8. UCLA and Nonstandard Analysis: 1962-1967
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CHAPTER EIGHT UCLA and Nonstandard Analysis: 1962-1967 Mathematics is ajungle, the Jungle of the Infinite. —Ian Stewart' Mathematics is not a deductive science—that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation , guesswork. —Paul R. Halmos2 T H E POSSIBILITY of bringing Abraham Robinson to the Los Angeles campus of the University of California arose during the visit he made to southern California in the spring of 1961, when he was working briefly at Berkeley while on leave from the Hebrew University. Although he was invited by the Mathematics Department, the Philosophy Department was just then considering ways to replace Rudolf Carnap (who was about to retire), with the hope of luring Alfred Tarski from Berkeley . Robinson, having expressed his interest in UCLA, offered an attractive alternative, one that would also serve to continue the department's strong reputation in mathematical logic. As R. M. Yost (then chairman of philosophy, soon to be replaced by E. A. Moody) wrote to Robinson in early April of 1961: Dear Professor Robinson: Professor Angus Taylor and I were delighted to learn, just before your visit to UCLA, that you were willing to consider the possibility of joining us permanently in 1962-1963. After an informal consultation, we concluded that by pooling our prospective resources in position and money, we could in all probability offer you a joint appointment in our two departments . My own department, no less than the Department of Mathematics, would be highly pleased and honored if you should decide to come to Los Angeles . Our own understanding is that if you should accept a joint appointment at UCLA, you would offer at least one course per semester in the Philosophy Department. Out of concern for the interests of my department , I should indicate to you the kinds of courses that would be of special value to us. We feel that our graduate students, especially those who l Stewart 1991, p. 75. 2 Halmos 1985, p. 321. 306 - Chapter Eight intend to go on for doctorates, should in some degree become acquainted with the most important developments in logic that have been made during the last generation. But most of these students will never attain the technical proficiency to master these subjects. We therefore hope that you would be willing to offer an advanced undergraduate course in which such important ideas as deducibility and completeness are presented discursively to those of our serious students who do not intend to specialize in logic. We hope also that you would be willing to offer a graduate course in our department in which topics in logic are presented to students who, though fairly well trained in the techniques of mathematical logic, have not had a complete undergraduate background in mathematics. From my conversations with Professor Taylor, I have the strong impression that the courses you would offer in his department could presuppose as much mathematical background as you wish. Meanwhile, Professor Taylor and I will press arrangements for your appointment as vigorously as we are able so long as you do not signal us to stop.3 Writing in support of Robinson's appointment was Alonzo Church, who endorsed Robinson's reputation as among the very best, internationally , despite the fact that he was still comparatively young (Robinson was forty-two), yet already well known as a major figure among logicians: There is no question that Robinson is a man of the highest standing in scholarship and research, and I have no hesitation in recommending him to you in the strongest terms in this regard. He has contributed to various branches of mathematics, but his most important work and that with which I am most familiar is in mathematical logic and in the important and rapidly developing intermediate field between logic and abstract algebra. Indeed the credit for originating the application of modern logic to algebra must be shared equally between Robinson and Tarski, who introduced the method independently of each other at about the same time. (It happened in my case that I first heard of this important idea from Robinson, though I afterwards learned that similar work was being done by Tarski.) Your request for as definite an estimate of Robinson as possible led me to ask myself, just who and how many of those who have done original work in mathematical logic I would rank as superior to...