Rationality, universality, and individuality in a functional conception of theory

International Journal of Psychophysiology 62 (2006) 411 – 426 www.elsevier.com/locate/ijpsycho

Rationality, universality, and individuality in a functional conception of theory Jiří Wackermann ⁎ Department of Empirical and Analytical Psychophysics, Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstrasse 3a, D-79098 Freiburg i. Br, Germany Received 29 July 2005; received in revised form 24 October 2005; accepted 5 January 2006 Available online 20 February 2006

Abstract In the present paper we reflect on some critically important issues in theory construction from the point of view of a practicing scientist. The starting point is to suggest the need for a minimal base of common agreement on the role of successfully working theories. It is proposed that scientific knowledge is not composed of singular facts but rather of relational structures connecting facts. Useful theories are both receptive and productive. Theories provide models, i.e., idealised representations of reality, expressed, in their most developed phases, in a mathematically formalised language. We further focus on the notions of rationality and universality, and show that these are mutually related and actually inseparable. Universality means description of observable phenomena in terms of universally valid laws that are essentially of a rational character, i.e., stated in terms of relational invariants preserved in variant, contingent conditions. Law-like components of a theory are universal by definition, not given by circumstances, and rational by their form, not by their content. Facts, on the other hand, are irrational elements unless they can be derived from law-like relations of another theory. Relational definition of rationality is self-consistent and independent from vaguely defined notions like ‘reason’. Pertinent to studies of human nature, including psychophysiology, is the problem of individuality. To reconcile the claim of universality with an adequate account of unique individuality, we advocate a ‘distributed nomothesis’, distinguishing first-order laws ruling in an individual ‘idioversum’, from the higher-order, universal laws. Idioversal laws play the role of ‘facts’ in construction of universal theories. © 2006 Elsevier B.V. All rights reserved. Keywords: Functional conception of theory; Idealisation; Idioversal laws; Individuality; Universal laws

1. Introduction What is theory? According to the Webster's Encyclopedic Dictionary (1996), ‘theory’ is a name for “a coherent group of general propositions used as principles of explanation for a class of phenomena; e. g. Newton's theory of gravitation”. However, the dictionary lists no less than six additional definitions, ending with “contemplation or speculation”, and “guess or conjecture”. This illustrates the variety of connotations, but also a confusing multitude of interpretations of the word ‘theory’.

⁎ Abtl. Empirische und Analytische Psychophysik, Institut für Grenzgebiete der Psychologie und Psychohygiene, Wilhelmstrasse 3a, D-79098, Freiburg i. Br., Germany. Tel.: +49 761 2072170; fax: +49 761 2072179. E-mail address: [email protected]. 0167-8760/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpsycho.2006.01.009

In common understanding, theory is a polar opposite of praxis, speculation as opposed to action directed towards the goals of real life. Theory is ‘why’ and ‘what if’, while the practical life is about ‘how’, ‘when’, and ‘for what’.1 There is, however, a domain of human activity where theory is not an opposite but rather an integral part of praxis: it is science. Yet science is not identical with theory. Different scientific disciplines are not equally prone or committed to theoretical thought. Is this non-uniformity due to essential differences between disciplines, or is it merely contingent, perhaps a sign of different degrees of their maturity?

1 “Gray, worthy friend, is all your theory/And green the golden tree of life” (Goethe, Faust, Part I, transl. by C. T. Brooks). But note that this is Mephistopheles speaking!

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In some disciplines, and even more so in inter-disciplinary research fields like psychophysiology, the lack of understanding of the role of theory is remarkable. There is only little, if any, agreement about what theory is or theories are; what are the criteria distinguishing good theories from not-so-good ones; and whether we need theories at all. Empirical research driven by the rapid development of instrumentation and experimentation technology seems to thrive and flourish even in an atheoretical modus operandi. Why, then, should we be concerned about questions of ‘just theoretical’ interest, that is to say, according to the popular notion of theory, apparently irrelevant for the everyday practice of research? In a series of reflections it will be shown that questions about the nature and role of theory are not merely the idle musings of scientists, but rather that these questions are of crucial importance for the practice and understanding of science. 2. Aspects of theory 2.1. Theory as a form of knowledge and as a form of life A look back to the origins of the word may be revealing. ‘Theory’ derives from the Greek word theōria, which means ‘watching’ or ‘contemplation’, and it is related to the verb theomai = ‘I watch’. The word ‘theatre’, Greek theatron, lat. theatrum, meaning ‘what’s given to one’s look’, a ‘show’, is derived from the same stem. However, theōria did not mean just any show, but originally meant attendance at ritual, religious festivities, or an excursion to such a festivity. This usage suggests that theōria referred to a divine revelation (theos = God) in an act of contemplation. In a broader sense, the word theōria refers to ‘observation’, ‘contemplation’, or ‘insight’, and therefore refers to a form of knowledge. Aristotle (1984a) in the first book of his Metaphysics draws the distinction between mere experience and theoretical knowledge: With a view to action experience seems in no respect inferior to art, and we even see men of experience succeeding more than those who have theory without experience. The reason is that experience is knowledge of individuals, art of universals, and actions and productions are all concerned with the individual (Met. 981a). Aristotle gives an example of a physician healing always a certain individual, never a human being in general; but then he continues If, then, a man has theory without experience, and knows the universal but does not know the individual included in this, he will often fail to cure; for it is the individual that is to be cured. […] But yet we think that knowledge and understanding belong to art rather than to experience, and we suppose artists to be wiser than men of experience […]; and this because the former know the cause, but the latter do not (Met. 981a). In summary, Aristotle holds that in particular cases action based on empirical knowledge may be as efficient as theoretical

knowledge, or even more efficient than the latter, but proper knowledge is oriented towards the universals and the true principles of things (‘causes’), not to particulars, and is thus superior to mere experience. The connotations linking the word ‘theory’ to its socioreligious origins can be found in Aristotle's (1984b) Nicomachean Ethics, where he distinguishes “three prominent types of life; that just mentioned [vulgar type, life of enjoyment], the political, and thirdly the contemplative life” (Nic. Eth. 1095b). The latter, bios theōrētikos, lat. vita contemplativa, is the best life of all: in Nic. Eth. 1177b–1178a Aristotle presents arguments for the absolute and almost divine superiority of the contemplative, intellectual faculty over all other human activities and preoccupations. Contemplation of truth, theōria, is essentially an ethical category.2 Since ancient Greece, the two aspects of theōria, the epistemic and the ethical, were amalgamated in the concept of vita contemplativa as the most elevated life. However, the dawn of the modern epoch brought a radical re-evaluation of all values, including those of science and knowledge. Nonetheless, the ideal of a life as service to the truth, excluding egoistic material interests, remained a constitutive part of the ethos of science. According to this tradition, bios theōrētikos is the proper life form of the scientist, since scientia = theōria.3 2.2. Theoretical faculty and division of labour in science Nowadays, the words ‘theory’ and ‘theoretical’ do not denote a scientist’s life form, but rather refer to a certain form of scientific practice. The distinction between empirical (observational or experimental) disciplines and theoretical disciplines is orthogonal to the ‘topical’ distinctions, identifying sciences by regions of reality of their interest (physics, chemistry, biology, psychology, etc.) or their particular topics (e. g., optics or thermodynamics as parts of physics, morphology or physiology as parts of biology, etc). This distinction is visible in teaching and research, witnessed by the names of institutes, journals, and societies. Where does this distinction come from, and what does it reveal about the working of science, and the role of theory in it? First, we may think of science as a process of acquisition of collective knowledge, as the cognition of a collective subject, say, a work-group, a community of specialists or, ideally, an educated part of mankind. Here, as well as in individual subjects, we can distinguish two functions, namely the formation of ‘primary representations’ of reality (percepts) and of ‘secondary representations’ (concepts). Then we may identify primary 2 The threefold typology of life forms reminds of the metaphor of life as Olympic games, traditionally attributed to Pythagoras: some people come to the games for commercial business, seeking material profit; some do participate actively in the games, seeking fame and honour; and some come for unselfish and pure pleasure of observing the course of games. 3 In Spranger's typology derived from analysis of value systems, the ‘theoretical’ life form was one of six basic types; but “theōria of Plato and Aristotle is not identical with a purely scientific mind, but contains also aesthetic and religious moments” (Spranger, 1930, p. 121). Among modern philosophers, the late Heidegger (1954) took a most radical position and straightforwardly identified science with the ‘theory of the real’, but at the same time he reproached the modern techno-science for ‘forgetting about Being’.

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representation with observation (data gathering) and emergence of secondary representations with the formation of theoretical concepts. However, we soon realise that these two functions or faculties, perceptual and conceptual, are actually two aspects of one process. There is nothing like a raw sensation or purely perceptual datum. Percepts are more or less structured forms; their formation follows certain structural laws, as demonstrated by gestalt psychology (Wertheimer, 1938). Even seemingly elementary perceptual acts contain cognitive components beyond ‘pure perception’. Past experience precipitated as ‘protoconcepts’ based upon prior percepts, co-determine the formation of later percepts, and thus in-form the present experience.4 We will see (Sections 3.2–3.3) a similar relationship between the ‘percepts’ and ‘concepts’ of science, i. e., facts and theories. Following further this parallelism, we might examine the biological foundations of the basic cognitive faculties, their role in psychological mechanisms of perception, differentiation and integration, learning, etc. (cf. Robinson, 2006-this issue), in an attempt to derive a ‘biological theory of knowledge’. But this is not our aim, since we are more interested in the logical structure of these faculties than in their material implementation. The differentiation between perceptual and conceptual faculties manifests itself in the organisation of science. With a certain license we can say that experimental laboratories and theoretical institutes are like specialised organs of a structured body of each scientific discipline. As in the case of comparative physiology, which studies the functional differentiation of organisms from an evolutionary perspective, the history of the organisational differentiation within science may shed some light on the functioning of its collective body and its ‘theoretical organ’.5 The division of labour between empirical and theoretical research is a relatively late development. At the origins of modern natural science, we see great theoretical achievements and experimental/observational discoveries made by the same persons (e. g., Galileo, Huygens, Newton)—the original unity of faculties. Scientists might have followed their natural inclinations, as illustrated by the contrast between two great astronomers, Tycho Brahe, the observer, and Johannes Kepler, the theorist (cf. also Robinson, 2006-this issue, Section 8). However, in their time, the division of labour was not yet institutionalised. The origins of differentiation can be seen in mathematical physics, particularly, in analytical mechanics (d'Alembert, Lagrange, and others; cf. Mach, 1960): physical problems motivate mathematical developments, and their success is judged by internal criteria (generality, consistency and economy of formalism, etc.), not necessarily by turning to experiment. During the formative period of physics (17th–19th

4 The notion of in-formation used here is obviously more extensive than the notion of information as used in communication theory. Information is not knowledge; but in-formation is an a priori condition of knowledge. 5 For example, the two-volume work by C. Jungnickel and R. McCormmach (1986), from which we quote later, is a thorough study of the rise of theoretical physics in German speaking countries between 1800 and 1925. In spite of its exclusive focus, their book provides valuable insight into social and psychological mechanisms of such a differentiation process, and is a highly recommended reading.

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century), we can see other sciences developing their theoretical fundaments with a delay or at a slower pace. But even in the late 19th century there was a truly universal mind, H. Helmholtz, contributing his theoretical and experimental work across diverse scientific disciplines as physics and physiology. Thus it may be slightly surprising that Helmholtz, probably the last representative of the original unity of faculties, argued in favour of separation between experimental and theoretical departments. In his opinion, lectures on experimental physics were not the proper place to introduce a “complete and rigorous formulation of the laws of nature, which demands a mathematical formulation” (Helmholtz, quoted by Jungnickel and McCormmach, 1986, vol. 2, p. 41). The lectures to which Helmholtz was referring to were attended by a broad audience, including students of medicine, pharmacy, etc., and they had to communicate the ‘knowledge’ of physics as experimentally demonstrable phenomena. In Helmholtz's judgment, this obviously was not the most essential part of physics, which should be the “complete and rigorous formulation of the laws of nature”—this is theoretical physics. In sciences which successfully accomplished the process of functional differentiation, the division of labour between experimentalists and theorists is now taken for granted. In other scientific disciplines, particularly those studying human nature, this differentiation process is not yet complete. Thus, for example, the inspired work of I. P. Pavlov still exhibits the inseparable unity of experimental invention and theory construction. On the other hand, this may indicate that the field has not yet reached the stage of maturity. In the next section we will pay attention to factors that obstruct this maturation process. 2.3. Against theory: radical empiricism and the myth of ‘pure observation’ Harmonic division of labour between theoretical and experimental departments is part of the ‘official’ image of science, but reality is far from the ideal harmony (Barry, 2006this issue). Some disciplines, like psychology, display a multitude of particular theories with different areas of applicability, but these possess no firm and unitary theoretical fundaments. This stimulates a skeptical attitude towards interpretations and theories, while experimental data seem to be certain and indisputable. Experiment, instead of being derived from theoretical reasoning, is elevated to be the superior arbiter deciding between competing theories. In the extreme case, scientific practice is de facto identified with experimental research, that is divorced from theoretical thought at all; this is the attitude of radical empiricism.6 A radical empiricist believes in pure observation, not contaminated by any theoretical concepts; and considers theories as harmful to the unprejudiced scientific exploration of nature, being nothing else than limitations and restrictions of

6 Among working scientists, ‘empiricism’ is often an unreflected attitude rather than an expressed and articulated philosophical position; cf. Section 5.1.

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the search for new facts.7 Claude Bernard (1949) preached that “theories should be left outside of the laboratory door”, and maintained that [m]en who have an excessive faith in their theories or in their ideas are not only poorly disposed to make discoveries but they also make very poor observations. They necessarily observe with a preconceived idea and, when they have begun an experiment, they want to see in its results only a confirmation of their theory. Thus they distort observation and often neglect very important facts because they go counter to their goal. […] they take into the results of their experiments only what fits their purpose, by neglecting what is unrelated to it, and by very carefully avoiding whatever might go in the direction of the idea they wish to combat. (Bernard, quoted by Duhem, 1954, pp. 180–181) The origins of radical empiricism are often attributed to Francis Bacon and his pamphlet Novum Organum (Bacon, 1854), which is still considered a canon of the inductive method. It may be instructive to take a closer look at his arguments and motives.8 Bacon was utterly skeptical not only about metaphysical notions, but about abstract concepts in general. He wrote: The subtilty [sic] of nature is far beyond that of sense or of the understanding: so that the specious meditations, speculations, and theories of mankind, are but a kind of insanity (Bacon, 1854, §10). Bacon's notion of idols, obstacles to true knowledge of things, which are either inherent to human mind, acquired by education, or imposed by authority, is well known. Most important for his anti-theoretical stance are the ‘idols of theatre’,9

theory-driven experiment—only Bacon wrote it more than two centuries earlier: All superstition is much the same, whether it be that of astrology, dreams, omens, retributive judgment, or the like; in all of which the deluded believers observe events which are fulfilled, but neglect and pass over their failure, though it be much more common. But this evil insinuates itself still more craftily in philosophy and the sciences […] [I]t is the peculiar and perpetual error of the human understanding to be more moved and excited by affirmatives than by negatives […]” (Bacon, 1854, §46). Bacon's anti-theoretic eloquence becomes tiring, and we are more interested in the positive elements of his doctrine. Then we soon find that Bacon's doctrine is not that of pure empiricism, as it may seem from a first, superficial reading. In fact, Bacon was well-aware of the two faculties, perceptual and conceptual, and the dangers of both extremes: Those who have treated of the sciences have been either empirics or dogmatical. The former like ants only heap up and use their store, the latter like spiders spin out their own webs. The bee, a mean between both, extracts matter from the flowers of the garden and the field, but works and fashions it by its own efforts. The true labour of philosophy resembles hers, for it neither relies entirely or principally on the powers of the mind, nor yet lays up in the memory, the matter afforded by the experiments of natural history or mechanics in its raw state, but changes and works it in the understanding. We have good reason, therefore, to derive hope from a closer and purer alliance of these faculties, the experimental and rational, than has yet been attempted (Bacon, 1854, §94, italics ours).

which have crept into men's minds from the various dogmas of peculiar systems of philosophy, and also from the perverted rules of demonstration […] For we regard all the systems of philosophy hitherto received or imagined, as so many plays brought out and performed, creating fictitious and theatrical worlds (Bacon, 1854, §44).

[V]ague and arbitrary experience is […]mere groping in the dark, and rather astonishes than instructs. But when experience shall proceed regularly and uninterruptedly by a determined rule, we may entertain better hopes of the sciences (Bacon, 1854, §100, italics ours).

Bacon never gets tired of pointing out sources of errors in human cognition, and has occasionally precise insights into the mechanisms of these errors, as in the following fragment. It reads almost exactly as Bernard's above-quoted criticism of

Now, what else is Bacon's “determined rule” than a theoretical idea, abstracted from experience, and giving direction and guidance to future experiments? This interpretation is further corroborated:

7 A popular saying goes that “one shouldn't watch the world through narrow peep-holes”. But it was invention of the telescope and the microscope—indeed, peep-hole-like instruments amplifying our sight in a chosen direction while restricting our sight in other directions!—what elicited the rapid progress of natural science in the 17th century. Theoretical devices—modelling, idealisation, and mathematical formalism (see Sections 3.4 3.5 3.6) should play similar instrumental roles. 8 Agassi (1983) observed that “[i]t is admittedly dangerous to cite Bacon to support any interpretation of his philosophy—since he was so often flagrantly inconsistent”; this applies also to popular interpretations of Bacon as a plain empiricist. 9 Bacon, however, does not refer to the common root of words ‘theory’ and ‘theatre’ as we did in Section 2.1.

When we have […] a collection of particulars we must not immediately proceed to the investigation and discovery of new particulars or effects […] transferring the experiments from one art to another […] many new experiments may be discovered […] yet comparatively insignificant results are to be expected thence, whilst the more important are to be derived from the new light of axioms, deduced by certain method and rule […] Our road is not along a plain, but rises and falls, ascending to axioms and descending to effects (Bacon, 1854, §103). It seems that empiricists swearing on Bacon's ‘canon’ did not read him far enough, or not attentively enough. Instead of one-

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way induction, he was actually advocating mutual exchange of induction and deduction. We only have to replace the word ‘axioms’ (which has nowadays an entirely different meaning) by the word ‘theorems’, to read his words as favorising the concept of theory-driven experiment! Bacon's eloquent rejection of ‘theories’ must be understood as rejection of void speculation, not as approval of the accumulation of raw, ‘theoryfree’, observations and findings, against which he actually warns.10 It is true that theory totally detached from experience is prone to dogmatism, false a priori's, and misperception of facts. As far as the empiricist's criticism is motivated by a wish to avoid these faults, it should be honoured as honest and justified. But in its extremely zealous forms,11 empiricism suffers from its own specific form of misperception, namely, a blindness towards the real function of working theories, which is the topic of the next section. 3. The working of theories 3.1. Two functions of theory A wide-spread concept of scientific theory is that it is a complex assertion about reality, about ‘how things are’, which may be either true or false. The ‘truth’ of a theory is usually understood in the sense of the ‘correspondance conception’.12 Such a concept (i) largely ignores the function a theory has in the process of the development of knowledge, and (ii) it implicitly refers to a reality beyond the interchange of theory and experience. A very different concept of the validity of a theory was expressed by Pierre Duhem: [A] true theory is not a theory which gives an explanation of physical appearances in conformity with reality; it is a theory which represents in a satisfactory manner a group of experimental laws. A false theory is not an attempt at an explanation based on assumptions contrary to reality; it is a group of propositions which do not agree with the experimental laws. Agreement with experiment is the sole criterion of truth for a physical theory (Duhem, 1954, p. 20–21). In a similar vein, we will advocate a functional conception of theory. The function of theory is twofold: a theory has to be

10 At present, a-theoretical research tends to be a truly ‘ant-like’ activity, seeking to find and do all what ‘has not been done yet’ in a mechanical combinatorics of experimental conditions and instrumental techniques. We should only wish that Bacon's warning be taken seriously. 11 For the lack of space we omit discussion of other sources of anti-theoretical prejudice, ranging from Feyerabend's ‘anarchic epistemology’ (Feyerabend, 1987) to post-modern criticism of science. While we may feel sympathy with critical self-reflection on science's goals and methods, we should not overlook that these post-modern movements are usually of extra-scientific origin, offering nothing but unproductive rhetoric, and becoming a true obstacle to the progress of science. 12 According to this conception (Tarski), the proposition ‘snow is white’ is true due to the fact that snow is white. This sounds plausible — until we realise that there is no privileged access to the real colour of real snow except through language, that is, via propositions acknowledged as true; cf. also Footnote 15.

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receptive and productive with respect to empirical facts. A theory is receptive to the extent that facts can be adopted or represented by the theory; a theory is productive to the extent that it generates propositions that can be tested experimentally (discussed later in Section 3.7). The attributes ‘receptive’ and ‘productive’ have grades, they are ‘more’ or ‘less’ judgments, not just logical valuators. Instead of saying a theory is ‘true’ or ‘false’,13 we may say a theory is ‘good’ or ‘bad’, depending on whether it is ‘doing well’ or ‘not doing well’. Evaluation of a theory is not a once-and-forever assignment of a logical value; it is a pragmatic judgment about how well a theory fulfills its function. The judgment is up to scientists themselves. Logicians and historians may reflect, retrospectively, on the logical structure and material content of theories; but the daily practice of science is the only proof-stone, and the scientists’ own words give the best definition of a theory's ‘doing well’. Let us take an example from an early period of electrophysics; in 1828 G. Th. Fechner wrote to G. S. Ohm: [It was] only through your theory that I obtained clarity about the conditions of the circuit, which were apparently so complicated and are now so simply resolved because of it. […] [The law] connects a great area of phenomena, which previously remained unconnected in a chaotic and puzzling way, [in a] beautiful linking of facts. (Fechner, quoted by Jungnickel and McCormmach, 1986, vol. 1, p. 59) Here we have a condensed account of what we mean by the receptive function of theory; and more: it is not only that singular phenomena are adopted by the theory (i. e., all found to be consistent with the theory), but they are now also “connected” in a “beautiful linking of facts”. This phrasing alludes to the intermediate role of structured facts, and to the relational and ‘holistic’ nature of theories in general, aspects of theories which we will discuss later (Section 3.7). The productive function is usually understood as the ability of a theory to make testable ‘predictions’. This is, in principle, correct, but should not be taken too literally. Prediction refers to a future event, it is a statement about ‘things to come’. The notion of causality is traditionally linked with direction of time: cause (earlier) → effect (later). This may suggest that a theory is successful because it is able to ‘trace the paths of causation’ from the past to the future: a clear fallback to metaphysical ‘correspondence’ between the ‘true’ theory and ‘true’ reality. Nothing like this is implied here: the future dimension of ‘prediction’ refers simply to ‘observations/tests not yet made’. From the logical point of view, it does not matter whether a theory specifies an event in the future (e. g., a lunar eclipse), observation of which confirms the theory (‘prediction’ in the narrow sense of the word), or specifies an event in the past that may have gone unnoticed. We may call the latter ‘postdiction’, or even better, subsume both variants under a single

13 Duhem's expresses himself in the language of the traditional logic, ‘true’/ ‘false’, but he fortunately circumvents the problems inherent to the ‘correspondance’ conception of truth.

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term, indiction.14 Later we will argue that the proper productive function of a theory is not to make singular predictions, but rather to provide a recipe, or a generating principle, for indictions. 3.2. Relational nature of facts Science derives from scientia = knowledge. Knowledge is often understood as a name for a totality of ‘known facts’,15 or simply ‘facts’. Facts are propositions about states of the world. We may believe that (i) the pool of ‘known facts’, shared by all members of scientific community, constitutes the collective knowledge of science, and that (ii) the task of science is to extend the pool of ‘known facts’. However, this concept of knowledge is defective for several reasons. Firstly, we should note that not all facts contribute to knowledge, and, of those which do, not all contribute equally. Consider the following facts: a: b: c: d: e:

Today is Sunday.16 The author's given name is Jiří. René Descartes died in 1650. Water boils at 100°C. Lead melts at 340 °C.

Volatile facts like a have no place in scientific knowledge, even if they are subject to general agreement: if it is Sunday, everyone knows it is Sunday, but the agreement is only circumstantial. Facts of merely private interest, like b, unrelated to other facts, do not contribute either; if the author's first name was different, ceteris paribus, nothing would change. Facts like c are usually considered a matter of knowledge (a student of philosophy is expected to know c), but they do not significantly differ from b; no important consequences can be derived from c, or only trivial ones, e. g., ‘Descartes could not know Kant's writings’.17 Facts d and e seem to be undoubtedly scientific facts and thus constitute the matter of scientific knowledge. Yet we must distinguish: d is not an empirical fact at all, but rather a

14 The sole purpose of this nomenclature is to avoid apparent asymmetries. Take, for example, two facts accounted for by Einstein's general relativity theory: secular changes of Mercury's orbit (M), and the deflection of light rays in the gravitational field of the Sun (S). Fact M was established by astronomical observations made since the 1840s and only post hoc explained by the theory. Fact S was really predicted by the theory, and triumphally confirmed by the results of Eddington's 1919 solar eclipse expedition. For a theorist, both theoretical indictions are equally important, while for sociologists, historians and biographers, they were two events of clearly unequal impact (cf. Clark, 1972, pp. 258–259, 284–291). 15 The form ‘I know that –’, where the free place ‘–’ is filled with various propositions, is potentially confusing. The words ‘I know that’ are void (Wittgenstein, 1975, §§6,15,58); saying ‘I know that p’ instead of p is as redundant as saying ‘proposition p is true’ instead of simply asserting p (Wittgenstein, 1956, §I.I.6). 16 This paragraph was really written on Sunday. 17 Trivial from the point of view of natural science, focusing on law-like regularities in reproducible phenomena. For history, of course, the consequences of singular facts are highly significant.

quotation from the definition of the centigrade temperature scale (Celsius). On the other hand, e clearly constitutes scientific knowledge: it applies generally to a broad class of experimental situations, and thus allows one to draw various conclusions under various circumstances; for example, ‘I have heated the probe up to 1000°C and it did not melt: therefore, this metal cannot be lead.’ In sum, it is not that every true proposition about the state of world can be acknowledged as a (scientific) fact. Volatile, private, singular facts, as well as ‘facts by definition’ do not qualify. On the other hand, facts positively contributing to the body of knowledge must exhibit a certain degree of generality, and a sufficient potential to relate to other facts. (This, of course, does not imply that such propositions make up the totality of knowledge.) The above-listed examples may suggest that facts are elementary or ‘atomic’ propositions of type ‘S is P’ or ‘S has property P’, as we know them from traditional logic. But we must distinguish between simplicity of expression and simplicity of its content. Actually, a statement about the melting point of lead (sub e) is not atomic at all: it refers to a virtually infinite multitude of experimental situations; the singular name, ‘lead’, refers to the concept of a chemical element, and to a variety of physical and chemical tests identifying the element of interest, Pb; the critical temperature specified by the fact refers to the concept of temperature, to various techniques of temperature measurements, etc. All this speaks against a comfortable but incorrect ‘atomism of facts’: Facts are not elements but relational structures linking together observable phenomena.18 3.3. Relational nature of theories Natural science is not interested in merely ‘historical’ facts, or protocolar statements about singular events, say, ‘on Thursday, June 9, 2005, at 20:05, Dr Fox has observed that the mercury column in the glass capillary tube reached a red mark labelled 80.’ In particular, ‘logical positivism’ attempted to build a strict logic of research upon such ‘atomic’ propositions, but these attempts remained sterile. As shown in the preceding section, there are really no atomic facts; facts are of a ‘molar’ nature. With this premise we proceed to discussion of the nature of theories. The reader may have noted in Section 3.1 that, in Duhem's account, a theory is said to represent ‘a group of experimental laws’, not ‘of experimental observations’ or ‘facts’ as we may have expected. But there is actually no contradiction: the expression ‘experimental law’ stands precisely for the ‘molar’ (i. e., intrinsically relational) nature of ‘facts’. Here we prefer the expression observational regularities, which may apply to observations under natural as well as in artificial conditions in a

18 Cf. E.R. Guthrie (1946): “A fact has a peculiar and intricate structure. […] Objects and events are not facts; they are merely objects and events. They are not facts until they are described […] it is in the nature of that description that the quintessence of fact lies. Only when an event has been given a very specific kind of description does it become a fact”.

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laboratory. Duhem's language is naturally influenced by his background in physics, where the relational structure making up an ‘experimental fact’ can be stated in a law-like form of mathematical equations. But whatever language we choose, the important question is what makes the ‘beautiful linking of facts’ (cf. quote from Fechner, Section 3.1). Firstly, we should note that even a statement of a relation between two relatively simple facts requires a sort of theory, or at least ‘proto-theory’: a seemingly simple comparison of two phenomena with respect to some dimension (e. g., colour) implies an act of abstraction from other experiential dimensions (e. g., size or shape), and an elementary notion of comparable magnitude. These ‘proto-theoretic’ acts may be, in their very elementary forms, implemented by the conceptual aspects of purely perceptual processes, as argued in Section 2.2. In a more abstract vein, also complex relational structures may be recognised as special cases of even more complex relations. This is where mathematical description of multivariate relational structures becomes not only useful but, in fact, indispensable. For example, all three ‘minor laws’ of physics of gaseous bodies, relating pairs of state variables V (volume), p (pressure), and T (absolute temperature), can be obtained as partial expressions from a general form, the ‘state equation’, pV ¼ const: T

ð1Þ

Finally, the most developed form of the creation of relational structures with the highest degree of generality is their construction by pure reasoning from primary postulates by means of mathematical formalism. Newton's law of gravitation is a notorious example (Feynman, 1965): knowledge of the law allows us to calculate trajectories of celestial bodies, whether real or just thought of, and to observe that their paths conform to Kepler's laws of planetary motions (observational regularities). However, the law of gravitation is nothing like a generalisation or extrapolation of Kepler's observational laws but, rather, a theoretical postulate of its own. Another example is given by Planck's quantum theory of black body radiation, yielding a formula for the energy spectrum from which Stefan– Boltzmann's and Wien's ‘experimental laws’ can be derived as special cases (Trigg, 1971). At the highest levels of generality and abstraction, the knowledge acquired consists in knowledge of principles and forms upon which the theory relies.19 Consequently, the test of ‘agreement with facts’ may consist of a rather abstract process of mathematical treatment and the matching of entire functional forms, not merely comparison of singular experimental measure ments. Experimental tests are thus inevitably penetrated by theoretical reasoning, which summarises and abstracts obser-

19 In scientific disciplines that have attained the mature stage of division of labour, it is usually only this latter type of work that is considered ‘theoretical’ in the proper sense of the word. Such theories are obviously not built to merely fit observed data post hoc: they either meet or miss the phenomena; cf. also Footnote 14.

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vational data to relational structures comparable with indictions made by the theory tested. These points will be elaborated in the following sections. 3.4. The role of models Theories are often intimately linked with models. The word ‘model’ has as diverse meanings as the word ‘theory’ itself, and opinions about the role and virtue of models in science vary, from the die-hard realist's claim, ‘models are of no interest, we want to know the true reality’, to the provocative anti-thesis, ‘a good model is all we may wish for’. Naturally, a model is something different from the reality modelled. Saying “A′ is a ‘model of A’”, we understand that A′ ≠ A; but what makes A′ a model of A? The key notion is that of mapping. First, consider real geographic maps of, say, the Black Forest. These may be smallscale or large-scale, sketchy or detailed. None of the maps is really identical with the Black Forest, and no person of sound reason would ever call the Black Forest itself a ‘true map of the Black Forest’. Maps (i) depict selected features of the modelled reality, e. g., traffic paths and roads, while (ii) abstracting from other features, e. g., local altitudes, and (iii) thus provide a basis for further inferences, e. g., about the possibility of reaching b from a by walking in less than an hour. Maps, as models in general, are not ‘true’ or ‘false’, only more or less useful, due to structural or functional similarity with the reality modelled. In a more formal language of algebraic structures (MacLane and Birkhoff, 1968), models are morphisms mapping elements from A to A′ so that the relational structure of our interest is preserved. The structure serving as a model may be a physical, e. g., mechanical system, or a purely mental construct, i. e., an abstract system. Structural/functional analysis of the model allows one to make backward inferences on structural/functional properties of the modelled system; modelling thus occurs as an efficient instrument of the productive function of a theory.20 Model-based theorising emphasises the functional aspect of a theory (Section 3.1). Since models are by definition different from the reality modelled, it does not make sense to ask whether a model is ‘true’; all that matters is whether the model ‘works fairly well’ for a given purpose, that is, with respect to properties of our interest. If we accept the functional conception of theory, we may daringly say that ‘good theories’ are nothing else than successful models of relations between empirical facts—or between ‘laws’ of a lower level of generality.21 In physics and engineering, the use of mechanical models has a long tradition; in psychology and behavioural sciences, the

20 Under some circumstances the roles may be reversed so that a theory is actually produced by the model (cf. McMullin, 1968). We are thankful to one of the reviewers for reminding us of this alternative. 21 The functional concept of model is similar to Hertz's concept of ‘pictures’ (Bilder), which was originally introduced in a discussion of various forms of mechanical theories (Hertz, 1894), but is applicable as well to other branches of physics or other sciences.

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more abstract models inspired by cybernetics and computing science are now popular. However, the material structure of the model is irrelevant for the purpose of model-based analysis and inference. For example, a mass hanging on an elastic spring, and a series RLC circuit, are two instances of a harmonic oscillator, that are described by the same differential equation and, consequently, are functionally equivalent. What matters in theoretical analysis is only the abstract form of a whole equivalence class of models, which is ideally expressed by mathematical equations.22 3.5. The role of idealisation Even if material elements play a role in model constructions, these are usually not things of the real world but, rather, elements with idealised properties. Physicists are trained to think of systems consisting of components such as perfectly rigid rods, perfectly elastic springs, incompressible fluids, etc.; more abstract constructs like ideal gases or absolutely black bodies belong to the same family. A nonphysicist may wonder, then, how models made of such idealised, i. e., fictitious, unreal objects, may yield theories that successfully describe empirical reality? A common misunderstanding is that this is because these ideal entities are ‘good enough’ approximations of real-world objects and situations: almost rigid rods, almost frictionless motions, etc. This is not always true, and, more importantly, misses the proper meaning of idealisation in science. Strictly speaking, just the opposite applies: after a certain degree of abstraction, sciences do not deal directly with the real world, but with constructs consisting of thought elements endowed with ideal properties. Not the ideal approximates the real, but the real world appears as a more or less good realisation of the ideal.23

22 An example from the history of physics may illustrate the point. Concerning Maxwell's theory of electromagnetic field, W. Thomson (later Lord Kelvin) wrote, “I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I understand it. As long as I cannot make a mechanical model all the way through I cannot understand, and that is why I cannot get the electromagnetic theory of light.”—In contrast, H. Hertz concluded, “To this question, ‘What is Maxwell's theory’ I cannot give any clearer or briefer answer than the following: ‘Maxwell's theory is the system of Maxwell's equations’” (both quotations from Duhem, 1954, pp. 71–72 and 80). These comments of two eminent physicists on the then recent theory reveal totally differing concepts of modelling and theory construction. Cf. a quotation from R. Feynman: “Maxwell's discovery of electrodynamics was first made with a lot of imaginary wheels and idlers in space. But when you get rid of all the idlers and things in space the thing is O.K. […] [M]athematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or […] mechanical feelings, is not an efficient way” (Feynman, 1965, p. 57). 23 This was correctly recognised by Husserl (1970) in his analysis of modern, mathematical natural sciences. However, it would be foolish to criticise sciences for only using fictitious, ideal entities, since this has proven to be an immensely efficient strategy for theory building and theory-based inferences. The criticism is justified if the fictitious constructs are interpreted as the only and ‘true’ reality, of which our experience gives an incorrect and incomplete account—a misinterpretation, leading to a regrettable ‘ontological reversal’ (Dahlin, 2003). Mach's crude phenomenalism and the late Husserl's discovery of the primacy of the ‘life world’ were two attempts to oppose this reversal and put things–those ideal as well as those real–back to their correct places.

But if this is so, how should we understand the relation between a theory operating on ideal entities, and an experiment arranged in the real, material world?24 This is an important point: the essential elements of experimental setups are, in fact, material realisations of ideal constructs, derived from the theoretical rationale of the experiment. The fusion of the theory and the experimental setup goes so far that, [w]hen a physicist does an experiment, two very distinct representations of the instrument […] fill his mind: one is the image of the concrete instrument that he manipulates in reality; the other is a schematic model of the same instrument, constructed with the aid of symbols supplied by theories; and it is on this ideal and symbolic instrument that he does his reasoning, and it is to it that he applies the laws and formulas […] (Duhem, 1954, p. 156). The conception of an experiment as a simple question posed to Nature, and giving a simple answer ‘yes’ or ‘no’, is unrealistic and, worse, utterly naive (cf. Section 3.7). The more elaborated the theoretical background, the greater the distance between observational data and final conclusions that must be overcome by the interpretation. The immense potency of theory-based experiment manifests itself in the fact that the ideal can be ‘extracted’ from the empirical realisation by means of built-in compensations or post hoc calculated corrections. In all cases, these compensations, corrections, and further data manipulations must necessarily be theory-based. Contrary to the myth of ‘unprejudiced’, theory-free observation (cf. Section 2.3), we now realise that an experiment involves (i) theory of the phenomena of interest, defined in the language of ideal entities, and (ii) theory of the experimental apparatus, linking the ideal scheme with the material realisation. Consequently, a theoretical rationale must precede the experiment, if the latter be susceptible to a meaningful interpretation.25 Interestingly, at the dawn of scientific psychology, the importance of idealisation was clearly seen and articulated by J. F. Herbart: Why do mathematics treat of a mathematical lever which has no reality? Why do mechanics treat of the motion of points, of simple pendulums, of the fall of projected bodies in vacuo? Why not directly of the material lever, of matter in motion, of the path of the projectile in the atmosphere? In a word, why does that science use so many fictitious, auxiliary quantities, why does it not directly compute what is found and what occurs in the real world? The answer is contained in the question: those fictions are real helps, those abstract quantities are means to analyze, or limits between 24 In the understanding of many experimentalists (and their students) experimental protocols are something like industry standards, or guarantees of quality production, or cooking recipes, based on accumulated experience and specifying ‘how to do things right’, e. g., how to produce a phenomenon of the experimenter's interest. This may be partly true, but does not give a full account of the meaning of experiment. 25 In a brilliant shortcut, G. Bachelard (1970, p. 3) observed: “En physique, l'expérience ‘pour voir’ de Claude Bernard n’a pas de sens.” (For Bernard's empiricist position, see Section 2.3.) Ernst Mach maintained that the dependence of experiment on theory applies equally in physiology as in physics (Mach, 1926, Footnote 3 in p. 202).

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which the quantities of observation must be included to approximate the latter with greater and greater accuracy. (Herbart, 1877, p. 259). 3.6. Laws, mathematics and ‘economy of thought’ It is commonly understood that sciences aim at discovery of the ‘laws’ governing reality. However, the expression ‘law of nature’ is clearly metaphorical, and requires clarification. In this section we are dealing only with the role and form of laws in working theories; other aspects will be discussed in the context of special problems of rationality and universality (Section 4.1). We have met the notion of ‘law’ in two different contexts (cf. Sections 3.1, 3.2, 3.3): low-level ‘experimental laws’, which we have named ‘observational regularities’; and high-level ‘laws of nature’ as theoretical constructs, generating the lowlevel laws as their consequences and, in this sense, ‘explaining’ them. But this distinction is merely provisional. There is, in our opinion, no strict dichotomy, rather a continuity: laws of lower level express certain regularities, forms of which are the ‘facts’ for the theories of higher levels, and their laws. In natural sciences,26 laws (at all levels) are usually expressed in mathematical form. This means that the elements of their theories–observational data as well as unobservable theoretical constructs–are represented by quantities. The ‘interface’ between experienced reality, given in observation or experiment, and the idealised ‘reality’ to which the theory actually applies, is the quantification of qualities, i. e., the process of measurement. Measurement is not simple theory-free observation; contrary to the common notion, measurements are not just ‘readings’ made on things, as we read prices from tags attached to goods in a store. Measurement is a model of the property measured, based on a morphism from the domain of objects or states of our interest onto the domain of real numbers. Consequently, measurement models themselves are subjects of theories. Fundamental measurements of physical properties usually conform to the classic theory of measurement,27 elaborated by Helmholtz, Hölder, and later Campbell (1957). In this theory, additivity with respect to a certain physical operation (aggregation, composition) plays an essential role.28 The ‘composition’ operation, i. e., the observer's Sometimes called ‘exact sciences’; note that the ‘exactness’ refers to the idealised form of their theories, not to the precision of their measurements or predictions. For example, astrophysics belongs to this class, although its data may be subject to large uncertainties. 27 We should note explicitly that this is a mathematical theory, constructed on axiomatic foundations. Such theories generate normative prescriptions, no propositions testable against empirical reality. We may evaluate such a theory in pragmatic terms (‘is this concept of measurement useful?’), but not in terms of agreement with facts. 28 The meaning of additivity has been often misunderstood. Additivity of the measured quantity is a requirement stated by the theory, not an empirical fact to be eventually tested. Also, additivity is a necessary condition for a construction of ratio scale of the quantity meaningfully related to the physical reality. Stevens’ classification of measurement scales in terms of admissible transformations (Stevens, 1951) diverted attention of psychologists from the morphisms between two domains, to merely formal properties of relations within the co-domain of the measurement morphism—with regrettable consequences. 26

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action within the physical reality, is thus part of the definition of the quantity measured.29 What, then, is the role of laws in theories? In the process of elaboration of a theory, various relations may be designed and probed against the factual ‘matter’ of the theory. In a complete theory, its content, i. e., the relational structure proposed by the theory, and the statement of its laws are identical.30 Since the law is typically expressed by an equation, or a system of equations, the function of a theory is revealed in theory-based calculations. This aspect of laws was emphasised by Ernst Mach in his principle of ‘thought economy’.31 Using Snell's law as an example, he wrote [t]he economical purpose is here unmistakable. In nature there is no law of refraction, only different cases of refraction. The law of refraction is a concise compendious rule, devised by us for the mental reconstruction of a fact (Mach, 1960, p. 582). Mach is perfectly correct reminding us that there are no laws in nature—only in our theories. But his reduction of the law to merely computational outcomes is too far skewed towards Mach's empiricist background, linking all contents of theories immediately to sensory data. The reduction makes, to some extent, sense if applied to low-level observational regularities, but fails if applied to higher levels of laws generating other laws. However, the ‘principle of thought economy’ is more useful if detached from Mach's naturalist concept of knowledge, and rephrased as a principle of economy of representations. Theories provide simple forms condensing large amounts of their factual matter, and providing thus easily manipulable elements within theoretical structures at a higher level. Laws are mathematical expressions of these simple forms. Low-level laws yield data via numeric calculations; high-level laws yield other mathematical forms via symbolic calculations. 3.7. Experiment as a test of theory There is a general consensus that theories should agree with facts. But what are the criteria of the agreement? How to interpret an evident disagreement? As recognised by Bridgman (1927), although his ‘operationalism’ was effectively ignored by physics, and largely misinterpreted in psychology (Green, 1992; Grace, 2001). 30 Whether we call the content of a theory a ‘law’ or a group of ‘laws’ is merely a matter of convention or didactic purpose. (Cf. also Hertz's quote, Footnote 22.) We may say that the theory yields the law(s) as its outcome, but this makes sense only insofar as we follow the theory in our thoughts. Our mental reconstruction of a theory may be a process extended in time; but its logical structure is a-temporal, and so is the relation between the form of its law (s) and factual contents. This justifies our lack of emphasis on ‘predictions’, and introduction of a time-neutral title, ‘indiction’, in Section 3.1. 31 This principle was frequently and legitimately questioned, but also inaptly ridiculed by Mach's critics. N. R. Campbell remarked, in a somewhat frivolous tone, that “[t]he best way to attain economy of thought […] is not to think at all. Science is a branch of pure learning; thought is its object. To engage in science not to think would be as sensible as to engage in commerce in order not to make money” (Campbell, 1957, p. 222). As amusing as this remark is, it grossly misses the target. 29

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In simplistic accounts of scientific knowledge, a theory either agrees with observations or not. A theory predicts that, under conditions C1, C2, …, we shall observe effects E1, E2, …. It is impossible to test a theory's predictions for all possible conditions; on all objects belonging to its universe of discourse; at all places on the Earth and at all times. Thus, we can never state with certainty that the theory is in perfect agreement with observable facts; but we can be certain that, if we meet just a single disagreement between the theory's prediction and the observed fact, that the theory has failed. We can never verify, but we can with certainty falsify a theory. This would suggest that the progress of scientific knowledge consists not in designing good theories, but in the progressive elimination of bad theories.32 For some philosophers of science (K. Popper) this is the cornerstone of the logic of scientific research. This seemingly convincing argument has been accepted by many researchers, particularly in the medical and social sciences, including psychology.33 Under the influence of the falsificationist doctrine, experiment is seen as the supreme instance that decides about the survival or extermination of a theory. This version of empiricism is weaker than the radical empiricism mentioned in Section 2.3, as it does not refute all theory as totally useless. However, the role of theory is only to stimulate experimental work which will lead, ultimately, to rejection of the theory; the virtue and dignity of theoretical work is, so to speak, that of suicidal heroism. If this is not radical empiricism, it is nonetheless a dangerously close variant of it: what both variants share, is the belief in the irrefutable ‘truth’ of experimental fact. The falsificationist concept is not satisfactory for many reasons. Firstly, it is at odds with the reality of scientific practice: in a given domain of scientific study, theories do not constitute a historical succession of absolute and despotic emperors, but rather form a living community of more or less powerful dynasties, each competing for more influence and importance. Less metaphorically: theories are not ‘true’ or ‘false’, but good or less good. The relation between a theoretical indiction and observation is not ‘agreement’ or ‘non-agreement’, in terms of bi-valued logic; it is gradual, more or less satisfactory approximation. Also, the performance of theories may differ between their two principal functions, the receptive and the productive (cf. Section 3.1). The falsificationist concept ignores the complex relational character of theories, but also of observational data, which are not ‘atomic’ facts but relational structures as well. Experiments are not peep-holes into ‘true reality’, but are more or less 32 In this account, theories are like candidates for a certain position, waiting in a queue for their opportunity; once they are elected and confirmed in their function, they stay until their first failure–e. g., a wrong decision, or a public scandal–after which they have to abdicate for ever. But things are not so simple in social life nor in science. 33 There seems to be an alliance between the falsificationist doctrine and the practice of statistical hypotheses testing based on the ‘tests of significance’ that are all-pervading in psychological research. What they have in common is a kind of negative logic, progressing towards knowledge by elimination of what has been proved wrong. However, the ‘hypotheses’ to be statistically tested may or may not be derived from a theory; they may be merely ad hoc assumptions, generalisations or carry-overs of facts from other fields.

complex arrangements of things and procedures, physically implementing the ideal conceptual structure (cf. Section 3.5). The function of each single element of the experimental apparatus depends on the working of many ‘local’ theories:34 “A physical law is a symbolic relation whose application to concrete reality requires that a whole group of laws be known and accepted”. (Duhem, 1954, p. 168).—In sum, prediction of the outcome of an experiment depends on an immense number of conditions and built-in theoretical assumptions. This was expressed by P. Duhem in his famous thesis, “an experiment can never condemn an isolated hypothesis but only a whole theoretical group” (Duhem, 1954, p. 183),35 from which the impossibility of a so-called ‘crucial experiment’ is self-evident. Instead of the testing and refutation of theories, we should more properly speak about the formation of theories. Evaluation of a theory is not a trial resulting in an irrevocable binary decision, ‘passed’ or ‘failed’; it is rather a continuous process of comparison between two series of regularities, those indicted by the theory and those obtained by observation or experiment. Differences between those two series create a challenge for a further development of the theory.36 The better theory may not be another one from a ready-made catalogue of proposals, but a modified form of the present theory. Thus, another measure of ‘goodness’ of a theory, not mentioned in Section 3.1, is its selfmodifying capability. Ideally, a theory utilises its productive function to generate indictions, and in this way probes its receptive function. A living theory exercises and perfects itself in a continuous process of probes and modifications. The schematic picture of the life-cycle of a theory, proposal → temporary acceptance → final refutation, insinuates an antagonism between the conceptual (theory building) and ‘perceptual’ (observing and data collecting) faculties of science (see Section 2.2). However, the differentiation of these faculties, a sign of maturity of a science, does not imply their antagonism but a co-operative unity. The theoretical faculty has to devise experiments as a mean of its development. Or, paraphrasing a well-known dictum on war and diplomacy, we could say that ‘experiment is a continuation of theoretical thought by other means’.

34 Sometimes unknown to or hidden from the experimenter, a fact often overlooked in interpretation of experimental results. For example, outcomes of brain imaging techniques are not direct photographs of ‘brain activity’, but the result of sophisticated computational procedures that rely on biophysical theories and mathematical theorems. Modern computer-based laboratory technologies lead to a state where even apparently simple measurements of physical quantities are outcomes of complex data-processing devices, rather than simple ‘readouts’ of measuring instruments. 35 The atomistic concept of theory testing was also questioned by Quine (1951), and the contemporary literature thus often refers to the ‘Duhem–Quine thesis’. It is true that both authors emphasised the complex structure and holistic (Esfeld, 2001) character of theoretical constructs under test. However, the motives driving Duhem and Quine were quite different, and thus “the two variants [of the argument] are better not confused” (Agassi, 1983). 36 This means: differences exceeding limits of approximation which are selfimposed by the theory. For a scientist accepting the functional conception of theory it is perfectly legitimate to declare, ‘my theory shall account for effects of first order and leave other effects out’. A believer in the correspondence-totruth conception will consider such a theory as ‘false’.

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4. Special problems in theory construction 4.1. Rationality, universality, and ‘scientific laws’ Rationality and universality are two frequently named attributes of scientific knowledge. How do they relate to each other, and what is their place in our concept of scientific theories? Are these attributes characteristic properties of scientific thought? Are they ideal requirements imposed on science? We begin our discussion with the idea of ‘law’ as a meeting point of the two notions in question. We have seen the key role of ‘laws’ in theory construction. We can say, with a certain license, that any theory of a certain domain of phenomena is not finished until the law(s) ruling these phenomena is/are found. Historically, interpretation of what happens as a law-like, regular, natural process is the key event in the development of science, and has its origins in ancient Greek thought, as has the concept of Nature, fysis, itself. The very notion of ‘law’, of course, belongs to the domain of human affairs, and its application to the physical domain is a metaphoric extrapolation. Saying that something happens or exists ‘by law’ or ‘lawfully’, we postulate a certain order, opposed to the notion that things happen just randomly or by someone's arbitrary will. The invention of universal law as a mean of organising society and bringing order to human acts and words (tending by nature to chaos and injustice) was a great step in the history of human civilisation. Singularly in Greek culture, the transition to forms of social life ruled by equal measure of law, isonomia, was accompanied and followed by the transition from mythical interpretation of the world to its logical interpretation and explanation. Nature, fysis, was seen as an organised and harmonically structured whole, kosmos. The order of Nature gives cause to think of an ordering principle behind observed phenomena, that is, a law, nomos. Similarly, the state of political order was described in geometrical and physical terms: equality, isotēs, static balance, isorropia (Vernant, 1982). Out of this background, the idea of a ‘natural law’, one divine and universal order in Nature and human society arose; in the classic formulation, “one eternal and unchangeable law […] valid for all nations and all times and there will be one master and ruler, that is, God, over us all, for he is the author of this law” (Cicero, 1928). We must be aware of this socio-cultural construct not to get stuck with a metaphysical vision of the lawful order of Nature, which is discovered and revealed by science. Compare, for contrast, Karl Pearson: The civil law involves a command and a duty; the scientific law is a description, not a prescription. The civil law is valid only for a special community at a special time; the scientific law is valid for all normal human beings, and is unchangeable as long as their perceptive faculties remain at the same stage of development (Pearson, 1900; quoted by Mach, 1926, p. 450). Here, the binding power of the scientific law applies to us, human beings, observers of nature. In this, and only this sense, the laws posited by sciences are universal. In terms of regions of validity, i. e., applicability, their laws are only conditionally

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universal. Their universality is limited from outside, by the boundaries of the universe of discourse of a given theory,37 and also from within, by the limitations of idealised and formalised models, on which the theories are built: [L]aws are always provisional; not […] that a physical law is true for a certain time and then false, but at no time it is either true or false. It is provisional because it represents the facts to which it applies with an approximation […] Physical law is provisional not only because it is approximate, but also because it is symbolic: there are always cases in which the symbols related by a law are no longer capable of representing reality in a satisfactory manner (Duhem, 1954, p. 172–174). Scientific knowledge, expressed in laws, is thus knowledge of the conditional yet, within the domains of their applicability, immutable and invariant order in the continuous flux of phenomena. It is knowledge of what is accessible to reason, leaving aside merely factual sensory evidence. This leads us to the second important topic of this section. Rationality refers to the rational faculty, ‘reasoning’. Reasoning is obviously not simply equivalent with ‘thinking’; weird world-views, or pseudo-scientific constructs, too, may arise from thought. Rational thinking is that which operates with relations and proportions, ‘pondering’ pros and cons, searching for measure and balance. It is not by chance that numbers that can be expressed as a proportion of two integers (i. e., intuitively and immediately understandable parts), are called ‘rational’.38 Scientific thought is rational by definition, not just as a matterof-fact. Now, the symbolic expression of physical laws reveals the rational character of the theory; yes, it incorporates the very ideal of rationality in a mathematical form. Consider, for example, the state Eq. (1).39 The expression is constant for a certain gaseous body across a variety of its states; the value per se is irrelevant for the statement of the law. The law can be more properly written in the form p1 V1 p2 V2 ¼ ; T1 T2

ð2Þ

where the indices 1 and 2 refer to two states. This expression does not involve any numerical constants, i. e., any elements external to the law. It merely specifies a relational invariant, which describes

37 Unconditionally valid laws–and, by the same argument, ‘theories of everything’–have no place in real science. 38 This concept of ‘rationality’ has also deep roots in ancient Greek thought. 39 We should notice that the example concerns the state equation of the ‘ideal gas’—cf. Section 3.5. Laws approximating state varieties of real gaseous bodies are more complex (e. g., van der Waals' equation). Characteristically, the ideal form of the law occurs as a limiting case of the more realistic (and more complex) law. This illustrates the role of ideals in the definition of concepts within a theory: we could properly say that a ‘perfect gas’ is defined by the ideal form of the law, and, consequently, that ‘real gases under low temperatures or high pressures are not perfectly gaseous’.

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the variety of all possible states of the system under varying conditions. Keeping one of the state variables, e. g., temperature T, constant, we may derive similar rational expressions of special laws. Virtually all ‘phenomenological’ laws of physics–Ohm's law in electrophysics, Kepler's 3rd law in celestial mechanics, etc.– possess this paradigmatic rational structure. In a more general form we meet this rational expression of relational invariants in universal principles applicable across particular universes of discourse of separate theories, e. g., about conservation principles. Conservation of a certain quantity throughout the variety of states implies that the physical theory specifies a n-placed function F of state variables v1, … , vn such that the variety of states of a system described by the theory is described by the relation

4.2. The problem of individuality

On the right hand side of the expression we have not only state variables T and V, and m as a measure of material content, but also a constant, c, characteristic for the given substance. Laws expressed in purely relational, that is, rational form, are valid without reference to, e.g., measurement units or material standards. To be useful for practical purpose, laws transcribed to ‘calculation formulas’ involve material constants like densities, specific heats, molecular weights, etc.. These elements are aliens in the rational structure of the theory, and, in this sense, irrational. They are pure facts that cannot be derived from the theory.40 Such merely factual elements are as irrational as singular observations, not subordinated to any (known or hypothetical) observational regularity, or as purely sensory41 data, not subordinated to any perceptual or conceptual framework.

The Latin word individuum means originally ‘undivided’ or ‘indivisible’. In modern usage, ‘individual’ means something or someone of unique identity, not interchangeable with anything or anyone else of the same sort. The notion of the human being as an individuum is a pre-scientific concept, occurring with the modern social and political order. Individuality refers to the integrity of a complex (biological, psychological, social) entity, and does not imply just ‘atomic’ simplicity. Natural science searches for universal laws, so the notion of individuality does not play any role: the law of gravitation applies to all material bodies, without exceptions. However, in sciences studying human beings, like psycho(physio)logy, the substrate of phenomena of our interest is an individual, bringing in her/his unique identity, unique biography, etc. We are thus facing a conflict between the aspiration to universality of science, and the uniqueness of individuals as objects of its study. In the past the problem was recognised but, as to our knowledge, never solved in a satisfactory manner. One such attempt was made by distinction between ‘nomothetic’ and ‘idiographic’ method, drawn by German neo-Kantian philosophy [(Rickert, 1986), cf. also (Oakes, 1988)]. According to this proposal, the task of physical sciences is to posit universal laws of Nature (nomothetic approach, nomos = law). The individual qua a unique being can be grasped only by a singular case description (idiographic approach, idios = private, on its own; graphō = I write). Obviously, this was no real solution but a declaration of defeat: the individual was thus, by definition, expelled from the realm of the lawful. Nonetheless, the preliminary distinction proves to be useful for further discussion. The individual as an aggregate of properties.—As long as we are studying universal regularities of psychophysical functioning, we can safely apply the same approaches as when studying mechanical or electrical properties of inanimate bodies. Individual subjects in our studies are not studied in their unique individuality, but merely as singular instances of the functional relationships of our interest. However, even on these elementary levels we find inter-individual differences—e. g. in thresholds of reactivity to physical stimuli, reaction times, etc. As we proceed from the elementary to complex actions as components of purposeful, motivated behaviour, and finally to self-reflected properties of the individual, inter-individual differences become even more pertinent. We realise that each individual can be described by her/his unique composition of properties.42 This is, generally, the approach of the ‘psychology of personality’, an attempt to find an order in the variety of the aggregates of characteristic properties, and to reduce them to a

40 If a rational theory ‘explaining’ their values is developed, it is a theory of a broader scope and different content from the theory, in which the factual elements originally occur. 41 Noteworthy, C.G. Jung (1921) in his theory of four basic psychological functions classifies sensation as irrational function.

42 In natural science, a vague analogy of individuality could be identities of pure chemical substances. This, however, is a case of collective identity — all atoms of silver, all molecules of water have the same properties. In contrast, human individuality implies singular identity, which is evident prior to cataloging and comparison of individual properties.

Fðv1 ; N ; vn Þ ¼ 0:

ð3Þ

We may call the form (3), expressing the content of a theory in a most rational manner, the isonomic form of the law, referring to the ancient Greek idea of isonomia. In textbooks, laws are usually not presented in the isonomic (‘closed’) form but, rather, in an ‘open’ form, allowing explicit calculation of certain quantities, given that values of other quantities are known. This seemingly supports the concept of a law (or of a theory positing the law) as just a handy ‘calculating device’ (cf. Section 3.6). By now it should be clear that we consider this ‘practical’ aspect of theories rather as a side-effect. But the explicit transcription of isonomic laws reveals something more. Consider, for example, the expression for a pressure p of m mass units of a gas, enclosed in a volume V at temperature T: p¼c

mT : V

ð4Þ

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a

φ [Hz] 20

b

Subject 1

10

0

c

φ [Hz] 20

423

Subject 2

10

0

10

φ [Hz] 20

Subject 3

0

20 Σ [ μ V]

d

20 Σ [ μ V]

10

0

φ [Hz] 20 0 20

0 10

10

10 50 20 10 5

0

0

10

20 Σ [ μ V]

0

0

10

20 Σ [ μ V]

Fig. 1. Sections a, b, c: State-space portraits of individual varieties of functional brain states during sleep. Σ = integral power, Φ = generalised frequency. Data based on 27-channels-EEG recordings during one whole night. Each data point represents a 20s data segment. Section d: System of k-isolines in the (Σ, Φ) space; individual baselines copy shapes of these isolines, determining individual values of k.

few underlying principles in a framework of a ‘theory of personality’. The individual as an idioversum.—Rather than treating individuals as elements of a universe (human beings in general) or sub-universe (participants population, pre-defined in terms of race, gender, social status, etc.), we may consider a given individual as a unique universe, or idioversum, of her/his momentary states sampled during a certain time period.43 These states can be characterised by simultaneous measurements of, say, m state variables (psychological and/or physiological) the sample portrait of the individual idioversum thus would consist of n points (n ≫ m) in a m-dimensional state space. Distributed nomothesis.—We propose an essentially nomothetic approach, oriented towards universal laws; but it is a ‘distributed’ nomothesis, proceeding on two levels. (1) On the first level, individual data are treated separately, within their idioversa, and idioversal law(s) describing intra-individual observational regularities are sought. No attempt is made to construct a ‘universal’ theory applicable to all individuals under study. (2) On the second level, variety of idioversal laws, expressed by logical or mathematical forms, is collected and treated as individual facts. Inter-individual comparisons thus does not focus on the variety of primary data but, rather, on the variety of individual forms. Thus, instead of reducing data across individuals to achieve a common description–which implies that they are all subject to a ‘universal’ law–, data are first reduced in terms of idioversal descriptions, and only then

43 The adjective ‘momentary’ has to be understood as ‘very short’, relatively to the duration of the entire observation period’.

subordinated to a common law. This law is universal in the sense that its mathematical form generates idioversal regularities as its particular cases, via suitable parameterisation. (Assignments of values of these parameters to individuals are a kind of ‘derived measurements’ on individual subjects.) Individual varieties of functional brain states (FBS), quantified by means of global descriptors of brain electrical activity (full-scalp EEG) during one night, may serve as an example (Wackermann, 1999, pp. 70–73). Fig. 1 shows such idioversal portraits of individual varieties of brain states, characterised by two state variables (Σ, integral power, and Φ, generalised frequency), for three individual subjects. The individual FBS varieties show similar shapes (Fig. 1abc) but occupy different places in the (Σ, Φ) space. Their forms can be expressed by equation RU ¼ k;

ð5Þ

where k is an individual constant physical dimension of which is [k] = μV · s− 1. Fig. 1d shows a system of theoretical curves for various k's in the (Σ, Φ) space. Obviously, superposition of individual data clouds in a common state space would grossly blur the picture; and the same applies to usual ‘normalisation’ procedures, e. g. transformation to common mean and standardised variance. In such a case, data reduction is applicable only after transformation which takes into account the real form of the idioversal laws. Another, superordinate law should characterise the statistical distribution of k's, or relate them to basic neurophysiological or neuroanatomical characteristic of the brain.—The approach is here illustrated by exclusively

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physiological data, but is applicable to psychological data, or product spaces of psychological and physiological data as well.

large—a philosophy that must be demanded of every special investigator (Mach, 1960, p. 610).

5. Concluding remarks 5.2. Towards a methodological physicalism 5.1. Philosophy of science and scientist's philosophy In the preceding sections we repeatedly touched themes which are usually considered special topics of the philosophy of science: the nature of human knowledge, relations between experience and theory, the concept of law, etc.. The reader may be surprised by the absence of references to philosophy of science, and the lack of a link between our and their views and positions. This should not be misinterpreted as a symptom of dumb ignorance or plain arrogance. We do not ignore the philosophy of science and its role in the elucidation and interpretation of scientific thought. However, we realise that the interests and aims of philosophers of science are not necessarily identical to those of a philosophically minded scientist. Traditionally, philosophers tended to study science from outside; they were interested in scientific thought and its ‘morphology’ as far as it concerned general themes of knowledge and its relation to reality. Such studies may have interpreted concepts, methods, or theories to identify and elaborate philosophical problems invoked by sciences; but they were never immediately facing the question occurring to a working scientist: ‘How do I understand my concepts and methods? What impact has my understanding of them on my own research and the interpretation of its results?’ Another point of divergence is the dialogic character of philosophy. A philosopher of science ‘taking a position’ to a certain problem does so, primarily, to maintain and defend a particular position in a dispute with professional colleagues. In contrast, a working scientist ‘takes a position’ by decisions made in daily practice; whether reflected and articulated or not, the position taken codetermines the understanding of data, results, conclusions, and communication strategies in the scientific community. This applies especially to the scientist's position concerning the role of theory in his field. Fortunately, we are witnessing a trend in the contemporary philosophy of science which is increasingly driven by the needs and deeds of scientists active in their respective fields of interest. This supports our point of departure, and strengthens our sympathetic link to early authors like Duhem, Mach or Bridgman, who were all working scientists, and, at the same time, independent thinkers reflecting science from within, before the philosophy of science became a professional option. If we are scientists by vocation (not just ‘doing research’ as it happens), we cannot avoid the need to reflect on the principles and ultimate goals of our work; it is a task we cannot delegate to specialists in the next-door department. Ernst Mach, who decidedly refused to be called a philosopher, and defined himself rather as a ‘rambler in varied fields of knowledge’, had seen this clearly when he wrote: A philosophy is involved in any correct view of the relations of special knowledge to the great body of knowledge at

In this essay we have frequently used illustrative examples, or anecdotal material, from the field of physics. As this paper will be read by psychophysiologists of various backgrounds (psychology, psychiatry and other medical disciplines, etc.), it is possible arguments against the author's ‘physicalism’ will be raised. More than just a few readers may feel, ‘all this may well work in physics, a science dealing with simple inanimate systems; but things are different in psychology’; and some will perhaps add that ‘physics should not be considered the ideal of science in general, and psychology will profit of getting rid of this misleading ideal as soon as possible’. The statements above are free quotations: discussions with young scientists and students teach us that the ‘uprising against the dictate of physics’ is now fashionable. One of our objectives is to oppose this fashion, and to make a case for a non-reductionist concept of the unity of science. We are not afraid of naming our position physicalism; but we should add that this is a methodological, not ontological, physicalism. That is, we do not subscribe to the strong reductionist programme of translating all conditions and/or manifestations of the mental to the language of neurophysiology or neurophysics. Such a programme would indeed degrade psychophysiology to a non-sensical ‘double accounting’ for one and the same physical reality; this is not our intent. Physicalism does not have a good name in psychology; neither has the ideal of formalised theorising in terms of mathematical postulates and laws in the manner, say, of C. L. Hull (1935); the behaviouristic past still throws long shadows. Concerning laws and their formulation, psychology has a notorious problem with the concept. It has been observed that “[t]here are not many ‘laws’ in psychology”, and even those counted as the most stable and venerable, like the Yerkes and Dodson (1908) law, occur as a rather deliberate construction of generations of researchers (Teigen, 1994). We may also object that since Wundt there have been rather too many ‘laws’ in psychology, designed at a writing desk as general principles. It is true that psychology has strikingly few established law-like regularities expressed in quantitative terms as, e.g., Hick's law (Hick, 1952). Regularities of this sort may be the factual basis for higher-order laws to be developed from neurophysical and psychophysical models; cf. Usher et al. (2002). Such theories would provide theoretical ‘explanation’ of observational regularities in psychology, in a similar manner as the kinetic theory of gases explained phenomenological laws in macroscopic physics. Paul Häberlin once properly noted that “the destiny of all biology and physiology is to become either physics or psychology” (Häberlin, 1923, p. 131). This is perhaps too strong a formulation, but it reveals the fact that the two accounts, the physicalist and the mentalist, act as asymptotic attractors in our interpretation of biological and physiological phenomena. But, if the physical and the mental are conceptualised as two different ordering structures for the same reality, that is to say,

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psycho-physically neutral experience (Mach, 1959), rather than two ontologically different realms, there is no objection against a unified methodology applicable in both physics and psychology. We believe that the ideal of rational theory sketched above— involving idealisation and mathematical formalism44—provides such a unifying principle.

earlier draft of the manuscript, and Dr. H. Atmanspacher for his comments on a revised version. The author is also indebted to two reviewers of this paper for their helpful critiques. Data shown in Fig. 1 are results from a cooperation with Dr. W. Szelenberger and his workgroup (Warsaw).

5.3. Consequences for education in psychology

References

From what has been said above, a number of consequences should be drawn for the revision and reform of study programmes in psychology. In spite of their desire to specialise, students should be aware of the position of their discipline in the broad context of natural sciences, and of the historical development of their concepts and methods. It is unlikely that they will understand fundamental concepts of measurements and quantitative description of reality without a comparative study of these concepts in various scientific disciplines. It is unlikely as well that they will understand the problems of theory construction in their own discipline if they have no understanding of the logical structure and historical development of theories in other sciences. In addition, wherever possible, the ‘historical-critical method’45 should be preferred to dictionarylike overviews and enumerations. The deficient scheme of experimentation as the machinery of ‘hypotheses testing’ should be removed from textbooks, and replaced by the exposition of the relations between theory construction and empirical evidence in their richness and complexity. Accordingly, more emphasis should be laid on the theory development on deductive grounds, in a relative independence from an empirical database, on model building and analysis, and on understanding of the role of theory-laden elements in experimental designs and their implementation in experimental procedures and devices. Experimental work should be presented as a sort of materialised reasoning, motivated by theoretical thought, not as a game played by its own rules on an isolated playground. The ideal form of a science as a fully developed theory of its subject must be presented to students as clearly and challengingly as possible; and this sub speciae of the supreme ideal of the unity of faculties, and, ultimately, of the unity of science. Acknowledgements The author wishes to thank Dr D. L. Robinson for his invitation to contribute to this special issue, and for his critical remarks on an 44 Mathematics should be understood in its broadest meaning, that is, not restricted to classical instruments of mathematical physics (calculus, differential equations). Modern branches of mathematics, especially theory of algebraic structures, may play equal or greater role. In fact, every formalism elaborated to a sufficient degree of precision tends to become ‘mathematics’ of its own domain. 45 Pioneered by Ernst Mach in his studies of fundamental concepts in mechanics, thermics, and optics. Incidentally, it was Mach's Science of Mechanics–originally in German, ‘Die Mechanik in ihrer Entwickelung historisch-kritisch dargestellt’–that had a deep influence on the young Einstein (Holton, 1970).

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