[FOM] ETH report

Harvey Friedman friedman at math.ohio-state.edu
Wed Sep 11 14:27:26 EDT 2002

Gebhard Fuhrken has translated this interesting story written by a 
journalist from Jerusalem concerning logic at ETH, into English. I 
have his permission to post this transcription.


End of a tradition of reasoning
Last meeting of the Logic seminar at the ETH Zurich

On July 2, with a lecture about "The splendor and misery of Logic", 
at the ETH Zurich a scientific tradition comes to an end. The 
following contribution describes the rise and history of the Zurich 
Logic seminar.

In the year 1934 said circumstances in Germany lead to good fortune 
for Zurich. The mathematician Paul Bernays had to move from Gottingen 
to the city on the Limat. Bernays, because of his belonging to the 
Jewish religion, was robbed of a modest position at the world famous 
institution; the reputation of being a brilliant logician preceded 
him. Born as a Swiss in London in 1888, he studied first engineering 
then mathematics in Berlin. The young doctor got his venia legendi [a 
higher doctorate] in Zurich and taught for five years as Privatdozent 
[unpaid assistant professor] at the University.

One day the famous mathematician Daivd Hilbert visited Zurich. During 
a walk on Mount Zurich he became aware of the talented Bernays and 
offered him a position in Gottingen. Though the Privatdozent was 
already in his thirties, he did not consider it beneath himself to 
move as assistant to the great Hilbert to Gottingen. The extremely 
fruitful collaboration culminated in the two volumes "Foundations of 
Mathematics", in which the authors set out to build the edifice of 
mathematics completely on symbolic logic.

But on the horizon gathered already the brown clouds of the Nazi 
regime. The mathematical teaching staff in Gottingen, who to a good 
part consisted of men (and a single woman Emmy Noether) of Jewish 
faith, were chased away by Hitler's henchmen. Hilbert was dejected 
about the departure of Bernays, as about that of all other Jewish 

*The prime of logic in Switzerland*

Gottingens' loss was Zurich's gain, since the arrival of Bernays rang 
in the beginning of the flowering of logic in Switzerland. At the 
ETH, he was first a lecturer, then an Extraordinarius (non-line item 
professor) with half a teaching load. Together with Ferdinand Gonseth 
and George Polya he conducted for the first time, during the winter 
semester 1939/40, a logic seminar, which he then would lead for 
decades. Attendance at the seminar was free. Bernays, not being 
employed by the university full-time, could have asked the 
participants for a fee, but then most likely not many students would 
have come.

Even after his retirement in 1958, on into this high age, Bernays 
continued to attend this especially lively seminar. A former student 
remembered, how he once stood at the blackboard in order to present a 
recently published article. Hardly had he begun his presentation when 
Bernays already asked a first question. This lead to a debate, until 
Professor Hans Lauchli stepped to the board, and, with chalk in hand, 
tried to solve the problem. Whereupon Professor Ernst Specker ran to 
the board to present another version.

Now Bernays wanted to give more weight to his point of view, pressed 
forward and the conversation became more and more heated. The poor 
student, today a respected professor at the University of Lausanne, 
could barely, with effort, finish his own presentation.

Bernays died 25 years ago, on September 18, 1977. Afterwards the 
tradition of logic was kept up by Bernay's former colleagues Lauchli 
and Specker. When Specker retired in 1987, he was urged by the 
assistants and students to continue the seminar, which he did for 15 
more years. Several participants of the seminar are today professors 
at universities the whole world over.

*Classical and many-valued logic*

But with the academic year 2001/2002 this era comes to an end. 68 
years after the arrival of Bernays in Zurich the logic seminar will 
be conducted for the last time. Lauchli's and Specker's chairs for 
Logic and Foundational Research at the ETH have been filled in the 
meantime differently. Thus there is, at the ETH, for some time now no 
longer research in the area of logic and foundation of mathematics. 
In the future, the desire for learning on part of students can be 
satisfied only by introductory courses in the division of computer 
science and by guest lectures.

One of the last meetings of the seminar was conducted under the title 
"four logics". There is, besides classical logic, for example also 
many-valued logic, which admits besides a proposition and its 
opposite still other possibilities. While e.g. in classical logic the 
opposite of "good" is "bad", in many-valued logic there are between 
black and white also tones of gray.

At the mentioned meeting two [female] students from the Italian part 
of our country presented results of intuitionistic logic. This logic 
distinguishes itself by the fact that, in contrast to classical 
logic, the maxim "tertium non datur" (The proposition of the excluded 
third) is not valid. That means that a proposition does not 
necessarily have to be true or false. The intuitionistic logic admits 
also the evaluation "no comment". About these and similar niceties 
the two [female] students reported. Perfectly choreographed they 
alternately wrote formulas at the board, which, after a while, only 
reminded of Egyptian hieroglyphs. It soon went over the head of a 
non-specialist's, but then Specker injected here and there a remark, 
and the situation became clarified. And if at the end for certain 
participants still not everything was perspicuous, the discussion 
could be continued at the equally important "Nachseminar" [post 
seminar] in the the restaurant Sonnegg.

George Szpiro, Jerusalem

On Tuesday, Juli 2 at a quarter past five Professor Ernst Specker 
will give a lecture in the Aula [main hall] of the ETH (Main Building 
G 60) about "The Splendor and misery of logic".

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