Andrzej Grzegorczyk
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Andrzej Grzegorczyk

Andrzej Grzegorczyk
Grzegorczyk in September 2012
Born22 August 1922
Died20 March 2014 (aged 91)
Resting placeCemetery in Pruszków, Poland
52°10?N 20°48?E
NationalityPolish
CitizenshipPoland
Alma materJagiellonian University
University of Warsaw
Known forGrzegorczyk axiom
Grzegorczyk formula
Grzegorczyk functional
Grzegorczyk hierarchy
Grzegorczyk induction
Grzegorczyk iterator
Grzegorczyk logic (S4Grz)
Grzegorczyk logic (CD)
Grzegorczyk non-Fregean logic (LD)
Grzegorczyk method
Grzegorczyk rule
Grzegorczyk schema
Grzegorczyk semantics
Renata Maria Grzegorczykowa (Majewska) (m. 1953)
ChildrenAgnieszka Grzegorczyk-Przeciszewska
Tomasz Grzegorczyk
AwardsStefan Banach Prize (1957)
Knight's Cross of Order of Polonia Restituta (1997)
dr. h.c. of Blaise Pascal University (2010)
dr. h.c. of Jagiellonian University (2013)
Officer's Cross of Order of Polonia Restituta (2014)
Scientific career
FieldsLogic
Ethics
Mathematics
philosophy
Religious study
Social issues
Education
InstitutionsUniversity of Warsaw
University of Amsterdam
ThesisOn Topological Spaces in Topologies without Points (1950)
Doctoral studentsStanis?aw Waligórski (1964)
Stanis?aw Krajewski (1975)
Bohdan Misiun (1992)
InfluencesCzes?aw Bia?obrzeski
Jan ?ukasiewicz
Mieczys?aw Milbrandt
Henryk Hi? (Henry Hiz)
Jan Salamucha
Micha? Walicki
Bogdan Suchodolski
Zygmunt Zawirski
Andrzej Mostowski
Helena Rasiowa
Roman Sikorski
Stanis?aw Le?niewski
Stanis?aw Ja?kowski
Alfred Tarski
Kurt Gödel
Alonzo Church
Arend Heyting
Bertrand Russell
Mahatma Gandhi
Martin Luther King Jr.
InfluencedGeorge Boolos
Andrzej Trybulec
Signature
Notes

Andrzej Grzegorczyk (['andj 'rtk]; 22 August 1922 - 20 March 2014) was a Polish logician, mathematician, philosopher, and ethicist noted for his work in computability, mathematical logic, and the foundations of mathematics.

## Historical family background

Andrzej Grzegorczyk's foundational family background has its origins in the Polish intellectual, religious, patriotic, and nationalist traditions. He was the only child to the Galician family of well-educated and wealthy parents, his father Piotr Jan Grzegorczyk (1894-1968) was a polonist and historian of Polish literature involved into literary criticism, bibliographic studies, and chronicles of the Polish cultural life. Andrzej's mother Zofia Jadwiga née Zdziarska was a Medical Doctor from a purely Polish landed gentry family.

Rich historical family background was the most fundamental element in the shaping of Andrzej Grzegorczyk's further both intellectual formation and professional academic career. In particular, this heritage laid the foundations of his philosophical system which was a specific apologetics which mixed the Christian doctrine with certain elements of the Communist Ideology, the ecumenic approach towards both the Roman Catholic Church in Poland and the Russian Orthodox Church, the manifestly friendly attitude to the Eastern European countries and their national philosophers, and problems in the social assimilation in the Western European countries which served him at most for short time visits.

## Educational formation

During the 1939-1944 Nazi-Soviet occupation of Poland in the course of the World War II, Grzegorczyk was a voluntary member of the Home Army, the dominant Polish resistance movement formed in February 1942 by the Union of Armed Struggle and other Polish partisans with allegiance to the Polish Government-in-Exile as the armed wing of the Polish Underground State. As an insurgent of the Warsaw uprising under the pseudonym Bu?ka, he provided a voluntary military service in the rank of Shooter in the 2nd Platoon of the Company 'Harcerska' of the AK Battalion 'Gustaw' of the 'Róg' Group of the Group 'Pó?noc' of the Home Army. As a result of the explosion of the Nazi heavy remote-control demolition layer Sonderkraftfahrzeug 301 Ausführung C Schwerer Ladungsträger Borgward B IV of the Panzer Abteilung (Funklenk) 302 on 13 August 1944 at the Jan Kili?ski street in the Warsaw Old Town, which took life of more than 300 Polish partisans and civilians, he was injured in legs and placed in a field hospital. Several days later he rejoined the division, but by the health condition he did not participate in the further fights and was forced to leave Warsaw on 31 August 1944 as a civilian in the evacuation by the city canals from the Warsaw Old Town to the Warsaw ?ródmie?cie.

He got primary education at a private School of the Roman Catholic Educational Society Future, the same as for other Warsaw Uprising's insurgent a Polish politician W?adys?aw Bartoszewski who under the pseudonym Teofil served to the Bureau of Information and Propaganda of the Headquarters of the Home Army in the rank of Corporal and in 1940-1941 was imprisoned in the Auschwitz concentration camp. Since 1938, Grzegorczyk had obtained the Polish secondary underground education at the 6th Tadeusz Reytan Lyceum in Warsaw to be matriculated in May 1940 on the day of France's capitulation. In order to be saved from a forced displacement to the Nazi Germany for a forced labour, he started another education at a chemical high school and then, when the Nazi authorities allowed vocational secondary education in the occupied Poland, at a 3-year chemical school localized on the area of the Warsaw University of Technology where in 1942-1944 he was taught by the professors of this university. At the same time, he completed a clandestine higher education at two then secret Polish universities - in physics at the University of Warsaw, where physics was taught by Czes?aw Bia?obrzeski and Leonard Sosnowski, and in philosophy at the University of the Western Lands, where among others W?adys?aw Tatarkiewicz had read to the students the parts of himself authored and then being created book O Szczciu (Analysis of Happiness), whereas history of philosophy was lectured by his protégé a Polish-Jewish philosopher Mieczys?aw Milbrandt who as an insurgent of the Warsaw uprising under the pseudonym Noemi since August 1944 during the assault on the Sejm in September 1944 lost a leg and died of the heavily injures in a field hospital. At the stage of higher education, Grzegorczyk was especially attracted to logic by a broadcast lecture on stoic logic by a logician and mathematician Jan ?ukasiewicz, who served as the Minister of Religious Denominations and Public Education of the Second Polish Republic in the 1919 government of a pianist and composer Ignacy Jan Paderewski, led the development of a Polish curriculum which replaced the Russian-German-Austrian curricula of the Partitioned Poland and focused on the early acquisition of elementary both logic and mathematics, in 1923 was awarded the Commander's Cross with Star of the Order of Polonia Restituta by President Stanis?aw Wojciechowski, in 1922-1923 and 1931-1932 was a rector of the University of Warsaw, in 1938 was awarded by doctor honoris causa title of the Westfälische Wilhelms-Universität Münster, and in May 1939 was elected a councillor of the Council of the City of Lwów as a representative of the Camp of National Unity based in the Sanation movement.

On the other hand, one of Grzegorczyk's underground teachers was a philosopher of science and culture Bogdan Suchodolski, a professor at the Chair of Pedagogy of the Jan Kazimierz University of Lwów since 1938, a professor at the University of Warsaw in 1946-1970 and a member of the PAU since 1946, since 1952 a member and in 1965-1970 a deputy of scientific secretary and in 1969-1980 a member of the presidium of the PAS, in 1953-1973 the chairman of the Committee on Education Studies of the PAS, the head of the Department of History of Science and Technology of the PAS for 1958-1974 and the founding director of the Institute of Pedagogical Sciences at the Faculty of Education of the University of Warsaw for 1958-1968, since 1968 a member of the Front of National Unity (FJN), in 1983 a member of its successor the Patriotic Movement for National Rebirth (PRON) created to demonstrate unity and support for the communist Poland's both government and governing party Polish United Workers' Party (PZPR) in the aftermath of the 1981-1983 martial law in Poland with a crucial role of a Polish centrist political party Alliance of Democrats and a pro-communist secular Roman Catholic organization PAX Association which in 1949 formed a publishing house Instytut Wydawniczy "Pax", in 1985-1989 a member and a Senior Marshal of the communist Poland's Parliament, in 1982-1989 the chairman of the National Council of Culture created by the martial law's main author Wojciech Jaruzelski, during more than four decades of the Polish People's Republic he was awarded by the crucial state decorations such like the Knight's Cross of the Order of Polonia Restituta, the Order of the Builders of People's Poland, the Medal of the National Education Commission, and twice the 1st class Order of the Banner of Work.

Similarly to another Polish mathematician Helena Rasiowa whose first unfinished master thesis in philosophy prepared under Jan ?ukasiewicz burned with all house during the Warsaw uprising, Grzegorczyk was able to complete his originally underground education only after the World War II finished. Already in 1945 at the Philosophical Faculty of the Jagiellonian University in Kraków, supervised by a renowned philosopher of physics Zygmunt Micha? Zawirski who in 1938-1939 was the Faculty's dean and in 1937 relocated to Kraków after uninterrupted nine years as the head of the Chair of Theory and Methodology of Sciences of the Adam Mickiewicz University in Pozna? and investigated the problems on the borderline of philosophy and physics, Grzegorczyk finished the first higher study by a magister degree in philosophy with the thesis The Ontology of Properties, wherein with a help of Kotarbi?ski's reism, also propagated by Henryk Hi?, in the formal version by Stanis?aw Le?niewski, he successfully presented interpretation of Le?niewski's elementary ontology as a theory of higher logical types. Soon after graduation, he got a postgraduate scholarship targeted to the study logic and the foundations of mathematics at the University of Warsaw, and on 26 May 1950 by examinations in philosophy and chemistry he completed a doctoral degree in mathematics with the thesis On Topological Spaces in Topologies without Points supervised by a famous mathematician Andrzej Stanis?aw Mostowski, in 1954 awarded by Knight's Cross of the Order of Polonia Restituta and in 1963 elected a real member of the PAS, who after the World War II also supervised Rasiowa's both master and doctoral theses in logic and the foundations of mathematics.

All the aforementioned teachers, both underground and post-war, by their teaching style and general attitude very deeply impacted onto Grzegorczyk's youthful mind. In his later years, the influence was strictly reflected by his various life choices, individual mental features, overall academic career both inside and outside Poland, both style and methods of research and teaching work. What is much more fundamental for his creativity, this impact straightforwardly shaped his personal world view which paradoxically mixed the ideas being in a deep mutual opposition, and resulted in the creation of a borderline philosophical system based on discrimination against the features of a human mind which are either inborn or beyond a personal choice.

In 1946-1948, he was an assistant to W?adys?aw Tatarkiewicz, and, since at this time Tatarkiewicz was the editor-in-chief of the first Polish philosophical journal Przegl?d Filozoficzny (Philosophical Review), he served also as the secretary of the editorial board. In 1948, he submitted a paper on the semantics of descriptive language to the 10th International Congress of Philosophy in Amsterdam, but, similarly to most Polish philosophers invited by the organizers or submitting papers, he did not get passport and could not participate in this event, although his abstract was included in the proceedings. This fact was the omen of a difficult political time, and at this time logic focused attention of many Polish philosophers, young Grzegorczyk selected the way of majority. Soon after completion of the doctoral degree, he was employed by the Institute of Mathematics of the PAS and after 3 years he completed qualification procedure to a docent position on the basis of a book Some Classes of Recursive Functions, what at this time was an equivalent of the habilitation procedure. In 1950-1968, he worked at a secondary employment for the Faculty of Mathematics and Mechanics of the University of Warsaw, in 1957 he was awarded by the Stefan Banach Prize of the Polish Mathematical Society, in 1961 he was appointed an associate professor of mathematics. In 1963, along with Andrzej Mostowski and Czes?aw Ryll-Nardzewski, he participated in the famous logical conference The Theory of Models at the University of California, Berkeley where he met Alfred Tarski and where his both individual research results and research results co-authored with Mostowski and Ryll-Nardzewski were the subjects of few lectures. When a famous Dutch logician Evert Willem Beth died in 1964, the University of Amsterdam offered him the position of the head of the chair after Beth, he came to Amsterdam for few months and returned to Warsaw because he could not find a mental place for himself in the Netherlands, at this time on the eve of the cultural revolution which made Amsterdam the 'magic centre' of Europe. Also in 1967 he lectured four months at the University of Amsterdam and was appointed a member and an assessor to the Division of Logic, Methodology and Philosophy of science and Technology of the International Union of History and Philosophy of Science, while in 1970 he lectured two months at the Sapienza University of Rome. In 1960, he contributed a philosophical essay to the festschrift volume to honor W?adys?aw Tatarkiewicz on the occasion of his 70th birthday anniversary, whereas his father contributed Tatarkiewicz's bibliography to this volume. In the aftermath of the March 1968 Polish political crisis, as a result of a long-lasting confirmed direct involvement into the anti-governmental oppositional actions such like signing every open letter against restriction onto freedoms under communist regime, the inconvenient political circumstances motivated him to leave the University of Warsaw for the Institute of Mathematics of the PAS, where, in the 1960s, he was appointed the head of the Department of Foundations of Mathematics after Andrzej Mostowski left this position and remained the head of the Chair of Foundations of Mathematics at the University of Warsaw. In 1972, he was appointed a Full Professor, in 1973 he organized the pioneering semester in mathematical logic at the Stefan Banach International Mathematical Center of the Institute of Mathematics of the PAS, also known as the Banach Center and formed in January 1972 by the mutual agreement between the PAS and the Bulgarian, Czechoslovak, East German, Hungarian, Romanian, and Soviet national academies of sciences, which started the 1973-1992 cyclic three-to-four-month long lectures and allowed both the logicians and philosophers of the isolated Eastern Bloc to interact with their Western colleagues. In 1974, by mutual agreement he left the Institute of Mathematics of the PAS for the Institute of Philosophy and Sociology of the PAS to work at the Section of Logic then headed by a model theorist Ryszard Wójcicki who founded the series 'Trends in Logic' and related conferences by the institute's oldest journal Studia Logica: An International Journal for Symbolic Logic, and to become the head of the Section of Ethics since 1982.

On the other hand, he was well known as an active member the Roman Catholic Church in Poland, in 1964 as one of the first Poles he appeared in the French commune Taizé, Saône-et-Loire, Burgundy to associate with an ecumenical Christian monastic group known as the Taizé Community, and this visit initiated the systematic contacts of the Polish Catholic intellectuals with this ecumenic group. He was a member of the Warsaw branch of the Club of Catholic Intelligentsia, particularly he was appointed a deputy president in 1972-1973 and a member of the government in 1973-1974 and 1976-1978, formed in 1956 after the Gomu?ka Thaw to stimulate independent thought and inform Polish Catholics on the Catholic philosophy in the countries outside the Eastern Bloc. Starting the 1970s, he practiced independent ecumenical activities, in particular the dialogue with the Russian Orthodox Church in Poland for which he organized encounters between the Polish Catholic intellectuals the Russian Orthodox intellectuals at his own apartment, which in the late 1970s and the early 1980s was also the location for the lectures of the Flying University organized by the Society of Scientific Courses (TKN). His model of the Catholic-Orthodox ecumenism found a good realization in the collaboration with the Russian Orthodox priest Alexander V. Men of Moscow, an eminent chaplain of independent Russian intellectuals who was murdered in 1990. He was a dedicated supporter of Russia and Ukraine, he felt that the Soviet Union was his second home, he actively collaborated with many Soviet and Russian scholars and claimed that Russians and Poles have a similar expression of the world and many in common by the culture. Among the anti-communist oppositionists in the Polish academia, he was well known as both supporter and propagator of the philosophy of nonviolence, a fight without making use of any kind of violence, and as the spiritual masters he followed the teachings of the leader of Indian nationalism Mahatma Gandhi, the leader in the civil rights movement Martin Luther King who got the 1964 Nobel Peace Prize, as well as both Henryk Hi? and his mentor Tadeusz Kotarbi?ski, who in 1958-1968 was a deputy chairman to the All-Poland Committee of the Front of National Unity of the communist Poland under first Aleksander Zawadzki and then Edward Ochab.

Censorship in the Polish People's Republic strictly blocked public information on Grzegorczyk, and, similarly to other Polish mathematician Stanis?aw Hartman of the University of Wroc?aw who got the Stefan Banach Prize in 1953, already in 1977 his name was enlisted for the strengthened control of the censorship. Every attempt of popularization of his name in the mass media (daily press, radio, TV, socio-political magazines) was immediately signalized to the directors of the central office of the state censorship directly controlled by the authorities of the communist party which then governed Poland. The censorship rules made exception solely for the publications in the specialist press, academic journals, and university lecture notes. However, as compared to the aforementioned famous case of Hartman, he had never been involved into a real political activity, such like direct supporting of anti-governmental student protesters, membership in oppositionist organizations, membership in a political party. Hence, he almost completely smoothly came through the communist period of Polish statehood and avoided the various unpleasant circumstances produced by the state authorities and services against their ideological enemies in the Polish academia, which usually included regular persecutions and repressions by sudden often brutal hearings, firing from a university teacher's job, ban on public lectureship, forced political emigration, internment during the period 1981-1983 of the martial law in Poland. Similarly to Hartman, for his oppositionist activity he was "exiled" from his alma mater to the Institute of Mathematics of the PAS. However, he always placed his personal intellectual development on the top priority, and made professional advancements both inside and outside the communist fatherland, particularly in 1979 he was elected a member of the International Institute of Philosophy (IIP) in Paris, France with respect to which he did not hide the critical views.

After the pioneering Revolution of 1989 in Poland, he was celebrated as an intellectual authority of the post-communist Republic of Poland. He was appointed a corresponding member of the PAU in Kraków after its finally successful restoration in 1989, and an active member of the Section of Philosophy of the Scientific Society of the KUL. In 1990, he took an early retirement and enhanced his organizational activity for the Polish philosophical academia as a director of research grant The Hundred Years of the Lwów-Warsaw School, within which there he organized a huge conference in Warsaw and Lvov on the occasion of Kazimierz Twardowski's centenary as the head of a chair at the former Jan Kazimierz University of Lwów, and translation of his book to Ukrainian language. In 1995, he was elected the chairman of the editorial board of the restored weekly Przegl?d Filozoficzny. In 1997, under the rationale 'for his outstanding merits to the Polish science' President Aleksander Kwa?niewski awarded him by the Knight's Cross of the Order of Polonia Restituta. In 1999-2003, he was both the first ever honorary member and the chairman of the Committee of Philosophical Sciences of the PAS, the Polish state body responsible for coordination and giving opinions on philosophical activities as well as analysis of philosophical publications and teaching programs in Poland. In 2011-2014, he was a member of the Committee of Ethics in Science of the PAS whose purpose is the diagnosis of ethical consciousness of Polish scientific community and recommendations for its improvements. In 2010, he was awarded by the honorary doctorate of the Blaise Pascal University, Clermont-Ferrand, France, whereas in 2013 he was awarded the honorary doctorate of the Jagiellonian University in Kraków . Finally, under the rationale 'for his outstanding achievements in the scientific and didactic work, for his merits to the development of science and the activity for the democratic transformations in Poland' in 2014 President Bronis?aw Komorowski posthumously decorated him by the Officer's Cross of the Order of Polonia Restituta.

## Legacy

### Mathematical logic and mathematics

Both inside and outside Poland he was most known for continuation of the Interwar period's intellectual traditions of the Lwów-Warsaw school of logic, in particular with the substantial help of Grzegorczyk and other Andrzej Mostowski's student Helena Rasiowa, as well as independently Alfred Tarski's student Wanda Szmielew, Warsaw rejoined the chart of the worldly foundational studies. He shared the view of Tarski and Mostowski that logical investigations should respect deductive sciences, in particular, mathematics, and was skeptical in the matter of a value of investigations, developed by ?ukasiewicz's school, which looks for the shortest logical axioms or the simplest axiomatic bases of various logical systems. It is important to notice that a role of both Grzegorczyk and Rasiowa for earlier unpublished work in computable analysis by Stanis?aw Mazur, a member of the Polish United Workers' Party who was a member of communist Poland's Parliament in 1947-1956 and the director of the Institute of Mathematics of the University of Warsaw in 1964-1969 awarded by the Officer's Cross of the Order of Polonia Restituta in 1946, the Stefan Banach Prize in 1949, and the Order of the Banner of Work in 1951 and 1954, who investigated nonlinear functional analysis and Banach algebras and who in 1936-1939 elaborated the concept of computable real numbers and functions along with Stefan Banach. It is well known that Mazur was unfortunate in extension of his pre-war work to general computable mathematical objects, and the results were successfully assembled and published only in 1963 just under edition of Grzegorczyk and Rasiowa, what had a comparatively small influence on development of computable analysis, but developed careers of both the editors at the University of Warsaw.

Among his achievements in logic, one can find the issues of computability and decidability such like recursive functions, computable analysis, axiomatic arithmetic, and concatenation theory. On the other hand, he made research in the system of logics such like logical axioms, axiomatic geometry, non-classical logics, and interpretations of logic where, in particular, he defended psychologism since the beginning of his research. His two famous articles of 1958 and 1961 co-authored with Andrzej Mostowski and Czes?aw Ryll-Nardzewski became the starting point for research in the axiomatic second-order arithmetic and the arithmetic with an infinite conclusion rule, in particular the 1958's paper introduces the second-order arithmetic formalized in the first-order logic wherein both numbers and number sets are taken into account. He contributed research of the fundamental importance for theoretical computer science and precursory for the computational complexity theory, in 1953 he described and investigated classes of recursive functions generated by superposition, restricted recursion and the restricted minimum operation from some prescribed basic functions which contain addition and multiplication, and satisfy the condition that every class in question includes more complicated primitive recursive functions, and he got the sub-recursive hierarchy which fills the class of primitive recursive functions and is named the Grzegorczyk hierarchy. This originally recursion-theoretic hierarchy takes into account a strictly increasing infinite sequence of classes of functions of which the sum is a class of primitive recursive functions considered earlier, the n+1-th level functions are generated by iteration of the n-th level functions the number of times indicated by one of the arguments and by the closure under primitive recursion scheme bounded from above by an already defined function.

In 1964-1968, he researched relational and topological semantics for the intuitionistic logic, what in the context of the famous work due to J.C.C. McKinsey and Alfred Tarski was also a semantics for modal logic. Inspired by Paul Joseph Cohen's notion of forcing and Evert Willem Beth's semantics for intuitionistic logic, on the basis of the Heyting arithmetic and Ja?kowski's formulation of the intuitionistic propositional calculus, he proposed the model theory for the intuitionistic logic of constant domains (CD) and found a modal formula which is valid in all partially ordered frames with descending chain condition but not in all topological spaces. Because the logic resulting from this semantics includes the intuitionistically unprovable Grzegorczyk's schema ${\displaystyle \forall x(A\lor B(x))\rightarrow A\lor \forall xB(x)}$, where x is not free in a sentence A, it is stronger than intuitionistic predicate logic. He proposed the semantics as a 'philosophically plausible formal interpretation of intuitionistic logic' independently of the near-contemporary work by an American philosopher and logician Saul Aaron Kripke, observed that his semantics validates the schema and modified the forcing relation for disjunctions and existential formulas to give an exact interpretation for intuitionistic predicate logic. Sabine Koppelberg née Görnemann first in her doctoral dissertation of 1969 proved completeness of a calculus related to Grzegorczyk's semantics by both Kripke's tableau method and an algebraic method which made use of a language with the logical symbols (${\displaystyle \land ,\lor ,\neg ,\rightarrow ,\exists ,\forall }$), and then in 1971, with independent results by Dieter Klemke in 1970-1971 and Dov Gabbay in 1969, proved that addition of the scheme to intuitionistic predicate logic is sufficient to axiomatize Grzegorczyk's logic. Grzegorczyk's model theory has a fixed constant domain and represents a static ontology, whereas Kripke's model theory involves a quasi-ordered set of classical models, where the domains can expand along the quasi-ordering, and represents an expanding ontology with new objects created in a growth of knowledge. In other words, Grzegorczyk's semantics for the intuitionistic predicate logic is the class of predicate Kripke's models which have constant domain function. From the point of view of non-classical logics, with a help of the necessity operator ${\displaystyle \Box }$ sometimes denoted by ${\displaystyle \bigtriangleup }$, he proposed to consider ${\displaystyle \Box (\Box (A\Rightarrow \Box A)\Rightarrow A)\Rightarrow A}$ what was later called the Grzegorczyk formula/axiom, which, although that is not valid in the Lewis normal modal logic S4, when added as a new axiom schema to S4, which can be equipped into the Lindenbaum-Tarski algebra, gives the intuitionistic logic which can be translated into the S4 calculus by virtue of Gödel's interpretation of an intuitionistic logic via provability operator. In particular, Krister Segerberg was the first who proposed for this emerging specific system of a modal logic the name Grzegorczyk's logic and the symbol S4Grz or S4.Grz, whereas George Boolos contributed the foundational investigation of Grzegorczyk's schema in the context of proof theory and arithmetic.

In 2005, Grzegorczyk gave a new proof of the undecidability of the first-order functional calculus without making use of Gödel's arithmetization, and, moreover, demonstrated undecidability of a simple concatenation theory, the operations of matching two texts understood as sequences of symbols into one text with the next text being a continuation of the first one. Grzegorczyk's undecidability of Alfred Tarski's concatenation theory is based on the philosophical motivation claiming that investigation of formal systems should be done with a help of operations on visually comprehensible objects, and the most natural element of this approach is the notion of text. On his research, Tarski's simple theory is undecidable although seems to be weaker than the weak arithmetic, whereas, instead of computability, he applies more epistemological notion of the effective recognizability of properties of a text and relationships between different texts. In 2011, Grzegorczyk introduced yet one more logical system, which today is known as the Grzegorczyk non-Fregean logic or the logic of descriptions (LD), to cover the basic features of descriptive equivalence of sentences, wherein he assumed that a human language is applied primarily to form descriptions of reality represented formally by logical connectives. According to this system, the logical language is equipped in at least four logical connectives negation (¬), conjunction (?), disjunction (?), and equivalence (?). Furthermore, he defined this propositional logic from scratch, argued that neither classical propositional logic nor any of its non-classical extensions can be applied as an adequate formal language of descriptions, whereas the paradoxes of implication and equivalence are due to classical logic's restricting itself to considering only one, admittedly the most important, parameter of the content of a claim, namely its truth value. He rejected all the classical logical tautologies except the law of contradiction and added two logical axioms: (LD1) represents an equivalence relation and obeys the appropriate Extensionality property, that is equal descriptions can be substituted for each other, and (LD2) joins some of the Boolean properties of descriptions, such like associativity, commutativity, and idempotency of ? and ?, distributivity of ? over ?, distributivity of ? over ?, involution of ¬ that additionally satisfies the De Morgan laws. His results in the concatenation theory and the propositional calculus with the descriptive equivalence connective provided an important addition to his signal achievements.

By his investigations in psychologism, he converted the paradox of Eubulides into a positive theorem (formally proved): an ideal human tackling a linguistically properly stated problem is able to think on this consistently, sincerely and fully consciously. In opposition to Alfred Tarski and other anti-psychologist logicians who taught that the natural language leads to contradiction by its very nature, he rejected this conviction and proposed a formal system of the Universal Syntax which imitates the versatility of colloquial language. On his approach, the axiomatization of quotation-operator is the best device which allows to marry logic with metalogic and prove the adequacy theorem for the notion of truth. He dealt with the problem on invasion of logic by postmodernity, because the deconstruction of logical rules is not at stake, there would be no logic, while the foundation of logic could be rocked. Despite that in the mathematical genealogy he was and a son of Andrzej Mostowski and a grandson of Alfred Tarski, he manifestly undermined and rebutted the classical anti-psychologism of modern logic. His best known logico-mathematical book is An Outline of Mathematical Logic: Fundamental Results and Notions Explained with All Details published in Polish in 1961 and in English in 1969. His book Fonctions Récursives became the standard handbook at the French universities. His other book Zarys arytmetyki teoretycznej (An Outline of Theoretical Arithmetic) became the basis for the Mizar system by the University of Bia?ystok's team of a notable computer scientist Andrzej Trybulec. In Poland, Grzegorczyk was the first who popularized logical calculus by the book Logika popularna (Popular logic), also translated into Czech in 1957 and Russian in 1965, and the problems of decidability theory by the book Zagadnienia rozstrzygalno?ci (Decidability problems).

He studied computable real numbers, in particular provided few different definitions of these numbers and the ways to development of mathematical analysis based only on these numbers and computable functions determined on these numbers. He investigated computable functionals of higher types and proved undecidability of different weak theories such like elementary topological algebra, he considered axiomatic foundations of geometry by the means of solids instead of points, he showed that mereology is equivalent to the Boolean algebra, he approached intuitionistic logic with a help of semantics of intuitionistic propositional calculus built upon the notion of enforced recognition of sentences in the frames of cognitive procedures, what is similar to the Kripke semantics which was created parallelly, and he studied Kotarbi?ski's reism. He proposed an interpretation of the Le?niewski ontology as the Boolean algebra without zero, and demonstrated the undecidability of the theory of the Boolean algebras with the operation of closure. He investigated intuitionistic logic, just a modal interpretation of the Grzegorczyk semantics for intuitionism, which predetermined the Kripke semantics, leads to the aforementioned S4.Grz. He sought logic as a vivid area placed in the mainstream of the European philosophy, and, although that he belonged to rather hermetic Lwów-Warsaw School of thought, in opposition to his intellectual masters and academic mentors he contributed the approach to logic by the means of psychology. For him, logic is a collection of principles which preserve the emphatic declarations of the majority of properly educated and free from either violation or corruption people, that is, he attributes logic to a perfect human mind formed as a result of ideal educational background, ideal upbringing process, and ideal propriety. On his idealist views, classical logic is a formal theory of existence lexicalized by the existential quantification, and all that is logical is nothing but a text. As a fervent follower of the classical Aristotelian attitude, he sought logic not only as the fundamental tool but also as the basic ontology wherein semantics dealing with human utterances is preceded by attributes of humankind such like rationality, life, and existence. In his methodological approach, logic lays the foundations of science and the overall European invention.

### Philosophy and ethics

In the field of philosophical logic he defended the ontological interpretation of the logical laws, on the basis of his personal belief on describing the world by these laws. In a straightforward opposition to the teachings by the fathers-founders of the twentieth-century European transcendentalism a German logician Gottlob Frege and an Austrian phenomenologist Edmund Husserl, thanks to which anti-psychologism also known as logical realism or logical objectivism dominated both the common understanding of logic and the formal reasoning in logic, he defended psychologism which he approached as a thesis about dependence of the relationship of meaning and determination on the human factor and its description attributed to a human behavior, what in itself was very far from continental philosophy and appropriate to an English Enlightenment philosopher John Locke and a British utilitarianist philosopher John Stuart Mill who was criticized by Husserl for the logical psychologism. According to Grzegorczyk's interpretation, any description is in a language of someone and done for someone, whereas logic is applied to describe the world strictly. As a result of such an approach, he produced the reinterpretation of the semantic antinomies which claims on limitations of applicability of concepts rather than self-contradiction of a language. Particularly, in the book Logic - a human affair, by the style appropriate to Tarski, he discussed with anti-psychologism and presented the formal construction of the Universal Syntax which led him to the hypothesis 'to say that a sentence A is true is equivalent to the statement of this sentence relativized to the domain wherein one applies the sentence A' which trivializes the notion of truth, but he also stated that 'the proof of this trivialization is trivial'. On his approach, the liar paradox, which lays the foundations of this construction, transforms the antinomy into the hypothesis on both the human nature and human condition: 'there is a problem about which a human can not think in an accordant, sincere, and fully conscious way, that is having full awareness of the recognized and unrecognized sentences'. Hence, in his fervent battle for psychologism, he linked formal logic to rather non-universal and subjective attributes of a human mind, and, moreover, claimed that anti-psychologist interpretation of meaning is inspired by the related idealist vision of the world as formed by ideally formed intellectuals. According to Grzegorczyk, independently on personal motivations for which one makes considerations, the criterion of the value of these considerations is logic, strictly speaking if a proof is logical, systematic, and self-conscious. Grzegorczyk approached logic as the morality of speech and thought, he sought in logic the foundations of moral discussions, and, therefore, made a straightforward cultivation of discrimination fully appropriate to the German idealists - he did not see a morality beyond a selected system and claimed the selected model of morality is the universal one. Despite that he conceived just logic by wide horizons, included the methodology of science into its foundations and claimed that logic is a basic component of the intellectual attitude which he identified with the European Rationalism, he limited both logic by rationalism and rationalism by logic. His model of rationalism is open to the realm of values, acquirable for a reliable knowledge, and advocates ethics in social relations, whereas logic appears therein as a pure attribute of a human mind - a rational European human. He fought for psychologism in logic, for him semantic relations are always relations for someone and are mediated by language. Consequently, paradoxes demonstrate the limits of concepts and systems rather than inconsistencies of a language.

In the matter of philosophical anthropology, on the basis of the ways of reasoning pivotal for the development of the European philosophy, he provided the systematic analysis of mutual relationships between the forms of thinking and cognition in the context of the beginnings of the European culture, gave precise description of the phenomenon of European rationalism, where rational means successful as well as efficient and well-founded, through joining this concept to the internal flow of intellectual life of the European civilization and to a specific literary topos, that is a place where this way of intellectual life is localized. Meanwhile, in the matter of ethics, he claimed that in a mind cleaned from egoism and disciplined by logic there should appear elements of a general human axiology whose presence in a human expression needs a deep ethical shock, experience of either own or others' strong testimony. Particularly, he sought it in the context of Christianity where cultivated saints are the sinners who came through the stage of a great internal conversion metanoi which principally demolished their earlier life's rules, and pointed out that this procedure was unsuccessfully attempted to be implemented on the area of a secular communist society. He specifically criticized mathematicians, thus including himself, by claiming that sometimes seeing on the might of mathematical brains focused on abstract problems it seemed that there is a satanic force which causes that the most able intellectually individuals are paid for the works meaningless for wellness of humans. By his ethics, he manifestly argued against his own life choices and looked for psychological either self-defense or justification, particularly he claimed that scientists are employed in an intellectual circus whenever they do not try to think on what really is worthy to do, and, for this reason, in the isolated intellectuals there should emerge a remorse and the will of more dedicated participation in realization of socially important tasks of either a country or the world, because quite well-paid mathematical games are a waste of energy which could be utilized for thinking on real actions having a good purpose. In the case of natural scientists, he claimed that they present a world view in a careless way, although by their scientific authority and reference to a concrete research they get a substantial expertise in general philosophic beliefs, but by propagation of unfriendly ways they propagate absence of precision because they avoid logical constructions of proofs in favour of a better visual impact. He sought logic as the method against epistemological particularism, for example, he claimed that a world view demands logical culture and analytic-philosophic insight, and the way against an intellectual trapping, for example, he had a radical and unpopular point of view that the only formal logic can be the security for language against the issues of a system of assessment by clear extracting, indicating and ordering. In his philosophy, a human condition is a free existence restricted by the various limitations. Accordingly, a human as an animal has the specific features, such like persistent enrichment of life quality, creation of an environment, sensitivity on values, spiritual sphere, investigating sainthood and transcendence, ability to creativity and creative thinking, and, moreover, usage of language and symbolic reasoning which gives a control over emotions. However, his psychologist approach collapses in absence of any of his determinants of a perfect human, what means that his philosophical system, including the psychologist logic, is case-dependent and applies to a selected group of humans by emergence on the basis of discrimination against intellectual features, often either inborn or independent on a personal choice.

He was interested in an ethical standpoint and the method of conflict solving known as nonviolence, what means an action without a violence. In relation to this of his research interests, he co-organized stays in Poland for a French pacifist Jean Goss and an Austrian Christian theologian and anti-war activist Hilderad Gross-Mayr, who in 2009 got the Pacem in Terris Peace and Freedom Award established by the Roman Catholic Diocese of Davenport in the U.S. state of Iowa to commemorate Pope John XXIII's the 1963 encyclical Pacem in terris (Peace on Earth) and in 1986 along with her husband got the Pope Paul VI Teacher of Peace Award by a Catholic peace organization Pax Christi USA. In particular, at the beginning of the Polish trade union federation Independent Self-governing Labour Union Solidarity, he organized the meeting of Jean Goss with the then movement leader Lech Wasa, who after being awarded by the 1983 Nobel Peace Prize to which the Goss couple were also nominated got also the 2001 Pacem in Terris Peace and Freedom Award to recognize his leadership non-violent attitude. The Goss couple became famous as the apostles of nonviolence, particularly for preparation of the 1986 People Power Revolution ('Yellow Revolution') in Philippines, and lobbying for recognition of the conscientious objection by the Roman Catholic Church during the 1962-1965 Second Vatican Council opened by Pope John XXIII and closed by Pope Paul VI. In 1991, just after the dissolution of the Soviet Union, Grzegorczyk was instrumental in organization of a symposium in Moscow dedicated to the nonviolence philosophy with participation of the Goss couple as well as a Canadian Catholic philosopher, theologian, and humanitarian Jean Vanier who was awarded by the 2013 Pacem in Terris Peace and Freedom Award and the 2015 Templeton Prize and an American political scientist and writer on strategy of a nonviolent struggle Gene Sharp who in 1983 was the founding father of the Albert Einstein Institution to explore the methods of nonviolent resistance in conflicts and in 2009-2015 was four times nominated to the Nobel Peace Prize. Despite of some kind of liberalism present in his thought, he was a definitely radical thinker, in particular, he propagated a nonviolent dialogue with everyone including terrorists, he was particularly fervent in forcing towards both logic and dialogue with everyone, and he claimed that going towards defense in any conditions of own dignity and inventory is harmful because the Christian Doctrine of turning the other cheek is correct. He applied his ethics to a conflict resolution, put a particular emphasis onto to the methods of nonviolence professed by Mahatma Gandhi and Martin Luther King, the laureate of the 1965 Pacem in Terris Peace and Freedom Award, he was also one of the first public figures in Poland who focused attention on the ecological issues, and, before it was widely understood in Poland, he popularized the warnings due to the Club of Rome which have claimed that the resources of our planet are scarce and the idea of permanent growth is dangerous.

### Morality and religious study

In his philosophical marriage between religious involvement and both reism and a specific variant of naturalism, the particular position was occupied by the moral dimension of the religious study from the point of view of Christianity. In his pseudo-essays, pseudo-sermons, and pseudo-treatises collected in the book Moralitety awarded in 1987 by the prize Warszawska Premiera Literacka (Warsaw Literary Award), he emphasized the central elements of the Christian doctrine such like the radical command to give a selfless care testimony, especially with respect to an enemy. He attempted to place himself in the role of a Catholic priest who claims that a self-demolition is not important if personal intentions are not allowed to be reduced, whereas in the book Europa: odkrywanie sensu istnienia (Europe: discovering the sense of existence) he emphasized the role of a logical reasoning in the foundations of civilization achievements to give an axiological theory of history. He claimed therein that the evolutionary development of humankind is accompanied by a specific participation of divine forces into development of human cultures, especially he pointed out altruism and a voluntary service as the examples of such either biological theology or theological biology. Without taking into account directly the Roman Catholic Church's domination in Europe and its enormous impact onto the foundations of the European philosophy in the form of various intellectual restrictions, such like in the most known cases of the Italian scholar Galileo Gailei and philosopher Giordano Bruno, he claimed European scientific theories were always logically ordered and based on deduction, empiricism and phenomenology, and limited the sense of the world to nothing but seeing the world as similar to an understandable text - hence he claimed that the explored world is already a humanly ordered structure. For him, history of religion is just deepening of this sense, with Abraham placed as the initiator of a new epoch of monotheism and a biblical reasoning as a pictorial system, which both married with the ancient Greco-Roman intellectual traditionalism gives the most appropriate philosophical system.

On his theory, Jesus Christ of Nazareth appeals for a well-defined individual testimony, and the issues of a daily life are nothing when compared to the extreme situations because Christianity for him is a realization of spiritual rather than vital values. He saw the teachings of Jesus as the acceptance of the European logic, he radically saw Jesus Christ as the provider of the European moral pattern because Jesus demanded and demonstrated coherent individual testimony. According to Grzegorczyk, in a wide sense logic lays the foundations of the European rationalism, with respect to which he identified himself as a cultivator, which says that any knowledge must emerge by logic and empiricism and must go only towards the essential points. By his personal religious standpoint shared with the passion to logic, he always fought against himself and was limited to no more than two possibilities: the way of ethics and its universality and allowing the inexpressible in order to kill the conflict between a reason and religion. Thus, by his point of view, a rational theology is useless in favour of an imprecisely defined spiritual religiousness merely based on ecumenic approach to Christianity, that is for Grzegorczyk the biblical traditionalism of Catholicism losses the intellectual value when compared to the moral testimony of its creator Jesus Christ - a reason married with an openness towards values. What is more interesting for Grzegorczyk's religious creativity, although his formal membership at the Roman Catholic Church he frequently expressed critical opinions on concrete policies of this religious organization, even on the pages of free-thinkers periodicals, and, similarly to a Russian religious philosopher Vladimir Slovyov, he manifestly ignored the East-West Schism between the Roman Catholicism and Orthodox Christianity, for example he took the Eucharist sacrament at both the Orthodox Church and the Roman Catholic Church. He was a fervent follower of Roman Catholics who felt an affinity to the Russian Orthodoxy, his religious reflection merged Christian morality to the European cultural tradition and by his views the same values lay the foundations of both Christianity and European rationalism. In his approach, history of Christianity, including its biblical roots, can be considered the history of how a sense and understanding of the world can be deepened by contemplating the sacred and transcendent.

He convinced that Modernity with its technological development creates the new challenges for humans, whose realization demands both an appropriate ethical mode, such like dedication to other and conscious self-limitations, and the rationalist standpoint. What is intriguing, in practice he realized this of his ideas for a general public in the form of a monk-like modest appearance joined with straightforward and often manifestly ignorant and arrogant if no blatant speech, which by virtue of the dogmatic Christianity could be interpreted in terms of either demonic possession or act of blasphemy. For example, in his article Odpowiedzialno filozofów (Responsibility of philosophers) he claimed that a philosopher whose texts are at the service of state authorities, creates a vicious circle of unquestionable truths which have not much in common with reality and strengthen the authorities's monopoly on a political violence, similarly to the Roman Catholic Church's theorists who referred to the holy books instead of commenting on the facts, whereas this article was published in May 1981 on the pages of the Polish Catholic quarterly Wi with death of the Primate of Poland Cardinal Stefan Wyszy?ski as the main subject of the issue and on the eve of introduction of the martial law in Poland by the communist authorities to crush the political opposition. It was not the only one and episodic case when Grzegorczyk could not clearly and unambiguously decide on his intellectual position with respect to the teachings of the Roman Catholic Church and the political ideology of the communist state authorities. He openly presented himself in a straightforward opposition to a religious organization when it was convenient and useful to his professional activities and when it gave him a professional advance or other at least societal profit, whereas he became suddenly manifestly religious when he sought any gains to support his ideology by a religion. In particular, the latter feature was ostentatiously expressed by his idea of ecumenism between the Roman Catholic Church and the Russian Orthodox Church, especially when he sought the profits in the academic contacts with Russian and Ukrainian academic professionals who humbly supported promotion of his borderline philosophical ideas motivated by himself arranged hospitability and grants.

The big gap in conformity with respect to both political and social association which he adopted from the Roman Catholic-oriented teachers of his war-time underground education supported by his father's attitude was completely filled with a big conformity towards his academic career based on the politicized part of the Polish academia independently on a political system of Poland, what he made with extraordinary intellectual autonomy and a coherent reasoning. Following his personal pseudo-clerical image and pseudo-homiletic written style formed on the dogmatic philosophical traditionalism appropriate to both the Fathers and Doctors of the Roman Catholic Church enriched by the arguments of neo-Thomism and Christian existentialism, he attempted to defend a manifestly old-fashioned model of academic work understood as a humble dedication to ideas and humanity rather than a professionalism. In particular, in his part of the 2005's survey Gdzie ta nasza filozofia? (Where is this Our Philosophy?) he sought new circumstances of philosophizing as generated by the current fashions and the collective factors such like massiveness of higher education and general commercialization of life, he compared the present-day both philosophers and generally all humanists to businessmen who first of all look for their personal professional success by the way of a relatively fast and an appropriately high return of the incurred hardships rather than a long and arduous effort which leads to a perfect product, and, moreover, he claimed that the sham achievements are fully able to give quite good living conditions to scientists and philosophers because social control over these products is already impossible as a result of development of an academic specialization beyond such control.

### Social issues

For Grzegorczyk, the greatest intellectual challenge was an axiological approach to history of the world. Taking from the Marxist sociology, he approached cultural conflict by wealth of a privileged social class as contrasted to poverty of the rest of a society marginalized and excluded from a system focusing on rich, powerful, and clever individuals. He enriched the Marxian thought by emphasis onto the role of intellectual divisions in perpetuation of conflicts, and, similarly to the creators of the Aryan race theory based on the common proto-language, contributed the Utopian necessity of a common language for agreement and reconciliation in the global scale, as well as the Utopian idea of an identical insight of all people in understanding the wholeness of human affairs. Furthermore, he attempted to convince that the suitable theoretical apparatus is the only way for the worldly peace, that since needs of everyone can not be satisfied there is the necessity to endure limitations collectively and introduce global regulations on the basis of a persuasive argument, and that a synthesis of scientific knowledge is necessary to serve the fair and peaceful coexistence, a theory solidified in 1956 by a Soviet leader Nikita Khrushchev in the Marxist-Leninist-inspired Soviet foreign policy at the 20th Congress of the CPSU and applied by the Soviet Union and the Soviet-allied socialist states such like the communist Poland during the 1947-1991 Cold War, especially in the phases Cold War (1953-1962) and Cold War (1962-1979). Grzegorczyk doctrinally did not respect any form of pluralism and any kind of diversity among humankind, he sought the order in a large scale uniformity which is appropriate to the political ideologies which laid the foundations of the 20th century totalitarianism in Europe - both German Nazism and Soviet communism. For this reason, implicitly, he sought the European totalitarianism as the consequence of the European cultural heritage supported by his logic. On the basis of the Universal Declaration of Human Rights, he appealed to the United Nations to take into account the principle that every person has the right to help any other person in a worse position than himself or herself in whatever country that person may reside, what in 1977 met the applause due to an American-Jewish leftist philosopher and left-wing activist Noam Chomsky who published a fragment of his correspondence with Grzegorczyk.

In the aftermath of the famous 1972's report The Limits to Growth by the Club of Rome, he developed his general Utopian idea of all-human solidarity by propagation of self-limitations on consumption and combating wastefulness. In contrary to his 'general well-being' utopia, in the case of political ethics he mostly contributed to criticism of the Solidarity, the Eastern bloc's first independent trade union recognized by a communist regime and created in September 1980 at the Vladimir Lenin Shipyard in Gda?sk under the leadership of Lech Wasa, in the time when the communist Poland was strongly divided between its supporters and opponents, and when there was not a place for the 'middle option' between the yes and the no for the anti-communist opposition. Despite that Grzegorczyk at this time was not an open supporter to the Polish government, it was understood as his direct conformity with the communist authorities in the name of his false concept of peace, and, consequently, the society of the Catholic intellectuals related to the magazine Tygodnik Powszechny (The Catholic Weekly) broke collaboration with him. Moreover, although he survived the 1939-1945 Nazi-Soviet occupation of Poland and was injured as an insurgent of the 1944 Warsaw Uprising, he manifestly demonstrated a glaring absence of sensitivity on the problem of the Holocaust, and also in this case his attitude entirely confirmed the crucial impact due to the war-time underground teachers of strictly nationalist-Catholic orientation. In 1993, he authored an article Dekalog rozumu (Ten commandments of reason) which proposed the moral rules 1. You will not clap, 2. You will not whistle, 3. Listen to the content, not the tone of expression, 4. Fight with an argument, not with a human, 5. Do not flatter other and yourself, 6. Distrust other and yourself, 7. Search for what is important, 8. Try to build something better, instead to look for scapegoats, 9. Do not generalize too hastily, 10. Do not use proverbs, they are usually a stupidity of nations, which imitated and caricatured the Ten Commandments by an Old-Testament Jewish leader Moses to ridicule the biblical foundations of Judeo-Christianity by comparing them to the academic work.

### Education

Grzegorczyk had a paradoxically formed mindset, a mind which was as modal as a modal logic. By the variety of his views, he criticized and was criticized by more radical exponents of various ideological positions - Catholics disliked his contacts with Atheists, Atheists accused him of clericalism, anti-communists disliked his attempts for searching the middle position, communists questioned his defense of freedom.[] He wanted to marry all with everyone, but his idea of unification was able to create only a borderline philosophical system whose followers create a dramatic minority even in the academic philosophy of Poland.[] The unpopularity of his system is contained in the open discrimination inherited with idealism, especially the German idealism such like of Friedrich Nietzsche which served as the philosophical basis for the Nazi Germany political ideology by Adolf Hitler.[] His logically trivialized philosophical views were inadequate for both communists and anti-communists, for both religious and irreligious individuals, for both philosophers and scientists, because he manifestly avoided a strict association with any concrete group and, in fact, participated in a one-person struggle for independence and freedom.

Despite that he was a well functioned academic personality among few major specialized groups - mathematicians, philosophers, Catholic intellectuals, people of art - and was active in the international society of socio-political activists, he solicitously worked on the public self-picture which presented him as independent on political, social, religious, and scientific relationships to get some popularity among students in the times when the Polish academia was directly dependent on the communist ideology and governed by the politicized scholars. Nevertheless, in his daily work, he tended to the goals which created the appraisal of an inexhaustible way towards extraordinary egoism and self-comfort with a help of conformity with any of the aforementioned systems, he simply used his social links and professional connections within these systems when it was necessary to him. For example, he manifestly declared in public to audiences and students that he had never tended to get any higher positions in academia, whereas actually he easily accepted all higher positions offered to him and abandoned a work only when he sought is as inconvenient with respect to his purposes, such like the cultural and political ones met in Amsterdam which were in a direct conflict with his religious and ideological views adequate to the reduced both intellectual and social expression in the communist Poland.

Since the time of his underground higher education, both he had supported and he was supported primarily by the politically involved academic teachers such like Bogdan Suchodolski and also Jan ?ukasiewicz. When Suchodolski organized interdisciplinary meetings for professors in the Palace of Congresses and Conferences of the PAS in Jab?onna near Warsaw in presence of a meticulously chosen audience, in particular the students who had the preferred 'social origin', then he served humbly as the pillar. In the time of the dominant socialist orthodoxy, he presented himself as the 'Jesus Christ' of the Polish humanities - for students his philosophy was beyond the bias, intellectual enslavement and hardline correctness of the state ideology. For the communist Poland's state authorities he was officially a persona non grata secured by the politically useful historical family background, whereas for the academic youth he served as the 'socrealist Messiah' against the system teachings. He was a talented speaker towards the youth, in both philosophizing and personal action he avoided biased and emotional notions, particularism, cultivation of a scheme, routine, institution in favour of an individual, and impressive words. He impacted onto an authentic individual attitude by his analytical, synthetic and globalist reasoning, criticism on own activities, selflessness in cognitive actions, promotion of a selective truth, constant attention and control over research by the selective values based on the specific union of the Christian theology and liberalized Marxist thought.

On the one hand, his style of giving opinions was particularly distinctive in both criticism and straightforwardness, often manifestly explicit and giving the impression of directly either conflicting with or fighting against the ideals which he supported theoretically, but, on the other hand, he expressed opinions only when it was fully convenient and safe for his professional and intellectual position and preserved his personal world view. His logically radicalized philosophical system was the specific mixture of the Christian theology and the Communist Ideology which directed his primary logical thought onto the intellectual margins to walk on the borderlines with a liberation theology and a religious communism, and to visit these extremist and anarchistic territories time by time for an intellectual explosion. In a clear opposition to pluralism of the world, he manifestly claimed existence of the selective values which are absolute and universal in the earthly scale. His theoretical pedagogy, more precisely philosophy of education, was based on the specific ideological mode of nonviolence philosophy, which was particularly attractive in the period of development of anti-communist opposition and political repressions in the communist Poland. He left an explicit context of the Communist Ideology in favour of his own ideology on both similarity of life and creativity, and action and rationalism which by an ecumenic approach married the Christian theology with selected concepts of Marxism with the background in logic. However, his philosophy was able to inspire educational theory and practice in Poland by freedom, tolerance, independent choice, individual rights, and the dictate of the related professional duties of an educator. On the other hand, also his ideology of democracy was attractive for some young intellectuals of the communist Poland, because it employed the concepts of a civil society and discussion community formed by a scattering between totalitarianism and anti-totalitarianism.

## Family

In 1953, he married Renata Maria Grzegorczykowa née Majewska who is an internationally renowned Polish philologist and expert in polonist linguistics, since 2001 a professor emeritus at the Section of Grammar, Semantics and Pragmatics of the Institute of Polish language of the Faculty of Polish Studies of the University of Warsaw. In 1964 she got a doctoral degree for a thesis in Polish verbs, in 1974 she completed habilitation with a book in semantic and syntactic functions of Polish adverbs, in 1976-1979 she was a deputy-director and in 1981-1984 was the director of the Institute of Polish Language, she was appointed an associate professor in 1983 and a Full Professor in 1995, and, in 1982-2001, she was the head of the Section of Grammatical Structure of Modern Polish Language. Grzegorczykowa is a full member of the Warsaw Scientific Society, in 2007-2011 she was a member the Phraseology Commission and the Commission of Language Theory, and to which in 2015-2018 has been a collaborator along with the Ethnolinguistic Commission, of the Committee of Linguistics of the PAS. In 1997-1999, she was the head of an international project in comparative lexical semantics at the University of Warsaw in collaboration with specialists from the universities of Prague, Moscow, Kiev, and Stockholm. She contributed to word formation, syntax, and semantics of Polish language, her interests were also related to slavistics, neopragmatism, and philosophy, in her investigations she made use of the methods of structural linguistics, cognitive linguistics and generative grammar. In particular, she investigated the semantic-syntactic interpretation of language and text based on the analysis of predicate-argument structures, the logical structure of Polish sentences such like reference and modality, semantic-pragmatic relationships studied in the context of the theory of speech acts and functions of language and text, linguistic foundations of cognitive science and its role for language mechanisms. By many years until retirement she was a member of the Commission of Grammatical Structure of Slavic languages of the International Committee of Slavists.

Her father, Polish mining engineer and industrialist Leszek Majewski, in 1920-1948 was the director of the Pruszków factory of pencils Majewski St. i S-ka, created by his father a Polish engineer, industrialist, and writer Stanis?aw Jan Majewski who was a member of the Legislative Sejm (1919-1922) and the 1st Parliament (1922-1927) of the Second Polish Republic as a representative of the Popular National Union, and on 2 May 1924 was awarded the Commander's Cross of the Order of Polonia Restituta by President Stanis?aw Wojciechowski. Stanis?aw's brother a Polish scientist and novelist Erazm Majewski created the foundations of the Polish academic archeology and in 1919 was appointed the head of the Chair of Prehistoric Archeology of the University of Warsaw. Similarly to Grzegorczyk, during the World War II her older brother Second Lieutenant and Sub-Scoutmaster Jacek Majewski was an insurgent of the Warsaw uprising pseudonymed Sielakowa in the rank of acting Commander of Platoon, since 1942 he served in the Assault Groups of the Gray Ranks which was the underground paramilitary of the Polish Scouting Association, in 1944 he commanded the 1st Platoon Sad of the 2nd Company Rudy of the AK Battalion 'Zo?ka' of the Diversionary Brigade Broda 53 of the 'Rados?aw' Group of the Home Army, and was killed on 31 August 1944 at the Biela?ska street in Warsaw during the unsuccessful attempt of transfer of the Group Pó?noc soldiers, including young Grzegorczyk, by the city canals from the Warsaw Old Town to the Warsaw ?ródmie?cie, and he was awarded by the Cross of Valour. Since her mother Maria née Borsuk was the only daughter of a Polish physician-surgeon Marian Stanis?aw Borsuk, an active member of the Warsaw Medical Society who in 1907-1923 was the head of the Surgical Department of the former Wolski Hospital in Warsaw and whose origins were in the Wilno Voivodeship of the Second Polish Republic which is a part of the modern-day Lithuania, the family members include also her younger brother a famous Polish mathematician Karol Borsuk of the University of Warsaw and his only daughter a Polish paleontologist and phylogeneticist Maria Magdalena Borsuk-Bia?ynicka who is a Full Professor at the Roman Koz?owski Institute of Paleobiology of the PAS. Grzegorczyk's other kins are also her husband a Polish algebraic geometer Andrzej Szczepan Bia?ynicki-Birula who pioneered in differential algebra and is both a full member of the PAS and a Full Professor at the University of Warsaw, his older brother a Polish theoretical physicist Iwo Bia?ynicki-Birula who is a full member of the PAS with the positions of a Full Professor at the Center for Theoretical Physics of the PAS and a professor emeritus at the University of Warsaw, and his wife a Polish theoretical physicist Zofia Bia?ynicka-Birula née Wiatr who is a Full Professor at the Institute of Physics of the PAS.

One of Grzegorczyk's publicly known grandchildren are a Polish physician-internist Franciszek Grzegorczyk who has worked for a few hospitals in Warsaw, including the academic Institute of Tuberculosis and Lung Diseases which was earlier the former Wolski Hospital, an economist Jacek Przeciszewski who graduated at the Warsaw School of Economics and is an activist of the Warsaw branch of the Club of Catholic Intelligentsia, and a lawyer Jan Przeciszewski.

Grzegorczyk died of natural causes in Warsaw on 20 March 2014 at the age of 91. His body is buried in the Cemetery of Pruszków.

## Famous quotes

"The achievements of Alfred Tarski were the most brilliant result of a favorable cultural entanglement which took place in Poland in the first half of the twentieth century." - from the book Alfred Tarski: Life and Logic (2008) by Anita Burdman Feferman and Solomon Feferman

## Selected publications

### Journal articles

• Grzegorczyk, Andrzej (2013): Wizja warto?ci i dramat wyboru warto?ci w my?li europejskiej. Wspólnotowo i Postawa Uniwersalistyczna: Rocznik PTU 2012-2013, Number 8, pp. 5-20
• Grzegorczyk, Andrzej (2012): ?wiatopogl?dowa integracja ludzkiej wiedzy. Przegl?d Filozoficzny - Nowa Seria, Volume 21, Issue 2, pp. 29-48
• Grzegorczyk, Andrzej (2011): Filozofia logiki I formalna logika niesymplifikacyjna. Zagadnienia Naukoznawstwa, Volume 47, Issue 190, pp. 445-451 (Errata: Zagadnienia Naukoznawstwa, Volume 48, Issue 194, p. 318)
• Grzegorczyk, Andrzej (2010): Uczciwo w nauce. Próba podsumowania (The moral integrity of the scientific research). Kwartalnik NAUKA, Number 3, pp. 194-200
• Przecki, Marian; Grzegorczyk, Andrzej; Jadacki, Jacek Juliusz; Bro?ek, Anna; Baranowska, Ma?gorzata Maria; Stró?ewski, W?adys?aw Antoni (2009): Inspired by the Bible (Z inspiracji biblijnej). Kwartalnik Filozoficzny, Volume 37, Issue 2, pp. 137-160
• Grzegorczyk, Andrzej (2008): Prawdziwo cecha wa?na, ?atwa do okre?lenia, trudniejsza do osi?gni?cia (Felieton filozoficzny). Przegl?d Humanistyczny, Volume 52, Number 2, Issue 407, pp. 71-81
• St?pie?, Antoni Bazyli; Krajewski, Rados?aw; Grzegorczyk, Andrzej (2005): Gdzie ta nasza filozofia? - Dyskusji ci?g dalszy. Miesi?cznik Znak, Issue 602-603, pp. 107-114
• Heller, Micha? Kazimierz; Chwede?czuk, Bohdan; Szahaj, Andrzej Jaros?aw; Przecki, Marian; Buczy?ska-Garewicz, Hanna; Sady, Wojciech Henryk; Bo?tu?, Piotr; Pi?at, Robert; Grzegorczyk, Andrzej; Koj, Leon Józef; Por?bski, Czes?aw; Ziemi?ski, Ireneusz; Marciszewski, Witold (2005): Gdzie ta nasza filozofia? - ankieta. Miesi?cznik Znak, Issue 600, pp. 29-54
• Grzegorczyk, Andrzej (2005): Undecidability without Arithmetization. Studia Logica: An International Journal for Symbolic Logic, Volume 79, Issue 2, pp. 163-230
• Grzegorczyk, Andrzej (2004): A Philosophy for That Time: The Philosophy of Selflessness. Dialogue and Universalism, Volume 14, Issue 5-6, pp. 167-171
• Grzegorczyk, Andrzej (2004): Decidability without Mathematics. Annals of Pure and Applied Logic, Volume 126, Issue 1-3, pp. 309-312
• Grzegorczyk, Andrzej (2003): Czasy i wyzwania. Wspólnotowo i Postawa Uniwersalistyczna: Rocznik PTU 2002-2003, Number 3, pp. 5-20
• Grzegorczyk, Andrzej (2002): Europe: discovering the meaning of existence. Dialogue and Universalism, Issue 6-7, pp. 111-126
• Grzegorczyk, Andrzej (2000): Racjonalizm europejski jako sposób my?lenia. Wspólnotowo i Postawa Uniwersalistyczna: Rocznik PTU 2000-2001, Number 2, pp. 5-8
• Grzegorczyk, Andrzej (1999): Antropologiczne podstawy edukacji globalnej. Forum o?wiatowe, Number 1-2, Issue 20-21, pp. 5-13
• Grzegorczyk, Andrzej (1999): The vocation of Europe. Dialogue and Universalism, Issue 5-6, pp. 11-41
• Grzegorczyk, Andrzej; Morokhoyeva, Zoya Petrovna; Zapa?nik, Stanis?aw (1998): Universalistic Social Education. Dialogue and Universalism, Volume 8, Number 5-6, pp. 159-163
• Grzegorczyk, Andrzej (1993): Dekalog rozumu. Wiedza i ?ycie, Volume 3, pp. 18-20
• Grzegorczyk, Andrzej (1989): Dzia?ania pokojowe a postawy etyczne. Studia Philosophiae Christianae, Issue 1, pp. 141-159
• Grzegorczyk, Andrzej (1987): Wierno i ?wiadectwo. Studia Filozoficzne, Issue 5, pp. 33-39
• Grzegorczyk, Andrzej (1983): Poj?cie godno?ci jako element poznawczej regulacji ludzkiego zachowania. Studia Filozoficzne, Issue 8-9, pp. 57-76
• Grzegorczyk, Andrzej (1981): Odpowiedzialno filozofów. Wi, Volume 23, Issue 5, pp. 49-56
• Grzegorczyk, Andrzej (1981): My Version of the Christian Vision of Sense. Dialectics and Humanism: The Polish Philosophical Quarterly, Volume 8, Issue 3, pp. 51-53
• Grzegorczyk, Andrzej (1977): On Certain Formal Consequences of Reism. Dialectics and Humanism: The Polish Philosophical Quarterly, Volume 1, pp. 75-80
• Grzegorczyk, Andrzej (1974): Prze?ycie transcendencji a mity kultury. Znak, Issue 236, pp. 224-235
• Grzegorczyk, Andrzej (1971-1972): An unfinitizability proof by means of restricted reduced power. Fundamenta Mathematicae, Volume 73, pp. 37-49
• Grzegorczyk, Andrzej (1971): Klasyczne, relatywistyczne i konstruktywistyczne sposoby uznawania twierdze? matematycznych. Studia Logica: An International Journal for Symbolic Logic, Volume 27, Issue 1, pp. 151-161
• Grzegorczyk, Andrzej (1968): Logical uniformity by decomposition and categoricity in ${\displaystyle \aleph _{0}}$. Bulletin de l'Académie Polonaise des Sciences: Série des sciences mathématiques, astronomiques, et physiques, Volume 16, Issue 9, pp. 687-692
• Grzegorczyk, Andrzej (1968): Assertions depending on time and corresponding logical calculi. Compositio Mathematica, Volume 20, pp. 83-87
• Grzegorczyk, Andrzej (1967): Non-classical propositional calculi in relation to methodological patterns of scientific investigation. Studia Logica: An International Journal for Symbolic Logic, Volume 20, Issue 1, pp. 117-132
• Grzegorczyk, Andrzej (1967): Some relational systems and the associated topological spaces. Fundamenta Mathematicae, Volume 60, pp. 223-231
• Grzegorczyk, Andrzej (1965): Nasi bracia mariawici. Wi, Volume 12, Issue 92, pp. 40-45
• Grzegorczyk, Andrzej (1964): Recursive objects in all finite types. Fundamenta Mathematicae, Volume 54, pp. 73-93
• Grzegorczyk, Andrzej (1964): A note on the theory of propositional types. Fundamenta Mathematicae, Volume 54, pp. 27-29
• Grzegorczyk, Andrzej (1964): A philosophically plausible formal interpretation of intuitionistic logic. Indagationes Mathematicae, Volume 26, pp. 596-601
• Grzegorczyk, Andrzej (1964): Sprawdzalno empiryczna a matematyczna. In Kotarbi?ski, Tadeusz; D?mbska, Izydora (editors) (1964): Rozprawy logiczne: Ksi?ga pami?tkowa ku czci Kazimierza Ajdukiewicza. Pa?stwowe Wydawnictwo Naukowe, Warszawa, pp. 73-76. Republished as translation Mathematical and Empirical Verifiability in Przecki, Marian; Wójcicki, Ryszard (editors) (1977): Twenty-Five Years of Logical Methodology in Poland. D. Reidel, Boston & PWN-Polish Scientific Publishers, Warszawa, pp. 165-169
• Grzegorczyk, Andrzej (1963): Zastosowanie logicznej metody wyodr?bniania formalnej dziedziny rozwa?a? w nauce, technice i gospodarce. Studia Filozoficzne, Issue 3-4, pp. 63-75
• Mazur, Stanis?aw; edited by Grzegorczyk, Andrzej and Rasiowa, Helena (1963): Computable analysis. Rozprawy Matematyczne, Volume 33
• Grzegorczyk, Andrzej (1962): Uzasadnianie aksjomatów teorii matematycznych. Studia Logica: An International Journal for Symbolic Logic, Volume 13, Issue 1, pp. 197-202
• Grzegorczyk, Andrzej (1962): On the concept of categoricity. Studia Logica: An International Journal for Symbolic Logic, Volume 13, Issue 1, pp. 39-66
• Grzegorczyk, Andrzej (1962): A kind of categoricity. Colloquium Mathematicae, Volume 9, pp. 183-187
• Grzegorczyk, Andrzej (1962): A theory without recursive models. Bulletin de l'Académie Polonaise des Sciences: Série des sciences mathématiques, astronomiques, et physiques, Volume 10, pp. 63-69
• Grzegorczyk, Andrzej (1962): An example of two weak essentially undecidable theories F and F*. Bulletin de l'Académie Polonaise des Sciences: Série des sciences mathématiques, astronomiques, et physiques, Volume 10, pp. 5-9
• Grzegorczyk, Andrzej (1961): Le traitement axiomatique de la notion de prolongement temporel. Studia Logica: An International Journal for Symbolic Logic, Volume 11, Issue 1, pp. 31-34
• Grzegorczyk, Andrzej (1961): Aksjomatyczne badanie poj?cia przed?u?enia czasowego. Studia Logica: An International Journal for Symbolic Logic, Volume 11, Issue 1, pp. 23-30
• Grzegorczyk, Andrzej; Mostowski, Andrzej; Ryll-Nardzewski, Czes?aw (1961): Definability of sets in models of axiomatic theorems. Bulletin de l'Académie polonaise des sciences. Série des sciences mathématiques, astronomiques, et physiques, Volume 9, pp. 163-167
• Grzegorczyk, Andrzej (1961): Metafizyka rzeczy ?ywych. Znak, Issue 80, pp. 154-162
• Grzegorczyk, Andrzej (1960): Metafizyka bez spekulacji. Znak, Issue 77, pp. 1417-1421
• Grzegorczyk, Andrzej (1960): O nie najlepszym rodzaju apologetyki. Znak, Issue 76, pp. 1343-1344
• Grzegorczyk, Andrzej (1960): Axiomatizability of Geometry without Points. Synthese, Volume 12, pp. 228-235
• Grzegorczyk, Andrzej (1959): Analiza filozoficzna, kontemplacja, warto?ciowanie. Studia Filozoficzne, Volume 5, Issue 14, pp. 161-173
• Grzegorczyk, Andrzej (1958): Mi?dzy dyskursywnym a kontemplacyjnym my?leniem. Znak, Issue 43, pp. 36-57
• Grzegorczyk, Andrzej; Mostowski, Andrzej; Ryll-Nardzewski, Czes?aw (1958): The classical and the ?-complete arithmetic. Journal of Symbolic Logic, Volume 23, pp. 188-206
• Grzegorczyk, Andrzej (1957): Uwagi z historii logiki. My?l Filozoficzna, Volume 1, Issue 27, pp. 164-176
• Grzegorczyk, Andrzej (1957): On the definitions of computable real continuous functions. Fundamenta Mathematicae, Volume 44, pp. 61-71
• Grzegorczyk, Andrzej (1956): Some proofs of undecidability of arithmetic. Fundamenta Mathematicae, Volume 43, pp. 166-177
• Mostowski, Andrzej; Grzegorczyk, Andrzej; Ja?kowski, Stanis?aw; ?o?, Jerzy; Mazur, Stanis?aw; Rasiowa, Helena; Sikorski, Roman (1955): The present state of investigations on the foundations of mathematics. Rozprawy Matematyczne, Volume 9
• Grzegorczyk, Andrzej (1955): Uwagi o rozumieniu praw logiki. My?l Filozoficzna, Volume 1, Issue 15, pp. 206-221
• Grzegorczyk, Andrzej (1955): Uwagi o nauczaniu logiki. My?l Filozoficzna, Volume 1, Issue 4, pp. 174-177
• Grzegorczyk, Andrzej (1955): On the definition of computable functionals. Fundamenta Mathematicae, Volume 42, pp. 232-239
• Grzegorczyk, Andrzej (1955): Computable functionals. Fundamenta Mathematicae, Volume 42, pp. 168-202
• Grzegorczyk, Andrzej (1955): Elementarily definable analysis. Fundamenta Mathematicae, Volume 41, pp. 311-338
• Grzegorczyk, Andrzej (1955): The Systems of Le?niewski in Relation to Contemporary Logical Research. Studia Logica: An International Journal for Symbolic Logic, Volume 3, pp. 77-95
• Grzegorczyk, Andrzej (1953): Some classes of recursive functions. Rozprawy Matematyczne, Volume 4, pp. 1-45
• Grzegorczyk, Andrzej (1953): Konferencja logików. My?l Filozoficzna, Volume 1, Issue 7, pp. 340-349
• Grzegorczyk, Andrzej; Kuratowski, Kazimierz (1952): On Janiszewski's property of topological spaces. Annales de la Société Polonaise de Mathématique, Volume 25, pp. 69-82
• Grzegorczyk, Andrzej (1951): Undecidability of Some Topological Theories. Fundamenta Mathematicae, Volume 38, pp. 137-152
• Grzegorczyk, Andrzej (1950): The Pragmatic Foundations of Semantics. Synthese, Volume 8, pp. 300-324. Republished in Przecki, Marian; Wójcicki, Ryszard (editors) (1977): Twenty-Five Years of Logical Methodology in Poland. D. Reidel, Boston & PWN-Polish Scientific Publishers, Warszawa, pp. 135-164
• Grzegorczyk, Andrzej (1948): Próba ugruntowania semantyki j?zyka opisowego. Przegl?d Filozoficzny, Volume 44, Issue 4, pp. 348-371