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 Łukasiewicz'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 It is important to notice that a role of both Grzegorczyk and Rasiowa for earlier unpublished work in computable analysis by Stanisław Mazur, a member of the Polish United Workers' Party who was a member of communist Poland's Parliament in 1947–1956 and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 Czesław 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 Jaśkowski'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 Białystok'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 rozstrzygalności (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 Kotarbiński's reism. He proposed an interpretation of the Leśniewski 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.

Furthermore, he contributed a series of writings in philosophical anthropology and ethics in the methodological framework of philosophy which he named rationalism open for values, which was basically no more than a mixture of the Christian theology and the selected teachings of the Lwów–Warsaw school, and for which he developed the selected ideas of the Marxist thought in the context of theology and philosophy. The best example of the latter context is his book Mała propedeutyka filozofii naukowej (Short propedeutics of scientific philosophy) issued by the aforementioned pro-communist Catholic publisher Instytut Wydawniczy "Pax" on the eve of the fall of communism in Poland in December 1989, when the Marxist-Leninist references were removed from the July 1952 Constitution of the Polish People's Republic and the country was renamed to the Republic of Poland, the dissolution of the PZPR in late January 1990 by its last First Secretary Mieczysław Rakowski and the dissolution of the Warsaw Pact on 1 July 1991 in Prague. However, Grzegorczyk yet in his 1989's book fully and fervently developed the crucial ideas of the Marxist ideology, where in particular the name "scientific philosophy"' is not equal to philosophy of science understood as the standard philosophical discourse and is reserved to the unique significance of the ideological deformation of philosophy. The ideological misuses of the word "scientific" in the context of Marxism-Leninism are well-known: "scientific world view" is equal to the Marxist world view, "scientific religion" is equal to the Marxist-Leninist atheism, "scientific art" is equal to socialist realism also known as socrealism, while "scientific philosophy" is simply the synonym of both dialectical materialism and historical materialism – just making use of the term "scientific" was making the ideology. Indeed, similarly to ecumenism between different religions, this book, which met a devastative criticism by the Roman Catholic clerical scholars such like a Salesian metaphysicist Andrzej Maryniarczyk of the KUL, under the brightly banners of "pure philosophy" and "uniform approach to philosophy which can be the basis of teaching" proposed no more than an ideological uniformity of philosophy without a division onto the subjective branches such like Thomism, Existentialism or Platonism in order to get the alleged advantage of "maximal objectivity" of philosophy, where Grzegorczyk approaches philosophy as merely a convention based on the alleged values such like "seriousness" and "sincerity" claimed by him as the determinants of quality of philosophizing. He did not give the explicit definitions of these alleged merits, but provided some crucial hints on what is "serious and sincere philosophy": the most general thoughts and insights concerning the world and human life, systematic cognitive activity leading to construction of a philosophical world view, the philosophical views of brilliant writers and even scholars of other disciplines who in the margins of their specialty sometimes made interesting general considerations, amateur general reflection on any topic, professional statements which give very systematic and well exhaustive reflection, texts printed in special philosophical journals, and teachings of university professors. He introduced three categories of philosophers: amateur, traditionalists and professionals, where the only latter one can be performed in the "scientific" way, that is with a help of natural science and mathematics, but he did not make a difference between a speculation attributed to amateurs and a theoretical approach attributed to philosophy understood as an academic discipline, and, for this reason, made philosophy a part of the collectivist people's culture. The crucial element of his approach is the concept of reality divided onto observable reality formed by "objects (things) of different properties, joined by relations, creating different sets" by learning of which "we attribute certain properties to them and combine them into sets", and unobservable reality "composed of some separate things (...) with certain properties", where he attempted to apply his variant of dialectical materialism to justify an undefined materialistic spiritualism usually attributed to the Marxist-Leninist atheism. Comparatively, in his other book Życie jako wyzwanie (Life as a challenge), published already in 1993 when the primary socio-economic-political transformations were just implemented in the restored Republic of Poland almost free of the fallen Soviet occupation, he presented an unambiguously liberalized ontological declaration 'the world (...) contains objects (...) having various properties, connected by various relations, and belonging to various sets'. From a general philosophical point of view, this book resorted to all the basic notions such like good and evil as the links of the first semantic chain, that is the central ontological notion of an object with the notion of a state of affairs, and his analysis went further precisely along the second ontological chain, that is towards the notions of case and act. In general, the whole book reflected its author's full both conformity with and loyalty towards the economic-political transition, started with the 1990 Polish presidential election which made the leader of the anti-communist opposition and the 1983 Nobel Peace Prize laureate Lech Wałęsa the first freely elected President of the Third Republic of Poland, although until 2007 Lustration in Poland the Polish state authorities did not require a political either purge or thaw or at least a humble self-criticism among the Polish academia, and, moreover, until 2005 the successors of the PZPR – the Social Democracy of the Republic of Poland (SdRP) in 1991 and the Democratic Left Alliance (SLD) in 1999 – governed by Aleksander Kwaśniewski who won the 1995 presidential elections over Lech Wałęsa to be the 3rd President for 1995–2005 and to be instrumental in introduction of Poland into the North Atlantic Treaty Organization (NATO) in 1999 and the European Union in 2004.

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 Wałęsa, 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 Jr., 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 Odpowiedzialność 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 Więź with death of the Primate of Poland Cardinal Stefan Wyszyński 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 human history. 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 Gdańsk under the leadership of Lech Wałęsa, 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.

He had never attempted to be a favourite academic teacher, he openly avoided any close cooperations with his students and deflected their attention by lack of will to co-authorship with a parallel will to interact with them for knowing more about them, he preferred a bold individual research work although he had multiple collaborations. He was hungry for knowledge on world and people, such like in the "ecumenic dialogue" with the Soviets and the various Polish communists, but was never able to fully follow any concrete system, had never joined any political party, and was focused merely on collecting information only for construction of a possible either critique or irony. Even those very few students who decided to prepare their doctoral dissertations under his supervising, never felt to contribute in the work of their mentor and to continue his intellectual traditionalism, because emergence of an academic school dedicated to development of his heritage in mathematics, logic, ethics, philosophy was impossible by his attitude. He was able to attract the attention of students extremely rarely, the facts say for themselves in the best way – over more than six decades of his academic work, he was able to produce no more than three doctoral students with 10–20 years of difference between the graduations, he supervised a computer scientist Stanisław Waligórski's thesis in mathematics Equations in closure algebras and their applications (1964), a Polish-Jewish philosopher and mathematician Stanisław Krajewski's thesis in logic Nonstandard classes of satisfiability and their applications in investigating of some extensions of axiomatic theories (1975), and an aesthetician Bohdan Misiuna's thesis in ethics Philosophical analysis of disgust phenomena and its axiological consequences (1992).

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 Łukasiewicz. When Suchodolski organized interdisciplinary meetings for professors in the Palace of Congresses and Conferences of the PAS in Jabłonna 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.