Thanks to a loan from YY several months back, I am currently reading Gaisi Takeuti’s “Memoirs of a Proof Theorist“. This is a compilation of English-translated articles on Godel originally written by Takeuti in Japanese. Unfortunately, the book suffers from some awkward English sentences. The grammar of some sentences could also be further improved. I hope that some editors will improve on this book in future.
I do not have any “genuine understanding” (to use Takeuti’s term) of logic and many of the technical areas discussed in the book are beyond me. Nonetheless, I’ve always had an interest in mathematical logic (which has a history of close association with the treatment of philosophical paradoxes) since my university days and I enjoy reading about famous logicians and their weird and interesting results.
In Takeuti’s book, I enjoyed reading anecdotes and memories of Godel. It was very clear to me that one of the main reasons for this book was for Takeuti to set the record right about the general and mistaken impression of Godel as an “eccentric” or “misanthrope” in view of his social reticence, which Takeuti attributes to Godel’s weak health. It is well known that Godel refused medical treatment in his last days, but the following incident concerning Godel is not well known (See pages 110 and 111) :
In 1970, an acquaintance of his introduced him to a famous doctor in New York and he received treatment. This doctor administered narcotics without informing him, which profoundly upset him, because he believed that narcotics damage the brain. This treatment was an extremely unpleasant experience and I imagine he was afraid more than anything else that it might be repeated.
In an Appendix called “On Godel’s Continuum Hypothesis”, Takeuti also revealed:
Godel sent a five page memo to the Proceedings of the National Academy of Science. It was hand written, with nonsensical definitions and style, and it gives an impression of doodle. The reason why this happened is that Godel came under the care of a famous medical doctor in New York, who prescribed narcotics without informing him. Under the influence of narcotics, Godel believed he had obtained a beautiful solution of a longstanding question, which he wrote out and submitted.
In Takeuti’s writing, it was also clear to me Takeuti is a frank and humble person, compared to say Gregory Chaitin. His frankness is is some times funny. For example, in article recounting his reading of “Godel Remembered”, he writes of Kreisel as follows:
The last article is “Godel’s excursions into intuitionistic logic” by Georg Kreisel. This is a big article occupying 122 pages of a booklet of 186 pages. It has played a substantial role in giving the booklet the style of a book. Typically for Kreisel, it contains too much information in various forms. It is a bit dense to read through, even for me, whose specialty is close to his. Therefore, I read here and there, looking for parts of interest to me. One is Godel’s view of Gentzen, in which can be read: He often called Gentzen a better logician than himself.
Here are some passages that I found amusing (the first is found on page 3 and typical of conversations by mathematicians):
Now, returning to my fundamental conjecture, Godel appeared to think that, if its proof were to be extremely impredicative, then there would be a counter-example and the state of things similar to the Incompleteness Theorem would hold. In fact, what is interesting about my fundamental conjecture is that, if one admitted an extremely impredicative demonstration, then it would become trivial. When I told his to Godel, he was very surprised and he seemed to become more interested in the problem. Godel asked me if I had published that fact, and I replied that I had not because it was trivial. He then said: “Publish it by all means.! Many people will change their views on your conjecture.” As a result, I published a trivial article against my will.
Here is a funny anecdote about Raymond Smullyan on page 4:
Thanks to Godel, during the two years of my stay at the Institute, many logicians such as Bernays, Schutte, and Feferman were there. Smullyan and Putnam were at the University as well. They held a logic seminear every week, and the logic group was very lively. In particular, there were two proof-theorists in the rare Gentzen style together (Schutte and Takeuti), and so we were were high-spirited. Smullyan would make me laugh by referring to us in a joking manner: “Is your name TakeSchutte?”. It is my sense that the energy and morale of logicians in Princeton was due to Godel’s kindness, cheerfulness and warmth.
Here is another amusing passage on Page 108:
The last article is “Godel’s impression on students of logic in the 1930s by Stephen C. Kleene. His writing is very typical of Kleene.
Unless there is some fault of the translation, this seems to me to be an absolutely “trivial” observation.
