Incompleteness

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Incompleteness Page 21

by Rebecca Goldstein


  Gödel, as Borel explained to me, had wanted Milnor to come to the Institute as much as any of the mathematicians had. But he couldn’t bring himself to oppose the director’s authority. It was Gödel’s unchallengeable adherence to authority’s rights that provoked the rest of the mathematicians to decide “that there was just no possible argument” [with Gödel], as Borel put it to me, continuing:

  The logic was just so strange. There just could be no discussion, not even a common way to discuss the matter. He was always with the authority. Deane Montgomery and I, we were talking to Gödel, and the logic, it was just totally impossible. Here was a man who had had to flee the fascists in power in Austria. And yet, by his logic, one does not defy authority. The logic, it was just impossible. And it was so bad in the department that it was decided, by general consent, that from then on logic would be handled separately.

  What this meant was that Gödel would no longer be included in the discussions of the mathematicians on appointment; he wasn’t sent the files of prospective candidates, he wasn’t solicited for his opinion, he wasn’t present at the meetings. He was exiled to his own sphere: logic. He would decide on the appointments of logicians, conferring with the mathematician Hassler Whitney.

  This was in 1961, and after that almost all conversation between Gödel and the other mathematicians ceased. Only Whitney kept up any contact with Gödel. And the contact was only of the most professional sort, for this is how Gödel himself wanted it. At Gödel’s memorial service, Whitney recalled how he’d once gone to pay a visit to Gödel and Gödel had been taken aback, since there’d been no “precise issue” that had brought Whitney to Gödel’s door.

  Gödel also developed a strong preference for conducting all conversations over the telephone. Even if a colleague was a few feet’s stroll away from his office at the Institute, Gödel would instruct him to use the phone.

  There was a brief period, in the early seventies, when Gödel manifested what was, for him, a preternatural gregariousness. Simon Kochen told me that during this period Gödel would often call him, to catch himself up on the latest work in his field. In March of 1973, Abraham Robinson (1918–1974), a mathematician whose work Gödel admired, gave a talk at the Institute. Robinson’s work had used the techniques of formal logic, many developed by Gödel in the course of his proof of the first incompleteness theorem, to solve standard problems in algebra, engendering what is called “nonstandard analysis,” and such extensions of logic’s reach were always encouraging to Gödel. (Simon Kochen’s work as a very young logician had similarly brought formal logic to bear on a more traditional mathematical problem.) Robinson’s talk prompted the usually taciturn Gödel to rise to his feet to congratulate Robinson on his work.9 Nonstandard analysis, he said, was not “a fad of mathematical logicians” but was destined to become “the analysis of the future. . . . In coming centuries it will be considered a great oddity . . . that the first exact theory of infinitesimals was developed 300 years after the invention of differential calculus.”

  In the autumn of 1973, Gödel surprised everyone by holding court at that lawn party at which I got my one and only opportunity to meet him. Joseph Stalin’s daughter, Svetlana Alleluyeva, a minor celebrity memoirist of the 1970s, was, I remember, at that party as well, but who had eyes for a Stalin when a Gödel was there? I never caught another glimpse of him.

  Then Gödel managed to infuriate his colleagues once again, during the Institute cause celebré that produced waves so huge as to overspill onto the pages of the NY Times and such magazines as Harper’s and the Atlantic Monthly (whose cover for the February issue of 1974 read: “Bad Days on Mount Olympus: The Big Shoot-Out in Princeton”). Though the director was now a different one—Karl Kaysen, who had taken over the reins from Oppenheimer in 196610—the bone of contention was the same—namely, appointments.

  Kaysen had come to the Institute from Harvard’s economics department, but he’d taken a leave from Harvard in 1961 to work for McGeorge Bundy at the National Security Council in the Kennedy White House. This was already far too much of the real world for the mathematicians, and they—excluding Gödel—were already strongly inclined toward bristling skepticism about the new man on campus.11 But when Kaysen proposed establishing a new school of social science, promising that he would raise all the funding for this school on his own, the mathematicians, as well as many from the School of History, girded themselves for full-scale warfare.

  The first appointment was of Clifford Geertz, a cultural anthropologist from the University of Chicago, whose work addresses all aspects of culture and whose professional credentials were as unchallengable as a social scientist can hope to attain. He got by. It was the candidacy of Robert Bellah, a sociologist of religion at Berkeley, that converted the hostile rumblings into pitched battle. Though of course the weapons were words, they could be quite targeted, even deadly. The mathematician André Weil,12 for example, was quoted in the NY Times as saying, “Many of us started reading the worthless works of Mr. Bellah. I’ve seen poor candidates before, but I’ve never had the feeling of so utterly wasting my time.” Some supporters of Bellah objected that Weil, as a mathematician employing the high standards of his discipline, would find any attempt to study religion sadly lacking in rigor. Weil countered that on the contrary, he had a personal connection with such topics; after all, his sister had been the famous mystic, Simone Weil.

  Gödel once again agreed in principle with the mathematicians. Borel told me that Gödel had said that Bellah’s appointment would be the weakest in the history of the Institute. At the general faculty meeting during which Bellah’s candidacy was discussed—a meeting in which many unfortunate things were said in the heat of emotion that were then released to the press by the “dissident majority,” after Kaysen had made clear his intention to ignore the faculty’s vote—Gödel overcame his reserve and spoke up, delivering himself in cool and rational terms. (His allies were relieved at his consistent reasonableness throughout his public remarks; in a pow-wow before the faculty meeting, he had privately speculated that perhaps Bellah, who had originally come from Canada, was so favored by the board of trustees because its director had once been the Canadian ambassador and perhaps Bellah had been a spy for Canada! This, says my source for this story, who, after all these years, still wishes to remain anonymous, was typical of Gödel’s reasoning. Since Gödel had read Bellah’s works and found them unimpressive, he was seeking the sufficient reason that would render the authorities’ decision intelligible.)

  In the public meeting, Gödel distinguished, in true Gödelian fashion, the influence ideas may have from their objective truth. (Intimations of Plato, castigating the Sophists of his day.) Bellah’s defenders spoke only of the former, not of the latter. Bellah’s work, Gödel was reasonably pointing out, may have influenced many in his own field, but that, in itself, is no grounds for thinking them true. Fashionable ideas aren’t necessarily true ideas. The counterclaim that in such fields as sociology there is nothing but influence to consider, the notion of objective truth being inapplicable (Kaysen, responding to Gödel, pushed this line a bit) amounted, for Gödel, to the most severe delegitimatizing possible of a field like sociology. “He [Gödel] also pointed out that many scientists of great intelligence, originality, learning, and influence have produced completely wrong theories, for example, Stahl, the inventor of the phlogiston theory.”

  Yet when it came to the vote, Gödel was one of the few mathematicians who didn’t vote against the nomination, once again finding it impossible to defy authority. The final vote of the faculty was 13 against Bellah, 8 for, and 3 abstentions. One of the abstainers was Kurt Gödel. This was final confirmation for Gödel’s mathematical colleagues that “the logic, it was just impossible.”

  The whole sad business of the Bellah nomination was brought to a fittingly sad conclusion: Bellah’s daughter died, and Bellah, in grief, simply withdrew from consideration. Not too long after the Bellah affair, Kaysen left the Institute, exhausted by his
mathematical adversaries (as Oppenheimer and Flexner had themselves resigned, utterly wasted). The current director of the Institute is said by the mathematicians to be a reasonable man.

  So much passion had been generated by the Bellah affair that in speaking with some of the participants now, more than a quarter of a century later, I could still feel blasts of heat rising up out of the past. Kochen told me that during the troubles over Bellah, Gödel would sometimes call to speak to him about it. “He was very distressed at the incivility of the atmosphere.”

  So despite the fact that he had briefly been the ally of his mathematical colleagues at the Institute, judging the work of the proposed new member as they judged it, his isolated exile continued. In fact, if anything it deepened.

  “I Can Only Make Negative Decisions”

  Karl Menger, Gödel’s old acquaintance from the Vienna Circle, who was happily ensconced at Notre Dame, wrote:

  On every one of my admittedly infrequent trips to Princeton, I had long talks with Gödel. Apart for his friendship with Einstein and (especially after the latter’s death) with Morgenstern, Gödel seemed to me rather lonely. Once he asked to my surprise, “Where is Artin now?” [This is the algebraist Emil Artin.] And when I answered, “In Princeton; I spoke to him yesterday,” Gödel said, “I thought he left long ago. I haven’t seen him in years.”

  Even more sadly, Menger theorized that the isolation that Gödel experienced at the Institute contributed to his lack of publications:

  At no time in his life did Gödel need intellectual stimulation to conceive and develop original and unexpected ideas. But he needed a congenial group suggesting that he report his discoveries, reminding and, if necessary, gently pressing him to write them down. All this he had at the beginning of his stay in Princeton with regard to the publication of his two booklets and his article on Russell. And he presumably could have found such support later. But apparently he never looked for it, and no one seemed to volunteer. The fact is that I could not observe anything of the sort in the 1950’s. Rather, it soon became clear to me that he wrote up many brilliant ideas only for his desk drawer if at all. From the point of view of the outside world, his incomparable talent was lying lamentably fallow.

  It was in this deep isolation that the paranoid tendencies from which Gödel had suffered even in his youth took on substance. Perhaps this darkening of his mental outlook would have been inevitable with age. Still, the imposed isolation, laced with the genuine hostility of his immediate peers, certainly couldn’t have been good for him. As we used to say in the sixties: just because you’re paranoid doesn’t mean they’re not really after you.

  After Einstein’s death, Gödel’s deepest identification appeared to have been with Leibniz. So true was this that Gödel extended his own paranoiac fantasy of imperiled rationality so that it extended to the seventeenth-century rationalist.

  In Gödel’s estimation Leibniz was an even greater thinker than posterity has realized and had carried his ideas for a characteristica universalis—or an alphabet of thought which would be used to represent thoughts in a logical way, rendering their internal logical relations transparent—to a more advanced stage than the written testimony suggests. Gödel had confided in Karl Menger his suspicions that some of Leibniz’s “important writings . . . had not only failed to be published, but [had been] destroyed in manuscript.”

  “Who could have an interest in destroying Leibniz’s writings?” Menger had queried.

  “Naturally, those people who do not want men to become more intelligent,” was the logician’s reply.

  Menger then suggested that the iconoclastic free-thinker Voltaire would be a more likely target of censorship, but Gödel disagreed:

  “Who ever became more intelligent by reading Voltaire’s writings?”

  Menger mentioned the interchange to Oskar Morgenstern, who had something of his own to relate on the subject of Leibniz and Gödel. He, too, had been alerted by Gödel as to the deliberate suppression of Leibniz’s contributions and had tried to argue the logician out of his conviction. Finally, to convince Morgenstern, Gödel had taken the economist to the university’s Firestone Library and gathered together “an abundance of really astonishing material,” in Morgenstern’s words. The material consisted of books and articles with exact references to published writings of Leibniz, on the one hand, and the very works cited, on the other. The primary sources were all missing the material that had been cited in the secondary sources.

  “This material was really highly astonishing,” a flabbergasted (if unconvinced) Morgenstern admitted.

  Gödel had always worried that he wasn’t living up to what the Institute had expected of him; this made him feel not only guilty but also insecure. Hard as it is to believe, the man who had been cited by Harvard as having produced the most important mathematical discovery of the century—the thinker who is generally pointed to as second only to Einstein in establishing the Institute as the haunt of intellectual divinities touching down briefly upon Earth—would sometimes call Morgenstern in a panic, saying that he expected to be thrown out. He also reported his suspicions that there were those who were trying to kill him, that his wife Adele had given away all his money, and that his doctors understood nothing of his case and were conspiring against him.

  Oskar Morgenstern did remain a wonderful friend to Gödel, loyally devoted, Gödel’s one abiding link, beside his wife Adele, to the old days in Vienna. Even when Morgenstern was dying of metastasized cancer, a fact tragically apparent to all his acquaintances but Gödel, his journal entries are filled with his concern for the logician.

  Today . . . Kurt Gödel called me again . . . and spoke to me for about 15 minutes. . . . After briefly asking how I was and asserting that . . . my cancer would not only be stopped, but recede . . . he went over to his own problem[s]. He asserted that the doctors are not telling him the truth, that they do not want to deal with him, that he is in an emergency (exactly what he told me with the same words a few weeks ago, a few month ago, two years ago), and that I should help get him into the Princeton Hospital. . . . [He] also assured me that . . . perhaps two years ago, two . . . men appeared who pretended to be doctors . . . . They were swindlers [who] were trying to get him in the hospital . . . and he . . . had great difficulty unmasking them. . . . It is hard to describe what such a conversation . . . means for me: here is one of the most brilliant men of our century, greatly attached to me, . . . [who] is clearly mentally disturbed, suffering from some kind of paranoia, expecting help from me, . . . and I [am] unable to extend it to him. Even while I was mobile and tried to help him . . . I was unable to accomplish anything . . . . [Now,] by clinging to me—and he has nobody else, that is quite clear—he adds to the burden I am carrying.

  This was the journal entry for 10 July 1977. Sixteen days later, Oskar Morgenstern was dead. Hours after the economist’s death, Gödel called his house, expecting to speak with him, to pour out the content of his dark delusions. The news that his one trusted ally had just died so shocked him that Gödel simply hung up the phone without saying a word.

  Adele, too, was experiencing health problems and had to be hospitalized during this period, and so Gödel was left to fend for himself for the autumn months, and then into the winter. With Morgenstern dead, and Adele away, the logician’s decline was precipitous.

  Perhaps the only one who tried to make contact with Gödel during these last few months of his life was the faithful acolyte/logician, Hao Wang. Wang was out of the country from mid-September to mid-November of 1977, but right before his departure he called Gödel, to tell him that he was coming by to see him. Wang came bearing a chicken that his wife had prepared for Gödel. Always a valetudinarian, excessively watchful of what went into his body, with recurring fears that he was being poisoned, Gödel’s abstemiousness was now advancing to self-starvation. When Wang arrived at the house on Linden Lane, Gödel “eyed him suspiciously” and refused to open the door. Wang left the chicken on the doorstep and departed.
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  Wang did manage to gain entry into the Gödel house on 17 December and seems to have been reassured by Gödel’s manner and presence (though he must have been emaciated). “His mind remained nimble and he did not appear sick. He said, ‘I’ve lost the faculty for making positive decisions. I can only make negative decisions.’ ”

  Adele returned home from her own hospital stay at the end of December and on 29 December (with the help of Hassler Whitney) persuaded Gödel to enter Princeton Hospital. “It was said that G[ödel]’s weight was down to sixty-five pounds before his death and that, toward the end, his paranoia conformed to a classic syndrome: fear of food poisoning leading to self-starvation.”

  Kurt Gödel died in the fetal position on Saturday, 14 January 1978, at one in the afternoon. According to the death certificate, on file in the Mercer County Courthouse in Trenton, he died of “malnutrition and inanition” caused by “personality disturbance.”

  Karl Menger contributed one last anecdote:

  In one of his last telephone calls before his own death (in July, 1977) Morgenstern described an event that evoked in me memories that long ago had somewhat estranged me from Gödel13—but it evoked them by its contrast to those memories, so that Morgenstern’s story moved me very much. Once again it was a question of Gödel’s rights, where his punctiliousness knew no bounds. What had happened was that Gödel, apparently suffering severely, sought and was granted admission to a Princeton hospital, but soon thereafter insisted that he had no right to one of the benefits proffered, since his insurance policy did not provide for it. He therefore refused to accept the benefit. The details of the case escape me now, though of course I am convinced that Gödel’s logic in interpreting the insurance contract was superior to the hospital’s. But be that as it may, in his juridical precision, Gödel unshakably maintained his ground.

 

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