Abstract
The paper is a mathematical and philosophical essay devoted to mathematical logic school created and guided by Andrzej Mostowski. Firstly, we discuss some of the main—still actual—achievements of Andrzej Mostowski, then we discuss weak sides of his scientific project. They are computational and philosophical.
Scientific challenges of our times in logic are mainly computational. The Warsaw school of mathematical logic did not support this direction.
Partially because of the political situation in Poland public philosophical discussions were strongly influenced by hard politics, including personal politics in academic institutions. Therefore, many people think that isolation of the foundations of mathematics and philosophy was forced by the communist ideology. This impression is false. The abyss between philosophy and the foundations was basically independent of the political situation in Poland.
What can we learn from this experience?
The author “Marcin Mostowski” is deceased.
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Notes
- 1.
Some of the other topics are discussed in part 4 of this book.
- 2.
A very good monography of the topic can be found in [6].
- 3.
A good introduction to ZFA can be found in [5].
- 4.
Professor Andrzej Grzegorczyk at least twice told me that Alfred Tarski decided that the result by Presbuger was too weak for PhD. Undoubtedly intending this terrible mistake as a lesson for future supervisors.
- 5.
A proper boolean algebra can be obtained by adding all the complements of the elements of an ideal.
- 6.
Zero element in T S is easy to define and inessential from the point of view of characterizing models of this theory.
- 7.
The method is currently a standard one and can be found in many textbooks of mathematical logic. A good presentation of it can be found e.g. in [2].
- 8.
Pow(q, d) means that d is a power of a prime q.
- 9.
The ordering is defined by x ≤ y ≡∃z x + z = y and x < y means x ≤ y ∧ x ≠ y.
- 10.
Personal communication at the joint meeting LMPhS and LC in Uppsala, 1991.
- 11.
The argument given here is mine, but Per Lindström gave an argument in a similar style in a conversation with Michał Krynicki and me (see footnote 10).
- 12.
I remember, I was a teenager, a comment of my father Andrzej Włodzimierz Mostowski about the book on philosophy and non-classical logics. He said: This is neither on philosophy nor on logic, this is about who should be relegated and who can keep his position.
- 13.
I was her student in 1982–1983.
- 14.
Andrzej Salwicki told that they did not know works by Andrzej Grzegorczyk. Only later on they recognized his works as relevant and important.
- 15.
He is my father, and younger cousin of Andrzej Mostowski. Similarly as sons of Andrzej Mostowski: Tadeusz and Jan, he lived in a shadow of Andrzej Mostowski. I was the the first person in the family who took the topics of Andrzej Mostowski.
- 16.
He was in this time a very eminent professor working in mathematical analysis and mathematical physics. He was also deeply interested in the philosophy of mathematics.
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Acknowledgement
This work was supported by the Polish National Science Centre [2013/11/B/HS1/ 04168].
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Mostowski, M. (2018). Foundations and Philosophy of Mathematics in Warsaw, the School of Andrzej Mostowski and Philosophy. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_38
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