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C H A P T E R 3 REVOLUTIONS IN PHYSICS AND CRISES IN MATHEMATICS* 1. THE THESIS OF T. S. KUHN WE WILL now deal with two topics which, although separable, are closely connected with each other. The first and larger part of the chapter is concerned with the conception of a revolution in physics, as recently blueprinted in a provocative book by Thomas Kuhn.1 We will make observations which are seemingly in conflict with those of Kuhn, but I really intend to amplify and qualify some of Kuhn's theses rather than to dissent from them, and my approach is somewhat different anyhow. After that, we will make some observations on revolutions in physics as far as the underlying mathematics is concerned. And, finally, we will make some remarks on so-called foundation crises in mathematics, which may be viewed as a kind of revolution, and especially on a major crisis of this kind which is presumed to have taken place in the 5th century B.C. Kuhn, in his investigations into the nature of revolutions in science, analyzes both the inward ontological and epistemological nature of such revolutions and the psychological and behaviorist attitudes, resistances, and responses of practitioners of science, before, during, and after a revolution. Kuhn finds that revolutions in science are mostly internal revolutions, brought about by some scientists and then forced by the initiators on the scientific community at large. There is even an implied suggestion •Originally in Science, Vol. 141, No. 3579 (2 August 1963) pp. 408-411. Copyright 1963 by the American Association for the Advancement of Science. Somewhat revised. 1 T. S. Kuhn, The Structure of Scientific Revolutions (University of Chicago Press, 1962). [131] REVOLUTIONS AND CRISES IN SCIENCE that, in the beginning, a revolutionary innovation may be both desired and resisted by the same group of scientists, ambivalently. Kuhn makes a point of emphasizing that most scientists all the time, and all scientists most of the time, prefer peace to revolution, normalcy to anomaly, and the preservation of their "paradigms" to changes of paradigms, a "paradigm," according to Kuhn, being more or less a sum of "universally recognized achievements that for a time provide model problems and solutions to a community of practitioners" (see p. χ of the Introduction to his book). This finding is indeed meaningful, and as already noted by Gillispie,2 it is one that can be easily accepted. For my part, I found nothing singularly disturbing in the realiza­ tion that among scientists, as in other groups of human beings, the revolutionaries of today are likely to be the conservatives of tomorrow; that paradigms are not readily abandoned or changed unless anomalies make it impera­ tive; and that there may be diehards who will not give in even then. But if one is surprised and disturbed to find that resistance to innovation is widespread and even dominant among "professors" who are expected to be professionally pledged and conditioned to emphatically seek the truth and nothing but the truth, I think that there is no clear reason for singling out scientists from among scholars in general. Kuhn's diagnosis of innate conservatism does attach a certain stigma, and it is restrictive to the entire study to stigmatize scientists for something which philosophers and humanists also practice. Perhaps we can see evidence of the humanists' concern to preserve a paradigm in a well-attested event 3 which 2 C. C. Gillispie, Science, Vol. 138 (1962), p. 1251. 3 The main reference is to an article by Otmar Schissel in Real Encyclopadie der klassischen Altertums-Wissenschaft, edited by Pauly-Wissowa (1930), Vol. 28, cols. 1759-1767; the article is an authoritative interpretative digest from R. Asmus, Das Leben des Philosophen Isidores, von Damaskios aus Damaskus (Leipzig, Philosophische Bibliotek, 1911), Vol. 125. [132] RPVOLUTtONS AND CRISES IN SCIENCE occurred in the Neoplatonic school at Athens during the last 50 or 60 years before its dissolution by the Emperor Justinian in A.D. 529. At the time, leading circles in the gehool were opposed to the increase in Aristotelian fea­ tures in the "official" world picture, the result of certain influences from within. A leading exponent of Aristotelian ideas was Marinus, born in Neapolis (the Hebrew Sheehem) in Samaria, who eventually became head of the school, succeeding the much-adored "divine" Proclus (A.D. 411-484). Marinus,· when still in the junior position of tutor, was in charge of Isidorus, a student. One day Marinus showed Isidorus a commentary on...


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