Journey to the Edge of Reason: The Life of Kurt Gödel by Stephen Budiansky
My rating: 4 of 5 stars

The Word Made Flesh in Vienna

It was Alan Turing who discovered an important implication of Kurt Gōdel’s Incompleteness Proof. One of the consequences of the impossibility of finding a justification for the logic of arithmetic is that some mathematical propositions, although true, cannot be shown to be so. The logical steps required to prove their veracity are infinite. In technical terms, this makes them undecidable. That is, both the proposition and its negation are possible without contradiction - a mathematical incongruity that stops reason dead in its tracks.

It strikes me that the central irony of Gödel’s life as described by Budiansky is precisely this kind of undecidability applied to himself. Gödel had incredible insight and ability in logical reasoning. But for him reason was a syntactical process, that is, a purely symbolic exercise. It had nothing to do with the world outside mathematics. Its semantics, that is the connection of abstract logic to the world outside of mathematics, was something Gödel had no interest in, and very little ability.

Gödel was not unaware of his handicap. In notes to himself quoted by Budiansky, he makes it clear that he is often simply incapable of what Immanuel Kant called Practical Reason, the logic of right action: “… [I]t takes me five to ten times as long to reach a decision than other people.” Budiansky reports that he filled page after page with procedures to employ in making decisions. But his self-diagnoses transformed routinely into self-fulfilling prophecies. It is as if his inner demon of abstraction and procedural inference had been given the task of correcting itself. The result was predictably not very encouraging. Yet he obsessively continued the practice of self-analysis and self-correction throughout his life, trying, it seems, to prove the reflexive paradox of his own Proof wrong.

His decisiveness and fluency in mathematics were entirely absent from his personal and social life. Taking action frequently made him ill with uncertainty. For example, leaving Vienna to take up a position at The Institute of Advanced Studies in Princeton, he became so distressed he had to return to Vienna. After his year long stay in America, he hospitalised himself almost immediately upon arrival home with concern about the prudence of his return. Then venturing again the following year to Princeton for his second stint at the Institute, he resigned almost immediately claiming stress and ill health. He had decided to return to an increasingly violent Austria in which university life had all but been destroyed! Subsequently when it was clear that Austrian fascism had annihilated the intellectual life of the country and the Anschluss by Hitler was only days away, Gödel was offered an appointment at the University of Notre Dame. Yet he dithered interminably and finally inexplicably rejected the offer. Neither sensible judgement nor fortitude were Gödel’s forté.

This profound indecisiveness was apparently accompanied by an equally profound fear of being observed, that is of being seen as a person apart from his mathematical accomplishments. He did give occasional lectures in front of colleagues and otherwise sympathetic audiences. But at his courses at Princeton, Gödel stood speaking with his back to the students facing the blackboard but never writing on it. Clearly he wanted his students attention solely on the ‘mask’ of his symbolic reasoning and not directed to his physical person. Yet his stance suggests not shyness or even a sense of threat but almost shame for betraying the guilty secret of mathematics as well as his own judgment in devoting his life to a ‘defective’ pursuit of truth.

So as an example of someone who identifies him or herself as their work, Gödel is hard to better. What seems especially significant though is that his quasi-paranoia was directed at himself rather than at those he perceived as observing him. This doesn’t appear to have been a form of autism - Gödel did frequently, and annoyingly, ignore events he found distracting but he could be charming and had a droll sense of humour. He was apparently a devoted and sensitive friend. It was his own physicality that Gödel did not trust, perhaps originating in his recognition that he was unable to make reliable decisions outside of mathematics, particularly about his own life. That he had discovered the black hole in mathematical reasoning could well have been as much as a psychic tragedy as much as a professional triumph.

This is obviously a terrible psychological burden to bear. It is a commonplace that mathematicians do their best work in their youth. Gödel berated himself in his mature years for his lack of work of the same quality that had made his reputation. No assurances from friends, colleagues or university administrators that he was still regarded as an important mathematician could convince him to mitigate his own self-reflective judgement. He simply could not be consoled. And as his German-speaking colleagues, especially Einstein, either died or left Princeton, Gödel showed full-blown signs of breakdown.

Another implication of Gödel’s Proof was developed by his friend Alfred Tarski. It turns out that not only are some propositions undecidable but also that even the notion of what constitutes truth is undefinable in arithmetic. Could this be the subconscious origin of Gödel’s indecisiveness and defensiveness? Certainly many others have lived out their neuroses in useful ways.

Perhaps Gödel’s life, therefore, was not only an example of total devotion to mathematics but also a physical manifestation of his primitive insight about it. He fought passionately against metaphysics using patently metaphysical arguments, arguing for example that his Proof showed both the Platonic reality of numbers and that this reality was permanently beyond human comprehension. As he matured is it possible the basic incongruity in his Self of abstract reason simply took its course to disintegration? That he became more himself in other words. I’m not being trite when I suggest that Gödel had a bug in his organic operating system, a genetic quirk that led him gradually into extreme self-alienation.

So for me the question this biography raises is something both personal to Gödel and yet general to the science of mind. Is it better, that is to say more accurate, more productive and in some ways more fair, to describe Gödel as a psychologically aberrant personality, or as someone who just lived out his fate as best he could? In more poetic terms Gödel seems very much the incarnation of his own mathematical word, a person of total although tragic integrity.

Might it be that each of us has some similarly in-built genetic logic that will have its way in whatever circumstances we might find ourselves, in fact motivating us to create those circumstances as well as respond to them?

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