daniel goldman cedarbaum - paradigms

DANIEL GOLDMAN CEDARBAUAP

PARADIGMS

We are like sailors who must rebuild their ship on the open sea, never able to dismantle it in dry-dock and to reconstruct it there out of the best materials.

Otto Neurath

My picture of our situation is not the famous Neurath picture of science as the enterprise of reconstructing a boat while the boat floats on the open ocean, but it is a modification of it. I would change Neurath’s picture in two ways. First, I would put ethics, philosophy, in fact the whole culture in the boat, and not just ‘science’, for I believe all the parts of the culture are inter-dependent. And, second, my image is not of a single boat but of a f7eet of boats. The people in each boat are trying to reconstruct their own boat without modifying it so much at any one time that the boat sinks, as in the Neurath image. In addition, people are passing supplies and tools from one boat to another and shouting advice and encouragement (or discouragement) to each other. Finally, people sometimes decide they don’t like the boat they’re in and move to a different boat altogether. (And sometimes a boat sinks or is abandoned.) It’s all a bit chaotic; but since it is a fleet, no one is ever totally out of signalling distance from all the other boats. There is, in short, both collectivity and individual responsibility. If we hanker for more, is that not our old and unsatisfiable yearning for Absolutes?

Hilary Putnam

Introduction

J’kite d’&re long, et je deviens obscur.

Boileau

‘THOSE WHO react negatively to your point of view,’ James B. Conant wrote to Thomas Kuhn in 1961, ‘will brush you aside, I fear, as the man who grabbed on to the word “paradigm” and used it as a magic verbal wand to explain everything!” In the same letter he expressed the hope that the work which he

,329 Harvard Street, Apt. 30, Cambridge, MA 02139, U.S.A. This paper is based on my senior honours thesis in the History of Science Department of Harvard College. I would like to thank Hilary Putnam, who has given me an insight into the world of the philosopher, and my adviser, John Beatty, who awakened my interest in philosophy of science, and without whom this thesis would not have been written. I am enormously indebted to Thomas Kuhn for sharing with me his recollection of the development of his ideas, for allowing me access to his files, and for writing The Structure of Scientific Revolutions. Finally, I owe a special debt of gratitude to my brother, Jonathan Cedarbaum, for his constant encouragement.

‘Letter from J. B. Conant to T. S. Kuhn, 5 June l%l, p. 1.

Stud. Hkt. Phil. Sci., Vol. 14, No. 3, pp. 173-213, 1983 0039-3681183 $3.00 + 0.00 Printed in Great Britain. 0 1983 Pergamon Press Ltd.

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had just read would ‘not only stir up opponents but win many adherents’;* the manuscript which Kuhn had sent him was entitled The Structure of Scientific Revolutions. Conant’s wish is reminiscent of Russell’s remark that Wittgenstein’s Tructatus ‘deserves . . . to be considered an important event in the philosophical world’.3 Since its publication in 1962, The Structure of Scientific Revolutions (hereafter Structure) has become nothing less than a bible for countless scientists, historians, sociologists and psychologists, and has at the same time been treated as nothing less than heresy by most philosophers of science. As Conant predicted, the focus of the controversy over the book has been Kuhn’s use of the word ‘paradigm’.

The fundamental obstacle to a proper understanding of Structure results from the fact that the term ‘paradigm’, as Kuhn has said of the book as a whole, ‘can be too nearly all things to all people’.4 Kuhn readily admits that he is partially to blame for this problem;5 only with great difficulty could he have left the concept of ‘paradigm’ more open to misinterpretation than he did. One sympathetic critic has shown that Kuhn uses the term in no fewer than twenty-one different ways.G This and related ambiguities are not the result of mere carelessness on the part of the author; rather, they reflect a lack of clarity in his views at the time he wrote Structure. Kuhn has good reason to remark that, ‘Monitoring conversations, particularly among the book’s enthusiasts, I have sometimes found it hard to believe that all parties to the discussion had been engaged with the same volume’;’ in an important sense, they usually had not been. To define precisely the nature and function of ‘paradigms’ in Kuhn’s conception of the scientific enterprise, and thus to separate the Structure

which Kuhn intended to write from those which others have read, is the object of the present study. That the book which Kuhn believed he had written is virtually unknown has, interestingly, been largely responsible for both the fanatical adulation and the opprobrium accorded to Structure.

Few books have been as widely read and as widely misunderstood as Structure. Since 1970, the University of Chicago Press has sold more than 380,000 copies of the second edition alone. In comparison, the same publisher has printed a total of fewer than 18,000 copies of Rudolf Carnap’s contribution to the International Encyclopedia of Unified Science (of which Structure is also a part). The popularity of Structure is made even more

‘Ibid. %. Russell, ‘Introduction’, in L. Wittgenstein, Tract&us Logico-Philosophicus, trans. D. F.

Pears and B. F. McGuinnnes (London: Routledge and Kegan Paul, l%l), p. ix. ‘T. S. Kuhn, ‘Second Thoughts on Paradigms’, in The Essential Tension (Chicago: The

University of Chicago Press, 1977), p. 293. 5Cf. Kuhn, ‘Second Thoughts’, pp. 293 -4, and T. S. Kuhn, The Structure of Scientific

Revolutions, 2nd edn. (Chicago: The University of Chicago Press, 1970), pp. 174ff. *M. Masterman, ‘The Nature of a Paradigm’, in Criticism and the Growth of Knowledge, I.

Lakatos and A. Musgrave (eds.) (Cambridge, U.K.: Cambridge University Press, 1976) pp. 61-5.

‘Kuhn, ‘Second Thoughts’, p. 293.

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remarkable by the fact that Kuhn’s book, like Carnap’s, is essentially a work of philosophy. This apparent anomaly has, however, a simple explanation; almost no one who reads Structure recognizes that its central arguments are philosophical.

At a recent meeting of the American Philosophical Association, a young philosopher greeted Kuhn with the query, ‘What are you doing here?“’ Indeed, trying to explain to most of Kuhn’s readers that Structure is concerned with some of the most fundamental issues in contemporary philosophy is like attempting to convince someone casually acquainted with evolutionary theory that the article ‘the’ does not precede the word ‘Species’ in the title of Darwin’s great work. In the latter case, however, a glance at the title page of the Origin will silence even the most recalcitrant anthropocentrist; in the former,

re-reading the entire book will probably persuade only a few that Structure is primarily a philosophical tract. Largely responsible for this misconception of the nature of his work is the fact that Kuhn, having had little formal training in philosophy, rarely uses the technical vocabulary of that discipline and refers to only a few philosophical texts. That Structure is far more complex than it appears is the principal reason that no adequate appraisal of the book has been written.

An insightful critic has remarked, ‘Just as the supporters of Herr Kant always reproach their opponents for not understanding him, it seems that some others believe that Herr Kant is right because they understand him.‘g Those who have struggled to make sense of a particularly obscure work often defend it without stopping to evaluate the views which their efforts have elucidated. Interestingly, a related, and perhaps more serious, problem is posed by works which are remarkable for their superficial simplicity. When not confronted by obviously difficult passages, challenging him to carefully reconstruct the arguments being presented, the reader may, on the one hand, be unduly impressed by a book’s apparent clarity and coherence, or, on the other hand, may be too quick to dismiss a book as trivial and its reasoning as lacking force. Structure has elicited both reactions.

That familiarity with the ‘Duhem - Quine Thesis’, Wittgenstein’s account of naming in the Philosophical Investigations, and Quine’s analysis of translation is a necessary, though by no-means sufficient, condition for fully understanding Structure is so far from clear from the text as to seem intentionally disguised. The most ardent admirers of the book have generally lacked this requisite philosophical background, and have thus been among those least well equipped to grasp the significance of Kuhn’s work. Indeed, no one who truly appreciated Structure could be as oblivious to the profound

“Kuhn, Lecture in Subject 24.853 at M.I.T., 11 February 1980. VI. C. Lichtenberg, The Lichtenberg Reuder, trans. and ed. F. H. Mautner and H. Hatfield

(Boston: Beacon Press, 1959), pp. 88-9.

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problems posed by the book as Kuhn’s most ebullient supporters have been; understanding Structure entails an awareness of its serious flaws.

The most perceptive comments on Structure have almost all, in fact, appeared in the context of largely negative appraisals written by philosophic- ally sophisticated critics.‘O Indeed, the opponents of Structure have had the best of the debate over Kuhn’s work; few of their charges have been adequately countered by the book’s advocates, including the author himself. Still, those whose philosophical expertise makes them capable of comprehend- ing Kuhn’s views (virtually all of whom are among the book’s detractors) have been almost as uniformly deceived by Structure’s aphilosophical fa2ade as have its more naive readers.” Few have even attempted to delve beneath that specious surface. Some, dismayed by the historical, psychological and sociological considerations found throughout the book, have decried Structure as proclaiming the irrationality of the scientific enterprise.‘2 Others, bewildered by Kuhn’s apparently reckless use of the book’s central term, have concluded that ‘paradigm’ is an empty concept and thus that the account of scientific development presented in Structure has no foundation.13 In showing that the question ‘What is a paradigm ?’ has a precise and meaningful answer, the essentially philosophical character of Structure will become evident. That process begins with an examination of some of the works which have directly or indirectly influenced Kuhn’s conception of the nature of science.

‘History,’ Structure begins, ‘if viewed as a repository for more than anecdote or chronology, could produce a decisive transformation in the image of science by which we are now possessed.“’ Thus regarded, the history of philosophy could also transform the vague and quasi-mystical image of ‘paradigm’ shared by most of Kuhn’s readers. Kuhn did not, of course, coin the term, nor did he introduce it into the philosophy of science. The word ‘paradigm’ was first used to denote a central component of the process of scientific development by a physicist and philosopher virtually unknown in the English-speaking world, Georg Christoph Lichtenberg, almost two centuries before Structure was published. Another philosopher, somewhat better known than Lichtenberg, in whose writings the term figures prominently was Ludwig Wittgenstein. Toulmin, however, in a footnote to Wittgenstein’s Vienna, has remarked that ‘The use of this term by Wittgenstein . . . (as well as by Lichtenberg . . . and other philosophers of language and philosophers of science) differs significantly from that made familiar recently by T. S. Kuhn in

‘OCf. D. Shapere, ‘The Structure of Scientific Revolutions’, Philosophical Review 73 (1964), 383 - 94.

“Cf. H. Putnam, ‘Philosophers and Human Understanding’, Herbert Spencer Lecture delivered at Oxford Unversity, November 1979.

“Cf. I. Scheffler, Science and Subjectivity (Indianapolis: Bobbs-Merrill, 1967). ‘Vf. Shapere, ‘The Structure of Scientific Revolutions’. “Kuhn, Structure, p. 1.

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his much-discussed book, The Structure of Scientific Revolutions.“5 That Toulmin is wrong is the principal conclusion of the following two sections of this paper.

The study of the paradigm concept in those two sections presents a difficulty which extends to the consideration of the historical development of any of the other elements of Kuhn’s view of science. The attempt to trace the history of an idea independently of the impact of that history on Kuhn’s work must be carefully distinguished from the attempt to locate those contributions which, directly or indirectly, helped to shape Kuhn’s thought. The present survey is concerned almost exclusively with the latter problem; an adequate account of all of the intellectual antecedents of Structure would require far more space than is here available. In fact, of those thinkers who have left their mark on Structure, only four will be treated in detail. The nature of the works of those four reveals a further restriction on the scope of this investigation.

The sources upon which Kuhn drew in writing Structure may be roughly classed as historical, psychological, sociological and philosophical. Almost all of the material considered in the following pages falls into the last category. Thus, the scope of this study is narrow, and many other thinkers might have been considered. The first two sections focus on Lichtenberg and Wittgenstein, respectively. The third is devoted to a book by Ludwik Fleck, Genesis and Development of a Scientific Fact [Entstehung und Entwicklung einer wissenschaftlichen Tatsache] (hereafter G.D.S.F.), compared to which the writings of Lichtenberg are as well known as those of Kant. That Fleck’s book has remained obscure since 1962 is surprising, since, except for A. 0. Lovejoy’s Great Chain of Being, it is the only work specifically mentioned in the text of Kuhn’s Preface to Structure. Kuhn there remarks that he is indebted to Fleck ‘in more ways than I can now reconstruct or evaluate’,lB and the aim of the third section is to reconstruct partially the ways in which G.D.S.F. influenced Kuhn’s conception of the scientific enterprise. The fourth and final section presents a precise characterization of the paradigm concept as used by Kuhn, and also examines the enormous impact of W. V. Quine’s philosophical speculations on Kuhn’s view of scientific development.

The philosophical background of Structure sketched in these pages should suggest what Kuhn himself recognized as early as 1953, that ‘Although much of the historical documentation for the monograph has been drawn from my own studies of the literature and has not previously been published, the project is primarily a work of synthesis.“’ This point is in no way intended to diminish the significance of Structure, only to facilitate a proper understanding of the

“A. Janik and S. Touhnin, Wittgemtein’s Vienno (New York: Simon and Schuster, 1973), p. 284, n. 12.

“Kuhn, Structure, p. vii. “Kuhn, ‘Plans for Research’, application for Guggenheim Memorial Fellowship, 1953, p. 3.

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book; that Newtonian physics and Darwinian evolutionary theory were both in large part syntheses of previously established concepts hardly detracts from those singular achievements. Kuhn continued his evaluation by proposing that ‘The ideas are original in this context; they are drawn from a variety of fields not normally treated together; and they contribute to a more realistic appraisal of scientific theories - a major desideratum.“8 This ‘desideratum’ reflects an extremely important sense in which Structure is fundamentally a work of philosophy, apart from the philosophical nature of Kuhn’s characterization of scientific development.

The opening sentence of Structure, cited above, is far more significant, and far more problematic, than it appears. The view that the history of science has relevance for philosophy of science was, and still is, anathema to most practitioners of the latter discipline. Structure, then, is as much about philosophy of science as it is about science itself. If in no other way, the book is philosophical in that it is a ‘meta-methodological’ prescription for philosophers of science. Wittgenstein wrote that the task of the true philosopher is, ‘whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions’;‘9 Kuhn argues that, in eschewing the evidence of history, philosophers have left the term ‘science’ meaningless. At the risk of overstatement, the account of scientific development proposed in Structure might almost be regarded as merely an example of what the correct approach to philosophy of science could produce. Richard Boyd is one of the few philosophers who have appreciated that one can disagree vehemently with Kuhn’s conception of the scientific enterprise and still be greatly influenced by Structure.20

Both those who claim to have been profoundly influenced by Structure and those who would rather the book had never been written often point to Kuhn and Paul Feyerabend as the leading exponents of the view that the scientific enterprise is irrational.2’ Although Feyerabend might be proud to admit that his is a theory of scientific irrationality, Kuhn would hardly be prepared to do the same. A confused attempt to identify Kuhn’s position with that of Feyerabend frequently results from a misinterpretation of Structure. The following pages will show that Kuhn’s method of ‘paradigms and revolutions’ is as far from Feyerabend’s ‘methodological anarchism’ as is Karl Popper’s method of ‘conjectures and refutations’.22 Indeed, Structure may well be the

“Ibid. leWittgenstein, Tractatus Logico-Philosophicus, p. 74. *OR. Boyd, ‘Metaphor and Theory Change’, in Metaphor and Thought, A. Ortony (ed.) (New

York: Cambridge University Press, 1979), pp. 356 -408. “Cf. P. Feyerabend, Against Method (London: Verso, 1975). “Cf. K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge (New

York: Harper and Row, 1%5).

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most rational characterization of the nature and development of science yet produced.

I

Everyone should study at least enough philosophy and belles lettres to make his sexual experience more delectable.

G. C. Lichtenberg

A great thinker once wrote that ‘a philosophical dream book could be written. . . . I know from undeniable experience that dreams lead to self- knowledge’. 23 The author of this remark was not Sigmund Freud, although Freud read it before writing The Interpretation of Dreams, but Georg Christoph Lichtenberg. Perhaps even more startling is the view of science which Lichtenberg proposed in 1789:

The more experiences and experiments accumulate in the exploration of nature, the more precarious the theories become. But it is not always good to discard them immediately on this account. For every hypothesis which once was sound was useful for thinking of previous phenomena in the proper inter-relations and for keeping them in context. We ought to set down contradictory experiences separately, until enough have accumulated to make building a new structure worth-while.*’

Most of Kuhn’s readers would be easily persuaded that this passage was taken from Structure. Were Lichtenberg a character of fiction, that he should also have introduced the term ‘paradigm’ into philosophy of science would render the story entirely implausible.

Perhaps no philosopher has been at once as little known and as influential as Lichtenberg. Born in 1742 near the German city of Darmstadt, Lichtenberg was the son of a Protestant clergyman for whom performing scientific experients was an avocation. A congenital deformation of the spine left Lich- tenberg with the sense that he was consigned to a life of observation rather than action, and this unfortunate circumstance may in part be responsible for the unfailing perspicuity of his comments on both the natural and social worlds. Financial problems resulting from the death of his father in 1751 prevented Georg Christoph from pursuing his higher education until he was able to gain a scholarship in 1763. In May of that year he entered the University of Gottingen.

Although founded less than thirty years before Lichtenberg came to Gottingen, the University had already acquired the reputation as a centre of

“Lichtenberg, The Lichtenberg Reader, p. 70. IdIbid., p. 94.


scientific learning which it maintains today. Lichtenberg began his studies with mathematics, but later devoted most of his time to physics and astronomy. The predilection for experimental science which increasingly drew him away from mathematics and theoretical mechanics is of central importance in the development of his philosophy of science. Whereas Kant’s ‘progress from applied science (geology and meteorology) to theoretical mechanics and hence to the philosophy of science made him increasingly suspicious of all reasoning that draws on analogy for its support’,25 Lichtenberg’s largely opposite path left him fascinated with the nature and function of analogy, a fascination which would later lead to his notion of ‘paradigms’. Also of great importance is the fact that Lichtenberg’s academic interests were not confined to the natural sciences; he read widely in many fields, including history, literature and philosophy. In addition, in late 1764 or early 1765, Lichtenberg began his lifelong practice of keeping ‘Waste-Books’ (he used the English term), notebooks ‘wherein I write everything, as I see it or as my thoughts suggest it to me’.26

Upon completing his studies in 1767, Lichtenberg, who had become known as a great Anglophile, began to tutor young Englishmen at the University. In 1770, he travelled to London, returning to Gottingen several weeks later as Professor of Mathematics and Astronomy; the highlight of the trip had been his first meeting with George III, who was the ruler of Hanover as well as the King of England. Except for another stay in England during 1774 and 1775, Lichtenberg spent all of the years between 1770 and his death in 1799 in Gottingen.

As a scientist, Lichtenberg was respected throughout Europe. His fame as a teacher was even greater, and he was the first in Germany regularly to use experiments as a pedagogic tool. *’ Many of the most eminent scientists of his day, including Herschel and Volta, travelled to Gottingen to visit Lichtenberg. Goethe and Kant were among Lichtenberg’s friends, and both expressed their deep admiration for the subtlety and power of his mind.*” Although he was elected to the scientific academies of London, Petersburg and Leyden, Lichtenberg made no outstanding contribution to science; his discovery of ‘electric figures’ (which bear his name today) proved to be of only minor importance. As the author of the Giittinger Taschen-Kalender (‘Pocket Almanac’), Lichtenberg came to be regarded as one of Germany’s wittiest writers; still, his published writings were not of the type that assures lasting renown. As a result, Lichtenberg’s fame both as a scientist and as a man of

*5J. P. Stern, Lichtenberg: A Doctrine of Scattered Occasions (Bloomington: Indiana University Press, 1959), p. 12.

*OLichtenberg, Notebooks (1775), cited in Stern, p. 15. ?‘F. H. Mautner, ‘Introduction’, in The Lichtenberg Reader, p. 5. 28Ibid., pp. 5, 24.

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letters began to wane soon after his death. Lichtenberg might well have been gradually forgotten had his literary

executor not made the fortuitous decision, shortly after Lichtenberg’s death, to publish selections from the sixteen ‘Waste-Books’ which he had filled since his days as a student. Those notebooks, and not the revolutionary scientific innovation for which he searched unsuccessfully throughout his life, would eventually ensure Lichtenberg’s immortality. The remarks in these books,

commonly referred to as Lichtenberg’s ‘aphorisms’, vary from single words to long paragraphs, and touch on almost every subject imaginable, from the most profound problems of philosophy to the most superficial questions of manners and mores. Mach was familiar with these aphorisms, and his admiration for Lichtenberg seems to have been largely responsible for the renascence of interest in the latter’s work which occurred on the Continent in the early part of this century.2g That his writings have remained virtually unnoticed in English-speaking countries is ironic, for Lichtenberg loved the English language and culture more than his own.

In one of the longer aphorisms, Lichtenberg presented a central aspect of his view of scientific development:

I believe that no heuristic lifting-gear is more useful than what I have called paradigmata. I really don’t see why we should not take Newton’s optics as a model for a theory of the calcination of metals. . . . But even the good mind has to be prodded into seeing something new; indeed, it is almost only by such means that new things can be found in a novel manner. If (as Kastner once conjectured) Newton arrived at the Law of Gravity by way of his interest in light, then that is a paradigm.30

A paradigm, then, for Lichtenberg, is an exemplary scientific achievement upon which the solutions of further problems may be modelled by an analogical process.

Lichtenberg’s choice of the word ‘paradigm’ was by no means capricious, and he was well aware of the technical use of the term in linguistics; in another aphorism he spoke of ‘paradigmata according to which to decline in the . . .

sciences’.3’ Just as, for example, in language, the conjugation of a particular verb serves as a pattern according to which other verbs may be conjugated without the need for explicitly articulated grammatical rules, so, in science, a widely acclaimed result may guide the researcher’s approach to another problem without the need for explicit rules relating the two. One student of Lichtenberg’s work, writing before Structure was published, characterized

Wf. E. Mach, ‘The Guiding Principles of My Scientific Theory of Knowledge and Its Reception by My Contemporaries’, in Physical Redity, S. Toulmin (ed.) (New York: Harper and Row, 1970), p. 38, n. 6, and Janik and Touhnin, p. 134.

Wited in Stem, p. 294. “Lichtenberg, Notebooks (1789- 1793), cited in Stem, p. 103.


paradigms as ‘formulas of procedure embodied in sensible form’.32 ‘Issuing somewhere between facts and laws,’ he continues, ‘these “paradigms” would in themselves be actual parts of natural science (as grammatical paradigms are parts of natural language). And, by virtue of the exemplary way they exhibit method, they would represent a host of cognate phenomena.‘33 Still, Lichtenberg’s ‘flash-like grasp of the importance of “paradigms” for logic, science, and language is as original as it is unsustained; both the bright idea and his failure to exploit it are characteristic of the man’.34 The same certainly cannot be said of Kuhn.

To judge whether Lichtenberg’s notion of ‘paradigm’ actually ‘differs significantly’ from that of Kuhn requires, of course, a preliminary sketch of the latter’s use of the concept. In the Preface to Structure, Kuhn succinctly describes his conception of ‘paradigms’. ‘These,’ he writes, ‘I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners.‘35 The term, he explains in a paper published twelve years later, ‘entered The Structure of Scientific Revolutions because I, the book’s historian-author, could not, when examining the membership of a scientific community, retrieve enough shared rules to account for the group’s unproblematic conduct of research. Shared examples of successful practice could, I next concluded, provide what the group lacked in rules’.36

In the preface to a collection of his essays published in 1977, Kuhn gives his fullest account of the reasons for his use of the word ‘paradigm’:

If scientists were not taught definitions, they were taught standard ways to solve selected problems in which terms like ‘force’ or ‘compound’ figured. If they accepted a sufficient set of these standard examples, they could model their own subsequent research on them without needing to agree about which set of characteristics of these examples made them standard, justified their acceptance. That procedure seemed very close to the one by which students of language learn to conjugate verbs and to decline nouns and adjectives. They learn for example, to recite, amo, amas, amat, amamus, amatk, amant, and they then use that standard form to produce the present active tense of other first conjugation Latin verbs. The usual English word for the standard example employed in language teaching is ‘paradigms’, and my extension of that term to standard scientific problems like the inclined plane and conical pendulum did it no apparent violence.37

Thus, Kuhn argues, for example, that Galileo’s discovery that a ball,

YStern, p. 103. ‘IIbid. l’lbid., pp. 166-l. 35Kuhn, Structure, p. viii. J’Kuhn, ‘Second Thoughts’, p. 318. S7Kuhn, ‘Preface’, in The Essential Tension, p. xix.

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starting from a given height on an inclined surface, acquires exactly enough velocity in rolling down the surface to attain the same height on a second incline, regardless of slope, served as a paradigm for his consideration of the motion of a pendulum, the bob of which is a point-mass. Huyghens, in turn, modelled his approach to the physical pendulum on Galileo’s analysis of point-pendula; by regarding the physical pendulum as an infinite collection of point-pendula, which could be separated instantaneously anywhere along the path of the bob, he was able to find the centre of oscillation of the latter. ‘After the bonds were released, the individual point-pendula would swing freely, but their collective centre of gravity when each attained its highest point would, like that of Galileo’s pendulum, rise only to the height from which the centre of gravity of the extended pendulum had begun to fa11.‘38 Daniel Bernoulli later patterned his research on the flow of water from an orifice on Huyghen’s solution of the pendulum problem. In effect, Galileo’s treatment of the inclined plane was the paradigm which enabled Bernoulli to determine the speed of efflux.38

In Structure, unfortunately, Kuhn tried to make this clear and simple concept carry more weight than it could bear, and in the process succeeded only in obscuring his original insight. (To characterize paradigms in a manner consistent with that original insight and yet able to support the burden imposed by Structure is the ultimate goal of this study.) Still, Kuhn’s notion of ‘paradigm’, as introduced and intended, far from being ‘significantly’ different from Lichtenberg’s, is virtually identical to it.

A striking compatibility of intellectual interests may help to explain why (setting aside the question of Lichtenberg’s influence on Kuhn) both were fascinated with the paradigm concept. Although one was the product of eighteenth-century Germany and the other of twentieth-century America, Lichtenberg and Kuhn had remarkably similar educational backgrounds. The scientific faculty of Harvard University was, like that of Gottingen of 1763, among the most respected in the world when Kuhn entered the College in 1939. As with Lichtenberg, though his field of concentration was physics, the breadth of Kuhn’s academic interests extended far beyond the bounds of the natural sciences; in addition to reading widely in the humanities, particularly philosophy, he was an editor of the college newspaper.

After graduating in 1943, Kuhn worked in a military radar laboratory in Cambridge until the end of the war. He was there exposed to the most practical aspects of science, and, despite the fact that he found the experience unrewarding,‘O he may well have gained from it a sense of the importance of analogy in the solution of scientific problems. Kuhn returned to Harvard in

“Kuhn. Structure, p. 190. ‘*Ibid. 40Conversation with T. S. Kuhn, 26 November 1979.


1945, receiving his Master’s degree in 1946 and his Ph.D. in physics in 1949; his doctoral dissertation presented a new technique for measuring the cohesive energy of certain types of metals. Both Lichtenberg and Kuhn, then, made their principal contributions to science in the domain of experimental solid- state physics. Further evidence that background in experimental or applied science is conducive to a view which emphasizes the importance of recognizing resemblances between situations, without articulated criteria of similarity, in the practice of science (or, indeed, in the use of language in general) will be provided in the following sections.

However closely related their notions of ‘paradigm’ may be, the fact remains that Kuhn had not heard of Lichtenberg before 1962, much less read any of his work. If a connection is to be established between their uses of the term, then, a third thinker must be found who, influenced by Lichtenberg and known to Kuhn, can serve as a bridge between the two. Fortunately, such an intermediary is not difficult to locate.

I therefore believe myself to have found, on all essential points, the final solution of the problems. And if I am not mistaken in this belief, then the second thing in which the value of this work consists is that it shows how little is achieved when these problems are solved.

Wittgenstein

In reading Lichtenberg, anyone familiar with contemporary Anglo- American philosophy is immediately struck by the central place accorded to language in the aphorisms. Indeed, the essence of Lichtenberg’s speculations may be captured in one line. ‘Our entire philosophy,’ he wrote, ‘is a correction of linguistic usage.“’ That Proposition 4.0031 of the Tructatus Logico- Philosophicus begins ‘All philosophy is a “critique of language”‘42 is by no means coincidental; although his thought has dominated British philosophy, Wittgenstein, like Freud, was the product of a Viennese intellectual milieu in which Lichtenberg’s writings were greatly revered.

The son of a wealthy industrialist, Ludwig Wittgenstein was born in Vienna in 1889. As a result of being privately tutored until the age of fourteen rather than sent away to school, he was fully exposed to the intellectual turmoil of fin-de-sitkle Vienna, of which his home was a cultural centre. Also as a result of that education, Wittgenstein lacked the training in Greek requisite for

“Cited in G. H. von Wright, ‘Georg Christoph Lichtenberg’, The Encyclopedia of Philosophy (1%7), Vol. IV, p. 464.

“Wittgenstein, Tractatus Logico-Philosophicus, p. 19.

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admission to the Gymnasium, and so entered the Linz Realschule in 1904. Having demonstrated a remarkable talent for constructing machines as a child, he decided to study engineering; like Lichtenberg and Kuhn, Wittgenstein began his academic career with mathematics and theoretical physics. Early in his studies, he was introduced to Heinrich Hertz’s great work, The Principles of Mechanics, which profoundly influenced his thought; Wittgenstein often quoted Hertz in later years, and may have admired him even more than Frege.43 Another idol of Wittgenstein was Ludwig Boltzmann, with whom he hoped to study after leaving Linz in 1906, a dream which was shattered by Boltzmann’s suicide that year.

Wittgenstein instead enrolled in the Technische Hochschule at Charlotten- burg, in Berlin, to pursue his work in mechanical engineering. Two years later, in 1908, he travelled to England, where he became a research student of engineering at the University of Manchester. As with Lichtenberg, his first trip to England had an enormous impact on Wittgenstein, although in a different way. While at Manchester, he read Russell’s Principles of Mathematics, and the book so impressed him that he decided to abandon his career as an engineer to study with Russell at Cambridge. After being admitted to Trinity College in 1912, Wittgenstein devoted himself zealously to mastering the techniques of logic, and soon began the investigations which would culminate in the Tractatus. Believing that an environment free from distractions would facilitate the development of his ideas, he journeyed to Norway in the latter part of 1913, where he lived alone until the outbreak of World War I.

Always guided by a strong sense of duty, Wittgenstein joined the Austrian Army as a volunteer. He continued to write while serving with the artillery, often carrying his notebooks into battle. Wittgenstein completed his Logisch-philosophische Abhandlung in August 1918, but, with the work in his possession, was captured by the Italians in November of that year. He succeeded in communicating with Russell from the prison camp, and was eventually able to send him the manuscript.

After being released in the summer of 1919, Wittgenstein returned to Vienna, where he offered the book to a publisher. In December he and Russell met in Holland to discuss the work, for which Wittgenstein asked Russell to write an introduction. The essay which Russell sent him several months later, though, seemed to Wittgenstein so entirely to misrepresent his intentions that he could not include it with the Abhandlung. That decision became moot, however, for the publisher subsequently rejected the book. In July 1920, Wittgenstein informed Russell that he would no longer attempt to publish the work, and that Russell was free to dispose of the manuscript as he saw fit. The German text appeared in 1921 in the Annalen der Naturphilosophie, and was

“Janik and Toulmin, p. 175.


published the following year in London, with an English translation, as the Tractatus Logico-Philosophicus.

Wittgenstein began teaching in an elementary school in a small village in Austria in the autumn of 1920. He later moved to another town, where he continued to teach until 1926. After considering joining a monastery, he was persuaded by a friend, Paul Engelmann, who had been commissioned to build a mansion for one of Wittgenstein’s sisters in Vienna, to help with the design; he was occupied with the work for two years. In 1929 Wittgenstein returned to Cambridge. Although what prompted this move is difficult to determine, a lecture by L. E. J. Brouwer on the foundations of mathematics, which Wittgenstein heard in Vienna in 1928, is often credited with having reawakened his interest in philosophy. He submitted the Tractatus as his doctoral dissertation, and received his Ph.D. and a research fellowship from Trinity College. Shortly thereafter, he wrote a paper, ‘Some Remarks on Logical Form’, which, except for the Tractatus, was the only one of his works published during his lifetime.

Wittgenstein began to lecture again in 1930. He soon became convinced that the Tractatus contained ‘grave mistakes’, and, in the summer of 1936, travelled to Norway to begin writing the Philosophical Investigations.44 Two years after his return in 1937, Wittgenstein succeeded G. E. Moore as Professor of Philosophy. During World War II he again left Cambridge, working in military hospitals from 1941 to 1944. After resuming his lectures in the latter year, he became increasingly disenchanted with his teaching, and finally resigned his chair in 1947. Wittgenstein spent the remaining years before his death in 1951 composing the Philosophical Investigations. That book, on which he was still working at the time of his death, was first published in 1953.

The first sections of the Philosophical Investigations present an overview of the workings of language, and introduce a concept which has become emblematic of the entire book. ‘One day when Wittgenstein was passing a field where a football game was in progress,’ Norman Malcolm relates, ‘the thought first struck him that in language we play games with words.‘45 Wittgenstein proposes in the seventh remark that ‘We can also think of the whole process of using words in (2) [an example of a simple language] as one of those games by means of which children learn their native language. I will call these games ‘language-games’ and will sometimes speak of a primitive language as a language-game. . . . I shall also call the whole, consisting of language and the

“L. Wittgenstein, Philosophical Investigations, trans. G. E. M. Anscombe, 3rd edn (New York: Macmillan, 1958), p. vi.

‘Tited in G. Hallett, A Companion to Wittgenstein’s ‘Philosophical Investigations’ (Ithaca: Cornell University Press, 1977), p. 68.

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actions into which it is woven, the “language-game”.‘46 Wittgenstein goes on to consider specific aspects of language, focusing

initially on the process of naming. In section 50, he discusses a notion fundamental to his conception of language-games:

There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris. - But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the language-game of measuring with a metre-rule. - Let us imagine samples of colour being preserved in Paris like the standard metre. We define: ‘sepia’ means the colour of the standard sepia which is there kept hermetically sealed. Then it will make no sense to say of this sample either that it is of this colour or that it is not.

We can put it like this: This sample is an instrument of the language used in ascriptions of colour. In this language-game it is not something that is represented, but is a means of representation. . . . And to say ‘If it did not exist, it could have no name’ is to say as much and as little as: if this thing did not exist, we could not use it in our language-game. - What looks as if it had to exist, is part of the language. It is a paradigm in our language-game; something with which comparison is made.”

Although now functioning on a more general level, Wittgenstein’s ‘paradigms’ remain, like Lichtenberg’s, concrete examples which permit the solution of certain problems (the domain of which has been extended from science to language as a whole) by means of an analogical process. Indeed, ‘Lichtenberg’s writings were . . . the source of the term.“*

Far from merely being familiar with his work, Wittgenstein classed Lichtenberg with Kierkegaard and Schopenhauer as the greatest of all modern philosophers.4g (Kierkegaard, incidentally, had referred gratefully to Lichtenberg as a ‘voice in the wilderness ‘.50) Nor was Wittgenstein the only Viennese intellectual enraptured with the thoughts of that eighteenth-century genius; Karl Kraus, for example, whose preoccupation with a ‘correction of linguistic usage’ also had a profound impact on Wittgenstein,s’ deeply admired Lichtenberg.52

That Wittgenstein’s knowledge of Lichtenberg’s writings was not confined to the aphorisms,53 though, is particularly remarkable, for he read comparatively little philosophy. ” Wittgenstein cites Lichtenberg in several places, 55 and he frequently referred to him in conversation, once exclaiming to

‘*Wittgenstein, Philosophical Investigations, p. 5. “Ibid., p. 25. “Janik and Toulmin, p. 176. ‘*Cf. Janik and Toulmin, p. 176. ‘OCited in Mautner, ‘Introduction’, p. 3. Vf. Janik and Toulmin, p. 93. S2Janik and Toulmin, p. 90. “Hallett, p. 770. “Janik and Toulmin, p. 176. Vf. Wittgenstein, Philosophical Grammar, R. Rhees (ed.), trans. A. Kenny (Berkeley:

University of California Press, 1974), p. 461.


G. H. von Wright, ‘Lichtenberg is terrific !‘56 That he gave Russell a book by Lichtenberg before World War I is a further indication of the great esteem which Wittgenstein accorded to the physicist from G6ttingen.57 Indeed, the aphoristic style of both the Tractatus and the Philosophical Investigations was inspired by Lichtenberg.SB Interestingly, however much Lichtenberg influenced Wittgenstein, Wittgenstein’s influence on Kuhn, although not nearly as evident, was equally important.

Having been asked by Charles Morris to contribute the ‘history of science’ volume to the International Encyclopedia of Unified Science, Kuhn began work on the project which would become Structure in 1953. Since he had outlined the issues which he planned to consider in a series of lectures at the Lowell Institute in 195 1, and had already done much of the historical research, Kuhn hoped to complete the book by the summer of 1955.58 Other obligations, however, prevented him from devoting his full attention to the work for several years, and he had not yet begun to write Structure when he accepted a year’s fellowship at the Center for Advanced Study in the Behavioral Sciences in 1958. At Stanford he quickly produced the draft of a chapter on revolutionary change in science (in which the term ‘paradigm’ is used only in its usual sense),Eo but found himself at an impasse in the spring of 1959. Although he was convinced that some form of consensus governs the interludes between scientific revolutions, Kuhn was unable to specify how such a consensus could make possible the unproblematic conduct of research characteristic of ‘normal science’.” Wittgenstein provided the answer.

Though Kuhn had read a typescript of The Blue and Brown Books in 1950, he had not read any of Wittgenstein’s other writings before 1959.6* When he came upon the Philosophical Investigations that year, he found in its account of naming the key to the working of normal science for which he had been searching.6J (Perhaps more consequential than his actual reading of the Philosophical Investigations were Kuhn’s frequent conversations with Stanley Cavell, who was at the time writing his doctoral dissertation on Wittgenstein’s later philosophy.8’) Although he does not remember taking the term ‘paradigm’ from Wittgenstein, Kuhn does allow that, alone among the philosophical works with which he was familiar, Wittgenstein’s treatment of naming in the Philosophical Investigations may have had a crucial impact on his formulation of the paradigm concept in the spring of 1959. Just as, for

Vited in Hallett, p. 770. “Hallett, p. 770. “Janik and Toulmin, p. 176. 6sKuhn, ‘Plans for Research’, p. 3. ‘OKuhn, ‘Chapter I - Discoveries as Revolutionary’, draft of Sfructure, 1958. O’Kuhn, ‘Preface’, in The Essential Tension, p. xviii. Vonversation with Kuhn, 26 November 1979. 851bid. “‘Cf. Kuhn, Structure, p. xi.

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example, the standard metre plays a ‘peculiar role’ in the language-game of measuring with a metre-rule, so Newton’s Laws play a peculiar role in the ‘language-game’ of classical physics; both are ‘paradigms’, things ‘with which comparison is made’. (That this comparison is particularly apt will be seen in the last section.) Moreover, just as the question of whether the standard metre is one metre long makes no sense within the corresponding language-game, so, for Kuhn, the question of whether Newton’s Laws are ‘true’ is meaningless within the framework of classical physics. ‘What looks as if it had to exist’, Wittgenstein writes, ‘is part of the language’;65 without the paradigm, the language-game cannot be played.

Perhaps even more important to the development of Kuhn’s ideas than section 50 (cited above) was a related passage which appears several pages later (in which, however, the word ‘paradigm’ does not occur). In sections 66 and 67, Wittgenstein addresses the question of what justifies the application of a name:

Consider for example the proceedings that we call ‘games’. I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all? - Don’t say: ‘There must be something common, or they would not be called “games” ’ - but look and see whether there is anything common to all. - For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don’t think, but look! - Look for example at board-games, with their multifarious relationships. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. When we pass next to ball-games, much that is common is retained, but much is lost. - Are they all ‘amusing’? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. . . .

And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail.

I can think of no better expression to characterize these similarities than ‘family resemblances’; for the various resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way. - And I shall say: ‘games’ form a family.”

That this account of naming is the only philosophical theory discussed in

detail in Structure evinces its central role in Kuhn’s conception of scientific development. In the chapter entitled ‘The Priority of Paradigms’, Kuhn writes:

What need we know, Wittgenstein asked, in order that we apply terms like ‘chair’, or ‘leaf’, or ‘game’ unequivocally and without provoking argument?

66Wittgenstein, Philosophical investigations, p. 25. 66Ibid., pp. 3 1 - 2.


That question is very old and has generally been answered by saying that we must know, consciously or intuitively, what a chair, or leaf, or game is. We must, that is, grasp some set of attributes that all games and that only games have in common. Wittgenstein, however, concluded that, given the way we use language and the sort of world to which we apply it, there need be no such set of characteristics. Though a discussion of some of the attributes shared by a number of games or chairs or leaves often helps us learn how to employ the corresponding term, there is no set of characteristics that is simultaneously applicable to all members of the class and to them alone. Instead, confronted with a previously unobserved activity, we apply the term ‘game’ because what we are seeing bears a close ‘family resemblance’ to a number of the activities that we have previously learned to call by that name. For Wittgenstein, in short, games, and chairs, and leaves are natural families, each constituted by a network of overlapping and criss-cross resemblances. . . .

Something of the same sort may very well hold for the various research problems and techniques that arise within a single normal-scientific tradition. What these have in common is not that they satisfy some explicit or even some fully discoverable set of rules and assumptions that gives the tradition its character and its hold upon the scientific mind. Instead, they may relate by resemblance and by modelling to one or another part of the scientific corpus which the community in question already recognizes as among its established achievements.B’

‘If, for example,’ Kuhn continues, ‘the student of Newtonian dynamics ever discovers the meaning of terms like “force”, “mass”, “space”, and “time”, he does so less from the incomplete though sometimes helpful definitions in his text than by observing and participating in the application of these concepts to problem-solution.‘6B

Wittgenstein further argues (in section 68) that the notion of a ‘game’ is not ‘rigidly limited’: ‘For how is the concept of a game bounded? What still counts as a game and what no longer does? Can you give the boundary? No. You can draw one; for none has so far been drawn. (But that never troubled you before when you used the word “game”.)‘ss In ‘Second Thoughts on Paradigms’, Kuhn devotes several pages to the discussion of a child’s acquisition of the terms ‘swan’, ‘goose’ and ‘duck’. Given drawings of swans, geese and ducks separated according to species (the paper on which the drawings are made representing the child’s ‘perceptual space’), he proposes, the child might, in effect, ‘draw closed nonintersecting curves around each of the clusters. . . . What results is a simple Venn diagram, displaying three non-overlapping classes. All swans lie in one, all geese in another, and so on. . . . Given such boundaries, Johnny now can say what the criteria are for membership in the class of swans, geese, or ducks. On the other hand, he may be troubled by the very next waterfowl he sees’.‘O ‘If . . . each new experience can demand some

O’Kuhn, Structure, pp. 45 - 6. s’Ibid., p. 47. 6eWittgenstein, Philosophical Investigations, p. 33. ‘#Kuhn, ‘Second Thoughts’, p. 314.

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adjustment of the class boundaries,’ Kuhn contends, ‘one may well ask whether Johnny was wise to allow philosophers to draw any such boundaries for him. The primitive resemblance criterion he had previously acquired would have handled all these cases unproblematically and without continual adjustment.‘” That ‘resemblance criterion’ is learned by repeated exposures to paradigms. (Kuhn’s emphasis on the role of ostension in paradigm-based learning was also derived from Wittgenstein.72)

G. H. von Wright once remarked ‘that the two most important facts to remember about Wittgenstein were, firstly, that he was a Viennese and, secondly, that he was an engineer with a thorough knowledge of physics’.73 His Viennese upbringing introduced him to the writings of Lichtenberg, and his training as an engineer conditioned his appreciation of the paradigm concept. These elements of his background, then, were largely responsible for

making Wittgenstein an ideal bridge between the works of Lichtenberg and Kuhn. The Philosophical Investigations, though, represents far more to the

development of Kuhn’s thought than a mere conduit for Lichtenberg’s ideas.

Interestingly, while Wittgenstein was in Vienna in 1927, another man was visiting the city, although almost certainly unknown to Wittgenstein, who would profoundly influence Kuhn’s conception of the scientific enterprise.

III

We are supposedly in possession of ‘correct thinking’ and ‘correct observation’, and therefore what we declare to be true is ipso factor frue. . . . This arch-nave view, which prevents the building up of a scientific epistemology, reminds us very much of the theory of a French philologist of the eighteenth century who claimed that pain, sitos, bread, Brot, panis were arbitrary, different descriptions of the same thing. The difference between French and other languages, according to this theory, consisted in the fact that what is called bread in French really was bread.

Ludwik Fleck

In the late 192Os, much to Wittgenstein’s dismay, the members of the ‘Vienna Circle’ proclaimed the Tractatus to be the bible of their philosophical

movement. ” That the ‘logical positivism’ which they espoused dominated European conceptions of science in 1935 was in part responsible for the fact that only 640 copies of a book by Ludwik Fleck were published that year, of which a scant 200 were sold. Hans Reichenbach was among the few who knew of the work, entitled Entstehung und Entwickiung einer wissenschaftlichen

“Ibid.. p. 316. ‘%Zonversation with Kuhn, 26 November 1979. “Cited in Janik and Toulmin, pp. 28-9. “Cf. Janik and Toulmin, pp. 24.216.


Tatsache, and citing it in 1938 in Experience and Prediction, he entirely misrepresented Fleck’s views.75 That footnote, though, would eventually play a major role in the creation of the discipline today known as the sociology of science.

Ludwik Fleck, like Lichtenberg, was only an ‘amateur’ philosopher of science. Born in Poland in 1896, he went to elementary school and high school in his native Lvov. That city, interestingly, was predominantly German- speaking, a legacy of the time when Lvov (then known as Lemberg) had been part of the Austrian Empire. Fleck studied medicine at Lvov University, from which he received his degree in 1922. He was engaged in research on typhus between 1920 and 1923, at the Typhus Investigation Laboratory of the University and at the State Hospital for Infectious Diseases, after which he did work in bacteriology in Vienna. Returning to Lvov, Fleck became head of the bacteriological and chemical laboratories of the State Hospital in 1925, where he stayed until 1927; he spent the latter year at the State Serotherapeutic Institute in Vienna. Back in Lvov in 1928, Fleck directed the bacteriological laboratory of the Social Sick Fund until he was dismissed, as a result of being Jewish, in 1935.

Before 1935 Fleck had published many articles on topics in general serology, hematology, experimental medicine, immunology and bacteriology. Of particular interest to him were the serology of typhus fever, syphilis and the nature of pathogenic microorganisms. In addition, Fleck wrote several papers on the methodology of science and the history of discoveries, and, in 1934, completed G.D.S.F. That work, which could not be published in Germany because of Fleck’s religion, was published in Switzerland in 1935.76

Using the history of conceptions of syphilis and the discovery of its relation to the ‘Wassermann reaction’ as an illustration, Fleck presents, in G.D.S.F., a philosophy of scientific development in which the scientific community, rather than the individual scientist, is of primary importance. The similarities between his views and Kuhn’s are numerous and striking. Fleck’s statement of his fundamental methodological conviction, for example, might well have appeared in Structure. ‘Who today,’ he asks, ‘would study anatomy without embryology? In exactly the same way epistemology without historical and comparative investigations is no more than an empty play on words or an epistemology of the imagination.“’

After a preliminary account of the origins of the modern concept of syphilis, Fleck proposes that:

“Kuhn, ‘Foreword’, in L. Fleck, Genesis and Development of a Scientific Fact, T. J. Trenn and R. K. Merton (eds.), trans. F. Bradley and T. J. Trenn (Chicago: The University of Chicago Press, 1979), p. viii.

“T. J. Trenn, ‘Biographical Sketch’, in Fleck, pp. 149-50. “Fleck, p. 21.

Paradigms 193

Once a structurally complete and closed system of opinions consisting of many details and relations has been formed, it offers constant resistance to anything that contradicts it. . . . What we are faced with here is not so much simple passivity or mistrust of new ideas as an active approach which can be divided into several stages. (1) A contradiction to the system appears unthinkable. (2) What does not fit into the system remains unseen; (3) alternatively, if it is noticed, either it is kept secret, or (4) laborious efforts are made to explain an exception in terms that do not contradict the system. (5) Despite the legitimate claims of contradictory views, one tends to see, describe, or even illustrate those circumstances which corroborate current views and thereby give them substance.‘B

In discussing the first point, Fleck argues that ‘When a conception permeates a

thought collective strongly enough, so that it penetrates as far as everyday life

and idiom and has become a viewpoint in the literal sense of the word, any

contradiction appears unthinkable and unimagineable.‘7g Similarly, Kuhn,

using the term to refer to ‘complete and closed systems of opinions’, contends

that paradigms ‘[ilnevitably . . . restrict the phenomenological field accessible

for scientific investigation at any given time’.*O

In Structure, Kuhn describes in detail a psychological experiment,

performed by Bruner and Postman, in which subjects were asked ‘to identify

on short and controlled exposure a series of playing cards. Many of the cards

were normal, but some were made anomalous, e.g., a red six of spades and a

black four of hearts’.8’ The results of the experiment were extremely

interesting:

Even on the shortest exposures many subjects identified most of the cards, and after a small increase all the subjects identified them all. For the normal cards these identifications were usually correct, but the anomalous cards were almost always identified, without apparent hesitation or puzzlement, as normal. The black four of hearts might, for example, be identified as the four of either spades or hearts. . . . One would not even like to say that the subjects had seen something different from what they identified. With a further increase of exposure to the anomalous cards, subjects did begin to hesitate and to display awareness of anomaly. . . . Further increase of exposure resulted in still more hesitation and confusion until finally, and sometimes quite suddenly, most subjects would produce the correct identification without hesitation. . . . A few subjects, however, were never able to make the requisite adjustment of their categories.”

Kuhn concludes that:

Either as a metaphor or because it reflects the nature of the mind, that psychological

lmIbid., p. 27. ‘Orbid., p. 28. “Kuhn, Structure, pp. 60- 1. O’lbid., pp. 62-3. “Zbid., p. 63.


experiment provides a wonderfully simple and cogent schema for the process of scientific discovery. In science, as in the playing card experiment, novelty emerges only with difficulty, manifested by resistance, against a background provided by expectation. Initially, only the anticipated and usual are experienced, even under circumstances where anomaly is later to be observed.83

When an important anomaly is perceived, ‘laborious efforts are made to

explain’ it in a manner consistent with the accepted paradigm. ‘More and more attention,’ Kuhn writes, ‘is devoted to it by more and more of the field’s most eminent men. If it still continues to resist, as it usually does not, many of them may come to view its resolution as the subject matter of their discipline.‘8’

A ‘structurally complete and closed system of opinions’, for Fleck, characterizes a particular ‘thought style’, the latter being inseparably tied to a ‘thought collective’:

If we define ‘thought collective’ as a community of persons mutually exchanging ideas or maintaining intellectual interaction, we will find by implication that it also provides the special ‘carrier' for the historical development of any field of thought, as we/I as for the given stock of knowledge and level of culture. This we have designated thought styIe.B5

Kuhn’s ‘scientific communities’ are examples of such ‘thought collectives’, and the term ‘thought style’ might often be substituted for ‘paradigm’ in Structure; in those cases, in fact, Kuhn treats the scientific community as the ‘carrier’ of a paradigm.

Perhaps Fleck’s greatest insight was his recognition of the importance of a sociological analysis of scientific communities for an understanding of the scientific enterprise:

When we look at the forma1 aspect of scientific activities, we cannot fail to recognize their social structure. We see organized effort of the collective involving a division of labor, cooperation, preparatory work, technical assistance, mutual exchange of ideas, and controversy. Many publications bear the names of collaborating authors. Scientific papers almost invariably indicate both the establishment and its director by name. There are groups and a hierarchy within the scientific community: followers and antagonists, societies and congresses, periodicals, and arrangements for exchange. A well-organized collective harbors a quantity of knowledge far exceeding the capacity of any one individual.‘@

Indeed, Kuhn acknowledges that reading G.D.S.F. led him to realize that his

“Ibid., p. 64. “‘Ibid., pp. 82-3. 05Fleck, p. 39. lOIbid., p. 42.

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ideas ‘might require to be set in the sociology of the scientific community’.87 Although the ‘importance of sociological methods in the investigation of intellectual activities was already recognized by Auguste Comte’, Fleck argues, and ‘stressed by Durkheim’s school in France and by the philosopher Wilhelm Jerusalem among others in Vienna, . . . [a]11 these thinkers trained in sociology and classics, . . . no matter how productive their ideas, commit a characteristic error. They exhibit an excessive respect, bordering on pious reverence, for scientific facts’.BB Fleck, in fact, ‘seems to have been the first systematically to apply sociological principles to the origin of scientific knowledge’.88

Among the most important aspects of the thought collective, Fleck noted, is the relation between the corresponding thought style and the language shared by the members of the community. (That such linguistic considerations play a central role in Structure will become apparent in the following section.) Fleck claims, for example, that:

Words as such do not have fixed meanings. They acquire their most proper sense only in some context or field of thought. This delicate shading of the meaning of a word can be perceived only after an ‘introduction’, whether historical or didactic.OO

The essential element of that ‘introduction’, for Kuhn, is the assimilation of paradigms. Those paradigms permit ‘the application of . . . concepts to problem-solution’ through which, rather than from ‘the incomplete though sometimes helpful definitions in his text’, ‘the student of Newtonian dynamics [for instance] . . . discovers the meaning of terms like “force”, “mass”,

“space”, and “time”.‘e1 Fleck’s description of this professional ‘initiation’ might well have been

written by Kuhn:

Any didactic introduction to a field of knowledge passes through a period during which purely dogmatic teaching is dominant. An intellect is prepared for a given field; it is received into a self-contained world and, as it were, initiated. If the initiation has been disseminated for generations as in the case of introducing the basic ideas of physics, it will become so self-evident that the person will completely forget he has ever been initiated, because he will never meet anyone who has not been similarly processed.

One could argue that, if there were such an initiation rite, it would be accepted without criticism only by the novice. , . .

But the expert is already a specially molded individual who can no longer escape

“Kuhn, Structure, p. vii. “Fleck, pp. 46 - 7. “Trenn, ‘Descriptive Analysis’, in Fleck, p. 154. e°Fleck, p. 53. “Kuhn, Structure, p. 47.


the bonds of tradition and of the collective; otherwise he would not be an expert. For the introduction, then, factors which are not subject to logical legitimization are also necessary, as well as essential both to the further development of knowledge and to the justification of a branch of knowledge that constitutes a science in itself.92

For Fleck, just as for Kuhn, the principal instrument of that indoctrination is the scientific textbook.93

Such a process of initiation inevitably makes communication between thought collectives problematic:

Since all words bear a more or less distinctive coloring conforming to a given thought style, a character which changes during their passage from one collective to the next, they always undergo a certain change in their meaning as they circulate intercollectively. One could compare the meaning of the words ‘force’, ‘energy’, or ‘experiment’ for a physicist, a philologist, or a sportsman; the word ‘explain’ for a philosopher and a chemist, ‘ray’ for an artist and a physicist, or ‘law’ for a jurist and a scientist?

Communication between successive thought collectives in the same discipline is similarly restricted; in medicine, for example, the ‘old concept of disease . . . becomes quite incommensurable with the new concepts and is not replaced by a completely adequate substitute’.” The importance, for Kuhn, of the notion of the ‘incommensurability’ of theories associated with distinct paradigms can hardly be overstated.96

Thus, that communication between thought collectives must be incomplete results from the fact that their members adhere to different thought styles. Much like Kuhn’s ‘paradigm’ (in its expanded sense), Fleck’s ‘thought style’ serves as ‘a definite constraint on thought, and even more; it is the entirety of intellectual preparedness or readiness for one particular way of seeing and acting, and no other’.g7 Although the myth that ‘A person wants to know something, so he makes his observation or experiment and then he knows’, is widely believed, Fleck argues that:

[T]his situation does not obtain - and perhaps never does, originally, in any field - until tradition, education, and familiarity have produced a readiness for stylized (that is, directed and restricted) perception and action; until an answer becomes largely pre-formed in the question, and a decision is confined merely to ‘yes’ or ‘no’,

“Fleck, p. 54. “Cf. Fleck, p. 54, and Kuhn, Structure, p. 46. “Fleck, p. 109. “Ibid., p. 62. Wf. Kuhn, Structure, p. 148. “Fleck, p. 64.

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or perhaps to a numerical determination; until methods and apparatus automatically carry out the greatest part of our mental work for US.~*

Assimilation of the thought style (or the paradigm), then, provides the requisite ‘readiness for stylized perception and action’, for ‘[dlirect perception of form [Gestaltsehen]‘.9a

Once that educational process has been completed, Fleck contends, ‘All

empirical discovery can . . . be construed as a supplement, development, or transformation of the thought style.“” Substituting the term ‘paradigm’ for ‘thought style’, this observation would serve as an excellent characterization of Kuhn’s conception of ‘normal science’. Also, for both Fleck and Kuhn, ‘The more developed and detailed a branch of knowledge becomes, the smaller are the differences of opinion’;‘01 that is, the more fully articulated the paradigm, the broader the consensus which unites the scientific community.

Although the word ‘paradigm’ appears several times in G.D.S.F., Fleck uses it only in its usual sense.‘02 A more significant difference between G.D.S.F. and Structure is that the notion of a ‘scientific revolution’ does not occur in the former; indeed, Fleck devotes almost no attention to the nature of scientific change. Nevertheless, Fleck’s work is clearly more than a mere essay in the history of medicine, a fact which some of the eleven reviews of G.D.S. F. (published between 1936 and 1938) failed to note.‘03 Those reviews were largely favourable, though rarely enthusiastic; one perceptive critic remarked that G.D.S.F., unfortunately, would probably not be fully appreciated for many years.‘04 The book was not mentioned in Isis, which was, by 1935, the most important journal of the history of science.‘Os In fact, Kuhn’s acknowledgement of G.D.S.F. in Structure seems to have been the first published reference to the work since 1938.1°6

Between 1935, the year in which G.D.S.F. appeared, and 1939, Fleck practised medicine privately in Lvov and conducted research in his own microbiological laboratory. Among other accomplishments, he discovered a way to increase the sensitivity of the Wassermann reaction, and found a new method for distinguishing true serological reactions from pseudoreactions.“” After the Russians took over Lvov in December 1939, Fleck,was appointed director of the City Microbiological Laboratory, and was also named to the

Oarbid., p. 84. osZbid., p. 92. “‘OZbid. ‘O’lbid., p. 83. ‘Vf. Fleck, pp. 76, 121. ‘O’Trenn, ‘Preface’, in Fleck, pp. xvii-xviii. ‘O’Trenn, ‘Descriptive Analysis’, in Fleck, p. 164. ‘O’Trenn, ‘Preface’, in Fleck, p. xviii. ‘061bid. ‘O’Trenn, ‘Biographical Sketch’, in Fleck, p. 150.


faculty of the microbiology department of the State Medical School. In addition, he became head of the microbiology section of the State Bacteriological Institute in Lvov and served as a consultant at the State Institute of Mother and Child Welfare.

In 1941 the Germans occupied Lvov, and Fleck was made director of the bacteriological laboratory of the city’s Jewish Hospital, where he stayed until December of that year. The terrible living conditions in the city produced a typhus epidemic, and Fleck developed a rapid diagnostic test for the disease and was able to manufacture a crude but effective vaccine. Arrested with his family in 1942, Fleck only survived the war because the Germans had need of his immunological expertise. He was deported to Auschwitz, where he was forced to produce his vaccine in the camp hospital. Transferred to Buchenwald in 1944, Fleck was again made to prepare his formula for the Germany army. After the camp was liberated in 1945, Fleck returned to Poland, where he became assistant professor of microbiology and head of the Institute of Microbiology at the Marie Curie Sklodowska University of Lublin, which had just opened.

In 1947 Fleck discovered a clumping of white blood cells associated with inflammation, which he called ‘leukergy’, and this phenomenon occupied much of his research during the next ten years. During that time, Fleck and his students published approximately forty articles on the subject.‘08 Fleck also served as an expert witness at the Nuremberg trials in 1948. He was made full professor of microbiology at the University in 1950, a position he occupied until being appointed director of the Department of Microbiology and Immunology at the Mother and Child State Institute in Warsaw. In 1953 he received the state scientific prize of Poland for his research on typhus, and was elected to the Polish Academy of Sciences in 1954. The following year Fleck was awarded a doctorate of medical science, the highest scientific degree in

Poland.‘O’ After many years of effort, Fleck was able to emigrate to Israel in 1957. He

became head of the Section of Experimental Pathology at the Israel Institute for Biological Research in Ness-Ziona, where he developed new serological tests for brucellosis and measles. In 1961, Fleck was asked to deliver a series of lectures on philosophy of science at Hebrew University, but illness prevented him from presenting them. He died in June 1961, just one year before Structure was published.

In 1949, the man who would write Structure was, as a Junior Fellow at Harvard, beginning the intellectual explorations which would culminate in that book. Reading Reichenbach’s Experience and Prediction, Kuhn noticed

‘08Ibid., p. 151. ‘OnIbid., p. 152.

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the footnote on G.D.S.F. and was immediately struck by the unusual title of Fleck’s work. (Lacking an ‘established bibliography’ for his subject, Kuhn recalls, his reading often owed ‘much to serendipity’.“O) Fortunately, Widener Library had one of the seven copies of G.D.S.F. available in the United States,“’ and Kuhn was soon immersed in Fleck’s book. He was so impressed by G.D.S.F. that he purchased a copy from Fleck’s publisher in Base1 in 1950.“a (That the book could still be obtained is surprising.)

Assessing Fleck’s influence on Kuhn is far more difficult than determining the extent to which the views of the two coincide. ‘I have more than once been asked what I took from Fleck,’ Kuhn writes, ‘and can only respond that I am almost totally uncertain.“13 ‘Very probably . . . ,’ he continues, ‘acquaint- ance with Fleck’s text helped me to realize that the problems which concerned me had a fundamentally sociological dimension. . . . But I am not sure that I took anything much more concrete from Fleck’s work, though I obviously may and undoubtedly should have.“14 Part of the reason for this uncertainty is that at the time Kuhn ‘found Fleck’s German extraordinarily difficult, partly because mine was rusty and partly because I possessed neither the background nor the vocabulary to assimilate discussions of medicine and biochemistry’.“5 The question of how well Kuhn understood Fleck is raised, for example, by a remark in Kuhn’s Foreword to the English translation of Fleck’s work in which he confuses ‘thought collective’ with ‘thought style’.‘is Still, the many marginal markings throughout his copy of the book suggest that Kuhn read G.D.S.F. extremely carefully, if slowly and with great difficulty, a characterization with which he does not quarrel.“’

Although, in the Preface to Structure, Kuhn cautiously calls G.D.S.F. ‘an essay that anticipates many of my own ideas’,“B the importance of Fleck’s work for the development of Kuhn’s thought would certainly seem to be greater than this appraisal allows. In addition to the impact which the passages cited above may have had on him, Kuhn admits that ‘Fleck’s discussion . . . of the relation between journal science and vademecum science . . . may . . . be the point of origin for my own remarks about textbook science.“‘g Also, Kuhn allows that Fleck’s discussion of, and emphasis on, Gestalt psychology may have awakened his own interest in the field;‘?O that contribution alone would

““Kuhn, ‘Foreword’, in Fleck, p. viii. “‘Trenn, ‘Preface’, in Fleck, p. xviii. “‘Conversation with Kuhn, 26 November 1979. “‘Kuhn, ‘Foreword’, in Fleck, p. viii. “‘Ibid., pp. viii - ix. ‘16Zbid., p. ix. “aZbid., p. x. “‘Conversation with Kuhn, 26 November 1979. “‘Kuhn. Structure, p. vii. ‘*°Kuhn. ‘Foreword’, in Fleck, p. ix. Cf. Fleck, pp. 118 -20. ‘*°Conversation with Kuhn, 26 November 1979.


make G.D.S.F. enormously significant in the formation of Structure. Perhaps an even more intriguing question is that of whether Fleck was

familiar with Lichtenberg’s work. Although the evidence is even less conclusive than in the case of Fleck’s influence on Kuhn, Fleck’s background suggests that he might well have read Lichtenberg. The breadth of Fleck’s intellectual interests was remarkable, and he read avidly in many fields;“’ in addition, he was educated in schools in which the German language was used, at a time when interest in Lichtenberg was at its peak. Fleck was well acquainted with Mach’s writings,12* and these might have aroused a curiosity about Lichtenberg. Regardless of whether a connection between the two can be found, the writings of Fleck and Lichtenberg are remarkably similar in at least one respect: both contain many startling remarks. Fleck argues, for

example, that:

Facts are never completely independent of each other. They occur either as more or less connected mixtures of separate signals, or as a system of knowledge obeying its own laws. As a result, every fact reacts upon many others. Every change and every discovery has an effect on a terrain that is virtually 1imitless.‘23

Asked to identify the author of this passage, almost any student of philosophy would quickly name a prominent American logician, who also profoundly influenced Kuhn’s conception of science.

IV

Ontology recapitulates philology. James Grier Miller

Just as, in 1935, the intellectual climate helped to assure that Fleck’s work would hardly be noticed, so, in 1962, a very different intellectual climate made possible the phenomena1 success of Structure. The hegemony of logical positivism, reflected in the enthusiastic reception of another book which appeared in 1935, Karl Popper’s Logik der Forschung, was, by the early 196Os, at an end. No single work played a larger role in freeing philosophy from the sway of that movement than an article by W. V. Quine, ‘Two Dogmas of Empiricism’, published in 1951. The arguments of that paper became so fundamental to Kuhn’s epistemological position that they remain almost entirely implicit in Structure.

“‘Trenn, ‘Biographical Sketch’, in Fleck, p. 149. “‘Cf. Fleck, p. 9. “3Fleck, p. 102.

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The first ‘dogma of empiricism’ which Quine discusses is the ‘belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truths which are synthetic, or grounded in fact’.12’ Rejecting several attempts to explain the notion of

analyticity, Quine concludes that, ‘for all its a priori reasonableness, a boundary between analytic and synthetic statements simply has not been drawn. That there is such a distinction to be drawn at all is an unempirical dogma of empiricists, a metaphysical article of faith’.lz5 The second dogma, which, Quine argues, is intimately related to the first, is reductionism, ‘the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience’.‘26 Claiming, following Duhem, that ‘our statements about the external world face the tribunal of sense experience not individually but only as a corporate body’, Quine contends that reductionism, like the assumption of an analytic-synthetic distinction, rests on an illusory depiction of the nature of knowledge.‘*’

Having argued that two of the principal tenets of logical positivism are without foundation, Quine summarizes his views at the end of the essay:

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. . . . Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. Even a statement very close to the periphery can be held true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws. Conversely, by the same token, no statement is immune to revision. Revision even of the logical law of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?‘28

Although the effect which this last sentence had on Kuhn will, unfortunately, never be known, the impact of Quine’s theory of knowledge on Structure is

unmistakeable; Kuhn writes, for example, that

It has often been observed . . . that Newton’s second law of motion, though it took centuries of difficult factual and theoretical research to achieve, behaves for those committed to Newton’s theory very much like a purely logical statement that no

“‘W. Van Orman Quine, ‘Two Dogmas of Empiricism’, in From a Logical Point of View, 2nd edn (New York: Harper and Row, l%l), p. 20.

Ybid., p. 37. ‘aeIbid.. p. 20. jz71bid., p. 41. “‘Ibid., pp 42 - 3.


amount of observation could refute, [and] the chemical law of fixed proportion, which before Dalton was an occasional experimental finding of very dubious generality, became after Dalton’s work an ingredient of a definition of chemical compound that no experimental work could by itself have upset.‘29

The views expressed in ‘Two Dogmas of Empiricism’ underlie Quine’s

account of ‘radical translation’ in the second chapter of Word and Object (published in 1960). Quine considers a field linguist ‘out to penetrate and

translate a language hitherto unknown’, without any aid from interpreters.lJO

‘The utterances first and most surely translated in such a case,’ he writes, ‘are

ones keyed to present events that are conspicuous to the linguist and his

informant. A rabbit scurries by, the native says, “Gavagai”, and the linguist

notes down the sentence “Rabbit” (or “Lo, a rabbit”) as tentative translation,

subject to testing in further cases.‘13’

Quine defines ‘the affirmative stimulus meaning of a sentence such as

“Gavagai”, for a given speaker, as the class of all the stimulations (hence

involving ocular irradiation patterns between properly timed blindfoldings)

that would prompt his assent’, and ‘the negative stimulus meaning similarly

with “assent” and “dissent” interchanged’.‘32 The stimulus meaning is then

the ordered pair of the two. ‘a3 With this definition, Quine argues,

Stimulus synonomy of the occasion sentences ‘Gavagai’ and ‘Rabbit’ does not even guarantee that ‘gavagai’ and ‘rabbit’ are coextensive terms, terms true of the same things. For, consider ‘gavagai’. Who knows but what the objects to which this term applies are not rabbits after all, but mere stages, or brief temporal segments, of rabbits? In either event the stimulus situations that prompt assent to ‘Gavagai’ would be the same as for ‘Rabbit’. Or perhaps the objects to which ‘gavagai’ applies are all and sundry undetached parts of rabbits; again the stimulus meaning would register no difference.“’

Quine concludes that such translation is ‘indeterminate’:

. . . one has only to reflect on the nature of possible data and methods to appreciate the indeterminacy. Sentences translatable outright, translatable by independent evidence of stimulatory occasions, are sparse and must woefully under-determine the analytical hypotheses on which the translation of all further sentences depends. To project such hypotheses beyond the independently translatable sentences at all is in effect to impute our sense of linguistic analogy unverifiably to the native mind. Nor would the dictates even of our own sense of analogy tend to any intrinsic uniqueness;

“‘Kuhn, Smcture, p. 78. ‘lOQuine, Word und Objecf (Cambridge, Mass.: M.I.T. Press, 1960), p. 28. ‘“‘Ibid., p. 29. 1321bid., p. 32. ‘Illbid., p. 33. ‘341bid., pp. 51 -2.

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using what first comes to mind engenders an air of determinacy though freedom reign. There can be no doubt that rival systems of analytical hypotheses can fit the totality of speech behavior to perfection, and can fit the totality of dispositions to speech behavior as well, and still specify mutually incompatible translations of countless sentences insusceptible of independent control.‘35

Qume’s influence on Kuhn extends far beyond the latter’s reading of ‘Two Dogmas of Empiricism’ and Word and Object. While a Junior Fellow at Harvard between 1948 and 1951, Kuhn became personally acquainted with Quine, who was (and is) a Senior Fellow. ‘a8 In the Preface to Structure, Kuhn credits Quine with having ‘opened for me the philosophical puzzles of the analytic - synthetic distinction’. ‘H Indeed, having read relatively little twentieth- century philosophy, Kuhn gleaned much of his knowledge of that field from his frequent conversations with Quine; thus, Kuhn’s entire philosophical perspective has a distinctly ‘Quinean’ cast.‘38 Also, like Kuhn, Quine spent the academic year 1958 - 9 as a Fellow of the Center for Advanced Study in the Behavioral Sciences at Stanford, preparing Word and Object for publication. Kuhn read a draft of the second chapter of that book during that winter, just a few months before formulating the paradigm concept.‘38 (Kuhn’s comments on the chapter are acknowledged in the Preface to Word and Object.‘““) That Quine’s work on both the underdetermination of theories and the indeterminacy of translation has had a profound impact on Kuhn, though, is rarely appreciated; the following interpretation of Structure should make clear how crucial Quine’s contribution to that work was.

And now, as a noted Harvard philosopher is fond of saying before lecturing on his own theories, for the truth. In ‘Metaphor and Theory Change’, Boyd suggests that the domain of philosophy of science is a subset of that of philosophy of language. “’ Although the relation between the two disciplines is probably far more complex than this view allows, no adequate account of theory change in science can ignore the significance of concomitant linguistic revision. Indeed, in Structure, Kuhn proposes that meaning change is the central element in theory change and the source of the revolutionary character of that process; and that semantic upheaval produces theoretical incommensurability, an often misunderstood and highly controversial concept. Ironically, Hilary Putnam, an avowed opponent of the notion of incommensurability, provides, in ‘Models and Reality’, an excellent example

*35Ibid., p, 72. “‘Conversation with Kuhn, 26 November 1979. js’Kuhn, Structure, p. vi. “‘Conversation with Kuhn, 26 November 1979. ‘3gIbid. “OQuine, Word and Object, p. xi. “‘Boyd, ‘Metaphor and Theory Change’, p. 360.


of incommensurable mathematical theories.14*

The essential constituents of a paradigm, for Kuhn, are an axiom system

and a model (in the technical sense’43) for that system. The model, though, is

not defined by formal correspondence rules; rather, it is fixed by exemplars

shared by all members of a particular scientific community, ‘concrete problem

solutions, accepted by the group as, in a quite usual sense, paradigmatic’.‘44

(Indeed, that such correspondence rules play a minor part in the actual

practice of science is central to Kuhn’s argument.) The axioms and the model

are only theoretically separable, separable in the same sense that the ‘given’

can be isolated from the ‘interpretation’ in epistemological discussion. This

interpretation preserves for shared problem solutions the central place

accorded to them in Kuhn’s introduction of the term ‘paradigm’; such

examples, he writes, ‘provide models from which spring particular coherent

traditions of scientific research’.‘45 (Kuhn here uses ‘models’ in the non-

technical sense, of course.)

The fundamental characteristic of a group of scientists committed to a

shared paradigm, then, is that its members, literally and figuratively, ‘speak the

same language’. A distinct scientific community is preeminently a distinct

linguistic community. The semantic model which is the common property of

each member of such a group permits the completely unambiguous

communication within that group which, Kuhn believes, is largely responsible

for the peculiar efficiency of the scientific enterprise. To the extent that that

model is confined to a particular group, it also renders interdisciplinary

communication difficult. A physicist and a biologist can each use the term

‘nucleus’ unproblematically, without any additional gloss, although they refer

to entirely different entities.

Of course, as Kuhn notes, a scientist can, and the most capable scientists

frequently will, belong to several communities simultaneously.‘46 The

possibility of communication between groups adhering to different paradigms

is further enhanced by the fact that their languages are almost never disjoint;

the physicist and the biologist often do ‘speak the same language’. This

similarity results from recognizing that scientific communities, and hence

paradigms, function at many levels, a consideration which Kuhn emphasizes

far more in writings before and since than in Structure.‘47 At one extreme,

three or four specialists within a field may comprise a discrete scientific

community; at the other extreme, all scientists share a commitment to the most

general form of paradigm, but a paradigm nonetheless. Although the physicist

“*Putnam, ‘Models and Reality’, The Journal of Symbolic Logic. “‘See Appendix, below. “‘Kuhn, ‘Second Thoughts’, p. 298. 74SKuhn, Structure, p. 10. ‘Wf. Kuhn, Structure, pp. 49 - 50. “‘Cf. Kuhn, ‘Chapter I - Discoveries as Revolutionary’.

Paradigms 205

and the biologist may well differ as to what constitutes a proper solution for a given problem, they will almost certainly agree as to whether a particular approach to a problem is ‘scientific’.

Kuhn argues that the student’s initiation into the scientific community is entirely analogous to the child’s learning of ordinary language. Both processes rest largely on the imitation of examples and the gradual assimilation of a non- criteria1 similarity relation. I48 ‘Proponents of different theories,’ he contends, ‘are . . . like native speakers of different languages.“48 In each case this form of education inculcates fundamental knowledge which can rarely, and then only incompletely, be articulated for the outsider. Just as, for example, one who is not a native speaker can almost never acquire the Frenchman’s feel for the use of the imperfect tense, the physicist trained in the nineteenth century would almost certainly not have the same facility with problems involving discontinuous motion as the researcher committed to the quantum mechanical paradigm. Although a new theory can be learned much as a second language is learned, certain basic patterns of thought will not be assimilated unless the old theory (or the old language) is completely discarded. Barriers to communication are most difficult to overcome for groups committed to competing paradigms in a field, since that portion of the paradigm of each which must remain unintelligible to the other is a far more important obstacle to mutual understanding than in the case of communities in different disciplines.

Scientific revolutions, for Kuhn, are ‘those non-cumulative developmental episodes in which an older paradigm is replaced in whole or in part by an incompatible new one’. I50 At the core of such an event, therefore, is a linguistic revolution. Within a given discipline, the difference between successive semantic models separated by a revolution is generally far more significant than that between the uninterpreted scientific theories to which the models correspond - is, indeed, what delineates a new and distinct paradigm. The ,enormous conceptual reorientation represented by the shift from a geocentric to a heliocentric system, for example, is reflected less in the syntactic revision of the astronomical theory itself than in the fundamental incongruity between the Ptolemaic and Copernican models for that theory.15’ The term ‘sun’, for instance, on the traditional view of naming, has a different intension in the Copernican model than in that of Ptolemy, and the word ‘planet’ has both a different intension and a different extension in one model than in the other.

Kuhn proposes that the change from classical to relativistic mechanics might

‘Wf. Kuhn, ‘Second Thoughts’. ‘4sKuhn, ‘Objectivity, Value Judgement, and Theory Choice’, in The Essential Tension, p. 338. “OKuhn, Structure, p. 92. *‘*Cf. Kuhn, Structure, pp. 149-N.


well be viewed as the prototype for scientific revolutions. ‘Just because it did not involve the introduction of additional objects or concepts,’ he writes, ‘the transition from Newtonian to Einsteinian mechanics illustrates with particular clarity the scientific revolution as a displacement of the conceptual network through which scientists view the world.“52 That ‘conceptual network’ is, of course, essentially the language of the scientific community. Kuhn argues that Newtonian dynamics cannot, as is frequently claimed, be ‘derived’ from relativistic dynamics as a special case. Although Einstein’s equations may entail Newton’s laws in a purely syntactic sense, the two systems are semantically incompatible. The model for the Newtonian theory is not a submodel of the model for the Einsteinian theory. In the former, for example, ‘mass’ refers to a substance which is conserved, while in the latter it refers to a substance which is convertible with energy. In fact, the two theories are incommensurable.

Although central to the debate over Kuhn’s work, the concept of incommensurability has remained vague in most of the philosophical literature. Those who have attempted to define clearly the notion, both critics and admirers, have almost always misrepresented Kuhn’s intentions.ls3 Understanding what he means by incommensurability is greatly facilitated by examining the considerations which led him to choose that particular term. Kuhn is well aware that the paradigmatic use of the word pertains to the discovery of irrational numbers by Pythagoras;‘54 the hypotenuse of a right isosceles triangle is said to be ‘incommensurable’ with the side. The length of the hypotenuse and the length of the side are literally not ‘of the same measure’; the ratio of the two cannot be expressed as a fraction of integers. Still, as Eudoxus showed more than two thousand years ago, that ratio can be approximated by rational numbers to any desired degree of accuracy. Although fundamentally different, the hypotenuse and the side are certainly not incomparable.

Kuhn defines two theories to be incommensurable if they cannot be completely translated into a neutral language.15’ Any two theories separated by a scientific revolution are thus incommensurable. The ‘untranslatable’ words and structures associated with distinct paradigms are an important source of this limit to communication between scientific communities. Since Kuhn’s commensurability condition is equivalent to the possibility of establishing a unique mutual translation manual for two theories, Quine’s arguments for the indeterminacy of such translation provide a further basis for

lSaKuhn, Structure, p. 102. *Vf. D. W. Moberg, ‘Are There Rival, Incommensurable Theories?‘, Philosophy of Science 46

(1979), 244-62. “‘Conversation with Kuhn, 26 November 1979. ‘“Ibid.

Paradigms 207

theoretical incommensurability. As in the trigonometric case, incommensurability by no means implies

incomparability, although most philosophers have treated the terms as interchangeable.“’ (That several translations of Structure have rendered ‘incommensurable’ as ‘incomparable’ has been a source of consternation for Kuhn.15’) Putnam, for example, is unjustified in arguing that ‘To tell us that Galileo had “incommensurable” notions and then go on to describe them at length is totally incoherent.“58 That Galileo’s theories are incommensurable with those of contemporary physics does not preclude an approximate translation of his ideas into the language of twentieth-century science. Rather, what Kuhn argues against is the possibility of ‘objectively’ comparing the theories by phrasing them in a neutral language. The scientist cannot ‘hold both theories in mind together and compare them point by point with each other and with nature’,‘? much as he cannot compare English and French except from within one of the languages. He has no neutral position from which to evaluate the theories; he must either be committed to the Galilean paradigm or to the current paradigm. Still, a quantum theorist could describe Galileo’s physics ‘at length’.

Putnam further claims that if Kuhn’s view of incommensurability were correct, then ‘17th century scientists . . . would be conceptualizable by us only

.as animals producing responses to stimuli (including noises that curiously resemble English or Italian)‘.‘@ The reasons for questioning whether Galileo was a human being, however, are no more cogent than are those for doubting whether Quine’s speaker of ‘Gavagese’ is a human being. The explorer who discovers a previously unknown tribe does not find himself without grounds for believing that its members are men and women simply because of his philosophical conviction that communication between them must always be imperfect. If Kuhn believed that Aristotle’s work were entirely incomprehensible to a twentieth-century audience, he would presumably argue that the student of the history of science should not bother to read the Physics, which he certainly does not do; rather, he warns the student that his understanding of Aristotle will be incomplete as a result of his commitment to a non-Aristotelian paradigm.

Even if incommensurability did entail a complete failure of communication between advocates of theories associated with different paradigms, though, the twentieth-century physicist would be well justified in considering Galileo a human being. Since paradigms are found at many levels, virtually all scientific

‘Wf. Putnam, ‘Philosophers and Human Understanding’. “‘Conversation with Kuhn, 26 November 1979. j5*Putnam, ‘Philosophers and Human Understanding’, p. 1 I. “OKuhn, ‘Objectivity, Value Judgement, and Theory Choice’, p. 338. ‘a0Putnam, ‘Philosophers and Human Understanding’, p. 11.


revolutions involve changes only in certain parts of a language. Galileo and Einstein were both members of a single ‘higher order’ scientific community, although each also belonged to scientific communities to which the other did not. The shift from Galilean transformations to Lorentz transformations reflects a scientific revolution in which one paradigm was replaced by another, but the language of Galilean science was only partially overthrown in the process. Assuming, for the sake of argument, that the portions of Galileo’s physics which were discarded in that revolution are totally meaningless to those committed to the relativistic paradigm, Putnam still has a basis for regarding the ‘noises’ Galileo made as human language.

In ‘Philosophers and Human Understanding’, Putnam argues that Kuhn’s notions of ‘paradigm’ and ‘scientific revolution’ represent important contributions to the philosophy of science, but that ‘incommensurability’ is an incoherent concept.‘6’ He has also stated that he has recently come to accept Quine’s arguments for the indeterminacy of translation.‘62 The above considerations, however, show that Kuhn’s conception of paradigms and scientific revolutions, together with the indeterminacy thesis, leads inevitably to the incommensurability of theories. Moreover, in ‘Models and Reality’ Putnam unintentionally outlines an excellent defence of the basic elements of Kuhn’s position.

Putnam argues, for example, that a society which had developed a high level of mathematics based on principles incompatible with the axiom of choice could not be regarded as simply having made a mistake.‘63 (See Appendix.) Although acceptance of that axiom is supported by various mathematical intuitions (as well as by its enormous fertility), none of the evidence which points to the veracity of the proposition is so decisive as to render rejection of ‘choice’ irrational. If both systems of set theory, that which includes the axiom of choice and that which does not, are rational, then to term one true and the other false seems meaningless. The axiom of choice is satisfied in one ‘intended’ interpretation and is not satisfied in another ‘intended’ interpretation; the two set theories lie in different models, so neither need be erroneous. These set theoretical frameworks constitute distinct mathematical paradigms, and the mathematical theories associated with them are incommensurable.

Putnam claims, though, that the set theoretical case is essentially different from, say, that of phlogistic theory and modern chemical theory, in that in the former the reference of words in both theories is unproblematic while in the latter words like ‘phlogiston’ seem not to refer at a11.‘64 If, however, as

“‘Ibid., p. 9. “‘Putnam, Lecture in Philosophy 247 at Harvard University, 3 December 1979. “‘Putnam, ‘Models and Reality’, p. 14. ‘Wonversation with Putnam, 13 December 1979.

Paradigms 209

Putnam believes, the ‘principle of charity’ allows the reconciliation of Newtonian mechanics with relativistic mechanics, then the principle also permits the reconciliation of phlogistic theory with atomic theory. The Einsteinian revolution, as Kuhn notes, is fundamentally similar to, only more subtle than, the chemical revolution. 165 To argue that Newton’s term ‘mass’ referred ‘in fact’ to a substance convertible with energy is no more reasonable than to argue that the term ‘phlogiston’ referred ‘in fact’ to the valence electrons of oxygen atoms.

More importantly, from the perspective of ‘internal realism’, which Putnam advocates as the only tenable form of realism, a classical truth criterion can be applied to a theory when, and only when, a model for that theory has been established. Indeed, without such a model the notion of a ‘correspondence with reality’ is meaningless. ‘The search for the “furniture of the Universe”,’ Putnam argues, may ‘have ended with the discovery that the Universe is not a furnished room.“ss Models are constructed, not given, and paradigms provide those models. The principles of phlogistic theory are as valid within the phlogistic paradigm as the laws of modern chemistry are within the current paradigm, and the reference of ‘phlogiston’ is as unproblematic within the former as the reference of ‘hydrogen’ is within the latter. Kuhn does not, as Shapere claims, deny ‘the objectivity and rationality of the scientific enterprise’; “’ rather, as an ‘internal realist’, he recognizes that that objectivity and rationality are only meaningful with respect to a given model.‘68

In ‘Philosophers and Human Understanding’, Putnam laments the fact that ‘the two most widely known philosophies of science produced in this century’, logical positivism and ‘anarchism’ (which he associates with Kuhn), ‘are both incoherent’.‘Bg If the above considerations are at all correct, though, the state of philosophy of science may not be as sorry as Putnam believes.

‘05Kuhn, Structure, p. 102. ‘a’Putnam, ‘Models and Reality’, p. 34. ‘YShapere, ‘The Paradigm Concept’, Science 172 (1971), 709. lsaIn a companion paper to Boyd’s ‘Metaphor and Theory Change’, Kuhn has recently proposed

accepting the ‘new theory of reference’ for proper names but not for kind terms. This view of naming, however, is inconsistent with the basic arguments of Structure. For Kuhn to claim, for example, that a ‘unit’ of phlogiston ‘tagged’ (call it ‘Harry’) during the early part of the eighteenth century is. in any meaningful sense, the same individual after the chemical revolution seems ridiculous. More importantly, his position requires that the common name ‘individual’ itself (or an appropriate synonym) be a ‘rigid designator’, contrary to Kuhn’s stipulations. He could, of course, argue that the term ‘individual’ is the only common name to which the ‘new theory of reference’ applies, but such a response, in addition to being entirely ud hoc, would undermine Kuhn’s own view of scientific development; ‘individual’ is precisely the type of term which, Kuhn wants to allow, can change ‘meaning’ during scientific revolutions. Still, Kuhn’s original conception of theory change remains far more coherent than most of his critics claim.

‘OePutnam, ‘Philosophers and Human Understanding’, p. 16.


Perhaps no paradox has more profound philosophical implications than that discovered by the Norwegian mathematician, Thoralf Skolem. Largely as a result of the deceptively simple formal resolution of the apparent contradiction, however, most philosophers have greatly underestimated the importance of the ‘Lowenheim - Skolem Paradox’. Nonetheless, Putnam and others argue that the antinomy extends well beyond the boundaries of mathematical logic, and that its resolution reveals a fundamental misunderstanding of the nature of realism. The paradox, as presented by Skolem in 1922, may be developed as follows.

A ‘model’ for a theory is a logical interpretation of the theory, a choice of a universe of variables over which the quantifiers range and an assignment of denotations to the term letters, under which all of the axioms of the theory are true. The ‘Lowenheim - Skolem Theorem’, one of the most important results of modern logic, states that a satisfiable first-order theory, in a denumerable language, has a denumerable model, where a first-order theory is one in which predicates do not have other predicates as arguments and in which predicate quantifiers do not occur.

A set is defined to be ‘non-denumerable’ if it is ‘larger’ than the set of positive integers, that is, if no bijective mapping between that set and the set of positive integers exists. That the real numbers are non-denumerable is a theorem, proved by Cantor, which may be expressed formally as:

(1.) - ( 3 R) (R is one-to-one. The domain of RcZ+. The range of values of R is S).

where R is a relation, z’ represents the set of positive integers, and S stands for the set of real numbers. Thus, any axiomatized set theory contains the statement that a certain set, S, is non- denumerable, and S must be non-denumerable in all models of, say, Zermelo - Fraenkel set theory (the most powerful form of set theory known). All models of ZF, then, are non-denumerable, ZF since a denumerable universe cannot contain a non-denumerable set. But ZF is a satisfiable first- order theory, and, by the Lowenheim - Skolem Theorem, must therefore have a denumerable model; thus, a contradiction appears.

In fact, the formal problem is readily solved. Once a denumerable model for the set theory has been chosen, the existential quantifier, ( 3 R), in (I .) no longer ranges over all relations on Z+ x S, but only over those relations included in that model. (A relation is itself a set.) Thus, given a model for ZF, (I.) simply holds that a particular type of mapping between two sets cannot be found within the model. A certain set S can be non-denumerable with respect to a denumerable model, h4, and yet be denumerable ‘in reality’, if a bijection between Sand Z+ exists but lies outside of M. Therefore, as Skolem noted, ‘denumerable’ and ‘non-denumerable’ are relative terms, and, by similar arguments, even such notions as ‘finite’ and ‘infinite’ may be shown to be model- dependent.

Most logicians regard this relativity of set theoretic concepts as the somewhat surprising truth established by an apparent contradiction. Van Heijenoort, for example, writes, ‘the existence of such a “relativity” is sometimes referred to as the Lowenheim - Skolem paradox. But, of course, it is not a paradox in the sense of an antinomy; it is a novel and unexpected feature of formal systems’. However, as Putnam argues, with the resolution of the logical paradox a philosophical antinomy appears.

Almost all philosophers agree that the existence of such ‘unintended’ interpretations, of models in which ‘non-denumerable’ sets are ‘in reality’ denumerable, ‘shows that the “intended” interpretation, or . . . the “intuitive notion of a set”, is not “captured” by the formal system’. Indeed, Skolem’s arguments demonstrate that a formalization of all of science, or even of the totality of human belief, could not preclude ‘unintended’ interpretations of the concept of a set. If neither axiomatic set theory, nor, in fact, the entire use of the language, can determine a unique interpretation, then the question of what does ‘capture the intuitive notion of a set’ poses a serious problem. To allow that the understanding consists of more than the manner in which language is used is anathema to a naturalistic epistemology. The Platonist will contend that these considerations support his claim that the mind has an inexplicable ability to perceive ‘forms’. The verificationist will argue that the paradox shows that a correspondence theory of truth is

“OThe following is meant only to be a summary of Professor Putnam’s work as presented in ‘Models and Reality’.

Paradigms 211

untenable, and that to understand a statement like ‘The real numbers are non-denumerable’ is simply to know what would count as a proof of the proposition, not to define a unique model. The more moderate philosopher who would like to preserve a classical conception of truth, and to regard ‘set theory as the description of a determinate independently existing reality’, however, is faced with an enormous difficulty.

Still, the lack of a single ‘intended model’ for set theory may seem irrelevant to mathematics, as long as all of the models satisfy the same sentences. The mathematician, after all, is essentially only interested in which propositions are true, not in the intrinsic nature of the sets described by those propositions. An extension of Skolem’s arguments, however, points to a relativity of the truth-values of certain set theoretic statements.

The ‘theoretical constraints’ imposed upon set theory must, for a naturalistic philosophy, be grounded in human decision or convention, or in human experience. That these two sources could ever produce a complete set of axioms for set theory (that is, a group of axioms which together implied every conceivable set theoretic proposition or its negation) is virtually unimagineable. If such a set of axioms is unattainable, and if no single ‘intended’ model is fixed by theoretical and operational constraints, ‘then sentences which are independent of the axioms which . . . will [be] arrive[d] at in the limit of set theoretic inquiry really have no determinate truth value; they are just true in some intended models and false in others’. An example of a set theoretic statement whose truth-value is model-dependent is readily available.

In 1938, Gbdel proposed adding the axiom ‘ V = L ’ to set theory, where ‘L ’ is the class of all constructible sets and ‘ V’ is the universe of all sets. Thus, ‘ V = L ’ states that ‘all and only sets are constructible’. Using the inner model for set theory in which ‘V = L’ is true, he proved the relative consistency of ZF and ZF with the addition of the axiom of choice and the generalized continuum hypothesis. Since then, however, Godel has reached the conclusion that ‘ V = L ’ is, in fact, false, and most set theorists are inclined to agree with him. Still, that, though consistent with set theory, ‘V = L’ is ‘in reality’ not true is an intuition which seems unjustifiable, as the following theorem helps to illustrate.

An ‘o-model’ for a set theory is a model in which the natural numbers are ordered as they are ‘in reality’. Consider the proposition that ‘ZF plus V = L ’ has an w-model which contains any given denumerable set of real numbers, the proof of which is not particularly difficult. A denumerable set of real numbers can be coded as a single real, so all that must be proved is that, given any real number r, an M exists such that M is an u-model for ‘ZF plus V = 15’ and r is included in M. The Lowenheim-Skolem Theorem has a strong form, called the ‘downward Skolem - Lowenheim Theorem’ which holds that a satisfiable first-order theory, in a denumerable language, has a denumerable model which is a submodel of any given model for the theory. That is, if P is a non-denumerable model for such a theory, then a denumerable model P ’ for that theory may be found such that the ‘universe’ of P ’ is a proper subset of the universe of P, and such that the predicate symbols in P’ denote the same relations (restricted to the smaller universe) as they do in P. Therefore, the above statement is true if and only if, given any real number r, a denumerable M’ exists such that M’ is an w-model for ‘ZF plus V = L’ and r is included in M ’ .

A denumerable o-model, like a denumerable set of reals, can be coded as a single real number. As such, the predicate ‘M is an o-model for “ZF plus V = L” and r is included in M’ ’ may be represented as ‘a two-place arithematical predicate’ of real numbers M’, r. Thus, the above sentence containing this predicate has the logical form ‘(r) ( 3 M’) (. . . , M’, r, . . .)‘, which is referred to as a rt, sentence.

Consider the inner model ‘ V = L ‘. Given any r in that inner model (in other words, any r in L), a model exists (L itself) which satisfies ‘ V = L ’ and contains r. Therefore, by the ‘downward Skolem - Lowenheim Theorem’ a denumerable submodel of L may be found which includes r. As Godel has shown, that submodel itself is contained in L, and so is the real number used to label it. So, the sentence ‘(r) ( j M’) (. . . , M’ , r, . . .)’ is true in the inner model ‘ V = L’. Also, Schoenfield has demonstrated that II, sentences are absolute, that is, that if such a statement is true in L, then it must also be true in V. Thus, the proposition is true in V, and the theorem is proved.

Now, assume that ‘ V = L’ is ‘in reality’ false, and that, as Godel believes, a non-constructible real number exists. A /&model is one ‘in which the “well orderings” relative to the model are well orderings “in reality” ‘. The predicate ‘is constructible’ is absolute in /3-models, so that any model which contains a non-constructible real number r cannot satisfy ‘r is constructible’ and be a fl- model. However, by the above theorem, an o-model containing r exists that does satisfy ‘r is constructible’ (since the model satisfies ‘ V = L ‘, which holds that everything is constructible).


Finally, let T be a denumerable set which includes all physical magnitudes in the universe that intelligent beings can measure. (That a non-denumerable number of such magnitudes exists is almost inconceivable.) Let R represent the set which assigns to each member of Tthe actual value of that magnitude at any given rational space- time point. All of the restrictions which ‘operational constraints’ might impose upon a scientific theory, then, are implicit in R. Assume, further, that the entire language of science is formalized within the set theory ‘ZF plus V = L’. By the above theorem, since R is a denumerable set of real numbers, an o-model for ‘ZF plus V = L’ exists which contains R. Thus, even if R is non-constructible ‘in reality’, a model for the language of science can be found which satisfies ‘ V = L’ and which pairs each element of Twith its correct value at all rational space-time points. To argue that ‘ V = L ’ is ‘in reality’ false, then, is to claim that this model is not the intended model. But, for a naturalistic philosopher, that position seems untenable. The model satisfies all theoretical constraints, and, as the preceding discussion shows, also meets all operational constraints, since no physical measurement could ever produce a real number not in the model.

The suggestion might be raised that ‘ V # L’ (or a proposition which implies the negation of ‘ V = L ‘) be included among the axioms of set theory as ‘an additional “theoretical constraint” ‘. From a realist perspective, however, whether ‘ V = L ’ is a fact independent of human decision. Therefore, if the ‘intended interpretation’ is determined only by theoretical and operational constraints, and if ‘ V # L’ is not established by those theoretical constraints (that is, if ‘ V = L’ is not made false by convention), then ‘intended’ models will exist in which ’ V = L’ is true. Thus, in addition to a ‘relativity of set theoretic notions’, the Lowenheim - Skolem Paradox suggests a relativity of the truth-value of ‘V = L’, and, as similar considerations show, of the truth-values of the axiom of choice and of the continuum hypothesis.

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