Abstract
During the 10th Congress of Logic, Methodology and Philosophy of Science (Florence, August 19–25, 1995), I took part in a panel discussion on the situation of logic in Eastern Europe during the time of Soviet domination. This essay, originally written to celebrate the 50th anniversary of the Polish Academy of Sciences1, is primarily based on the paper I presented on that occasion2. The list of people with whom I consulted while preparing first the Florence paper and then the present one is rather long.3 I appreciate the assistance of all of them. My special thanks are due to Wojciech Buszkowski, Andrzej Grzegorczyk, Witold Marciszewski, Wiktor Marek, Roman Murawski, Jerzy Tiuryn and Jan Zygmunt, who in addition to offering various suggestions, remarks and criticism provided me with brief overviews of selected areas of logical investigations carried out by Polish logicians. The postwar Polish logic is too rich and too diversified for one person to be able to present it in an adequate manner, and I would not have been able to complete this paper without these people’s kind assistance. Yet, it goes without saying that the final responsibility for this paper is mine. I tried as far as I was able to evaluate critically all pieces of information I was offered and occasionally revise them. In this manner, the Polish version of this survey was prepared in cooperation with Jan Zygrnunt, who was also the author of the initial draft of its English version. The latter was accessible on the Studia Logica home page for quite some time. Eventually, I rewrote its various parts taking into account suggestions offered to me by its readers. Of those, I particularly appreciate the remarks and comments offered by Z. Adamowicz, J.M. Dunn, W. Marek, R. Murawski, Z. Pawlak, J. van Benthem, and H. Wansing. I also express my gratitude to Tom Brunty who took the effort to polish this translation.
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Reference
The Polish version “Logika polska okresu powojennego, pr6ba rzutu oka wstecz” of this paper was published in Nauka 4(2002), 157–175.
The Postwar Panorama of Logic in Poland“, in: Logic and Scientific Methods, eds. M.L. Dalla Chiara et al., Kluwer 1997,. 597–608.
Various suggestions regarding the earlier “Florence” version of this survey were offered by: Janusz Czelakowski, Andrzej Grzcgorczyk, Jacek Malinowski, Marcin. Mostowski, Roman Murawski, Ewa Orlowska, Witold A. Pogorzelski, Kazimierz Swirydowicz, Max Urchs, Jan Wolenski, Andrzej Wojcik, Jan Zygmunt. While preparing this version of the survey I received assistance front: Zofia Adamowicz, Wojciech Buszkowski, Janusz Czelakowski, Witold Marciszewski, Wiktor Marek, Roman Murawski, Jan Mycielski, Mieczyslaw Omyla, Jerzy Pogonowski, Jerzy Tiuryn, Anita Wasilewska, Andrzej Wisniewski, Jan Wolexiski, and Jan Zygmunt.
One might think that by extending the notion of logic to its limits, logicians behave like “logical imperialists” who try to invade other branches of mathematics. This is not so. Logic and its methods are both the source of inspiration and the basic research tool for mathematics. Applying the term “logic” to the foundations of mathematics enables the experts on foundational issues to establish their scientific identity. It also enables them to see their highly varied field of research as a whole that differs from the rest of mathematics.
It was formed by a group of philosophers, logicians, sociologists, and other scientists who upheld the tradition initiated by the seminars and writings of Kazimierz Twardowski, an eminent psychologist and philosopher from Lvov University. Precise analysis and lucid argument were the virtues that Twardowski considered indispensable both in scientific inquiry and philosophical analyses. Logic was regarded as the basic tool for meeting this requirement. It is not odd then that the Lvov-Warsaw School attracted logicians while at the same time logicians and their works essentially influenced the School. An impressive monograph on the School was written by Jan Wolenski, Logic and Philosophy in the Lvov-Warsaw School, Kluwer 1989. A brief and informative article on Polish logic of the interwar period can be found in The Routledge Encyclopaedia of Philosophy, vol 7, Routledge, London and New York, 1998, 498–500, “Polish Logic” by J. Zygmunt.
This subject was examined in many Polish and foreign centers. In Poland it was examined by: A. Krawczyk, M. Krynicki, L. Szczerba, W. Szmielew, M. Zawadowski, and others. Its computational aspects were analysed by A. Pawlak, H. Rasiowa, and E. Orlowska.
A. Mostowski (in collaboration with A. Grzegorczyk, S. Jankowski, J. Log, S. Mazur, H. Rasiowa, and R. Sikorski), “The Present State of Investigations on the Foundations of Mathematics”, Dissertationes Mathematicae 9 (1955), 1–48.
A. Mostowski, Thirty Years of Foundational Studies; Lectures on the Development of Mathematical Logic and the Study of the Foundations of Mathematics in 1930–1964, Acta Philosophica Fennica 17 (1965), 1–180.
The group of close collaborators of A. Mostowski included Janusz Onyszkiewicz, Stanislaw Krajewski, and Konrad Bielinski. These names are well known to all who witnessed the democratic changes in Poland (J. Onyszkiewicz was the Defense Secretary in two cab- Mets, S. Krajewski remains one of the most prominent members of the Jewish community in Poland, and K. Bielinski was one of the leaders in the underground Solidarity movement). Of course there are other logicians (e.g. Jan Waszkiewicz) and scientists close to logic (e.g. Klemens Szaniawski, Rector Electus of Warsaw University) who were deeply engaged in the political movement that sought to promote democratic changes.
In a letter I received as part of correspondence concerning this paper, J. Mycielski wrote: “Since there was a close cooperation (exchange of papers and ideas) between Mostowski’s and Tarski’s schools, one can say that there was just one Berkeley-Warsaw school and it is impossible to discuss one without discussing the other.”
Not only philosophical ones. Tarski’s concept was the subject of numerous formal analyses and generalizations. An interesting survey of this topic can be found in S. Krajewski’s essay “Prawda” in: Logika formalna. Zarys encyklopedyczny z zastosowaniami do informatyki ti lingwistyki, edited by W. Marciszewski, PWN 1987, 144–156.
Tarski’s contribution to the development of logic is discussed in J. Zygmunt’s “Alfred Tarski” in: Polska filozofia powojenna, vol. II, edited by W. Mackiewicz, Agencja Wydawnicza Witmark, Warszawa, 2001, 342–375.
The note “From the Editor” found in the first issue of Studia Logica reads that the journal will publish papers devoted to all areas of logic, including formal logic, mathematical logic, inductive logic, theory of definition and of classification, etc., and that SL invites especially works on the history of Polish logic.
Its membership included: N. D. Belnap, Jr and J.M. Dunn (USA), B. I. Dahn (DDR), L. Esakia (USSR, Georgia), D. Follesdal (Norway), R. Gilles (Canada), J. Hintikka (Finland), L. Maksimowa and V. A. Smirnow (USSR, Russia), R. Routley (Australia), I. Ruzsa (Hungary), P.Weingartner (Austria), and P. M. Williams (UK).
This “party vigilance” was not unjustified. Since the scientific periodicals were not censored, there was a danger that some of the papers might have been written by “enemies of socialism”. Studia Logica committed this kind of crime by publishing a review of A. A. Zinoviev’s (one of the leading Soviet dissidents) book Logical Physics (SL 35, 1976). It was a book free from ideological issues, but still the members of the Soviet Academy of Sciences protested.
According to the contract, the periodical remains one of the publications of the Institute of Philosophy and Sociology of the Polish Academy of Sciences, and the main Polish libraries receive it at reduced prices
The aim of this newsletter (founded by the section of logic of Inst. Phil. Soc. Pol. Ac. Sc. in 1973) was to extend international cooperation and indirectly promoting Studia Logiea. Since 1991 it has been published by Lodz University and edited by Grzegorz Malinowski.
Studia Semiotyczne (founded by J. Pelc and published by PoLskie Towarzystwo Semiotyczne) has also played an important role in this area.
It requires a competence to which the author of this survey cannot aspire, nor probably can the workers in this discipline, because of its size and scope. On the other hand it would be odd not to mention the foundations of mathematics. The results of this discipline are strongly related to those of logic.
The work of Andrzej Mostowski is discussed in five papers written by: A. Grzegorczyk, W. Guzicki, W. Marek, L. Pacholski, C. Rauszer, and P. Zbierski in: A. Mostowski, Foundational Studies: Selected Works, vol I, PWN, Warszawa, North-Holland, Amsterdam 1979. The monograph which summarizes his metamathematical research in set theory is: A. Mostowski, Constructible Sets with Applications, PWN, Warszawa, North-Holland, Amsterdam, 1969.
H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, PWN, Warszawa, 1963 (3rd edition, 1970 ).
If by laws of logic one means the laws of classical logic, then they can be characterized by the laws of Boolean algebra. Non-classical logics can be represented by “non-Boolean” algebras(e.g. intuitionistic logic is characterized by pseudo-Boolean algebras). H. Rasiowa, An Algebraic Approach to Non-Classical Logic, PWN, Warszawa, North-Holland, Amsterdam, 1974.
Studia Logica 2, 1955, 151–212.
This notion was also explored by Spanish logicians.
These two conceptions were discussed in section 2. The extent to which they differ from each other can be illustrated by the following. The system of 3-valued Lukasiewicz logic in its inferential meaning has two “non-trivial” extensions, while the same system in its sentential meaning has only one extension. This result (obtained by R. Wôjcicki) was later generalized (G. Malinowski, W. Dziobiak). It makes clearer some of the “paradoxical” results obtained earlier by H. Hiz and Rasiowa, which were concerned with the sentential meaning of the logical system. The distinction between logic understood as a set of tautologies and a logical consequence enables us to show (R. Wôjcicki) that we cannot define classical logic by the use of the constants of intuitionsitic logic in the inferential case (which is possible in the sentential case).
The papers addressed here are: J. Los, R. Suszko, “Remarks on Sentential Logic”, Indagationes Mathematicae 20, 1958, 177–183, and R. Wôjcicki “Some Remarks on the Consequence Operation in Sentential Logics”, Fundamenta Mathematicae 68, 1970, 269279.
The results mentioned here as well as those of other logicians (W. Blok, H. Hiz, J. Los, D. Pigozzi, H. Rasiowa, W.A. Pogorzelski, and others) are discussed in: R. Wôjcicki, Theory of Logical Calculi; Basic Theory of Consequence Operations, Kluwer, 1988. Some of these results were applied to the theory of automatic theorem proving (cf. Z. Stachniak, Resolution Proof System, An Algebraic Theory, Kluwer, 1996 ).
This research is discussed in the monograph: J. Czelakowski, Protoalgebraic Logics, Trends in Logic, Studia Logica Library, Kluwer, 2001.
A thorough discussion of their proceeds with a comparison to the proceeds of other centers results ca,n be found in: W. Buszkowski “Mathematical Linguistics and Proof Theory”, Handbook of Logic and Language (collective work edited by J. van Benthem and A. ter Meulen, Elsevier and MIT Press).
S. Jankowski “On the Rules of Suppositions in Formal Logic”, Studia Logica. Wydawnictwo poswigcone logice i jej historji, nr 1, Scminarium Filozoficzne Wydz. Matematyczno-Przyrodniczego Uniwersytetu Warszawskiego, Warszawa, 1934. This series was to be published under the editorship of J. Lukasiewicz. Unfortunately only one volume was published. Postwar Studia Logica (cf. section 12) referred to it but did not comprise its continuation.
n order to make S. Jaskowski’s system better known J. Slupecki and L. Borkowski elaborated a version of it (and published it in the book Elementy logiki i teorii m,nogosci, PWN, 1963; translated as Elements of Mathematical Logic and Set Theory, Pergamon Press 1967) and presented the possibility of applying it to mathematical reasoning.
This project is supported by international grants (from EU and NATO, e.g. Ph. D. scholarships in Germany and Japan) and its main aim is to complete an online encyclopedia of mathematics (comprising a collection of computer verified proofs of theorems). There is also a quarterly: Formalized Mathematics - A Computer Assisted Approach published there, edited by R. Matuszewski.
A good introduction to this subject is a book by G. Malinowski, Many-Valued Logics, Clarendon Press, Oxford 1993.
I,1. Urchs is mentioned here because of his strong connections with Polish logic. He came to Poland as a young man from the DDR and began to study in Torun.
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Wójcicki, R. (2003). Polish Logic in Postwar Period. In: Hendricks, V.F., Malinowski, J. (eds) Trends in Logic. Trends in Logic, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3598-8_2
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