Mycielski mentioned how Mostowski influenced his mathematics and
his philosophy:
1. My first teachers of Logic and Foundations were J. Slupecki and
J. Los at the University of Wroclaw. But I learned much more more from
Mostowski's book "Logika Matematyczna" and Kuratowski & Mostowski
"Teoria Mnogosci". At that time the Completeness Theorem of Godel and
the Skolem Lowenheim theorem were the great insights that attracted me
to LF.Slupecki told me that Mostowski was the most talented logician in
Poland, and when I was in Warsaw I always tried to attend his seminar.
2. Now, as an old mathematician and logician I admire the tact and
skill of Mostowski. Whenever I had a chance I told him my questions and
ideas, and always gotobjective and admirably witty comments. Eventually
his "30 Years of Foundational Studies" gave me a stimulating overview of
the subject.
3. I remember a conference on algebraic textbooks. The text books
of Mostowski and Stark had just appeared. Los was one of the organizers,
and he had nothing good to say about their work. And yet it was the
deepest and probably the best series of such textbooks in polish. There
was astark contrast between the briliant but destructive wit of Los and
the constructive wit of Mostowski during that conference. Los kept
picking at their textbooks comparing them with thevan der Waerden
classic, while Mostowski defended his and Stark's work and challeged Los
to write better texts (which never happened).
4. About 1953, the Mostowki family and mine were spending a summer
vacation in Ustka. I spend many hours on the beautiful beaches of the
Baltic shore talking about mathematics and swimming. The weather was
splendid, but every 20 minutes or so a patrol of jet fighters flew at a
very low altitude along the shore just above our heads with a terrific
noise. I remember Mostowski's remark "we live in an insane azylum".
He gave me a little problem, to define a sequenceof natural numbers with
a certain growth condition that he needed for a proof in one of his
papers. I was able to do it and it made me very happy.
I had read earlier a lecture of Mostowski thatgave me a bit of cold
feeling since he mentioned materialism in a positive way. I suspected
that it was a whiff of Marxism or political correctness. When we talked
about it he told me "materialism is a beautiful idea". At that time
Poland was reeling under the suffocating propaganda of Soviet Marxism,
with vague slogans such as "the principle of unity ofcontradictions",
"the law of quantities turning into qualities", etc. Then I realizedthat
Mostowski's philosophy was close to Kotarbinski's nominalism and there
was nothing vague in it.
At that timeI thought that we are free to believe any ontology
consistent with verifiable facts. Besides the Soviet rule in Poland was
dehumanizingand Catholic personalism was anadmirable opposite of the
ideology ofcollectivism and politicization imposed byCommunists. So I
did not understand why I should not accept the Catholic ontology, say
Thomism, which was presented by the theologians whom I knew.
It took me a few years to realize (about 1954) that we are not free to
accept arbitrary theories consistent with facts. That we have to obey
our innate preference for theories that are the simplest or alternatives
of the simplest (at a given level of agreement with facts). And then I
understood Mostowski.
5. I studied the proof of the non existence of finite axiomatizability
of Peano's Arithmetic invented by Ryll-Nardzewski but written by
Mostowski, and Mostowski's own proof of this theorem.But at that time
these papers were very difficult for me. In contrast Mostowski's
presentation of Godel's constructible setswas admirably clear, and it
entailed my admiration for axiomatic set theory.
6. I submitted to Mostowski several papers that he presented to the
Bulletin of the Polish Academy of Science.
7. It was a shock when I learned of Mostowski's death.