected problems result from temporal factors of lies. Can a projective utterance be called a lie? “I will never leave you!” Consider a famous example: St. Peter swears to his Lord. Soon after he has betrayed him three times (though under the circumstances, it would be interesting to know who was morally responsible). In my opinion, only under very special conditions can promises denoting future events be true or false now. Sentences with uncertain logical status, however, can’t be components of a lie. Consequently, and deviating from usual talk, we shall admit that — normally — a braggart is not a liar. In order to make this precise we need tools to handle temporal aspects in the background logic. But the above suppositions have consequences for the extrapolation of the intuitive notion of lie as well. If true, it may well be the case, that there is no such thing as a general concept of lie. This wouldn’t be an outrageous result. Quite the same holds for such central concepts like causality, law, or duty. There is a standard way out in such a situation: one should split up the concept and start with the easy cases. So we might investigate the notion of a lie in special forms of standardized communication, e.g. in scientific discourse, legal context, or maybe even more specifically in criminal law and in civil law taken separately. What is more, there is no reason to exclude the possibility that an utterance may be a lie to some degree only. If the concept of lying turns out to be a comparative one, then things become really messy from the point of view of logical analysis.

4. The End To sum up the above review of hindrances for an adequate formal analysis of lies we put together the main points. • lies produce inconsistencies; • whether an utterance is a lie or not heavily depends on context; • according to background knowledge, a flic-flac effect may occur; • causal and intentional aspects are indispensable in an analysis of lies.

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To be sure, all these topics are handled by modern logic. And yet, to merge them into one formal framework, which remains practically feasible seems hard enough. So it is not surprising that a satisfactory logic of lying is still to come. As cold comfort, let me end with a little poem by one of the most underestimated German philosophical thinkers. It shows another aspect of our topic, which seems pretty remarkable, at least from my perspective. In my humble translation,4 it goes: If all things would remain what we — in lust and pain — have to each other said; if lies turned into hairs, we would be rough as bears and see not one bald head.

European Business School Chair of Philosophy of Science Schloss Reichardshausen 65375 Oestrich-Winkel Germany Uniwersytet SzczeciĔski Instytut Filozofii ul. Krakowska 61-69 71-017 Szczecin Poland E-mail: [email protected]

4

In fact, it was Scott Thompson who saved the rhythm of the verse. And he did a lot of god to the rest of the paper. In German, Wilhelm Busch’s pretty verse sounds like this: Wenn alles sitzen bliebe was wir in Hass und Liebe so voneinander schwatzen; wenn Lügen Haare wären, wir wären rauh wie Bären und hätten keine Glatzen.

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REFERENCES Ajdukiewicz, K. (1931). Paradoksy StaroĪytnych [The Paradoxes of the Ancients]. Filomata 35: 6-14; 36: 51-58. Antas, J. (2000). O káamstwie i káamaniu: Studium semantyczno-pragmatyczne. Kraków: Universitas. The Bible, American Standard Version. Bok, S. (1978). Lying. Moral Choice in Public and Private Life. Sussex: Harvester Press. Chudy, W. (2003). Filozofia káamstwa. Warszawa: Oficyna Wydawnicza Volumen. Falkenberg, G. (1982). Lügen: Grundzüge einer Theorie sprachlicher Täuschung. Linguistische Arbeiten, vol. 86. Tübingen: Niemeyer. Lem, S. (1974). Summa Technologiae. Kraków: Wydawnictwo Literackie. àukasiewicz, J. (1987). O zasadzie sprzecznoĞci u Arystotelesa. Warszawa: PWN. Meggle, G. (2000). Logik der Täuschung [The Logic of Deception]. In: Rationality, Realism, Revision, pp. 339-348. Berlin: de Gruyter. von Meinong, A. (1977). Über Annahmen [On Suppositions]. Graz: Akademische Verlagsanstalt. Stelzner, W. (1984). Epistemische Logik. Zur logischen Analyse von Akzeptationsformen [Epistemic Logic]. Berlin: Akademie Verlag. Sommer, V. (1992). Lob der Lüge. Täuschung und Selbsttäuschung bei Tier und Mensch [Praise of Lying]. München: C. H. Beck Tokarz, M. (2003). Lectures in Communication Theory. Unpublished manuscript. Urchs, M. (2001). Recent Trends in Paraconsistent Logic. In: H. Wansing (ed.), Essays on Non-Classical Logic, pp. 219-246. New Jersey, London: World Scientific. Witkowski, T. (2002). Psychologia káamstwa. Warszawa: Unus. Wuttich, K. (1991). Glaube, Zweifel, Wissen. Eine logisch-philosophische Studie [Belief, Doubt, Knowledge]. Berlin: Deutscher Verlag der Wissenschaften.

Jerzy Perzanowski IN PRAISE OF PHILOSOPHY*

Let’s not ask: Why philosophize? That’s obvious. Instead of that, let’s ask: How should we philosophize? Are there reliable rules for philosophizing? And if so, what they are? Let us however begin with some general comments on the place, source, and aims of philosophy.

1. The Place of Philosophy 1. Philosophy1 breaks up into a series of disciplines. They fall into groups for reasons of methodology and content. So the various areas in philosophy are differentiated by the methods, results and standards sofar worked out for them — from scientific philosophy in the strict sense (which involves, amongst others, fragments of the philosophy of

*

The paper is an English version of the Polish original (Perzanowski 2000). Translation by Dr. Matthew Carmody has been authorized. The work on it was carried out with support obtained from the Flemish Minister responsible for Science and Technology (contract Bill 2002/41) and from the Polish Minister of Science and Higher Education (grant 1H01A00230). 1

Notice that in the Polish tradition, following Twardowski and his disciples, philosophy is treated as a science.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 375-393. Amsterdam/New York, NY: Rodopi, 2007.

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language and science, the core of ontology and metaphysics, and, last but not least, logic) to philosophy of a semi-literary nature, which, even in the case of delimitation of its basic problems, facts and methods, works and improves its methods only with the greatest effort, thanks to the great number charlatans prowling, unfortunately, in this terrain. 2. Several disciplines are associated with philosophy, which do not themselves belong to philosophy, but can be linked to it and be useful to it. For example: the history of philosophy, the history of concepts, the history of ideas, the history of religion, cultural and social anthropology, psychology, theology as well as basic disciplines of the modern science: mathematics, physics, chemistry and biology. These areas are close to philosophy and knowledge of them is important in practicing philosophy. At the other extreme are various ideologies, world-views, areas of faith whose connections with philosophy, a fortiori with scientific philosophy, are weak and distant. It is very often the case that this connection is damaging to philosophy itself, although the converse doesn’t necessarily hold. 3. The role of philosophy is determined by its fundamental (and, for most people, naive) questions: What is the world and where does it come from? Why is it? And, how is it? What is, why is, and how is man and what is his role in the world? What is the mechanism of specifically human worlds and how does it work: the world of psychic experience, the world of culture and the world of social institutions? How is truth to be distinguished from illusion? How do we guard ourselves against all manner of errors? How should we live? And similar, naive but urgent, questions. Truly (Szymborska 1997, pp. 274-275): Znowu i tak jak zawsze

[Again, and as ever]

.....................

...........................

nie ma pytaĔ pilniejszych od pytaĔ naiwnych.

[the most pressing questions] [are naive ones.]

Two philosophical questions are certainly the most fundamental ones: The question of the nature of the world? And the question of

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humans, the question of their nature and destiny? With both questions are connected the question of Reason and the question of God. 4. Indeed, he who is not aware that philosophy belongs amongst the most important areas of our spiritual life lives in dangerous naivety. 5. Philosophy is one of the main forges of ideas. One should treat ideas, to use contemporary metaphor, as informational viruses, which, by means of language or other media, spread throughout the whole population — by jumping from head to head. Ideas either destroy minds or they enriches them. Hence epidemiological character of certain ideologies, and also fashions (including intellectual ones), especially today, in a world of global means of communication. 6. Philosophical ideas are either beneficial or harmful. Beneficial as, for example, Plato’s idea of the connection between the Good, the Beauty and the Truth; or Montesquieu’s idea of the dynamically understood basis of democratic social order, which demands for its stability the division and balance of power. Or Adam Smith’s idea of the free, self-regulating market which, in tandem with a universally accepted moral order (quite simply, honesty) is the basis of a healthy and mutually just social-economic system. Philosophical ideas can also be harmful, even harmful to the highest degree. For example, such is the naive idea of J. J. Rousseau, according to which people are by nature good, and only deprived by culture. Or Marx’s idea, that Heaven may be founded on Earth simply by taking from some and distributing the goods equally amongst the rest. Marx was evidently a victim of Rousseau’s illusion, that people are by nature angels. There are also racist ideas, present in two of the twentieth-century bloodiest ideologies: the pseudo-biological idea of Hitler and his comrades of the harmfulness of certain populations or races (Jews, Romanies, Slavs); and the communist idea, expressed by Lenin, Stalin and their cohorts, concerning the basic harmfulness of the looselydefined “races” of class enemies. Finally, let us also remind ourselves of an recently popular idea of the newest toxicity, that Truth is the enemy of Freedom. It is connected

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with an old, albeit vigorous sophistical piece of nonsense, that nothing differentiates Truth from Falsity along with the idea, that the measure of Truth, and thus the sphere of facts is Man. And also, that everything is a product of equally valid cultures, which are not subordinate to external judgment. We shall not go so far from common sense and reason. For following the above ideas in a strict and narrow way is a betrayal of Reason, one which prepares a new captivity for us. 7. Philosophy, in particular logic and ontology, occupy a key place in the structure of human knowledge. We conceive the world, one might say we grasp it, via concepts, that is, mental pictures of the aspects of objects under consideration. Concepts in turn are connected, according to the principles of an appropriate grammar, into propositions (logical judgments), that is, logical pictures of mentally-grasped fragments of the world. Concepts are junctions of information; propositions — its pieces. 8. From here comes the role of logic, being the basic theory of those pictures of the world, fragments of grasped information. The logic of names examines the relations between concepts expressed in a given language. The logic of sentences examines the relations between propositions. This leads to an examination of the recombinations of the initial group of pictures, that is, to an examination of possibilities. Their totality in turn constitutes the ontological space, the space of all possibilities. 9. Ontology, the true first philosophy, in this way creates the most general conceptual framework for the varied and diverse fields of human knowledge and strives towards the complete working-out of that framework. As a matter of fact, we owe to Leibniz the idea of the above modal definition of ontology and the opportunity of carrying out ontological research by pointing out the proper form of ontological questions: what is possible? And why? And, how is it possible? In turn, particular ontological questions, for a given x, sound as follows: how is x possible? We have amongst other: metaphysical questions — How is the world possible? How is existence possible? And: what, why and how is it that exists?; epistemo-ontological

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questions — How is knowledge itself possible? In particular, How is mathematical a priori knowledge of that which is real possible? Also questions of axio-ontology and antropo-ontology: What are values? How are they possible? How is evil possible? Why are people so evil? And many other questions of this form. 10. The problems of real philosophy are real and great. Therefore they will be with us for as long as will survive human curiosity. For all people by nature strive for knowledge (Aristotle, Metaphysics, I, 1), including the deepest one. 11. This is why it is so important that reflection on these questions be carried out by true philosophers. For if philosophy, at the insistence of skeptics or under the pressure of positivists, were to give up concerning itself with its real problems, then they would fall into hands of charlatans, causing great mental and social damage. Therefore people should not forget about philosophical questions and the right way to deal with them.

2. The Sources and Aims of Philosophy 12. The great philosophical problems produce real, sometimes great, philosophy. Therefore respect them, even if you stand no chance of contributing to their solution, and if also, as happens not infrequently, the philosophical assaults made so far leave you deeply unsatisfied. 13. If you philosophically mature, don't waste your strength on “small philosophy” or on petty analytic exercises. Such things are essential for beginners, to train the hand and mind. Per aspera ad astra. Be a true philosopher! 14. Whom do you mean, then, by the true philosophers? — Those for whom the truth is the spectacle of which they are enamored . . . (Plato The Republic 475e, tr. Paul Shorey)

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. . . wisdom is good and ignorance bad (Plato, Euthydemus 281e) . . . no gods ensue wisdom or desire to be made wise; such they are already; nor does anyone else that is wise ensue it. Neither do the ignorant ensue wisdom, nor desire to be made wise: in this very point is ignorance distressing, that a person who is not enlightened or intelligent should be satisfied with himself. The man who does not feel himself defective has no desire for that whereof he feels no defect. Who then, Diotima, I asked, are the followers of wisdom, if they are neither the wise nor the ignorant? Why, a child could tell by this time, she answered, that they are the intermediate sort, and amongst those also is [Eros]. For wisdom has to do with the fairest things, and [Eros] is a love directed to what is fair; so that [Eros] must needs be a friend of wisdom, and, as such must be between wise and ignorant. . . . (Plato, Symposium 204b; with one change: ‘Eros’ instead of ‘Love’)

15. Let us add to Plato’s words a Poetess reflection full of melancholy (Szymborska 1997, pp. 272-273): . . . Gáupota nie jest Ğmieszna MądroĞü nie jest wesoáa.

[. . . Stupidity isn’t funny] [Wisdom isn’t gay.]

16. Is it possible, and to what extent, to give consolation as we strive for understanding? Does understanding itself suffice, especially for those, who have broken hearts2? Philosophy is born out of a desire for wisdom, out of a hunger for understanding. It is produced by reason. By the light of reason — the soul. And it serves to satisfy it. It’s curiosity and love of wisdom. As Descartes wrote in Principles of Philosophy, Introduction (letter to Picot): To live and not philosophize is truly to have one’s eyes closed without ever trying to open them.

17. Human curiosity is not mundane. It embraces a very wide sphere, from matters of sciences, through matters of the worlds of culture and social institutions, to matters not of this world. It stems in

2

The heart is truly broken by unhappiness or envy or intrigue, and also betrayal, not however, by a typical short-lived romantic disappointment. Although the amount of suffering in this case may indeed be great.

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part from human fantasy. The main source of that human striving to such diverse knowledge is however the very special situation of man. For man is an edge-being, as if located at the intersection of at least five planes of being. The plane of things and natural processes TNP, including, above all, bodies and concrete things. The plane of psychic experiences PE includes not only perceptions, but also (subjectively taken) concepts, thoughts, imaginations, feelings and various phantasms, which take us outside of the sphere of the mundane. The next is the plane of objective counterparts of PE — beings, that is, the sphere of ideas, values, concepts, and other general objects along with the plane of their extensions (sets, aggregates, etc.). The fusion of both planes is the plane of ides and sets IS. And the plane of social and cultural institutions CSI, in which a human animal is first changed into a social animal, and then into a citizen. At least some others associate themselves with other planes, such as the plane of spirit S, which displays itself in the spiritual life of people. S

IS

CSI

TNP

PE

d 3

18. Thus man by his nature is a being having many assembled experiences from a variety of fields. The attempt to encompass them all

3

I abstract away here from the issue of whether this is a result of natural evolution and also from the issue whether this what is essential for a person has been instilled in him.

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in their totality, which is the duty of philosophy, seems to be a task of superhuman. 19. The main weapon we have in our struggle for knowledge is reason. The greatness of man is made manifest in it. Reason is truly a great and heavenly gift and one should believe in its capacity to understand the world. Those who undermine trust in reason therefore err and serve evil (see Miáosz 2000). 20. Let us add, that true lovers of wisdom are not threatened by to great a trust in reason. For a fundamental component of their position is criticism as expressed in the chief principle of rationalism: “I do accept only such arguments, which after consideration seems to me better.” (Socrates) And the related principle of common sense: Gentlemen respect facts and thus not argue as to whether a fact is a fact or not. And also the principle of concreteness: Check every philosophical speculation and its results — as long as they are connected with the world — through concrete examples, as if to put it against the world. Speculation which explains nothing, or nearly nothing, from the sphere of our basic experiences is not worth a great deal. Lovers of wisdom know that uncritical trust in anything, even in reason, is a sign of stupidity. Their faith in reason is thus critical. 21. The philosopher, as every educated man, strives for knowledge. That is to a systematized system of properly justified responses to clearly formulated questions. Philosophy looks for something more, however. It looks for understanding. For it is a discipline which not only gathers facts but is more — a discipline seeking understanding. It only appears when we find answers to well chosen and deep questions. 22. More important than the question of What is a response? is sometimes the question What is a question? This is exactly how it is in philosophy. Be therefore an aristocrat in the area of choosing and posing questions. In examining the problem, aim for understanding of the area.

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23. Remember as well the reasons of the heart. And that not all of the world is locked in the framework of reasoned discourse. Be open to impulses, outbursts and requests of the heart. Be sensitive to the non-verbal communications of other people. For the goal of philosophy is not empty and cheap comfort, but sympathy and understanding. Non ridere, non lugere, neque detestari, sed sentire et intelligere! 24. True philosophy therefore has a dimension of understanding and a dimension of sympathy. Its speculations are under the constant control of logical reason (in the dimension of argumentation and affirmation), practical reason (in the sphere of common sense and feelings) as well as the powers of judgment (in the sphere of actions and morality). And the powers of taste,4 which protects us from trifling matters, errors in our behavior, directing us as it should.

3. Hints How these regulations of the maximal, meaningful, and theoretical understanding of philosophy look? 25. Seek out first of all appropriate philosophical problems. A person blessed (by his/her nature) with a natural inclination to be curious will certainly not have any serious problems here. Remember, that in recognizing such problems, there are questionforms especially suiting philosophy which will help you: What? What type? From where? What does that mean? And the most basic: Why? How? How is it possible? Do not therefore avoid such questions, even if they sound naive to the ignorant.

4

For short, clear and up to the point explication of these powers see Zbigniew Herbert’s poem “PotĊga smaku” [The Power of Taste].

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26. In philosophy be motivated exclusively by a desire for knowledge. Remembering, that particular philosophical disciplines are, or should be, scientific, one must not give any answer whatever, but only those answers which conform to all principles of the scholar's art. Having formulated the problem, establish the initial data and put forward introductory hypotheses. Aim to solve the given problem via critical analysis and argumentation. 27. The entry point into philosophical investigation is a proper analysis of the data. This is as much a linguistic analysis as a conceptual analysis, and a logical analysis and an eidetic analysis (phenomenological). Practice the art of analysis by studying the examples of past masters and via systematic study. 28. It will turn out to be essential that one has knowledge of logic, the basis of ontology, and abstract rudiments of certain sciences: mathematics, informatics, physics, chemistry, genetics, etc. Remember that each of these disciplines undergoes change. Even exact, deductive disciplines, such as mathematics and logic, whilst having truths which are (under accepted assumptions) inviolable, are empirical in the sense that the issues and concepts may vary over time, often along with the background perspective and style of thinking. Always be prepared, therefore, for a fundamental revision of received truisms and “obvious” truths. Be certain, however, that the core of philosophy, the first philosophy, persists independently of the present state of our knowledge. The form may change, but not content. First philosophy is that what it is, because its problems. Because they are. 29. Philosophy is an autonomous field. It is not a lone island, however. Philosophize, therefore, whilst maintaining a tight connection with other disciplines, especially those mathematical and scientific. In philosophical anthropology and ethics, hold yourself close to biological anthropology, the cognitive sciences and social sciences.

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30. Separate which is autonomous and assumption-free in philosophy from that which employs other disciplines and enthymematic knowledge. Work on what is first in connection with what is second. 31. Don’t be ashamed of mistakes. For everyone errs. Even, he who does nothing, errs by his laziness and lack of care. Fight your own errors and those of others. This requires an internal freedom, whose mark is self-criticism, and simple courage. Remember that “Reason has the right to fight with error” (Thomas Jefferson). 32. Independently of the difficulties and obstacles, the fundamental aim of man, which expresses itself most fully in philosophy and science, is the search for the truth. Man is a being by nature curious and wanting to aim for truth. These reveals the intellectual and moral greatness of man. 33. . . . When one takes the truth away from a person, all attempts to liberate him become completely unreal, since truth and freedom either exist together or perish together. (John Paul II, Encyclical: Fides et Ratio, VII, 90).

4. The General Recipe for Scientific Philosophy 34. How should we therefore philosophize? The answer is: By respecting the work and achievements of our predecessors. Systematically. Respecting facts. Completely. 35. Philosophize completely. This means — try to embrace the whole world of man by responsible philosophizing. The concrete, material world surrounding him. And also the world of psychic experiences. The world of feelings and the world of thoughts. The world of man's creations and discoveries. The world of culture. The world of ideas and the world of values. The world of science. The world of the body and the world of the soul. Aim to restore to philosophy its character of wisdom and completeness.

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36. In philosophy we are, unfortunately, in permanent danger of word-splitting, sophistry, even charlatanry. Philosophy is full of false philosophers. Some people find also philosophy to be dark and too difficult. They thus try to introduce ersatz questions and considerations instead of real ones. This is, however, easy and cheap. 37. Doing philosophy be therefore5 scientifically as well as philosophically responsible. Try to develop philosophy as a science. Stay with true philosophical problems and methods. Be a true scholar and a true philosopher as well! 38. Scientific philosophy (in its extreme, strict form — logical philosophy) is created by those who in cultivating philosophy behave as scientists. For the recipe for scientific philosophy is simple. Cultivate it as scientists cultivate science. Remember that the true method of philosophy is no other than the method of the natural sciences (Franz Brentano), and that the method of philosophy is the method of the exact, that is rational, sciences (Kazimierz Twardowski) and that logic supplies philosophy with a method of research, just as mathematics supplies physics with such a method (Bertrand Russell). The main, but not the only, tool for cultivating scientific philosophy is logic: general logic in the preliminary conceptual analysis, and formal logic, during the development of that first analysis into a theory.

5. The Recipe for Logical Philosophy 39. Let us develop the above general recipe in the case of logical philosophy.

5

As Roman Ingarden taught us.

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I Begin with a clearly-put philosophical problems. Make them precise. Separate out the central questions in the issue under consideration, if there such questions. II Do not avoid difficult problems. Even the hardest questions — from the core of philosophy itself. For logical philosophy only carries out its task when it fruitfully takes up the main problems of real philosophy. III Avoid disrespectful moving away from hard problems and substituting replacement questions in their place. IV Remember that the key to success is breaking up complex problems into simple ones, hard problems into easier ones. V Do not be too hasty in judging the problems of real philosophy, even the dark ones, as pseudoproblems. VI Separate the wheat from the chaff. Begin with a preliminary analysis of concepts carried out by means of the basic techniques of philosophical analysis: linguistic, semiotic, phenomenological and, last but not least, logical. VII Analyze examples and counterexamples. Choose some of them as models. VIII Try to grasp what is in metaphors and myths and the sense of symbols, which turn up in connection that matter which interests you. They express a certain collective faith (pre-knowledge). A certain body of information. The results of pre-rational attempts at understanding.

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IX Collect information about the problems you are researching. Gather and think through that which has been carried by upright philosophers and that which, as regards related issues, the learned have established in other, relevant areas to the given problem. X Trust the experts. And your colleagues, if you have reason to. Remember that it is necessary to earn both for credence and for a loss of it. XI Use the works of the masters, try to learn their techniques, refer to their achievements, continue their work. XII Do not begin everything anew. Philosophy is a collective enterprise and not a show of soloists. XIII Share the results of your work with the others. Use the results of others’ work (not anonymously, needless to say). Let others use the results of your work. Read and discuss. XIV Aim to create a scholarly environment. XV Be an enthusiast. Remember that the work of those of little faith is usually of little value. XVI After having completed the preparatory work, begin the systematic research. Put forward hypotheses. XVII On the basis of a preliminary analysis, separate out the fundamental truths, the clear truths, the obvious truths and the intuitive truths. Treat some of them as axioms.

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Next, begin to work out theorems. Start deducing. The theorems of a theory are its fruits. Remember that you will recognize them by their fruits. XVIII Remember, that the goal of logical philosophy is the building of philosophical theories. Build up such a theory as far as is possible and sensible. When you therefore have already got axioms, draw conclusions. Reason. Do not look only for theorems but also for new proofs. Remember that not only axioms and models but also proofs give meaning to the theorems of an axiomatic theory. XIX Compare the old results of a theory and its theorems with your leading intuition and your initial intuition, as long as it differs from the leading one. XX Besides the basic principles of a critical rationalism laid out in §20 and the rules from points XVI-XVIII, steer yourself by common sense and a sense of reality. Even in admiring the results of some speculative philosophy, respect the deliverances of common sense, when they are necessary: Do not fly. Do not exaggerate. Respect the useful principle of Reverend KamiĔski,6 when you are pushed towards things that are contrary to healthy judgment (for example, when postmodernists tempt you): That far I will not go! XXI Be critical. Do not trust tools. Remember about limitations of logic. If a logical system is required, then the appropriate system will be found.

6

One of heroes of Henryk Sienkiewicz’s Trilogy.

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XXII Don’t simply try to make things better than they are. In particular, don’t force philosophical results through an arbitrarily-chosen logic. XXIII Do not lose a basic trust in classical logic. Remember that logic is the ethics of language and thought.7 XXIV Don’t withdraw immediately from that which you don’t understand. Remember that paradoxes ultimately broaden understanding. XXV Avoid overformalization. It is indeed true that formalization is the ideal. But an excess of it kills the ideal, just as an excess of sugar destroys the pleasure and use we have from. Don’t oversweeten things and philosophical matters as well.

6. The Place of Logical Philosophy 40. The greatest achievements of the axiomatic method supply logical philosophy with its paradigms: the axiomatization of geometry by Euclid, of mechanics and optics by Newton, of classical logic by Leibniz, Boole, Frege and others, of the arithmetic of natural numbers by Dedekind and Peano, of the theory of sets by Cantor, Zermelo and others, of topology by Hausdorff and Kuratowski, of classical mereology by LeĞniewski, and of deductive systems by Tarski. 41. In each of these examples, the axioms flow from clear and obvious and deep intuitions. The theories based upon may be said to develop the initial intuitions, stretching them to produce an ever wider domain. Logic plays the role of a light. It brings out of the dark fragments of the previously invisible landscape.

7

Dictum of Jan àukasiewicz, the father of Polish logical philosophy.

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42. From the point of view of logical philosophy, philosophy divides into logical philosophy and extralogical philosophy. The second of these divides into prelogical8 philosophy and illogical philosophy. PHILOSOPHY

LOGICAL

EXTRALOGICAL

PRELOGICAL

ILLOGICAL

43. Prelogical philosophy is that part of philosophy which is conceptually clear and logically consistent and consequent enough to be able to be shaped into the body of a theory of logical philosophy. The corpus of traditional philosophy is in essence prelogical philosophy. 44. Illogical philosophy consists all that in philosophy which does not tolerate clarity, the light of reason. That which lives in the dark is blind, not even knowing about it. And not wanting to know. Let us remind ourselves of Socrates’ sad statement: Neither do the ignorant ensue wisdom, nor desire to be wise: in this very point is ignorance distressing, that a person who is not enlightened or intelligent should be satisfied with himself. The man who does not feel himself defective has no desire for that whereof he feels no defect. (Plato, Symposium 204b)

Unfortunately, examples of such stupidity are legion. 45. Logical philosophy and prelogical philosophy (including traditional true philosophy) determine the criteria of the proper way to conduct philosophy, saving it from being wasted in the hands of illogical philosophers. 8

The name has been formed on the pattern of: pre-disposition, pre-existence, etc. Prelogical philosophy is therefore a philosophy with content, waiting for that content to be turned into precise theories.

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46. Last, but not least: logical philosophers differ from certain of their colleagues in going down those roads that they point out.

7. Conclusion 47. One should neither talk too much about philosophy nor, even more so, moan about it (that it is finished, that it has died, that it has wasted away). One should simply do it. In connection with logic and other disciplines, one should put forward problems and work on them with the appropriate means and measures. One should restore to philosophy its aspect of wisdom. 48. Think completely and in depth. Think logically. Philosophize clearly. Write in a precise manner. Justify your statements. Be critical. Be, at the same time, optimistic in philosophy. And be faithful in reason. 49. What does true philosophy yield? Most often, it does not yield the expected answers. It may however give a picture of the whole and a critical understanding. It may also bring consolation. And an idea about how to live. It also teaches us how to die. Is that not enough?

Uniwersytet JagielloĔski Department of Logical Philosophy and Cognitive Science Institute of Philosophy ul. Grodzka 52 31-044 Kraków Poland E-mail: [email protected]

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Ignatianum Chair of Logic ul. Kopernika 26 31-501 Kraków Poland E-mail: [email protected]

REFERENCES Miáosz, C. (2000). Czego nauczyáem siĊ od Jeanne Hersch [What I learned from Jeanne Hersch]. Tygodnik Powszechny 27 (2660; July 2nd, 2000). Perzanowski, J. (1989). Jak filozofowaü? [How to Philosophize?]. Warszawa: PWN. Perzanowski, J. (1991). Sentire & Intelligere. Znak — Idee 4 (MyĞląc o filozofii [Thinking about Philosophy]): 11-16. Perzanowski, J. (1993). Aim, Scope and Editorial Policy of the Journal. Logic and Logical Philosophy 1: 3-6. Perzanowski, J. (1994). Filozofia logiczna = filozofia/logika [Logical philosophy = philosophy/logic]. In: Filozofia/logika = filozofia logiczna 1994, pp. 69-75. ToruĔ: Wydawnictwo UMK. Perzanowski, J. (2000). O filozofii [On Philosophy]. In: Logika i filozofia logiczna (Logic and Logical Philosophy), pp. 13-26. ToruĔ: Wydawnictwo UMK. Plato, Euthydemus. Translated by W. R. M. Lamb. Loeb Classical Library. Cambridge, MA: Harvard University Press, 1925. Plato, Symposium. Translated by W. R. M. Lamb. Cambridge, MA: Harvard University Press, 1925. Plato, The Republic. Translated by Paul Shorey. Cambridge, MA: Harvard University Press, 1935. Szymborska, W. (1997). Schyáek wieku [The Century’s Decline]. In: Nothing Twice. Selected Poems (selected and translated by S. BaraĔczak and C. Cavanagh). Kraków: Wydawnictwo Literackie.

Roman Kubicki LOVE: IN SEARCH FOR THE FIRST PHILOSOPHY

1. Introduction According to the Polish proverb “A person is known by the company she keeps.” There is the spirit of hope hidden in this proverb, (good company may elevate us), as well as the spirit of forewarning (bad company will certainly ruin us). This saying does not determine whether we are somebody once and for all or whether we are incessantly in the process of becoming somebody. In all likelihood this depends on the nature of who (what) we associate with. Some of us succumb to the beauty of the Heraclitean river, others are seduced by its Parmenidean bank. In philosophy, as in the proverb, a question of a human being turns out to be a question of his company. Needless to say that not only philosophy asks about the company, but it also investigates which company is most suitable for us. For the Greeks such company was provided by Being, whereas for Christians by God. Experience of Being realizes itself through reason, whereas experience of God through heart. Most often the other person remained the name of the secondary problem — even a Christian did not have the right to enter the world of mystical experiences. Contemporary philosophy is torn apart. On one hand, during its search for a person’s ideal company, it finds it either — in case of Descartes — in thinking, or — in case of Hegel — in the State, or — in case of Marx

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 395-413. Amsterdam/New York, NY: Rodopi, 2007.

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— in a specific social group. On the other hand — more and more often philosophy attempts to identify this best company with the human himself. Such a human is understood in two ways. Posing the question of a human, Stirner and Nietzsche institute the history of metaphysics of secularized loneliness, which makes it possible to get to know oneself absolutely; only does a human see himself and only himself, when there is no need in him to observe other people. Conversely, Kierkegaard and Feuerbach see human’s best company not within himself, but in another person. Still, it is not every other person, but solely the person who loves only herself and at the same time is only loved by herself.

2. To Possess the Truth is to Possess Everything In spite of the fact that the human from the Antiquity did not sound dignified, first philosophers were striving to formulate conditions the fulfillment of which should warrant human’s ontic perfection and independence. Human life was fragile and in that sense also unserious. As long as people associate with what is contingent, mundane and earthly, so long they remain contingent, mundane and earthly. For that reason people should be provided with better company, as it is the only way to make them independent in a better — i.e. more real — existence. The question touching upon the possible metamorphosis of “unserious life” into “serious existence” seems the crux of all philosophical speculations. This question has been answered optimistically many times. All answers — with the exception of irresponsible yapping of sophists — describe the prospect of “serious existence” applying terms derived from the hope that cognition of existence is understood as coexistence with it. Being is scrubbed from inconstancy and uncertainty. A philosopher observing immortal order of things strives to reconstruct this pattern within himself. The last stage of philosophical cognition of Being consists in creation of oneself in its likeness: therefore, what’s immortal and secure finds its haven in a human, being perceived as mortal and uncertain.

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A philosopher examines Being by means of thoughts. But it is not possible to construct any “other more truthful world” solely from thoughts since such a world would be as transient as thoughts. Only a concept shows to thought the charm of its potential infinity and eternity. Therefore not all thoughts, but only thoughts that have succeeded in solidifying in poses of concepts, create the homeland of philosophers. Concepts make our thoughts go beyond the outlines of transitoriness. Constructing ourselves solely from thoughts, we build in the air, since thoughts still arouse in us and still fall asleep in us. It is different when we construct from concepts. Since in that case we entrust ourselves to language, which is older than each of us. The world of language is different: concepts do not arise in ourselves, but we strive to recognize ourselves in concepts. Only concepts open our eyes, and enable to see in ourselves the absence of eternity, i.e. to realize who for sure we are not. Hitherto he knew that he was not a tree that had burned down just a moment ago or a hare, which he was digesting. Everything that could wish to entice him with its existence went by, and thus he had no awareness of passing — even the sun shining that day was absolutely new to him. Everything changes with the advent of concept. Concept cannot be seen or touched — concept can only last. Therefore from the philosophical viewpoint, concepts, which have transformed into our own thoughts, provide the best company a human could ever think of; as long as you associate with concepts, similarly to them, you become serious and great. Nietzsche was convinced that cognition annihilates action, since to act we have to be veiled in illusions — in all those illusions, on which final cognition wages a tenacious war. Philosophical homeland of the Great Greeks was different: a necessity to act kills a possibility to cognize. Cognition on its part does not kill action, but it negates the necessity to initiate it. Aristotle finds that among thoughts these are free which can be chosen for their own sake, and those that lead to knowledge concerning something else, bear resemblance to slaves. We do not think in order to act, but in order to think. Who possesses the truth has everything. The one who possesses everything since he possesses the truth has no need to act.

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Therefore it is hardly surprising that when reading the Greek philosophers we frequently come across aversion towards mundane, earthbound problems and physical toil; the most devoted companions of life. Even if a daily, insignificant life calls for this physical drudgery now and then, we must do everything to escape from the trap that makes us relinquish discovering the truth. Significant life — and thus true life — commences with wisdom. Nothing but wisdom enables a human to live in the world adequate for him. If our dwelling is to be safe, concepts that are laid as its foundations cannot be captured in a net of apparent problems. For this reason Socrates searching for the ultimate truth feels disturbed by incessant yapping of Xantippe and cries of children. Worldly matters taking place here and now pose questions that are not worth answering, but worth always having an answer at hand. Therefore also Plato’s philosopher fulfills what he is to fulfill in life yet irrespective of time and place he remains faithful to philosophy and pursues such a daily schedule that promotes development of skills, memory and reasoning. Truth emerging from the texts of learned Greek reminds of a proverbial dog in the manger: although it does not consume the fruits of worldly life, it guards that nobody, for the sake of their final good, consumes them. Above all this ultimate truth has not developed a taste for vicissitudes of life. Nietzsche characterizes this indigestion saying that sages forever and a day thought that life is vanity . . . No matter where and when they were giving the same shout imbued with doubt, melancholy and weariness, the shout in defiance of life. Even dying Socrates, said that living is equivalent to being ill for a long time. He admitted that he should buy a cock for Asclepios. Even Socrates has had enough of life. So long is thought wise and hardens in a concept, as long it gets free from the Socratic ethereal and quotidian problems. In Greek scholé means free time, time to stop, take a break, have rest, be sluggish, idle, spend spare hours studying; and finally it means a school — a place where we make use of our free time. Spare time does mean neither rest nor end of work. On the contrary, work signifies the end of free time. In Aristotle’s writings those who work have no time; yet those who have no time do not master time (keep it under control); those who do not control their own time, by the same token cannot control

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themselves — they are not free and deprive themselves of the right to true happiness. Therefore we happen to be true humans during our free time — when we are free from matters, which do not deserve to be a subject of true thinking. The Stagirite proves that nature itself requires from us to know not only how to act appropriately, but also how to loaf. It is in inactivity where everything starts and thus it should be placed above work and work’s aim. Happiness we pursue is a type of a theoretical contemplation. There is no other happiness then happiness conceived and maturing in a concept thoroughly scrubbed from the rust of life.1 Path to a concept does not lead through mystic meditations abounding in obscure recesses and dark sources, but through philosophical, logically coherent (whatever this word means) considerations. Only such reflections lead to perfect happiness. What kind of person one becomes depends on the subject one cognizes. In the world of philosophers a binding rule holds: “Tell me what and (how) you cognize and I will tell you who you are.” Boredom is the twin sister of inactivity (idleness). As Leszek Nowak states categorically, philosophy is not conceived out of curiosity but out of boredom (Nowak 1998, p. 81). Hardships of everyday existence are not the only enemy of wisdom philosophers and those willing to become philosophers crave for. Wisdom does not also feel at ease in the world of feelings. Besieged by feelings, wisdom loses its authority, efficiency — and most importantly

1

Similar dislike for the toil of everyday life can be fund in some chapters of the Bible. Sirach from inspired authors claims that “the wisdom of a learned man cometh by opportunity of leisure: and he that hath little business shall become wise.” . . . Concrete task distances from wisdom. Wisdom is not granted to the one who “handles the plow, and who glories in the shaft of a goad, who drives oxen and is occupied with their work, and whose talk is about bulls?” (Sir. 38). It is also strange to craftsmen and artists (“So too is every craftsman and master workman who labors by night as well as by day; those who cut the signets of seals, each is diligent in making a great variety; he sets his heart on painting a lifelike image, and he is careful to finish his work” — Sir. 38.) All of them put trust in their hands. Sirach does not belittles physical work “On the other hand he who devotes himself to the study of the law of the Most High will seek out the wisdom of all the ancients, and will be concerned with prophecies” (Sir. 39).

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— reliability. In the prologue of our lives, we start to love with heart; in the epilogue, the point is to love with mind. Wisdom makes people control themselves. Therefore wise persons know that the aim of their life, only if it was not to go astray and vanish, is to reside in truth or the incessant search for truth. Common people are not wise and — as Plato warned — they do not worship beauty with eyes, but being at the mercy of pleasures, want to astride and possess beauty, as if they were a four-footed animal. Truly wise people overcome a physical desire of possessing the beloved one since only on that condition, as Plato promised, suddenly a miracle is revealed: beauty in itself, beauty in its essence. There opens in front of them a sphere towards which they targeted all their previous toils; they see eternal beauty, beauty that is not summoned, that does not perish or wither. Who knows hic et nunc will always know — he who understands himself today, harbors no fear of himself tomorrow. This is good knowledge since it provides a guarantee for the entire future.

3. The Way to God is through Wisdom Not through Heart Principles binding in the world of reliable cognition, rarely find application in the world of emotions. If I do not know how much “two plus two” makes, and one day I would like to discover it at long last, I have to undertake adequate examinations, cherishing a hope that sooner or later they will lead to an awaited solution. Having received one-sided education in the humanities, I may not be prepared to carry out such examinations (particularly nowadays at the time of so-called stress-free education, there are no ungifted children, only children “gifted differently”). But under such circumstances I count that there is somebody else who will lead me to the solution. If I have learnt this fact today, I will know it also tomorrow. Forgetfulness is the only threat on the way of my knowledge. But than I still know, that although I have forgotten how much “two plus two” makes, I can do my best to recall the result of this mathematical calculation: independently or taking advantage of kindness of other people or various artificial

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contraptions that humankind has evolved to help my failing memory. Knowledge by nature is transmittable and abhors “epistemological” loneliness, still on numerous occasions, particularly when knowledge debunks, it leads to a solitary life. If I am the only one in the know, it is as if I knew nothing. Therefore I have to share my knowledge — even if it is the Socratic knowledge about my ignorance. Undoubtedly I can assure that “I know something” and at the same time caution categorically, “for sure I am not going to tell anything to anybody,” still if I persist in my resolve too long, my assurance shall become groundless and empty for others. Yet with feelings it is a different matter. I love this woman and being vain I want the entire world to know about my love; but at the same time, I do not want all men to love the way I do. On the contrary I will do everything so no other man loves her. Love is not transmittable, whereas its future is uncertain and unforeseeable. Today I love this woman but unfortunately I have no guarantee that I shall love her tomorrow. Søren Kierkegaard, along with Ludwig Feuerbach, the greatest theoretician of love, in The Aesthetic Importance of Marriage makes an unusual declaration saying that there is something he is truly grateful to God, namely that his wife is the only one he has loved, the first one. He also adds that there is something he asks God with all his heart, i.e. to give him the strength not to wish to love another one. The pledges: “I will love you tomorrow” and “Tomorrow I will cease loving you” are formulated beside the sphere of life appropriated by love. What surprises in love is its beginning and end. Love itself does not surprise us since it is the source of happiness and we would always like to have more of it. The promise: “Even if tomorrow I will forget that I love you, the day after tomorrow I will do my best to remember” is preposterous. Kierkegaard’s man is aware of his own helplessness. He knows that if tomorrow he falls in love with another woman, there shall be no place for the one he loves today and today he wishes to love her eternally. Let us recapitulate, according to philosophers, good life is guided by reason understood both as a proper order of human soul and being. Plato’s man finds fulfillment when he discovers being. Christianity replaces impersonal being with personal God. Still, the path leading to

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God is not marked out by wisdom but by heart. Humans are not able to discover God but they may hope to love him. Who we become depends primarily on what or whom we love. Either we love worldly pursuits and are then penetrated by them, or we love God and have the grace to meet Him. In Confessions, we encounter an intriguing paragraph, in which St. Augustine ponders what it means to love God. First we learn what we should not and cannot love if we want to love God. And accordingly, we should not love physical beauty nor pleasures of worldly life, nor the radiance of light that pleases our eyes, nor the melodies of various songs, nor the delightful scent of flowers, oils or perfumes, nor the body that we would love to embrace. According to St. Augustine, these are not the things we love loving God. It seems that the lengthy answer provided by the saint borders on the tradition originated by Plato. He also assured that beauty would not be revealed in the form of any bodily part, nor a word, nor knowledge, nor the earth or heaven, but in the invariable and eternal form. Only one path leads to ideal and absolute ideas. It passes through the world that is radically purified of earthbound content as well as values that come into sight when people recognize themselves in the intensively sensual courage of coalescing with such qualities. Augustine being a Christian cannot be a thoroughly faithful child of Plato’s man whose soul was once punished and imprisoned in a human body. For the Father of the Church, Jesus’ body through which ChristGod instills human life with the hope of salvation was also human. God recognizes a man in himself, as this is the only way to help man. We remember that Socrates ordered his adherents to offer a cock to Asclepiads after his death. He was convinced that only death provides a seriously truthful answer to unserious questions of unseriously transient life. Jesus, the human son of divine God, in contrast to Socrates, the human father of divine philosophy, frightens death. In the Garden of Gethsemane “he began to be sorrowful and very heavy.” And he tells his disciples: “My soul is exceedingly sorrowful, even unto death; tarry ye here, and watch with me.” Fear accompanies him even at the time of his first prayer in the garden where he says: “O my Father, if it be possible, let this cup pass from me!” He painfully assures God: “Nevertheless not as I will, but as thou wilt.” During his

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second prayer he is more resolved: “O my Father, if this cup may not pass away from me, except I drink it, thy will be done.” Crucified, he shouts loudly a momentous question: “Eli, Eli, lema sabachthani? (My God, my God, why hast thou forsaken me?). For the Son of God, life is a positive value and thus he is more human than the father of philosophy. Doors belonging to philosophers, that tightly isolate life from its truth hardened in a concept, open a crack. Consequently St. Augustine must consider once again what he loves when he loves God. This time his answer becomes a positive declaration. He admits he loves a certain type of light, voice, fragrance, food and embrace, when his human body loves God in the form of light, voice, fragrance, food and embrace. Although thinkers give rise to words, it is history that shoulders the meaning of their utterances. Christian consent to love assumed in its command, originated from the spirit of the Platonic asceticism. This dictate, against its will, not only portends social ennoblement of feelings and sensuality, but also an obvious conflict between the ancient cult of hardened necessities and the charm of uncertainty that accompanies love. Almost one thousand and fifty hundred years passed and the philosophy of inhumanly divine atheist Feuerbach paradoxically commences in the place in which the theology of inhumanly holy Augustine terminated. Philosophers’ doors are pushed open: here paths leading from metaphysically founded love of personal God in another man to deprived of this metaphysical foundation love for man in a man commences. The concept of a neighbor that each Christian shall love as much as himself is a significant stop on this path. According to Leszek Nowak the command to love our neighbor is undoubtedly one of the most mighty blows aimed in the history of our culture into our sense of obviousness” (Nowak 2000, p. 73) since everyday experience teaches us all the time that neighbors hide behind the majority of our problems.2 Socrates’ man does not do harm to other man owing to a potential value of the other man, but because, any evil

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Sartre is right saying that “hell is others”; but he forgets to add that if we feel like remaining/persisting in this hell, this feeds on the presence of other people in our lives.

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has no value whatsoever and therefore doing evil is a metaphysically futile activity. According to him crime is never good nor beautiful thus we should not return crime for crime, no matter what we have experienced from other people. A Christian person does not do harm to another person since — in line with the logic of neighborly love — she loves the other. She must love him since she loves all people. But why does he love all people? The answer is evident — since every man is created in God’s likeness . . . It is not a coincidence that Saint Augustine, who explained to us what is means to love God, informs us also in detail, how we should love man: Non hominem, sed Deum in homine ama (“Not man, but God love in man”). Earlier prophet Jeremiah assured: “Cursed be the man that trusteth in man and maketh flesh his arm” (Jr 17,5). To sum up: Socrates’ man does not do evil to other man since evil has no value; a Christian does not do evil because every man, who would potentially fall prey to him, is — similarly to this who can do evil — the image of God and it is the reason of his value. Socrates’ man is self-centered and for this reason he “has no time” (since life is “brief “) to see another one, who he could make the victim of his crime; a Christian, who “would have not time” to see another one, would have no “time” to see God, whom each human being — and therefore also this other one — is a recollection. On the way that led Greeks to Being the other man is usually a hurdle and a stumbling block, on the Christian way he is a question, in which we should be able to recognize a signpost showing our way to God. Christian love of one man for another derives its sense from beyond the factuality and contingency of life of each of them; the grandeur of truthfulness of this love is decided upon by the grandeur and truthfulness of God’s domain, which does not depend on life, but which life presupposes. What is factual is loved as long as it is the image of what is divine and ideal.

4. One who Loves can only Love With the inception of contemporary times God, who till that time was loved in another human, vanishes away from humans. Descartes’ man

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exists because he thinks, not only does he think, but also more and more often he does think in a mathematical language. In the mathematical picture of the world, pathos of truth identical with the once searched being disappear. One hundred and fifty years passed and Pascal’s “order of the heart,” contrived as an ambitious attempt to oppose the omnipotence of “order of reason” and to invigorate once eternal values and old methods of their fulfillment, constitutes for modern Feuerbach an invitation to absolute cognition, not through love of God, but through love of another human, the human that I can love, because — as we remember — I have to love him. Contemporary times have deprived of pathos both ancient Being and Christian God. Being has become transformed into the universe understood as a perfect mechanism best comprehended through the application of mathematical formulas. Future gestures of today’s world have to be looked out for in rules, not in God’s intentions. Man addicted to them asks: How to live? Alas the answer does not come neither from the physical mechanism of the universe nor from God that ceased intervening into worldly matters. Crusaders conquering Jerusalem in 1099 were convinced that they acted upon God’s will, that they complied with Deus vult; they immodestly declared alliance with grandiose notions. Yet a contemporary person sporadically takes a stance towards such towering concepts. Respectable metaphysical ideas lose their vitality and meaning; devoid of explanatory power of rational actions, they vegetate in gestures of circumstances and disposition. John Locke, being a very learned man, was certainly familiar with Plato’s words that each pleasure and pain nails soul to body endowing it with physical qualities. Therefore the soul is under the impression that only the dictates of the body are true. In spite of this sentence, he wrote that it couldn’t be denied that good and evil, present and absent, shape human soul. According to Locke, our will is spurred to action by the anxiety of desire, directed at some absent good — either negative, which the suffering person discovers in painlessness, or positive, related to experiencing pleasure. Thus to understand a human, we do not have to search for the truth of his transient life in metaphysical concepts of good and evil, which elevated most outstanding philosophers and annihilated second-rate thinkers.

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Since the route leading to such truth lies in “the anxiety of desire. Locke notices that our Creator, knowing what determines our will, adequately to our physical system and disposition, equipped man with anxiety of hunger and other desires, that return every now and then to stimulate and direct his will towards self-preservation and preservation of species. An absolutely efficacious medicament (and thus a utopian one) treating all problems of this world is straightforward. It will suffice people delimit their activities to those motivated by inherent desires arising from a legitimate and exulting necessity to preserve oneself and our species. Therefore let us eat, drink and make love. Love for “bodily embrace,” described by St. Augustine, becomes autonomous in ontological, axiological and epistemological terms. First of all, only what can love and is loved exists (amo ergo es — amas ergo sum). Secondly, a binding principle says: “if you love you are free to do whatever you want,” and, thirdly: “I love thus I cannot doubt.” For Saint Augustine sins of a man marked the end of his humanity. One hundred and five thousand years later Nietzsche retorted that we should not kill your sins, but sanctify them — render them innocent. Each human is a potential “mirror of being” — so long “god in diminution,” as long he plucks the courage to admit that there is more wisdom in his body than in his reason. Formerly it was St. Augustine who spelled it out. Now it has been done by Feuerbach who was convinced that truthful and divine is only what does not require any proof, what is . . . as clear as daylight. But only sensual matters are as clear as daylight. Only where sensuality commences, doubts and arguments fade away. A person’s love for another person is fraught with a flesh of eternity. Kierkegaard expressed a similar opinion stating that what differs love from bliss is the brand of eternity. Those in love are internally convinced that they form a self-contained, unchangeable unity that is never to alter. Therefore the Danish philosopher promises that we can discover beauty in the fact that one man is everything to another although the slightest thing in the world around does not suggest it. Plato was convinced that particular, concrete and individual elements participating in beauty are perishable, yet beauty remains completely intact. Augustine’s man loved God and therefore could not

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fail to see the perfection (beauty and goodness) of the world by Him created. Love for God guarantees that we see the world the way it really is. In the second half of the 20th century, Adorno claims that not a single lover able to see the difference (and this is the condition of love) will let the beauty of his or her beloved one wither (Adorno 1994, p. 496). Contrary to Plato and Augustine the beauty of a beloved one more and more often constitutes not the first but the very last dimension of experiencing any absolute. Love sets free from intentional relation with God. In a human’s world of human problems, true love exists only if those in love have the courage not to seek durability of their relation beyond human experience. The point is not that a human shall be wolf or brother to a human but God (Homo homini Deus est). As Feuerbach accentuated, love loves human in a human and chains human to a human. For love heaven resides in worldly matters, and love finds the ultimate bliss in itself. What is finite love exalts to infinity. Love “for bodily embrace” is absolute: self-sufficient and infinite. For this reason those who love are brave enough to bracket epistemologically, ontologically and axiologically all that is not directly contained in the sphere of love. Mystic Eckhart had no doubts when he said that the most joyful is the one who lives in the greatest seclusion. It turns out that also lovers have no doubts whatsoever, they seek absolute loneliness, since only then they may thoroughly discover, exist and be significant to each other. A human does not love another human because this is the only way to love God; he or she does not love another human because this is the only way to love oneself. St. Bernard of Clairvaux would say: Amo, quia amo (I love because I love) . . . Those who love can only love: Franz Rosenzweig, not very frankly, warns that love for a human means to forsake oneself. — When she loves she is nothing more but the loving one. Self, which in other case would be the carrier of property, in love, in the moment of love, vanishes without a trace. In a loving human the human dies and is born anew. The sole reason for love is love itself, if we put it a bit differently and it is not necessarily the same — the only reason that love is able to discover, love finds within itself. God’s selfpresentation in front of Moses: “I am that I am” in the world of love finds its own secularized form. A man in love assures that he does not

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love his lady because of her wonderful breasts, shapely legs, alluring buttocks, slender waist, fair hair; neither does he love her because she thinks beautifully, is resourceful or dynamic or — on the contrary — touchingly lost in this world; he loves for one reason only — he loves her because she is the one. Love originates from nothingness — from you and me: it would not be here if did not exist, love has come with us, although it was not in us then. Kierkegaard is right when he says that the one who loves does not want to be taken for somebody else: neither for a better or worse person. Scientific knowledge has its ideal of certainty and infallibility; and by the same token love also has such an ideal, which according to Max Scheler — never wanders around and never makes errors provided that a human does not deceive oneself in respect of its existence, its truthfulness or object. God, the originator of the discourse of love has become its main pray: Feuerbach is convinced that love provides the only practical and organic passage from the Kingdom of God to the Kingdom of Man since love is practical atheism, negation of God in heart, thought, deed. Love is not blind but it sees differently: avariciously and with no irony. In the world of love consent to irony marks the beginning of its end: love stripped from dogma is neither naked nor true but miserable. “Fundamental terms” of the language of love are ‘everything’, ‘always’ and ‘everywhere’. Kierkegaard ponders if loving somebody means loving the entire world?” The one, who loves the entire world, cannot find a place he or she does not love, the place that would provide a more precise or different vantage point. The language of love knows no irony and is absolutely intensional; within the limits of its world, it is impossible to exchange “carriers” of supposedly the same goods: Kierkegaard is convinced that even if the most insignificant human loved the most talented, the later would have to understand that even greatest talents cannot bridge the abyss between people as only love can complete it. In the language of love each gesture is the inception of a twisted tautology and the answer for expectations love brings can be fund only within love itself. The starting point of the travel of Cartesian contemporary man is his own thinking; therefore it is hardly surprising that his own thinking will mark the end of this travel. Although Pascal’s man cannot put up

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with living in a Cartesian world, which is constantly distancing himself from God, he knows he will not find a different world. For Pascal’s man losing oneself in the order of heart was to assure man’s adherence to God, and thus to order, certainty and sense. Alas also this time Heraclitus was right: it is not possible to enter the same river twice. Pascal’s contemporary man not only knows that he should absolutely believe God and in God, but also he would like to absolutely believe both God and in God. Although he knows and wants to believe absolutely, he is not able to believe absolutely anymore, since his drama of metaphysical desires and disputes, he tries to inherit from Saint Augustine, takes places in the theatre of a different, postCartesian world. The greater optimist Pascal’s man is, the more rarely he laughs, the more often he laughs, the greater pessimist he becomes. Pascal’s man loves God, but on the other hand, he cannot find himself in the world created by God. Therefore Pascal advises that “the only and true virtue is to hate oneself. Although he comforts us in a next few sentences that the common good is in us, is a summary, he warns that it is not. So Pascal has no doubts whatsoever: the cause of a human’s love for a human is nobody knows what, and its effects are appalling. Even if Pascal’s man finds God, this is God to whom Cartesian world more and more rarely grants the right to speak about matters important to a human. Nature is said to abhor a vacuum. New silence of the world is filled by Hegel with the pathos of the state, whereas Kierkegaard and Feuerbach fill it with screaming whispers of one human’s love for the other. The drama of contemporary times is overshadowed by two transcendences. They include neither Greek Being nor Christian God. The first one (enacted by Hegelianism) is given shelter by the State, the second one (problematized by antihegelians) — by the human we love. Nietzsche will replete this silence with the will of life, will that turns its back both on the State and other human and can only love itself.

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5. Carnal Nudity of the Work of Art Is the Source of Hope, Not Shame Plato’s man lived truly only when he discovered being; Augustine’s man lived to the fullest only when he loved God. Contemporary times transform, on the one hand, cognition of being into a mathematical and physical cognition of the world and universe, and on the other hand — love of God into love for another man. These two transformations presuppose ontological, epistemological and axiological ennoblement of sensuality. Natural sciences that relay on experience, strive to find fulfillment in the physical arms of the world. Similarly love is true provided it finds fulfillment in a sensual relation with another human. Both “limbs” of the body of world, and “limbs” of the body of human turn out to be the only subject and source of valid cognition. Modern discourse of science and modern discourse of love co-create discourse of modern life. Human — the one who experiences and the one who loves — does not reside in the world, but in its picture, the picture that he has composed in a divine act of creation. Real is not only what is rational; real is also what is loved. The one who loves has everything. The one who has everything, since he loves, lacks any incompleteness— this and only this one becomes one of the beings of contemporary world. It is not only science and love that ennoble “bodily limbs.” Sensuality reveals its spiritual (theoretical) character also in art. Let us mention Schelling, who at the beginning of the 19th century identified the first philosophy with the philosophy of art, or art itself. For Schelling — and also for Kant — a work of art unifies nature and senses with consciousness — the sphere of ideal. Art enables a direct intellectual scrutiny of consciousness that perceives itself as an object. Art takes over responsibilities falling to philosophy and fulfills them from the place recognized as a limit of philosophical thought. Work of art — as Schelling writes in The System of Transcendental Idealism — reflects what is not reflected anywhere else, absolute identity that is divided even in the Self. Art through its miracle radiates what a philosopher divides in his very first act of consciousness and what is beyond any other scrutiny. New possibilities of aesthetic sphere open

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up due to the objective character of art. Art represents objectively what philosophy may represent solely subjectively. Schelling has no doubt: If we deprive art of its objectivity, it will cease being art and will transform into philosophy; if we give philosophy objectivity, it will cease being philosophy and will evolve into art. Although philosophy wishes to attain most elevated spheres, it takes there only a small fragment of a person. Whereas art takes a whole person, the way she is, to recognize these most elevated regions. Philosophy, whose natural motherland is concept, encompasses no more than a “particle of a person.” Only art may represent a “whole person” as only in a work of art, assumed concept is tantamount to a person’s body. In contrast to philosophy, art does not fear body, as the creation of freedom and nature- is present in every single work of art. The more a work of art exposes its physical character, the less it may be reduced to body. In the world of art, nudity of a work of art — similarly to nudity in the world of love — is not a source of shame but hope, dignity and grandeur. Work of art invites to a sensual contact that opens humans to values surpassing all sensuality. Inroads made by the philosophy of art into philosophy itself comprise an ambitious attempt to assign a new place to sensuality in the axiological sphere of human life. This intrusion, initiated by Kant, furthered by Hegel and the already mentioned Schelling, was completed by Nietzsche. A work of art becomes a material creation of a human, creation in which he fully recognizes him- or herself; and this recognition pleases him or her aesthetically. Thereby aesthetic and by the same token sensual bliss offered by the body of the work of art constitutes the only legally valid pleasure, that philosophy (aesthetics) willingly absolves, the only one that a human without detriment to his or her humanity may await or desire. In late modernism it turns out that nudity (the awareness of which is identical to the exile of the first people from paradise), acceptable in a surgery and atelier, is not only permitted but almost required (psychoanalytic debunking thought is of great contribution here) in “love embrace.” Although a contemporary person lied to sleep in the world of pleasures legitimized by aesthetics, he or she was falling asleep with the hope that sooner or later he or she would wake up in the world of pleasures legitimized by love.

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6. Although a Loved Person Gives Everything He or She Still Gives too Little It could seem that the discourse of modern life will be a consistently optimistic discourse. Alas it is not so. Leszek Nowak wrote that Heidegger’s greatness, among other aspects, lies in the fact of questioning one of the canons on which Western philosophy was propped from its very onset. This canon reads as follows: a human is connected with being by means of cognitive powers. Yet Heidegger shows the fallacy of this statement. Not only senses, reason, intuition, but also moods we experience every day are ontologically engaged. Cartesian definition of what there is holds: these are my cogitationes and everything they logically presuppose. Heidegger’s definition is different: there are moods of Being and everything which leaves its mark on them (Nowak 1998, p.85). Ontologically engaged moods appear as early as first philosophical discourses of love. Present in St. Augustine, who in contrast to St. Thomas, believed more in the power of questioning rather than answering. They flourish in Pascal’s writings, in which the reasons of the heart bring more vacillation than reasoning. Pascal’s man, in contrast to Plato’s and Aristotle’s man, is apprehensive of free time, which he could devote to himself; he can fill this time neither with the need of being nor with God and thus quenches the thirst of sense with streams of cheap, indiscriminate entertainment. Similarly eternal happiness of Kierkegaard’s man, who loves and is loved, is haunted by fear and trembling, which suck all joy of living out of him. In the language of love producing happiness, tragedies are written (needless to say each epoch has harlequins it has deserved), and their protagonists die since they have entrusted their lives to emotions. Only Feuerbach’s man managed to identify a beloved one not only with the absolute, but also to relive theological optimism of St. Thomas. Each theism, thus also Feuerbach’s “theism,” is crowned in some atheism. This time it is Stirner’s martyrly atheism and heroic atheism of Nietzsche. Not only the sky is empty. In the wake of God’s death there comes the time for human’s death — particularly the person who loves and is loved. Today, at the time of so called

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postmodern era, we see that also this human — like Being and God formerly — gives everything yet he or she gives always too little.

Uniwersytet im. A. Mickiewicza Department of Philosophy ul. Szamarzewskiego 89c 60-569 PoznaĔ Poland E-mail: [email protected]

REFERENCES Adorno, T. (1994). Teoria estetyczna. Translated by K. Krzemieniowa. Warszawa: PWN. Adorno, T. (1984). Aesthetic Theory. Translated by C. Lenhardt. Edited by G. Adorno and R. Tiedemann. London: Routledge & Kegan. Nowak, L. (1998). Byt i myĞl. U podstaw negatywistycznej metafizyki unitarnej [Being and Thought. On the Foundations of Negativistic Unitarian Metaphysics]. Vol. I: NicoĞü i istnienie [Nothingness and Existence]. PoznaĔ: Wydawnictwo Zysk i S-ka. Nowak, L. (2000). Gombrowicz. Czáowiek wobec ludzi [Gombrowicz: A Person in the face of People]. Warszawa: PWN.

Bert Hamminga IS THE ENLIGHTENED WORLDVIEW ON RETREAT?

During the centuries of the European Enlightenment, science was engaged in liberating more and more research loci from religious obstacles preventing proper light to shine. Philosophers were continuously engaged in redefining the borderline between science and religion. To most historians overseeing the course of these centuries, the process is regarded as the retreat of religious doctrines from areas amenable to scientific research. Starting from the mechanical behavior of bodies, science, in the course of the 16th to the 19th century conquered the areas of light, electricity, gases, the working of living organisms, finally to reach the human mind, the structure of social phenomena like trade and political organization. The triumph of science is one of largely unquestioned background assumptions of philosophy of science as it has taken shape in the past fifty years. But, an important hitch has occurred and grew in seriousness. This hitch is the subject of this paper. In short: scientific and technical development now has gained a pace that can not even longer be followed by the individual human, and is now determining every Westerners’ life, both in work and private. But the confrontation with the actual theories and methods underlying the techniques at work in home and job, even where the job is a scientific or technical one, has

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 415-444. Amsterdam/New York, NY: Rodopi, 2007.

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become very limited and fragmentized. The enlightened worldview does not anymore emanate in Western people’s personal lives as the evident way of seeing the world. Some first examples: as a teenager, you are no longer able to repair your scooter yourself; you go to a garage, where the repairman connects the vehicle to a computer that he does not understand. This computer tells the repairman to replace some part, the working and manufacturing of which he is unacquainted with. The price of the part is appearing on a screen in the garage office, in a way only known to the garage network operator, who himself has never been anywhere near a broken engine. The client pays with a credit card, a process technically understood neither by the customer, nor by the repairman, nor by anyone else in the garage. Some other examples: in the high tech office gardens of the mobile phone companies, youngsters, while working at the next generation mobile phone system, believe in astrology and aliens. On his way home, the head of this office pops in a drugstore to buy a homeopathic, infinitely diluted medicine to cure his little daughters cold. On minarets, the singers are replaced by speakers and amplifiers, technical children of the civilization of the Western sinners, and high in space even satellites may broadcast the mosque’s message, but down below, the mikes record talk about how to beat women, the bashful untouched virgins in heaven and its view down on hell. Is the worldview of modern citizens is getting immune to the general philosophical thoughts underlying scientific and technical developments in a way that would be incomprehensible to educated citizens of the 12th century world centers of civilization and science, Baghdad and Cordoba? When, in April 1970, the astronauts of Apollo 13 were in great danger after the explosion of an oxygen tank, the American people, including the astronauts themselves reverted to praying for their safe return (though astronauts and ground control took some more effective measures too). In the campaigns of US politicians, the word ‘God’ occurs in top frequency. Proposals to solve global health problems involving abortion, if only as an option, are blocked by the US government on arguments that are religious, hence alien to scientific analysis of the social processes to be tackled. More generally,

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the public morale in many circles, like those opposing a host of different kinds of research on plants, animals and man and promoting nature conservation and the life of primitive tribes is based upon the idea of Nature as not being Man’s business (and Punishment will follow if he tries to control!). That is exactly the key idea fought by Enlightenment from its start. The standard vocabularies in terms of which these moralism are extensively and repetitively expressed in mass media have long left the discourse of the sciences of the relevant fields. After the disaster of September the 11th, it was hard to tell whether God featured more prominently at the side of the attackers or the attacked (though it did not seem to solve anything). This is the problem of this paper: is there a retreat of the Enlightened worldview? That would obviously threaten to turn philosophy of science into a hobby for a few isolated academics, on equal footing with other, but less isolated hobbies like UFO search, sound healing, nature conservation, computer hacking, creationist biology, speed metal pop, etc. — if it is not so already, without many philosophers of science noticing.

1. Unbeliever Attitude to Religion: Disdain or Anthropology? Clearly, religious remnants float around in contemporary social consciousness, science has not eradicated them. The unbeliever (that is the unbeliever who considers himself enlightened) typically assumes an attitude to (contemporary) religion and the views on the contemporary world emanating it that comes close to shrugging one’s shoulders. Hence, the study of the modern and contemporary religions is, unfortunately, largely left to its believers. A short look at such believer studies may indeed add to the attitude of disdain of many contemporary scientists and philosophers. Believerauthors on the subject of religion are often seen as pseudo scientists whose errors and tricks are too simple even to analyze, or, if believed

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to believe in their own proposed doctrines, to be “backward fellow humans,” people whom that treasured growth of human consciousness which is the fruit of the Enlightenment itself has largely passed by. Unbeliever scientists and philosophers who do once in a while try to discuss the foundations of the religious worldview with believers often get frustrated by running after them in verbal circles and finally get into stalemates of a logical simplicity that no longer allows a serious consideration of the position of the believer discussion partner. Though this typical reaction of frustration and loss of interest is quite understandable, it is actually not suitable to the scientific mind. Scientists for instance successfully overcame the pitfall of treating the wisdom and customs of primitive tribes with disdain, as a heap of mistakes of “backward fellow humans.” This marked the birth of a cultural anthropology based on a clear distinction of the belief of the onlooker and that of the object, and a clear distinction between learning to understand a belief and starting to believe it. Once you creep, for the sake of understanding, into another culture’s purported truths they often turn out to form a logic that is, for the inquisitive mind, interesting to bring out, though this does not entail any defense of the system as whatever a kind of candidate alternative to whatever other belief systems. Another way to state my claim therefore, is: not enough good scientific and philosophical minds are set to the psychological, cultural anthropological, and other scientific aspects of the religions (and remnants of religions), their logic and the way they get and keep their hold on the minds of Homo sapiens well into the contemporary age of space travel and internet. In many academic circles it is still fashionable to claim with a laugh that one “does not understand” believing Christians, Muslims and Jews, as if this is something praiseworthy. Clearly, the distance between such academics and such believers has not yet reached the width necessary for the birth of a systematic cultural anthropology of believers. Which academic would dare to claim with a laugh not to understand Papua’s or San? That would simply mean to put yourself in the ranks of those in need to read a book or two, hardly something to confess easily, let alone loudly, let alone with a laugh, let alone in enlightened academic circles.

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Claiming that some academic subject is neglected is, in modern times, with its unprecedented eruption of literature, a precarious thing to do. I do not to mean to claim that it would be hard to come up with quite some pages of references to recent publications on the subject. My claim is that the scientific (that is: not religious) study of religion should not simply be one of the specialisms in one of the sub departments of academic intercourse, but, given the baffling avalanche of recent cultural developments that I specify in this paper and that are straightforwardly discomforting to the fans of the enlightened worldview, to which I, and, I reckon, most philosophers of science belong, deserves a much more general attention. That is because religions and remnants and reviving seeds of them are grossly underestimated key forces in the current revolution — of unprecedented pace — of cultural consciousness in the contemporary technical and scientific world.

2. Roots of Judaism, Christianity, Islam The dominant religions in the contemporary world are the religions of Semitic origin. The term ‘Semitic’ has, in politics, been misused in terms like ‘anti-Semitism’ that are supposed to refer to a hostile attitude towards Jews. In science, ‘Semitic’ is used as a category defined in terms of language similarities. The spreading of the Semitic languages is an indication of the spreading through history of the influence of Semitic tribes. Is does not unambiguously indicate the spreading of those tribes themselves, because the languages, especially Arab, were adopted by many a tribe subdued during Semitic conquests, especially the Muslim conquests 7th and 8th centuries AD (reaching from present day Pakistan to present day Spain and Portugal). To the Semitic language group belong northern African and Middle East languages, including Egyptian, Berber and Cushitic. The Semitic languages are divided into four groups: (1) Northern Peripheral, or North-eastern, with only one language, ancient Acadian; (2) Northern Central, or Northwestern, including the ancient Canaanite, Amorite, Ugaritic, Phoenician and Punic, and Aramaic languages and ancient

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and modern Syriac and Hebrew; (3) Southern Central, including Arabic and Maltese; and (4) Southern Peripheral, including South Arabic and the languages of northern Ethiopia. Cushites penetrated as deep down as Uganda. According to some findings of DNA research, some fairly closed Semite groups calling themselves Lemba, descending from the Jewish Cohanim priest class would have migrated even down to Zambia but in the course adopted a Bantu structure of language. Abraham, Isaac and Jacob feature as ancestors in the historical consciousness of most of these tribes, notably in the Arab and Jewish tribes. The myths surrounding these ancestral figures indicate an awareness, at least a conscious claim to common Semitic descent. Jewish, Christian and Islamic faiths are variants of Semitic religious tradition. The Christian and Islamic faiths later got adopted world wide by a wide range of peoples with no close genetic ties to Semitic tribes. The Northern Peripheral Semitic group, from the Ancient to Middle Stage, includes Acadian with its dialects of Babylonian and Assyrian, spoken in Mesopotamia from about 3200 BC until the Semites were chased out of Mesopotamia by a group of peoples merging under Hammurabi and ultimately forming part of the great Persian empire, the greatest world power and world civilization in the last millennium B.C.. Hammurabi, his followers and successors had driven the Semites out of Mesopotamia. This at first led them into a nomadic life in the deserts. This episode could well be the historical substance and clearly is an echo of what Jews, Christians and Muslims call the expulsion from paradise. And this forced journey by Abraham’s tribe into the desert is what definitively marked Semitic religious consciousness. The Semites lost the Mesopotamian territory and made into their God the One whose betrayal by themselves was believed to be responsible for their weakness. Expulsion from Mesopotamia made the Semitic religion a religion of the losers of an important war, fearing their mighty, wrathful God and deeply inclined to relive His act of expulsion as “punishment for their sins.” The feeling of being a sinner are cherished in these religions, both by their leaders and by their flocks. Conceding you are a sinner is an act of loyalty to your fellow sinners, of

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reconciliation with God, and hence of averting his anger and punishment. To show his consciousness of being sinful, a wide spectrum of rituals of abstinence of the pleasures of life has been made available to the believer, such as abstinence of sex, alcohol, food and interest on capital, though different currents of this belief system take different selections of these pleasures as target for abstinence, or limit the abstinence rituals to specific periods of the year. The expulsion-from-paradise metaphor, and the obligation to show your consciousness of being sinful classify Semitic religions as essentially traumatic, encouraging the believer to engage in (self-)traumatizing. The making of sacrifices is not specific for Semitic religions, the aspect that is specifically Semitic is to sacrifice yourself on the basis of a feeling of being sinful and guilty. This is the root of systematic attempts to approach God by showing Him one can hurt oneself and others. It is shown to God by abstaining from different types of pleasures and, in “fighting for God,” suppress your natural urge to have mercy with those whom you are told do not deserve it. This specifically Semitic type of sacrifice enhances the exertion of leader authority, reduces fear of death and thus encourages bravery (for more details, see http://mindphiles.com).

3. Heaven and Hell Further reduction of the fear of death was achieved by the introduction of heaven and hell. The first known variant of hell, defined as a torture department in the underworld, is found among the Greek (Tantalus myth). Jews never defined heaven — seat of God — as a place where dead people go. After death all people were thought to linger in a weak form in a dark place somewhere down. This was not thought to be preceded by some kind of divine verdict concerning the earthly life of an individual. Such divine jurisdiction, the so called Last Judgment, was a Christian invention. It was designed to oppose Roman jurisdiction at the time, thought by religious leaders to be too strong to fight at its home ground, the real world.

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Heaven and hell were taken over by Muslims, but for a different application. This time it was not to compete with the jurisdiction of an oppressor of Roman stature. It was primarily designed to convert Arab pagans, primitive desert dwellers. Muhammad wanted to propose a unified religion including Judaism and Christianity. In early stages of his efforts Muhammad thought that it would not be difficult to convert Jews and Christians because he regarded the doctrines of Judaism and Christianity essentially as part of the doctrine of Islam. After getting frustrated in his attempts to unite with Jews and Christians, he ordered the direction of prayer to be turned from Jerusalem to Mecca. Descriptions of hell in the New Testament and the Koran largely coincide. It involves fire, thirst, and no or disgusting food of too high, throat-burning temperature. Heaven is quite an abstract place in the Christian revelation, possibly due to the fact that articulation of the heavenly desires of Christian created the danger of bringing them back to the Roman oppressor’s ideas of pleasure. In the Koran, not inhibited by the threat of associations to what could be called the pleasures of the oppressor, heaven has been concretized all over the book, containing (in order of frequency) the following features: rivers, running streams, fountains, abundant fruit, peace, (soft) couches, bashful virgins, houris (be wedded to), silk, brocade, gold for clothing and covering, shade (shady trees), (pleasant) mansions, high pavilions, drinks abundant, no idle talk (no sinful speech), grace in Gods sight, pure nectar, no toil, descendants accompany, fathers accompany, conversation, questions, young boys, dishes and cups of precious metal, wine (rivers of), spouses accompany, no weariness, view down on hell, rivers of milk, no hatred, rivers of clarified honey, abundant meat, no sinful urges, no disease (for more details, see http://mindphiles.com).

4. Truth, a Revelist Concept The source and justification of these Judaic, Christian and Muslim religious ideas are revelations: a human individual (like Moses, Jesus and Muhammad) claims successfully to have received word by God

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himself about Universal Truth and man’s assignment on earth. Those human individuals assume the status of prophets. There is a succession of them, but the typical prophet, while paying tribute to former prophets, considers himself as the last and definitive one in the succession. Hence a revelation is to be considered as a final fixing of Universal Truth to mankind for the rest of eternity by its ruler and creator, God, through his chosen prophet. A believer in this kind of prophecy shall be called a revelist, and the Truth-concept of knowledge shall be called: revelism.

5. Revelation and Writing Semitic revelism is literary: Truth is fixated by means of sacred books, Torah, Bible and Koran, containing the word of God. This considerably adds to the static character a revelation already has due to the claim to have received the Definite Word of Universal Truth by the Only God. This deprives its believers from the prudent degree of sloppiness that oral traditions employ to adapt to changed circumstances, a strategy advocated by many wise men including Plato. This literal fixation has posed huge problems to the clergy and theologians of the Judaic, Christian and Islamic religions throughout history. The problem is that a fixed text, thought to have been revealed at a certain point in time as an eternal, general, universal Truth, is not designed to cover a process of historical development. It is frozen by its nature. Since history does not belong to the kinds of things that can be halted — though leaders of religions based on such revelations have tried and keep trying to halt historic developments with the cruelest of means — the problem of authorities in such religious traditions becomes to determine how the original revealed text relates to the changing historical circumstances. Should, for instance, an animal forbidden for consumption in Leviticus, after that species successfully evolved into immunity for the virus that in 1000 BC made it unsuitable for consumption, be kept on the list of barred food? Should another animal that falls prey to a dangerous new mutation of a virus be kept on the list of food allowed for consumption?

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In religions based on Torah, Bible and Koran, a large part of the activities through history of prudent religious leadership and scholarship consisted of relating new practice appropriate to new circumstances positively to the original frozen revelation (sometimes even going as far as disqualifying parts of the text handed down, as happened in the European Reformation, as apocryphal). This necessary bending and breaking of text by reinterpreting and disqualifying parts as smuggled into the texts by thugs naturally leads to change in the views of “what always had been meant.” Humankind must deem itself deeply lucky for these efforts to read the revelations in a way that harmonizes with modern ethics, civilization and human rights, but at the same time they create profound misunderstandings about such religions. The main misunderstanding, actively promoted, is that the ethics and social structure of modern revelist communities inspired by these revealed texts are “founded” upon their textual revelations in a logical sense. Since such revelist communities form majorities or at least large and politically and culturally relevant minorities in most regions from the American West coast Eastward to the Eastbound of Indonesia, the numbers of believers trying to believe and promote these misunderstandings are vast indeed. The stressful intellectual activity by believers of continuously updating the “real original meaning” of Holy Scripture leads away from the reading of the prophetic books in their original historical status. The chance in danger of being missed as a result, both of the attitude of insiders continuously reinterpreting the “immutable” texts, and of outsider disdain towards the claims that these texts are the “foundation” of the relevant religions in a logical sense is to study Torah, Bible and Koran as magnificent and truly invaluable sources for the understanding the early history of Semitic culture, the history from the times of Abraham, around 2000 BC, until the period in which Muslims were the first to reach the stage of Enlightenment, not much after 900 AD and culminating in the golden age of Arab science and scholarship of the 12th Century. For the history of Christian Europe, its meaning is even stretching some more centuries, until well into the Renaissance period, teaching us why the spreading of enlightened Arab ideas over the Christian community was counteracted by extreme oppression and

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violence (like the brutal and savage methods of killing of many of the opponents of Thomas Aquinas in Paris academic discussion, most notably Siger de Brabant, who was later put in the Heaven of Light in the brilliant company of 12 illustrious souls by Dante, in the Divine Comedy).

6. Arab Enlightenment: Khass and 'Amm In the period of Arab Enlightenment for the first time attempts were made to define the relation of religious belief to another type of belief thought to be somehow independent of it, that of scientific knowledge acquisition. The most explicit attempts handed over to us were those by the Muslim Cordovan scholar Ibn Rusjd. In Paris, though his name got corrupted there to ‘Averroës’, some put their life in danger by defending his line of argument. One of them was Siger de Brabant. He finally got stabbed to death by a clergyman Rome had assigned the task to accompany him everywhere he went. Ibn Rusjd had carefully molded his argument in Aristotelian terminology, using works lost in Europe, which, if you read them for the first time after an education, as the European catholic clergy had, of mostly Bible reading and a little Plato, badly handed over and intentionally mutilated by second rate catholic clergymen, astonishes by its logical precision. The most worrying aspect of Ibn Rusjd’s work was that he conceded that scientific knowledge (the result of the exercise of reason) can be, and often is, inconsistent with the literal text of the Koran. In such cases, Ibn Rusjd wrote, the Koran should be interpreted metaphorically. Since common people (’amm) due to their weak mental capacities, neither understand the exercise of reason not the idea of a metaphor, they should not bother about it and take the Koran literally everywhere. The problems of reason and metaphor are technical issues for specialists (elite, khass). Ibn Rusjd’s approach was meant to create loci for scientists to explore the real world freed from the time consuming obligation to logically connect their findings to the literal text of the Koran. It marks the stage of Arab enlightenment.

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It took quite some casualties in the European Christian world, but three centuries later similar points of view gained a beginning of acceptance there too. Moreover, due to the rise of the general level of education, khass gained, and ’amm declined in social importance in the western world, which finally led to the dechristianization process of the last century. Meanwhile, the Arab world was overrun, first by the Mongols and then by the Turks, who, after a first lapsing into savagery inspired by primitive versions of Islam, quickly (that is, in little more than a century) took over the enlightened Arab view on the relation of science and religion. This led to general technical superiority of the Muslim Turks over the Christian Europeans, also with respect to military hardware. This enabled the Turkish Empire to conquer Byzantium in 1453 and ultimately led to a prolonged military stand-off ending only in 1683 before the gates of Vienna. Most of the so called European technical inventions of this period, ranging from heavy duty precision cannons to croissants and cappuccino, actually found their way from the Muslim world to Europe in this historical development.

7. The True, the Real, and the Local The marked difference between the religions of Semitic origin and most other religions in the world is the claim of Universality, and corresponding zeal to convert mankind to its principles. There is only one place where I found something carrying a remote similarity: the pastoralist Karamojong tribe in North Eastern Uganda believe they were given all cows in the world and hence can take any cow they see anywhere because it must have been stolen from them. The Jews did not yet have such a far reaching claim of Universal Truth. And they never adopted it. There is, in Jewish revelation, only one God, Jahwe, that is, only one God for the Jews. But, for instance in the Torah, the Moabites, a tribe unlucky enough to inhabit the promised land before the rivers became, as we read, red of their blood and the promised was taken, had another God, and lost the war, according to the Torah, because their God was weaker than Jahwe. That is not a matter of uniqueness and generality, but of quality, which

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is quite a different issue. In defending their stance in situations of conflict and despair relating to problems with non-Jews, Jews are not accustomed to refer to God, as for instance Americans and Arabs do. Americans and Arabs, especially in political contexts, seem to think they are only convincing if they suggest that God is behind them. This behavior can be traced back to Jesus, who unambiguously made the transition to a claim of general, Universal Truth. There are no others. This was taken over by Muhammad: “There is only one God and his prophet is Muhammad.” Claims of revealed Eternal Universal Truth are hot potatoes. Its defenders are vulnerable to questions on observations made and other practical issues that seem to put the revealed doctrine into question. But, even worse, they are serious obstacles in practical negotiation under conflict and disagreement. Seeking compromise between two inconsistent Universal Truths is formally impossible, and if prudence nevertheless requires it, any such compromise should — by both parties! — be venerated as being wholly in harmony with their own Universal Truth. This is either impossible or leads to very complicated unperspicuous pieces of argumentation beneath which monsters keep active ready to raise their ugly heads. Well known utterly curious dogmatic compromises on historical meetings of revelist top clerics can testify, but a good example is also the Universal Declaration of Human Rights. At first sight this could seem an inappropriate example indeed: the Holy Scriptures abound with places where God and prophets encourage or even command the flock to commit human rights violations. But what underlies the Declaration is the (vain) revelist hope of universality, and so is its revelist practical use as a weapon against a political enemy. In short, claims of Universal Truth in practice have a disintegrating effect. This can properly be dubbed the inverse dialectics of universality aspirations. In the early stage of analytic philosophy, philosophers introduced the axiom that claims of universal truth are a hallmark of science. From a logical point of view, the universal quantifier was widely thought to be the first sign in any formula representing a scientific theory of law. This view is still widespread among philosophers of

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science, especially in the traditions in which works of for instance, Popper and Nagel are recognized as significant sources. In history, however, science progressed by local hypotheses, not by Universal Truth. It did not progress by replacing the integrated general body of human belief by another one, not even by trying to maximize its claim of as large an area of application as possible. Such a maximization strategy, blowing the balloon up as far as possible, is a type of revolution that reminds more of the birth of a new religion at the moment of a new revelation. On the contrary, in the course of Enlightenment, science wrestled its way out from under religion in a piecemeal way by establishing more and more local knowledge. That obviously was the wisest way to keep out of trouble with zealots. But by the same token, these claims of local, but independent area’s of knowledge acquisition by the early scientists were what mostly worried the Pope. Galilei did not get into trouble by his dealing with the structure of the solar system, which after all, even today, as is well known by contemporary popes, and can safely be assumed to have been anticipated by 16th century ones, is uninteresting, unknown or at least unclear even to most contemporary voters, consumers and certainly most regular church visitors in Western countries. The trouble was caused by Galilei introducing local claims to knowledge not based on revelation. Galilei may or may not correctly have been thought to have refuted the claim of universal Truth of Christianity, but what he put forward was much scarier than just another claim to universal Truth: he came up with a little bit of local knowledge that is, claims just resting on some partial interpretation of just a few things that one can only observe by using specialized equipment. Osiander, in his preface to Copernicus tries to explain that truth is a religious thing, not a scientific one: “He who takes as the truth what is devised for another goal will come out of this science with greater ignorance than the one he entered with” (Copernicus 1883). His words have turned out to be more scaring and unacceptable to Christian revelists than the actual results of the sciences: this new intellectual enterprise called science, claiming to produce valuable thoughts outside the realm of truth, made them unsure, with good reason, about how it could affect religious authority. As science progressed, its

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particular results have at many more occasions caused fear to revelists — think of the idea of evolution -, but nothing compares to the fear caused by Osiander-type explanations that the very notion of truth has nothing to do with science. This not only shook revelists. It aroused philosophers of science and induced them to attack such “instrumentalist” positions, and to defend “realism” against such scandalous scientific paganism. Nietzsche, as he realized, was far too early in claiming that the desire for truth is a Christian residue: “To laugh about yourself, as you should in order to laugh yourself out of the whole [idea of] truth . . . ” (Nietzsche, Die fröhliche Wissenschaft, Book 1, Section 1, p. 42) and his characterization of truth as the “weakest form of knowledge” (Book 3, Section 110, p. 152,). Now, in the 21st Century, more of us have enough experience with scientific and technological progress to start understanding what Nietzsche tried to say. Of course, claiming that science is about local knowledge does not mean to deny that in science, the establishment of more and more local knowledge led to attempts to integrate dispersed local knowledge suspected to be interrelated. Many of those integration projects turned out to be based on daring but useless assumptions and had to be abandoned. A few, and those are the famous ones, like the CopernicusKepler-Galilei-Newton-Einstein development, resulted in integrated structures that held modified forms of the initial local integration candidates, according to the logical relation that has been called dialectical correspondence (Nowak and Nowakowa 2000, pp. 185-188). But of course also the latest structure in any hitherto successful sequence will, just like the previous ones, not last for long in the future. As Osiander, Nietzsche and that part of the modern philosophers working along instrumentalist or idealizationalist lines express themselves: Theories are no truths. The best way to rid yourself of the idea of science as truth finding in the context of modern science is to study the method of idealization and concretization (Nowak and Nowakowa 2000). The idea is that scientific laws typically hold only under ideal conditions. Such conditions typically are never met and could never be met in the real world. In that sense such ideal conditions could be called “false,” but

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that notion of falsehood is a kind of category mistake if applied to ideal conditions. Ideal conditions are not meant to be “true.” Nevertheless, for revelists, truthists, realists, anti-instrumentalists and universalists it may be good as a first approach to think of laws as “false in the real world” and “only true in an ideal world.” It helps you to get rid of the romantic idea of science as the Quest for the Hidden Truth of the Universe. Stating that scientific laws are true in an ideal world, however is in itself a tautology: by — logical — definition, for every consistent statement there always are ideal worlds in which it is true. If this “falsity of laws” claim would have been the message of idealizational philosophy, the harvest would have been as small as Tarski’s definition of truth (‘p’ is true if and only if p) if taken as the message instead of the medium (Tarski 1956, pp. 152-278). The revelist notion leads to a modal logic: ‘p’ is a universal Truth, ‘p’ is a universal Falsity, or ‘p’ is neither. The first two options are interesting to the Enlightened mind only in logic and mathematics — and authority there is argument, no prophets or church leaders. It is a relatively small field. The Enlightened mind shades the enormous “neither” class in a subtle multitude of colors, always remaining ready to slightly shift color at any time. This is what has been reconstructed as the approximation strategy in the method of idealization and concretization. The idealization/concretization approach to scientific theories is meant to deal with this “neither universally True nor universally False” class and to replace their Truth with approximation. Approximation is a relation between a theory, a set of mathematical functions or a computational model, and the data sets the scientist works with at a particular time. Approximation is crunching numbers with functions (and crunching functions with numbers). Both math and data sets are continuously changing in reaction to the results of approximation calculations. Fantasy, and readiness to shift, in the light of approximation problems, from one fantasy to another is important in science but truth plays no role. Whoever, philosopher of science, propagandist or (would be) scientist, puts a rude metaphysics of “Truth,” “Reality” and “Universality” below the subtle and fluent development of modern scientific theories as an immovable or definitive “foundation” of science is a hypocrite or a fool: one day later, his “truth” has faded in

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the versatile minds of whatever scientists he took it from and he belongs to the past.

8. Revelist Remnants in Modern Science Though historically the process of Enlightenment is the triumph of science over revelism, science has been hampered by revelist remnants and sometimes even had its revelist revivals. The reader may have the inclination to see this section as dealing not with science but with “pseudo-science.” Such a distinction has, however, proven to be so treacherous and ideology dependent that I will not make it at all. Science is being understood here in a no nonsense way as what is done, said and written by those generally regarded as scientists by their society.

8.1. Interparadigm Argumentation The claim that scientific theories are not Truths is even in modern day science not an uncontroversial one. It can be seen contested, or at least overlooked, in the rhetoric of scientists’ debates as soon as beliefs are dogmatically expressed, especially beliefs in the deep theories underlying whole branches of science, such as relativity theory, thermodynamics, the theory of evolution and the theory of free market competition. In debates among scientists about the rival fundamental principles dubbed “incommensurable” by Kuhn, scientists have been shown not to be shy to defend revolutionary new points of view by reverting to the truthist and realist conversion strategies that remind of revelists. The subject we touch upon here is the “politics” of science in times of deep controversy and scientific “schism.” Because rival viewpoints are largely backed by what their pay off will be in solving the agenda of future applications (“puzzles,” as Kuhn called then), rival “political” leaders in science are in need of followers willing to have faith in the promise. Since research funds are scarce and the flock is constrained in size, to attract a sufficient number of research workers for a new approach is a territorial matter in which propaganda may be

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directed to what wins founders and followers over rather than to what private doubts scientific leaders may have about their own approach. An illuminating example is that of Avogadro refusing Gay-Lussac the right to round off 1.97/1 to 2 in the volume analysis of oxygenhydrogen reactions, while after having found 1/4.75 for the weight ratio of N and H in NH he wrote “because an integer remains easier in memory, we prefer the ratio 1:5 until a more precise ratio had been obtained” (Hooykaas 1976, p. 230). Nice also are the “bandwagon effects”: after scientists of authority have measured the value of a natural constant, there is a tendency of values close to it to be reported until another scientist of authority reports a significantly deviant value. This then marks the building up of a new “bandwagon.” Such social phenomena in science exist, despite the fact that science and Universal Truthism root in fundamentally different metaphysics. The message of Enlightened tolerance is to find local solutions for local problems. “Mechanics,” for instance, is a local solution. It is of little help in explaining most known phenomena. Those who have proclaimed mechanics as a universal solution, like materialists, lost their energy in revelist philosophies that did neither contribute to the growth of successful scientific applications of mechanics nor to the growth of any other field of scientific knowledge. The enthusiasm of such proponents of grossly universalist claims is at least quite similar to the phenomenon of lapsing back into revelist fundamentalism. As Thomas Kuhn noted, even once most of the leading research workers in a field feel that an old basic theory has been convincingly surpassed by a new rival, typically a gradually ageing group of die-hards will remain, defending it against the odds. At such occasions, Truth takes its toll. Such lapses no doubt have been seen most frequently — and seen up to totalitarian proportions — in universities and academic institutions. The paradox of the university world is that it depicts itself as the carrier of scientific progress, but in practice acts as the maintainer of scientific traditions, which is by nature a conservative task. Universities typically formalize a hierarchy in faculties and departments and thus impose requirements of discipline on those who should, according to the Enlightened worldview, be independent

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minds. Thus it is at least far from certain that universities are the institutions from which to expect the largest of contributions to the growth of knowledge. And indeed a surprisingly large amount of great minds of the Enlightenment lived in filthy garages, on dusty attics and in the wilderness. Such minds typically are either much poorer than university professors and not bothering about it, or much richer. No wonder totalitarian societies cherish their universities as useful instruments to counter Enlightened tendencies. Their very structures makes them suitable indeed for that purpose.

8.2. Scientific Backing of Political Ideologies This brings us to a second reason that some may be doubting the claim that science is not about Truth, let alone universal Truth. In many social and political situations, scientists, especially those with state or party university backgrounds are found backing political ideologies such as racism, nationalism, socialism, and communism. In their messianistic rhetoric they are typically drawing predecessor scientists into their camp, not infrequently putting them in roles reminding of that of the revelists’ prophets. Since such kinds of scientific developments in Nazi Germany and the Soviet Union have been covered extensively by its intellectual and political enemies, let us start with a 20th Century English example, the Eoanthropus dawsoni. In a series of discoveries in 1910–12, Charles Dawson, an English lawyer and amateur geologist, found what appeared to be the fossilized fragments of a cranium, a jawbone, and other specimens in a gravel formation at Barkham Manor, on Piltdown Common near Lewes in Sussex. Dawson brought the specimens to Arthur Smith Woodward, keeper of the British Museum’s paleontology department, who announced the find at a meeting of the Geological Society of London on Dec. 18, 1912. Woodward claimed that the fossils represented a previously unknown species of extinct hominid (Eoanthropus dawsoni) that could be the missing evolutionary link between apes and early humans. His claims were endorsed by some prominent English scientists. The primacy of Great Britain in the world was established by

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research in what is the True Foundation of Mankind: the earth’s crust, Sussex. The display of Eoanthropus dawsoni was opened by Her Majesty the Queen. A later examination of the Piltdown remains showed them to be the skillfully disguised fragments of a quite modern human cranium (about 600 years old), the jaw and teeth of an orangutan, and the teeth probably of a chimpanzee, all fraudulently introduced into the shallow gravels. Chemical tests revealed that the fragments had been deliberately stained, some with chromium and others with acid iron sulphate solution (neither chromium nor sulphate occurs in the locality) and that, although the associated remains were of genuine extinct animals, they were not of British provenance. The teeth, too, had been subjected to artificial abrasion to simulate the human mode of flat wear (Source: Encyclopedia Britannica). Research with similar aspirations abounds in Russia, China, the Holy Land and elsewhere. Governments have usually some interest in monitoring the results of home archeology and it is well known that many countries discourage the advent of foreign archeologists. Let us go to France. In 1952, Swedish dentist Sten Forshufvud read the recently published account of Napoleon’s death by Merchand (Forshufvud and Weider 1995). Based on his knowledge of toxicology, Forshufvud came to the conclusion that Napoleon had been murdered. Fortunately, a number of Napoleon’s staff had kept locks of the Emperor’s hair, which were passed down the generations, sometimes coming up for auction. In the 1960s this happened and in order to prove this theory Forshufvud turned to Glasgow University forensic scientist Professor Hamilton Smith, who had developed the nuclear techniques to record very small levels of arsenic. Since it has been established that hair grows at approximately one inch every two months, if it is shaved at the scalp and the date is known, then tests for arsenic in the hair can determine almost to the day when arsenic was ingested. Using these techniques it was shown that small quantities of arsenic were present in Napoleon’s hair. It was possible to poison a person without detection by slowly exposing him/her to small quantities of arsenic. This technique was known and was described in a book that Albine de Montholon had with her in St Helena. Forshufvud

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concluded that Napoleon had been murdered by the Comte de Montholon. This obviously had implications for the correct view on this episode of English and French political history. To investigate further details, Forshufvud went on search for more specimens of Napoleon’s hair. The French Academic network, however, had made sure that no further of the known specimens would be made available to Forshufvud’s research, a French academic attempt to keep French history French. (It failed. British scholars later found that the British wallpaper of Napoleon’s room at St. Helena contained some arsenic too, though — but the lobby behind this last addition has yet to be identified — not in lethal quantities). These are all fine examples, but the revelist remnant of revealing the hidden Truth in history, and fixating it in a Book has become the best known by the work of Karl Marx and the status that this work acquired in socialist and communist doctrines. Marx was well aware of the structural analogy of his view on history and that of the Bible, from the paradise of Genesis to John’s Apocalypse. Moreover, he gave his followers, in the form of Capital, their own Book. Lenin adapted the doctrine to make it fit the Orthodox Christian flavor of early 20th Century Slavic culture by molding it more emphatically into the eschatological sequence of Paradise (Original Communism) — Fall (Original Appropriation, Feudalism, Capitalism) — Satan-in-Chains (Dictatorship of the Proletariat) — Heaven (Final stage of Communism). In communist thinking, ideology covers all science in the same way as religion was stipulated to cover all science in the European Middle Ages. The Enlightened idea of science as objective research work done by independent minds is, in communist thought, rejected as a bourgeois mystification of the Truth of the scientific suppression of the proletariat under capitalism. Marxism was by far not the last scientific current backing political doctrines. In the second half of the 20th Century, the Last Judgment regained popularity: politics first saw scientists supporting the limited resources movement (Club of Rome, Meadows et al. 1972). After resources turned out not to be the most acute problem, the Western world saw the rise of the ozone layer/global warming movement,

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supported by an extensive scientific lobby. After a brief interruption by fear for a temperature jump inversion to an ice age quickly followed by the sudden fear of the possible collision of the earth with a meteorite, the attention of public opinion was turned back to the main world diseases, like AIDS, malaria, diabetes, obesity etc, all of them attributed the status of the globally most serious disease in the world, at least by the mass media, at least each of them in turn around the time of the annual world congresses of their respective medical research communities. So far for contemporary scientific backing of ideologies.

8.3. Realism and Anti-Instrumentalism in the Philosophy of Science Philosophers of science, often posing as “realists,” contest the claim that scientific theories are no Truths. They often label this view as “instrumentalism”: the idea that theories have no ontological claims in themselves but just hold together an integrated body of relations observed to hold approximately in the area’s covered by those who “work with” that theory. Philosophers of science infuriated by instrumentalism are not seldomly warning against it as a cultural danger. Their “realism,” the doctrine that good scientific theories are true in the real world (under a Mediaeval plethora of rival definitions of what is “truth” and what is “reality”), is claimed to save the world from the “instrumentalist” danger. Popularization of science in mass media. The revelist mistaken image of the scientist as a hero searcher and finder of hidden Truth is actively enforced by the popularization of science, for instance in the TV broadcasts of Discovery and of National Geographic Channel. There, the attention of the TV audience is turned emphatically from the nasty math to the face of the scientific prophet-Truth finder who, in an adventurous quest full of despair, finally uncovers the definitive Truth. Big media successes typically report on scientific research proving truth of claims occurring in ancient revealed texts, such as finding traces of habitation of the Black Sea floor and ruptures in the Bosporus area indicating a Noah type of flooding of the Black Sea basin

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due to global warming around 5000 BC. This mass media behavior suggests that Ibn Rusjd was not far off the mark with his Khass-’Amm distinction. Concluding: unfortunately it cannot be denied that scientific research every now and then degenerates into a Truth finding mission. Revelist approach to knowledge seems to keep an appeal allowing it to deform the image of science and even to creep in scientific procedures.

9. Superstition Given New Opportunities by the Present Big Bang of Science Despite liability to infection by revelist remnants, the contemporary growth of scientific knowledge is explosive. In the seventeenth century it had become impossible to acquire all available scientific knowledge in such a way as to be able to actively participate professionally in all fields. Nowadays, no one can be expected to keep updating the overview of even only the main results of the main fields of physics and biology. There is no evidence of any kind of decline of the acceleration of the growth of knowledge. Within scientific fields, finding and keeping track of related fields, the results of which are relevant to one’s own, is now constituting a major problem. No one can be sure not to have lost track of others whose results should have been monitored. Theories may start to diverge not due to conscious disagreement but simply due to lack of mutual acquaintance of the research groups working with them. The astonishing explosion of knowledge, the process crucial to the future, is uncoordinated, autonomous. Nobody is in charge. It just happens, and nobody it going to stop it. Every individual involved only sees (let alone controls!) a negligible fraction of it. Despite this historical process of loss of individual grip on history, the “We” ’s and “Mankind” ’s broadcasted by priests, networks and politicians have become more and more encompassing, and by now long has reached the stage that “We” have to save the earth (for some danger or another, by some means or another). “We” have responsibilities, tasks and missions. “We” discuss genetic research and nuclear

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proliferation as if “We” could exert any influence on its development. Everybody, scientists included, is ready to back up claims on the issues “We” have to address. “Mankind” is the standard subject to enter the ecoliturgy at the end of nature documentaries: “Whether this unique species will survive, depends on whether Mankind . . . ” The belief in “We” and “Mankind” as a collective subject is no doubt the chief item of contemporary superstition. It is found everywhere, until deep in the labs of the Nobel Prize winners. And it is this “Mankind” for whom the prophets wrote their revelations down. As far as Darwinist biologists and sociologists are concerned, it does not exist. But this is only the very summit of all opportunities that the Big Bang of science provides to superstition. Once science became an autonomous social process, Enlightenment became a feature of social structure: anyone who has any talent that is of any use to any fraction of science has a good chance to be absorbed in the process of scientific growth, be it in a lab, be it by on line partnerships between people working at common interests, be it in a company designed new types of products for industry or consumer. Whatever beliefs you have apart from this one talent that may suck you in the scientific social structure, is irrelevant. If you can deal well with UTMS communication software you will be hired, no matter whether you believe in aliens, are a pro-life pro-death penalty Methodist, or even a post-modern deconstructivist. Who cares? Enlightenment has become independent and autonomous nowadays and only tends to occupy a very small part of the human soul, the rest of it is free! The situation today is, of course, only one particular stage in a historical development of, it seems, ever increasing speed. At the beginning of the Enlightenment, the revelist idea of Truth prevailed: the idea that knowledge is Truth based on holy books and that (religious) authorities are in charge of interpretation problems. Such authorities do discuss controversies but, due to discipline of khass and illiteracy of ‘amm (to stick to the terms of Ibn Rusjd) only their common conclusions tend to reach the general public. Then, in the 16th, 17th and especially the 18th Century an intermediate stage was reached where the public still generally considered

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thought to be a specialism exerted by khass, but different and inconsistent khass-opinions started to spread wider among the general public (the spread of literacy, the introduction of newspapers, later the widening of democratic rights) and started to be discussed there. The general public was getting accustomed to the existence of divergence of opinions and discussion. At the contemporary stage, philosophers and scientist do not differ from any other social group like rock musicians, sportspeople, film stars, artists, film producers, TV documentary makers, web editors. Everybody develops his own thoughts fitting to his own life, and there is simply little time and little interest to study thoughts of those who lead other professional lives. The only ones who need to keep track of the development of thoughts other than those of their own group are those who work for politicians or for the selling departments of producers of mass consumption goods. Hence the observable features of their work (advertisements, political campaigns) are the only ones that are put to the test of general public approval (in terms of earnings and votes). These reflect the continuous multi-billion dollar research aimed at improving the operating system of societies, at least of the part that forms targeted consumers and voters, albeit a system that merely aims at having their members buy some product or cast their votes some way rather than another. The data of advertisement and public relation offices are the only wider ranging generalizations available. The contents of advertisements and political campaigns makes clear that this is not what many of us would like to think of as the main achievement of western civilization. Be this as it may, the contemporary fruit of the Enlightenment is that there is no social danger anymore in top soccer players wearing crosses from their necks (as long as they use the stretch strings given to them by the scientifically versed training staff), believing they should never step on the line when entering the field, rock stars believing in aliens, web editors believing in God and captains of industry cured from cancer by miracles. Frequency and depth of such beliefs are continuously monitored by the market research workers of politicians and mass producers, and as soon as they become socially significant, they enter the advertising and political campaigns. Scientific

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knowledge is an “objective” power, but it is not to be located in the consciousness of the public. As advertisements show, the public is not interested in the theories underlying cell phones, but in for instance, their helpfulness in getting into contact with someone desired to become a sexual partner. The public is not anymore interested in economic theories underlying political programs but in whom of the professional cheaters contending for some seats deserves their “trust.” Science is everywhere: no mass product, no political program can be successful without science, but it has become autonomous, unconscious, objective, collective, a force by itself. This process of Enlightenment becoming independent and autonomous is not to be identified with the Ibn Rusjd’s khass/’amm distinction. Whoever worked with the youngsters actually doing the developing work at the front edge of technology knows that in their office-gardens top soccer players believing they should never step on the line when entering the field, rock stars believing in aliens, and web editors believing in God are quite at home. Ibn Rusjd would probably conclude that today khass has disappeared because science did not need it anymore. The general image emerging is that science and technology now got so fragmented that the single individuals’ knowledge of it has become too small to allow for a rational worldview that reflects the state of available knowledge. The single individual, even if he is thoroughly schooled in some scientific or technical specialism lapses for the unoverseeable part of nature he is not specialized in, into the worldview radiated by TV channels, rock star albums, Popes, Imams, government press offices, deodorant advertisers or other public “authorities” at hand. It is as soon as they are seen as research objects, not to be argued against (for such arguments are easy to give and already satisfactorily supplied for many centuries) that the subject shifts to the peak of relevance to the humanities. Clearly the questions are: • What make the pre-Enlightenment metaphysics so tenacious and attractive that it has resurfaced as soon as Enlightenment gained autonomy? Why are notorious believers immune to the well known arguments against their religions? Why does this

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phenomenon of archaic belief extend not only over political leaders and exponents of top sport, but even to the ranks of scientists, research workers and skilful astronauts? • How do believers abundantly exposed to the fruits from the culture of Enlightenment prevent these fruits from entering the core of their being where they could deconvert them into nonbelievers? • Why do they do that? • What is the explanation for on the one hand, the inclination of believers to form social groups around a doctrine and, on the other to breaking them up in often bloody fraternal doctrinal strife?

10. Contemporary Science and the Contemporary Meaning of Theories Not wishing now to enter the skirmish between rival views in the philosophy of science we stick to the basics: roughly, scientists communicate and update with three things: data sets, functions and theories 1. data sets, containing variable values collected 2. mathematical and computational functions that have proven effective in restricting the possibilities in what data sets can result from the collection of variables. They allow obtained datasets to be labeled as standard, problematic, anomalous, etc. or to conclusions that some unmeasured parameters must have certain values. 3. theories about what’s going on, making sense of the functions that are thought useful in the process A striking thing of the explosively growing speed of scientific developments in the last decades is that the life cycle duration of this third element, theories (between adoption and dumping) has shortened enormously, even at a pace similar to that of consumer durables. In the 19th Century, adoption and dumping of theories still were big and emotional happenings, both to an individual scientist and

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to a research group. Nowadays, proposing to replace an old theory with a new one is a routine thing at every lab’s colloquium session. Like consumer durables, modern scientific theories have become lighter. They should just contain enough to visualize the processes studied in a way nicely symbolizing the math currently applied. Theories are not the big issue anymore. A theory is OK if it helps you thinking through the math you apply and how it does well in some and badly in other applications (think of the speed in which new proposals for new types of subatomic particles and new types of energy are succeeding each other in contemporary pure physics). The important thing for a scientific research worker is to be tolerant to may be even strange ideas that might come up in yourself and your colleagues. Though this seems where enlightenment has naturally taken us, at the same time it means that what formerly may have fiercely been fought as “superstition” is not such a big deal either, provided you keep doing the math and keep checking and worrying where and how data fit it nicely and where they do so unsatisfactorily. To contemporary scientists, theories are fun things to play with and no big deal to dump. In this respect, research workers are well integrated in the culture of homeopathy, astrology, fundamentalist fire arm lobby Christians, pro life pro death penalty Presbyterians, child pornography, nature conservation, anti-globalization, Catholic pedophilia, Muslim fundamentalism, Gay rights activism, aliens, worm architecture, UFO’s, anti-immigration politics, ozone layer defense, plane hijacking, animal rights, slavery reparation payments, post modern deconstructivism and everything else nowadays tried out in the mass media, on the internet and elsewhere. Modern scientists are product of a culture allowing you to deal as liberally, freely and smoothly with your ideas as toddlers do. After all, it is by now well established that as far as the speed of growth of knowledge is concerned, toddlers are superior by far to adults. It is no accident that nowadays adults acknowledge and admire this, while even fifty years ago, to adults toddlers were not more than inferior animals that could only hope to become human by eating and obeying. This is the trend in modern western society and this trend is unstoppable.

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True Enlightenment frees man of the burden to treat his theories as universal Truths. The astonishing explosion of light ideas and theories floating around in the worlds is not a token of the end of Enlightenment. It shows how playfulness makes scientists, artists and others astonishingly effective once they are unhampered by “Truth.” Enlightenment has become the obvious practice and thus disappearing from conscious considerations. Hence, as a conscious worldview it lost its necessity. It it turned into the fabric our social structure as happened with the free market economy, which, quite similarly started as an idea. Similarly, few are able to consciously ponder the differences between a market economy and a huntergatherer economy. The larger and most powerful part of civilization ceased to take matter of “Truth” as its daily object of thoughts and doubts. Its hands are free to create an unprecedented explosion of knowledge, technology and power. We have reached the stage where the gods, heavens and hells featuring in private homes, TV shows, computer games and holy places — apart from some escapes from the closet in the form of youngsters trying their computer shooting game at school or practicing the Koran maxims in aero plane raids — can do no more harm to civilization and the progress of knowledge than their competitors: aliens, stand up comedians, soaps, advertisements and political campaigns.

Conclusion Revelism got free of its roots and is now fully accepted among Enlightenment’s freely floating debris of theories.

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PHiLES Institute Jan Evertsenstraat 18 5021 RE Tilburg The Netherlands

REFERENCES Copernicus, N. (1883). De hypothesibus motuum coelestium a se constitutis commentariolus. With a preface by Osiander, To the Reader About the Hypotheses in this Work. Berlin. Dijksterhuis, E.J. (1950). De Mechanisering van het wereldbeeld. Fourth edition. Amsterdam: Meulenhoff, 1980. English translation: The Mechanisation of the World Picture: Pythagoras to Newton (Princeton: Princeton University Press, 1986). Encyclopædia Britannica (2002). Chicago: Encyclopædia Britannica, Inc. Feyerabend, P. (1970). Against Method. In: (Minnesota Studies in the Philosophy of Science, vol. 4). Forshufvud, S. and B. Weider (1995). Assassination at St. Helena Revisited. John Wiley & Sons. Galilei, G. (1982). Dialog über die beiden hauptsächlichtsten Weltsysteme. Stuttgart: Teubner. Hooykaas, R. (1976). Geschiedenis der Natuurwetenschappen [History of the Natural Sciences]. Utrecht: Bohn, Scheltema en Holkema. Kuhn, T.S. (1970 [1962]). The Structure of Scientific Revolutions. Second Edition. Chicago: Chicago University Press. Marx, K. (1975). Capital. Berlin: Dietz. Meadows, D.L. (1972). The Limits to Growth. New York: Universe Books. Mindphiles.com. Web Site for Nomadic Philosophy. http://MindPHiLES.com Mirowski, P.J. (1992). More Heat than Light: Economics as Social Physics, Physics as Nature’s Economics. Cambridge: Cambridge University Press. Nietzsche, F. (undated). Die fröhliche Wissenschaft. In: Gesammelte Werke, vol. 6. Muenchen: Wilhelm Goldman Verlag. Nowak, L and I. Nowakowa (2000). Idealization X: The Richness of Idealization. PoznaĔ Studies in the Philosophy of the Sciences and the Humanities, vol. 69. Amsterdam: Rodopi. Tarski, A. (1956). Logic, Semantics and Metamathematics: Papers from 1923 to 1938. Oxford.

Martti Kuokkanen BOXING AND VIOLENCE*

Boxing is an honorable sport. You don’t want anyone to get hurt more than they have to. — George Foreman

The paper first defines a concept of violence whose adequacy is discussed both theoretically and through some examples. It is applied to sports and a thesis that boxing is not violence is defended. Any kind of sport can and should be considered at two different levels: at the level of the sport itself, where the sport is completely comparable to any other social institution, and at the level of the tokens of the sport. It is argued that one cannot claim that boxing itself

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Several people have commented on the earlier drafts of this paper. I want to thank Heta Häyry, Matti Häyry, Timo Jukka, Heikki Kannisto, Kaarlo Miller, Tuula Pietilä, Gabriel Sandu, Tuija Takala and Risto Vilkko of the Departments of Philosophy, University of Helsinki; Leila Haaparanta and Timo Klemola, Department of Philosophy, University of Tampere, and Henrik Nordman, VTT Energy, Finland. My special thanks are due to my boxing friends at Helsinki Tarmo Boxing Club, including Ilmo Lindqvist, Erkki Luja, Kimmo Luja, Jaakko Lundén, Tuija Niironen, Turo Saarinen, Tiina Tuovinen and Juha Turkka. Mr. Roderick McConchie has kindly revised my English.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 445-460. Amsterdam/New York, NY: Rodopi, 2007.

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is violence unless one is willing to accept the view that many other social institutions, for example the business world, are violence. This thesis does not exclude the possibility that boxers may be violent in a bout or that the bout itself may contain violence. It is argued that these facts are insufficient for claiming that boxing is violence. Otherwise many social institutions — generally seen as nonviolent — become violence by the same argument. Moreover, it is argued that any criteria which are external to sport are inadequate in assessing the violence in sport. Finally, a criterion to assess the violence in boxing is developed. This criterion is internal to sport, theoretically justifiable by the core ideas of sport and it applies — mutatis mutandis — adequately to any combat sport as well as to some areas outside sport, for example to self-defense, to defending a victim of violence and to the police.

1. The Concept of Violence I start from a distinction introduced by John Harris (1980, Ch. 2). We may use the word ‘violence’ in a descriptive way or in a classificatory way (a violent act as against an act of violence). The problem of the descriptive use is that it does not appropriately differentiate acts of violence from other acts. In practice almost anything can be performed violently. For example a coffee cup can be hit violently against a wall. However, doing so need not be an act of violence. Poisoning a person is in itself a non-violent act. However, it is clearly an act of violence. The case in point is the following example from John Harris (1980, p. 16): To turn from fiction to fact, we are told that children in Belfast adopt the following tactic against British soldiers. Here is one of the children describing the method: That’s the street right? There are the lamp-posts and that’s the Army Land-Rover coming up the street. You tie your cheese-wire between two of the lamp-posts about six feet up. There’s always a soldier standing on the back of the jeep; even with the search lights he can’t see the wire in the dark. It’s just at the right height to catch his throat. No violent act but clearly an act of violence. So long as such tactics are employed no one would consider Belfast to be a violent-free city!

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The above examples clearly demonstrate that the descriptive use of violence does not appropriately differentiate the acts of violence from other acts. For this reason we need a definition of violence which is adequate at least in covering paradigmatic examples of the violence of everyday life. I propose the following definition. Definition of Violence: An act is an act of violence if and only if (1) the act is performed freely and autonomously, and (2a) the act presumably violates the autonomy of the other party, or (2b) the purpose of the act is to hurt the other party mentally or physically, or to restrict the freedom of the other party. The epithets ‘freedom’, ‘autonomy’, ‘the purpose of an act’ as well as ‘to hurt the other party’ occurring in the definition are difficult to some extent. It is impossible to ascribe any general, exhaustive meanings to these epithets because their meanings depend rather heavily on the context in which they occur. (For detail in a medico-ethical context, see for example Häyry 1991, Chs. 2, 3, 5, 6.) Next I try to argue that the conditions of the definition are mutually independent. In this sense the definition is formally correct. I proceed through some examples. First, blackmailing certainly, not only presumably violates the autonomy of the victim. The blackmailer may act freely or as forced. On the other hand, everyday life conversation presumably does not violate the autonomy of the conversation partner. However, defamation for example does. Thus, conditions (1) and (2a) are mutually independent. Second, consider conditions (1) and (2b). Street violence, slander and offensive language are acts whose purpose typically contains hurting the victim physically and mentally, respectively. Planning to kidnap someone is an act whose purpose contains the restriction of the freedom of the victim. Any of these acts can be performed freely or as forced. Thus, condition (1) is independent of condition (2b). Everyday life is full of free acts whose purpose is neither to hurt any other part mentally or physically nor to restrict the freedom of the other party. On the other hand, the purpose of several everyday life

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free acts may very well be to hurt the other party mentally or physically, or the intention may be the restriction of the freedom of the other party. Thus, condition (2b) is independent of condition (1). Consequently, conditions (1) and (2b) are mutually independent. A medical operation without or against the consent of the patient presumably violates the autonomy of the patient. However, typically the purpose of such an operation is neither to hurt the patient mentally or physically nor to restrict the freedom of the patient. Thus, condition (2b) is independent of condition (2a). A boxer may enter the ring with intention to hurt his opponent physically. However, no violation of the autonomy of the opponent occurs. The purpose in political arguing may very well be to hurt the opponents mentally. Typically no violation of autonomy takes place. A criminal is sentenced to the prison by the court, i.e., the purpose of the act of the court contains the restriction of the freedom of the criminal. However, the autonomy of the criminal is violated by no way. Thus, condition (2a) is independent of condition (2b). Consequently, conditions (2a) and (2b) are mutually independent. Several of my colleagues have proposed that the definition should be entirely conjunctive, i.e., conditions (2a) and (2b) should be conjoined by conjunction instead of disjunction. However, it seems that such a move makes the definition too narrow. As an example, consider a duel. Condition (2b) is always satisfied when it is relativized to the appropriate context, i.e., to the conditions of dueling. Condition (2a) is false in the context of dueling. Condition (1) is typically satisfied in the relevant context. Thus the conjunction of conditions (1), (2a) and (2b) is false and for this reason a duel does not contain any acts of violence, i.e., dueling is not a violent institution. However, this result seems extremely counterintuitive. Applied to boxing we get a completely analogous result. But it seems evident that a bout may contain acts of violence and boxers may perform acts of violence in a bout. I will consider later some examples of violence in boxing matches in detail. The above definition of violence is adequate in the sense that it covers the paradigmatic examples of everyday violence. Applying the definition yields the result that street violence and acts such as rape,

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torture, cruelty to animals, coercion, oppression, insult, defamation etc. are violence or contain acts of violence. Slander and offensive language are also violence in the sense of the definition. An objection to this definition may be that it is too wide. However, I think that its implicit context-dependence excludes the most serious counter-examples. For example (an effort at) coercion is mental or physical violence in the context of everyday life. However, it clearly is not violence, for example in the context of business and politics, at least not always. Correspondingly, stripping is not violence when it happens in a brothel for example. However, stripping in an ordinary restaurant is counted as mental violence to the same extent as improper suggestions are seen as mental violence. 1

2. Boxing and Violence There are kinds of sport which are associated with various amounts of physical violence. Cases in point are combat sports, for example boxing and contact karate. There are also team sports which are associated with violence, ice hockey and American football being typical examples. A commonsense approach to the problem seems to be the following. Violence in a sport depends simply on whether the sport contains risks

1

John Harris (1980, p. 19) defines violence as follows: an act of violence occurs when injury or suffering is inflicted upon a person or persons by an agent who knows (or ought reasonably to have known), that his actions would result in the harm in question. I think that Harris’ definition is not satisfactory. First, I think that an act of violence should be done freely and autonomously. If a person is forced to perform an act of violence, the person him/herself becomes the victim of violence and we may say at most that he or she is forced to act violently. But this is clearly separate from performing an act of violence. Second, Harris’ definition does not contain any reference to the violation of the autonomy of the other party. Consequently many medical operations for example are violence.

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of injury and permits acts which are violent in the descriptive sense.2 The commonsense approach is, however, to a certain extent inconsistent. In some cases the extent to which a sport directly resembles violence in the descriptive sense seems to be completely irrelevant. For example fencing as a sport resembles violence very much (fighting with swords). However, fencing is typically not counted among violent sports, because the risks of injury in fencing are negligible. On the other hand, the extent to which a sport exposes its contestants to serious injury is alone insufficient to characterize the violence involved in a sport, motor sports being cases in point. These examples clearly demonstrate that violence in a sport cannot be assessed appropriately if it is used in the descriptive sense. The problem should be approached from the classificatory sense of violence. Participating in a sporting contest, for example in boxing, presupposes the consent of all contestants. This applies to all parties in boxing: the boxers, their trainers and seconds, the jury, the referees, the judges and the audience. Violence in turn presupposes typically, although not always, an act without or even against the consent of at least one party. This feature of violence means a de facto violation of the autonomy of at least one party. Looked at from a slightly different angle we may say that sport in general and boxing in particular presupposes the autonomy of all participating parties. Moreover, any kind of sport presupposes mutual respect for the autonomy of the contestants. Violence in turn typically violates the autonomy of at least one party directly or indirectly, although not always. In particular, physical violence violates the bodily integrity of a person, which is essential to his/her autonomy. On the other hand, violence in combat sports can be looked at from the perspective of the extent to which the purpose of the acts permitted in the sport is to hurt the opponent and to what extent the consequences of the acts permitted in the sport may injure the opponent. Here violence in a sport should be looked at from two 2

See for example Joyce Carol Oates (1988), Joyce Carol Oates and Daniel Helpern (1990), and Edith Summerskill (1956).

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different angles: first at the level of the tokens which exemplify the sport, and second at the level of the sport itself which makes any sport comparable to any other social institution. Causing injury to the other party intentionally is a sufficient, but not a necessary condition of violence. If a person causes injury to the other person unintentionally, accidentally, from ignorance or from inadvertence he or she does not typically perform an act of violence. In particular, physical violence always presupposes an act whose purpose is to cause injury to the other person. However, an act of physical violence does not presuppose success. For example, an attempt to murder a person is an act of physical violence. If a person causes injury to another as an unintended and unforeseen consequence of an act after due consideration the act is not counted as violence. When the purpose of acts permitted in combat sports is considered at the level of the tokens of the sports there are no clear criteria for resolving whether combat sports contain violence. The motives and purposes of contestants may differ greatly from one another. A boxer may enter the ring with the intention of winning without injuring his opponent. In a bout there is, however, always a risk of injury and if in such a situation the boxer injures his opponent it is evident that doing so is an unintended consequence. Such a case clearly does not belong among acts of violence. Another boxer may enter the ring with the intention of winning the bout by injuring his opponent. A third may enter the ring with the primary intention of injuring his opponent. For a fourth boxer the fight itself may be the most important thing independent of winning or causing/getting injury. The cases above indicate that at the level of tokens, boxing may involve violence, depending on the motives and purposes of the contestants. However, one can only very exceptionally know with certainty whether a boxer is violent. This consideration may be objected to as follows. The crucial thing in considering the purpose of an act is those immediate consequences which may reasonably have been assumed to be known by the agent and others. The aspects of an act alone which are consistent with the description of the act of the agent itself are insufficient or even

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misleading in considering its purpose. According to this objection, if the purpose of an act is fixed only on the basis of the conscious motives and of the other related things the following untenable results follow: • when chopping wood in a forest flies are annoying. I squash a fly on the top of my companion’s head with the back of my axe. In the hospital I say: “I’m very sorry. I only intended to squash the fly.” • the primary purpose of the robbery with murder is getting money. A robbery with murder is therefore not an act of violence. • the primary purpose in war is to win. Thus war itself is not violence. Note first that all of the examples above are violence in the sense of the definition given above, except defensive war itself. In all of the examples, the autonomy of the other party is de facto — not only presumably — violated when the examples are relativized to their relevant contexts. For this reason these examples are acts of violence given that the relevant acts are performed freely and autonomously (which is obvious in these examples). Moreover, the objection contains a serious problem. There are no general, context-free and agent-independent criteria for fixing what are the immediate consequences of an act which may reasonably have been assumed to be known by the agent and the others. This problem shows in particular when the violence of acts is considered in which no party’s autonomy is de facto violated, and especially when the acts presuppose the consent of all parties. For example, is sadomasochistic sex violence? What is the purpose of having sadomasochistic sex? If a “normally sex-orientated” person happens involuntarily or against his/her will to be involved with sadomasochistic sex in some way or other, it is justified to say that he or she is involved with violence. However, I think it is wrong to claim in general that sadomasochistic sex is violence. If a sadomasochist him/herself says that the purpose of having sadomasochistic sex is sexual pleasure, sadomasochistic sex is not violence in the sense of the above definition. If he or she says that the purpose is to hurt the sex partner and/or him/herself then the related

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acts are violence. If he or she says that the purpose is sexual pleasure and hurting him/herself and/or the sex partner the situation is ambiguous. In such cases it remains open whether sadomasochistic sex is violence. As another example, consider euthanasia. The immediate consequence of euthanasia is the death of the patient. This is known de facto by all parties, the doctor and the others which may include the patient him/herself. Euthanasia is killing the patient which de facto or presumably entails the consent of the patient. However, killing a person in general or killing a person of one’s own free will is not the purpose of euthanasia. The purpose of euthanasia is to alleviate pain and guarantee a good death. For this reason euthanasia is not violence. If the purpose of euthanasia were killing a human being or killing a human being of one’s own free will, euthanasia would be accounted violence because killing a human being (of one’s own free will) is injuring a human being when killing human beings is considered in general, apart from all relevant contexts. Why is cutting a person, for example with a knife, generally separated from all relevant contexts, violence? Because it typically violates the autonomy of that person. This holds at least in the western cultures. Why is an operation performed by a surgeon not violence? Because it entails de facto or presumably the consent of the patient and the purpose of the operation is to improve the health of the patient. If a surgeon performed the operation just for fun or for his/her perversions his/her acts would be accounted violence. The examples above show that the relevant context of the acts and the conscious motives of the agents are relevant when the violence of acts is under consideration in situations which contain no violation of the autonomy of the parties. Second, the examples show that what are the immediate consequences of an act which may reasonably have been assumed to be known by the agents and the others cannot be resolved independently of the relevant context and of the agents. Only in the euthanasia example it is known that the immediate consequence is death. A sadomasochist knows when pain exceeds sexual pleasure for him/herself but not for his/her partner. For this reason sadoma-

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sochists use a so-called safety word which signals the limits of the game. In surgery there are operations which involve significant risks of death. The latter case applies well to boxing. If a boxer knew or could rationally expect to be injured in a bout he would presumably enter the ring only very exceptionally. Boxers know only that they take a more or less significant risk of injuring their opponent or getting injured themselves when they enter the ring. I think the above examples demonstrate that there are no general, context-free and agent-independent criteria for fixing the immediate consequences of an act which may reasonably have been assumed to be known by the agents and by the others. In some cases — for example in boxing — even (rationally) expected consequences are out of the question. Here you have only more or less significant risks. Consider next boxing as a sport. Boxing is regulated and controlled by clear norms the most important of which are the written rules of boxing. The task of the referee, the boxing doctors and the jury is to ensure that the rules are followed. The purpose of a bout is to win according to the rules. These rules also fix precisely which acts are permitted in the ring. The purpose of boxing considered as a sport is not injuring or hurting the contestants. Moreover, participating in a bout — in the ring as well as outside the ring — typically presupposes the consent of all parties. For these reasons boxing as a sport is not violence.

3. Violence in a Sport — an External Criterion The above thesis may be objected to as follows: Boxing as a sport is violence because the boxing rules allow acts which may injure one’s opponent, and in particular because winning by injuring one’s opponent is permitted in boxing. This objection is that the distinction between a violent sport and a nonviolent sport can be drawn relative to the norm of non-violence: (NV) Winning presupposes permissible acts which do not hurt one’s opponent.

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Applying the norm yields that boxing as a sport is violence because the norm does not hold in boxing, i.e., winning in boxing is permitted also by injuring or hurting one’s opponent. However, I think that the objection is not convincing for several reasons. First, one can argue that violence and the normative core of sports, fair play, are incompatible when fair play is relativized to the sporting context. The stronger form of fair play claims that to fight and compete for superiority or for victory in sports is incompatible with the intention to injure or hurt an opponent.3 According to the argument, so far as the purpose of the fight or the competition is to injure or hurt the opponent or so far as superiority or the victory in the game presuppose injuring or hurting the opponent, the fight or the competition is not a sport at all. Applying the argument, boxing is distinguishable for example from dueling and gladiatorial contests in ancient Rome. Second, independently of the preceding argument, it is noteworthy that neither the norm (NV) nor its appropriate transformation are applicable outside sport. The norm cannot be reasonably applied for example to institutions whose function is to save or protect citizens. As an example consider the Finnish door-man position in restaurants. The primary function of this job is to guarantee “a nice atmosphere in a restaurant.” To achieve the purpose the door-man is permitted to hurt or injure customers and related persons under certain conditions, if necessary. Despite this fact the Finnish door-man is not counted among violent institutions. The same holds for firemen, border-guards, the Customs, private guard and security services and at least partially for the police.

3

The weaker form of fair play contains two items: First, the rules guarantee that the game is fair. Second, the rules are (at least approximately) followed in the game. Adding to these two conditions the assertion that the basic purposes of sports and the intention to injure or hurt an opponent are incompatible gives the stronger form of fair play.

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Third, the norm (NV) appropriately transformed does not apply even to competitive institutions in general. Socially the most important competitive institution is the business world. Here the norm would transform to: (BW) Success in business presupposes acts which do not hurt other competitive enterprises. The norm (BW) clearly does not hold in business world. On the contrary, it is completely absurd. Moreover, it is argued that free competition including bankruptcies and compulsory wind-ups is or should be the core of business. So far as one commits oneself to the principle of free competition one should accept institutional violence in the business world, given that the meaning of violence is not changed: enterprises win, lose, succeed or fail. The principle of free competition permits an enterprise to succeed at the expense of compulsory wind-ups of other competitive enterprises. An enterprise is allowed even to force another competitive enterprise into liquidation by legal business methods. In business world there are also permissible acts which harm, hurt or even injure persons directly. For example the owner of a small firm may intentionally, using legal business methods, force another small owner into bankruptcy the foreseen consequence of these acts being that the other commits suicide. Or consider a chief in a big company who in a tough competitive situation notices that his/her company is going into liquidation because of the operations of the competitive companies and his/her own miscalculations. For these reasons he/she goes mad and has to be institutionalized for a long time. Both examples contain acts which are permitted in the business world and which injure or hurt persons directly or indirectly. In the former example the injury is foreseen. Despite these facts the business world is not included among violent institutions. The above considerations of course need not force a person to give up the claim that boxing as a sport is violence. However, for the sake of internal consistency the person should commit him/herself to the view that violence and sport are compatible. Moreover, he or she should agree that neither the norm (NV) which should separate violent sports from non-violent sports nor its appropriate transformation apply to

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any social institution outside sport. Or alternatively, he or she should agree that so far as the norm (NV) or its appropriate transformation are applied to competitive institutions, the business world is a violent institution given that the meaning of violence is not changed or restricted. These considerations show that the application area of the norm (NV) is extremely narrow, applying in practice to no social institution except sport. The justification of the norm is also problematic. It seems that it is impossible to justify this norm by arguments which are internal to sport. Finally, it seems that any justification of the norm presupposes that violence is used in the descriptive sense. This is a very weak theoretical starting point in itself. In the next section I formulate a criterion which applies to the problem of whether boxing matches are violence and whether boxers in a bout are violent. This criterion is compatible with the classificatory use of violence. It is also theoretically justifiable by arguments which are internal to sport. I will try to demonstrate that this criterion is an instance of the principle of fair play in the stronger form, which claims that violence and fair play in sport are mutually incompatible. Moreover, the criterion applies mutatis mutandis to areas outside boxing and other combat sports, for example to self-defense, to defending a victim of violence, to the door-man, to the police etc.

4. Violence in Boxing — an Internal Criterion The thesis stated above (that boxing is not violence) does not exclude the possibility that a boxer may be violent in a bout or that the bout itself may contain some violence. In assessing the violence in boxing the problem is that one cannot know and one cannot directly control the extent to which a boxer is violent in a bout, i.e., to what extent the purpose of a boxer is to hurt his opponent is outside knowledge and direct control. The rules of boxing constitute the norms which fix the permissible acts of boxers. One of the tasks of the referee is to ensure that boxers follow the rules.

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In amateur as well as in professional boxing, with somewhat looser conditions, both the referee and the doctor have the right and the duty to stop the contest. The contest should be stopped if the referee or the doctor suppose that the contestant is injured or that the risk of being injured is increased significantly. In general that means that the contestant is rated as unable to defend himself, as having an observable injury or that it is likely that he will be injured soon. So far as there are no clear or outrageous violations of the rules which entitle the referee to disqualify a contestant there is no other means of controlling the violence of the contestant. So, one can neither “see” nor directly control the violence of a boxer. In the end only the boxer himself, his trainer and his closest seconds know to what extent he is violent, i.e., to what extent his purpose is to hurt his opponent. Assessing the violence of a bout itself is at least as difficult as assessing the violence of a boxer. Outside of boxing there are no criteria which may indisputably apply to assessing the violence of a bout. First, neither street violence nor fictive violence apply to assessing the violence of a bout simply because there is hardly any element common to boxing and street or fictive violence. Most acts typical of street or fictive violence are forbidden in boxing. Although street and fictive violence contains punching and blows as boxing does, technically street and fictive violence has nothing to do with boxing. A boxing match only exceptionally resembles street and fictive violence and vice versa. Getting injured would work as a criterion of assessing the violence of a bout if its purpose were to injure one’s opponent. However, because getting injured in a bout is only one rather infrequent possible consequence, getting injured in a bout reflects the risky nature of boxing rather than violence. So, what remains as a criterion for assessing the violence of a boxing match is the extent to which the bout contains unnecessary suffering and risks relative to the outcome of the bout. This criterion is a special case of the stronger form of the principle of fair play in the following sense: so far as the point is to fight for superiority or for victory, letting the bout continue is unnecessary if

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the outcome of the bout is obvious. However, if the bout in such a situation is continued the reason for letting the contestants fight on is no longer superiority or victory, but something else. By the same token one steps outside of sport and boxing becomes violence. The relative nature of the criterion may yield some non-commonsense results. First, a win on points may be “more violent” than a knock-out. Second, both a win on points and a win by knock-out may be violent. Third, an even bout may be violent in the descriptive sense. However, it need not be violent in the classificatory sense. The criterion works in boxing in any case. Although the audience may often disagree about the outcome of a bout it is typically relatively unanimous on the question of when the contest should be stopped. Skilled referees, boxing doctors and the well-informed spectators typically recognize when there is no point to letting the fight continue. The above criterion also works satisfactorily in cases where amateur and professional boxing are compared to one another, there being clear differences between them. Substantially the main difference is perhaps that amateur bouts are stopped more easily than professional bouts. Because the outcome of a fight between two well-matched contestants is in practice unpredictable and there is always an element of surprise stopping the bout always leaves room to speculate on its outcome. On the other hand, the greater the financial stakes in a bout the less one wants to leave room for speculation. This fact explains why boxers, trainers, doctors and referees are willing to accept more unnecessary suffering and more risks in professional boxing than in amateur boxing. The same fact also explains why a win by knock-out is more preferable in professional boxing than in amateur boxing and why wins by knock-out are rather typical in professional boxing whereas they are rather exceptional in amateur boxing. The above criterion, appropriately transformed, applies to assessing violence also outside of boxing and other combat sports. For example, defending oneself or defending a victim of violence become excessive, i.e., violence, in the case of use of excessive force. A door-man in a restaurant behaves violently if he uses unnecessary force. Similarly, a

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policeman may behave violently, for example in controlling a demonstration, etc.

University of Helsinki Department of Moral and Social Philosophy P.O. Box 24 (Unioninkatu 40 B) 00014 University of Helsinki Finland E-mail: [email protected]

REFERENCES Harris, J. (1980). Violence and Responsibility. London: Routledge & Kegan Paul. Häyry, H. (1991). The Limits of Medical Paternalism. London: Routledge. Oates, J.C. (1988). On Boxing. London: Pan Books Ltd. Oates, J.C. and D. Helpern, eds. (1990). Reading the Fights: The Best Writing about the Most Controversial of Sports. New York: Prentice Hall Press. Summerskill, E. (1956). The Ignoble Art. Melbourne: William Heinemann Ltd.

Katarzyna Paprzycka ON WILLFULLY CONTRARIOUS BELIEFS

What is common to the conception of an ideal legislator, the idealizational conception of science, the adaptational interpretation of historical materialism, non-Marxian historical materialism, unitarian metaphysics and the interpretation of Gombrowicz in terms of the nonChristian model of human? Aside from their Author, it is the methodical application of idealization. But even that does not capture the gist of Leszek Nowak’s mind. This is easily seen when one considers not only the above conceptions but also the numerous, quite brilliant publications directed toward the general public. Then the only common denominator turns out to be the tendency to swim against the current, the tendency to move in exactly the opposite direction than the others, in other words — contrariness. If there is anything that constitutes the essence of Leszek Nowak’s thought, it is being against — against the received view, against what captivates our minds, against what appears to us to be true, against beliefs toward which we drift.

In: J. BrzeziĔski, A. Klawiter, T.A.F. Kuipers, K. àastowski, K. Paprzycka, P. Przybysz (eds.), The Courage of Doing Philosophy: Essays Dedicated to Leszek Nowak, pp. 461-471. Amsterdam/New York, NY: Rodopi, 2007.

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1. The Paradox of Contrarious Beliefs 1.1. Usually the concept of contrariness is related to our actions or to persons. In a paradigmatic case, α’s ϕing is contrarious when α ϕs (α’s ϕing is an action of α), α believes that someone expects that α not ϕ, α wants to act contrary to that person’s expectations and this belief and desire actually explain α’s ϕing. It is usually assumed that unlike actions, beliefs are involuntary. Thence derives one of Pascal’s dilemmas. One may want to believe in God and, having weighed all the reasons for and against the belief, decide that one will believe in God and yet nevertheless remain unmoved in one’s belief that, in fact, God does not exist. We may wish all we want to believe that the Sun is made from chewing gum, but we will not “install” this belief into us simply by wanting or deciding to believe it. We are passive toward our beliefs, as Hume puts it. 1.2. This suggests that the very concept of a contrarious belief is inconsistent. If something is contrarious, it is voluntary. Beliefs are involuntary, so they cannot be contrarious. It should be noted that this paradox concerns beliefs, not mere thoughts. We can represent to ourselves in thoughts what we do not believe to be the case. We can bring to mind various things pretty much voluntarily — even contrariously. What accounts for the difference that contrarious beliefs, but not contrarious thoughts, seem to be paradoxical is the fact that beliefs are tied to the notion of truth in a way in which thoughts are not. (We will consider this link to truth in §3.) 1.3. None of this, of course, throws any doubt on the possibility of as-if contrarious beliefs. It may very well be that someone holds a belief, which happens to go against the grain of accepted and expected opinion but whose origin has nothing to do with contrariness or any other exertion of the will. I will not try to decide which of Leszek Nowak’s beliefs are as-if contrarious and which are in fact contrarious. The witnesses to the

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origin of at least some of Nowak’s theories will have to agree that at least some of his beliefs fully deserve to be called “contrarious.” I will thus start with the assumption that there are contrarious beliefs (and so that they are possible too). I will try to find the sources of the above paradox in our way of thinking about beliefs rather than in the beliefs themselves. I will proceed in two stages. In §2, I will describe two ways of thinking about beliefs. The paradox of contrarious beliefs finds its natural grounding in the first view. This might already be enough to shed doubt on the inescapability of the paradox. However, Williams (1970/1973) has proposed quite a general objection that beliefs cannot be voluntary because of their connection with truth. In §3, I will attempt to answer that objection.

2. Two Ways of Thinking about Beliefs 2.1. The guiding metaphor of the atomistic-naturalistic view of beliefs is that of being hit. We acquire a belief as a result of being “hit” by certain fragments of the world. When we look at a red apple, the lightwaves reflected from the apple hit our retina and are processed by our perceptual apparatus. The end result of such a process is the belief that there is an apple in front us. (Locke’s or Hume’s empiricist theories of beliefs are good illustrations of this type of thinking.) Indeed perceptual beliefs are the paradigms of beliefs on this approach. On this interpretation of the notion of a belief, it is hard to imagine how voluntary beliefs in general, and contrarious beliefs in particular, could be possible. The subject is entirely passive with respect to her belief. 2.2. The guiding metaphor of the holistic-normative view of beliefs is that of a web. The contents of beliefs are related inferentially to one another.1 A belief is defined by its place in a web of rational

1

It should be noted that inferential relations are not limited to formal or logical relations; see Sellars’s (1956) distinction between material and formal inferential relations.

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(normative) relations to other beliefs. The central claim of holisticnormative theories of beliefs (e.g. Sellars 1963; Brandom 1994) is that to have a belief with the content p the subject must be able to master a sufficiently great number of the inferential relations that the content p enters into. Theoretical, not perceptual, beliefs are paradigmatic types of beliefs on this approach. This is not to say, however, that perceptual beliefs constitute something of an anomaly for such views. The representatives of the holistic-normative theories emphasize that the mere activation of some neurons in our brains is not sufficient for us to have a belief. To have the belief that there is a red apple in front of me, it is not enough that a group of neurons be activated even if those neurons are somehow correlated with the color red, apple-like shape or some other features of the red apple. To have the belief that there is a red apple in front of me requires that I am able to navigate the inferential net into which the belief enters. I must be able to draw the right inferences — that there is a colored apple in front of me, that there is a red fruit in front of me, and so on. This (sufficiently good) ability to replicate the inferential relations between the contents is a necessary condition for me to have the perceptual belief that there is a red apple in front of me. It is this ability that distinguishes a parrot from a person. A parrot can be taught to repeat “Red apple!”, quite possibly it can taught to repeat it in response to the presence of a red apple and only in those circumstances. This is not enough, however, for the parrot to have the belief that there is a red apple in front of it for the parrot is not able to move along the net of inferential relations into which the content “there is a red apple in front of me” enters. 2.3. The holistic-normative approach is much more congenial to the idea of a voluntary belief. The having of a belief, on this view, is not entirely passive. To the contrary, in order to have a belief we must demonstrate a certain ability to follow the inferential relations into which the content of the belief enters. Even though the subject is only required to have the ability to follow sufficiently many of the inferential relations, not to actually follow them, this still involves a

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different picture of the subject of beliefs as not passive but quite active (at least potentially). Even with this change in thinking about the subject of beliefs, one may be quite skeptical about voluntary beliefs. How can one want to believe something and, as a result of this want, actually come to believe it? One has to admit that the possibility of voluntary perceptual beliefs really does seem to be quite far-fetched unless, of course, the desire to believe that there is a chocolate ice-cream in front of me were to lead me to buy the ice-cream, to put it in front of me and, finally, to look at it triumphantly. But there are numerous other beliefs, which could be described as organizing or hypothetical, with respect to which the thought that they are subject to our will is not so foreign. Consider a detective story example. A detective investigates a crime. The evidence gathered points to one or two people from among numerous suspects. The detective tries to organize his knowledge about the crime committed. His task is to look for other evidence, to interrogate various people and, finally, to organize the knowledge that he has gathered so as to solve the puzzle. If one were to trust many detective stories, one good heuristic that detectives often use is to accept, as a working assumption, that the crime was committed by the person who is suspected the least. Presumably the justification for such a heuristic lies in the fact that a person who commits a premeditated crime must count with the possibility that she will be suspected and so she must plan the crime in such a way as to redirect suspicions at other people. When the detective accepts such a hypothesis as a working assumption, he tries to see how it organizes what he knows about the crime, how it explains puzzling facts, what sorts of questions it generates for further exploration, and so on. The detective thus accepts the hypothesis for the time being and tries to locate it among other beliefs he has. If the hypothesis turns out to be fruitful (if it tallies with other beliefs, if it leads to the discovery of new facts, and so on), the detective will find it more probable, until he accepts it as true. If such a hypothesis is accepted as true by the detective, the detective will have formed a belief that was at its origin a voluntarily accepted hypothesis. Of course, the hypothesis had to be confronted with other beliefs, it had to tally with them, and so it had to be

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appropriately related to reality, in order for the detective to have accepted it as true, in order for him to have come to actually believe it. Nonetheless this is an example of a voluntary thought, created at a whim, which was transformed into a full-blooded belief. If so then it is possible to have beliefs voluntarily though only on the additional condition that the beliefs can enter into a system of our other beliefs. One may suggest that the ability to form voluntary beliefs is characteristic of really flexible and creative minds. It might turn out that the inclusion of such a new hypothetical thought into a received belief system will require that some of the received beliefs be revised. In such a case, when someone revises his old beliefs in order to uphold the new hypothetical thought, it is hard to resist thinking that such a person really does want to believe that hypothetical thought.

3. Are Contrarious Beliefs Directed at Truth? The holistic-normative approach shows that the subject is not entirely passive with respect to the beliefs she holds. However, there is an objection in the literature which is designed to show that no belief can be voluntary. 3.1. Bernard Williams (1970/1973, p. 136) points out that, unlike acts of will, beliefs aim at truth. To believe that p one must believe that p is true. Someone who takes one’s belief to be false must also reject it. This close relationship between beliefs and truth is demonstrated by Moore’s paradox, for example: it is paradoxical to say “I believe that p but not p.” At the same time, desires do not aim at truth. There is nothing strange in saying “I desire p but not p” — quite to the contrary, the fact that the world is not the way that I desire it to be seems to give me additional reason to change the world so that it fits my desires. Williams argues as follows: If I could acquire a belief at will, I could acquire it whether it was true or not; moreover I would know that I could acquire it whether it was true or not. If in full consciousness I could will to acquire a “belief” irrespective of its truth, it is unclear that before the event I could

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seriously think of it as a belief, i.e. as something purporting to represent reality. (1970/1973, p. 148)

The paradox of a voluntary belief, in Williams’ view, relies on the assumption that the subject is aware of the fact that willing to have a belief is tantamount to abandoning one crucial feature of beliefs, viz. their aiming at truth. The paradox consists in the fact that, on one hand, we desire to acquire a belief, i.e. we desire to be in a state that aims at truth but, on the other hand, we know that the method of acquiring beliefs in response to desires is not good for it does not guarantee (it does not even make it more probable) that the beliefs acquired in this way will aim at truth. Putting the matter in this way is, first, subject to the objection that the paradox arises only on the assumption that a person has such meta-theoretical knowledge. This immediately gives rise to the possibility that there is nothing paradoxical about a voluntary belief as long as the person is unaware of the lack of connection between a willful belief and truth.2 We could, of course, acknowledge that a belief acquired in this way would have an arational origin but as long as it functioned in the belief system in the usual way (in particular, if the subject would be inclined to reject it in case it were to come into conflict with the subject’s other beliefs about reality) there would be no reason to disqualify it as a belief. 3.2. Williams’s argument invites another kind of response, however. For it opens the possibility that one might have certain metatheoretical views concerning the best methods of aiming at truth that would find a connection between will and truth. Williams works on the assumption that a willful belief is completely arbitrary as far as truth is concerned. L. Nowak has in particular advanced certain metatheoretical views, according to which there is a connection between contrariness and truth. If he were right then, even on Williams’ terms, there would nothing paradoxical about a certain kind of voluntary beliefs, viz. the contrarious ones.

2

Such an objection is presented by, for example, Scott-Kakures (1993).

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L. Nowak seems to hold the view that there is a connection between contrariness and truth or, more precisely, between commonsense (which is uncontrarious) and falsehood. He claims that contrarious beliefs have a better chance of being true than uncontrarious ones since uncontrarious beliefs conform to the established commonsense. He thus proposes to comply with the rule of nonstandard discoveries, i.e. with the assumption that “things are quite other than the majority assumes them to be” (2000, p. 162). In his (2000) book on Gombrowicz, Nowak has in mind a particular class of beliefs, viz. social and religious beliefs. In such cases indeed one might conjecture that there is a tendency for those beliefs to get entrenched that serve the ideological interests of certain groups of people. To use Marx’s classical example: one would expect individualist ideologies in a capitalist system of production because they tend to conceals class-based reality. One would expect pro-feminine cultural beliefs in a patriarchic society. And so on. However, the alleged connections between contrarious (and uncontrarious) thoughts and truth (and falsehood) are too elusive to be treated as holding for all contrarious (and uncontrarious) thoughts. One should wander especially whether scientific beliefs could equally be argued to serve ideological interests.3 There are, of course, social interests associated with the advantages of adhering to an accepted paradigm. It is unclear, however, why the accepted theory together with uncontrarious beliefs circling on its orbits should have any lesser claim to truth than alternative contrarious theories. Both seem to be equally prone to being false. 3.3. Nowak’s arguments that contrarious beliefs have a better chance of being true than uncontrarious ones are thus not fully convincing. This is not to say, however, that there is nothing to his thought. I have

3

One cannot, of course, be quite certain that scientific beliefs never conform to ideological interests. One could mention here a strand in the feminist critique of some research especially in biology, where it has been argued the patriarchal and misogynous ideology has influenced the content of what appeared to be topic-neutral investigations. See Tuana (1989).

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argued above (§2) that any voluntary belief has to be located among other already accepted beliefs, so that it inherits, as it were, the quality of aiming at truth from those other beliefs. I will now argue that one can use a broadly speaking Popperian (1959) methodology with a Gombrowiczian correction to show how especially contrarious beliefs may aim at truth though not as directly as L. Nowak (2000) would have it. (i) Let us accept that Popper’s methodology is basically right. The task before the ideal scientist is, first, to think of all the possible theories that could explain a given domain and, second, to try to falsify them. In the limit, all except one theory will be falsified, the true one. (ii) No scientist is an ideal scientist. In the first instance, no actual scientist would have the time (not to mention other limitations) to think of all the possible theories. However, it is the duty of actual scientists to try to approach the ideal as much as they can. One way in which to do this is by trying to think of as many theories as possible. The more theories we, as a scientific community, propose and the more of them we falsify, the closer we are to the goal of eliminating all false theories. It is here that we stumble upon the solution to our puzzle. In thinking up new theories — even ones that are going to turn out to be false — we participate in the research practice whose aim is to achieve the truth. Voluntary beliefs could thus aim at truth in this global sense of being part of a global research strategy aimed at truth. Contrarious beliefs are no exception. (iii) To see the special role for contrarious beliefs in a scientific research practice one would have to understand not so much certain facts about our limited natures but rather certain facts about our herd nature, as Gombrowicz would have it. We have an uncanny inclination to repeat clichés and platitudes, to subordinate ourselves to dominating intellectual fashions, to admire the views of the famous and the powerful, and if we dare to put forward some novel views, their novelty usually consists in some small deviations from the thoughts that overtake us. Note that if this is the case then we are in principle not the sort of creatures that can pursue a Popperian type of methodology (see also Kuhn 1962). For we are incapable of thinking up

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all the possible theories since our imaginations are completely captured by the status quo, i.e. by those theories that are dominant. Instead of freely exploring the space of all possible theories, we are tied by our herd nature to explore the orbits of what is currently fashionable. It is thus that we can finally understand the epistemological sense of contrariness. Given our herd nature, we require something like the ability to think contrarious thoughts to fully explore the space of possibilities. In fact, we can understand how such an ability actually plays a central role in our collective pursuit of truth. This is not to say, however, that contrarious beliefs have a privileged position with respect to truth, that they somehow have a greater chance of being true. It might, of course, happen that some contrarious belief will in fact turn out to be true. But it might likewise happen that some uncontrarious belief will in fact turn out to be true. In such a case, one might think, that the courage and the strength required to think contrarious thoughts, to organize scientific knowledge around them, was pointless. But this would be an illusion. The effort of contrarious thinkers is never lost — even if their theories actually move away from, rather than toward, the truth. For it is only thanks to them that we can be certain (as certain as we can be) that we are considering more theoretical possibilities than we would otherwise be prone to consider. Whether Leszek Nowak’s contrariness has brought us closer to the truth or further away from it, time will show.

Warsaw University Department of Philosophy Krakowskie PrzedmieĞcie 3 00-927 Warszawa Poland E-mail: [email protected]

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REFERENCES Brandom, R. (1994). Making It Explicit. Cambridge, MA: Harvard Univ. Press. Kuhn, T.S. (1962). The Structure of Scientific Revolutions. Chicago: Univ. of Chicago Press. Nowak, L. (2000). Gombrowicz: Czáowiek wobec ludzi. Warszawa: PrószyĔski i S-ka. Popper, K.R. (1959). The Logic of Scientific Discovery. New York: Harper and Row Publishers. Scott-Kakures, D. (1993). On Belief and the Captivity of the Will. Philosophy and Phenomenological Research 53: 77-103. Sellars, W.S. (1956). Empiricism and the Philosophy of Mind. In: H. Feigl and M. Scriven (eds.), The Foundations of Science and the Concepts of Psychology and Psychoanalysis (Minnesota Studies in the Philosophy of Science, vol. 1), pp. 253-329. Minneapolis: University of Minnesota Press. Sellars, W.S. (1963). Science, Perception and Reality. London: Routledge and Kegan Paul. Tuana, N., ed. (1989). Feminism and Science. Bloomington: Indiana University Press. Williams, B. (1970/1973). Deciding to Believe. In: Problems of the Self. Philosophical Papers 1956-1972, pp. 136-151. Cambridge: Cambridge University Press.