Towards Scientific Metaphysics, Volume 1
In the Circle of the Scientific Metaphysics of Zygmunt Zawirski. Development and Comments on Zawirski’s Concepts and their Philosophical Context
Table Of Content
- Title Page
- Copyright Page
- Outline of metaphysical research in Polish academic circles at the turn of the 19th and 20th centuries
- About the author
- About the book
- Citability of the eBook
- Part One: The philosophy of Zygmunt Zawirski
- 1 Philosophy of natural science and the philosophy of nature
- 1.1 Axiomatization of deductive theories
- 1.2 Epistemological foundations of natural science
- 1.3 Analysis of time, space and cosmology
- 2 Logic and methodology of science
- 2.1 Methodological problems in science
- 2.2 Many-valued and intuitionistic logic and their applications in physics
- 3 Meta-philosophy
- 3.1 Ontological structure of reality
- 3.2 Relations between the theory of reality and metaphysics, and science
- 3.3 The problems of scientific metaphysics
- Part Two: Critical remarks and comments on the concept of the scientific metaphysics of Zygmunt Zawirski
- 1 On problem-rising axiomatization of mathematical natural science
- 2 Justification in natural sciences and metaphysics
- 3 Disputes over the synthesis of particular sciences
- 4 On the relationship between science and metaphysics
- Part Three: Selected works of Zygmunt Zawirski
- 1 The significance of many-valued logic for epistemology and its connection with the probability calculus221
- 2 Importance of logical and semantic research for the theory of modern physics227
- 3 Comments on the natural sciences method232
- 4 Toward the analysis of the scientific synthesis233
The works undertaken in the field of logic, methodology and philosophy of science, and in particular the philosophy of nature and natural science testify to a solid preparation for the fundamental task of developing contemporary scientific philosophy. The emerging mathematical natural science did not have those possibilities that emerged in the 20th century and which Zawirski used. In the development of scientific metaphysics, he took into account both the achievements of modern logic and mathematics as well as physics. Zawirski builds scientific metaphysics by referring to empiricism, to broadly understood experience. Modern metaphysics should meet high standards of precision and uniqueness, which is why Zawirski attempts to apply the axiomatic method to both the analysis of the theory of physics and the scientific metaphysics.
The study of the concept of scientific metaphysics aims not only to show the historical importance of the achievements of native philosophy, but above all to pay attention to their timeliness. Conducted research on philosophy and the general theory of reality developed within its framework are to show how this project proposed by Zawirski was implemented by him, and to what extent it is still valid, due to the continuous development of natural science.
The first volume consists of three parts. In the first one, I discuss the most important areas of Zawirski’s colloquial research, highlighting many detailed issues that particularly demonstrate a very good knowledge of not only the ongoing methodological discussion outside of Poland, but also a very good knowledge of physical theories: relativity theory and quantum mechanics. Reflecting on the second law of thermodynamics, Zawirski developed the concept of time cycles, which is now one of the basic concepts of understanding the history of the Universe. Zawirski also notices that the content of new physical theories changes the understanding of many scientific concepts such as: causality principle, space, time, irreversibility of natural phenomena, etc. The leading issue, which Zawirski studies, is the possibility of applying the axiomatic method to the analyses of particular sciences. Zawirski was undoubtedly the first philosopher who used the axiomatic method in physics.←23 | 24→
When presenting the first part one cannot forget about Zawirski’s important achievements in the field of logical and methodological research. Zawirski developed many-valued logic, which he tried to use to develop quantum mechanics. In turn, the analysis of the results of methodological research is important because they have become recognized as permanently useful for the achievements of the philosophy of science. At the end of the first part we will go to the central issue of the two-volume monograph – the scientific metaphysics developed by Zawirski. At this point, I will discuss Zawirski’s views on the relation of scientific metaphysics to particular sciences and classical metaphysics and his position on the possibility of developing a synthesis of particular sciences.
In the second part, the previously discussed detailed problems of Zawirski’s philosophy will be subjected to critical analysis, taking into account parallel discussions in Polish academic circles. Confronting the results of Zawirski’s research with other methodological proposals and positions in the field of the possibility of synthesis of particular sciences and the development of scientific metaphysics, it will be possible to evaluate all of his scientific achievements and show them significantly for contemporary research. In this part we put a lot of questions-problems for which we will seek answers. We will be interested in the following issues: how and – if yes – whether all the results of Zawirski’s research in logic and methodology are in line with important scientific achievements? Is and – if yes – to what extent the building of scientific metaphysics can be recognized as a current research program? How much is the axiomatization of scientific theories still an important research venture? To what extent is it possible to build scientific metaphysics as a deductive system? Answers to the above questions will serve to compare the scientific results and scientific conception of metaphysics worked out by Zawirski with the results of scientific research of Benedykt Bornstein in the quest for the elaboration of an algebraic and geometric concept of scientific metaphysics.
In the third part, so as to document Zawirski’s research route, I will present some of his works from the most interesting areas of logic, methodology and meta-philosophy.
When analyzing Zawirski’s results of scientific research, it should be stated that he was a philosopher with a broad spectrum of interests in the ←24 | 25→philosophical assumptions and consequences resulting from the development of natural sciences. So as to arrive at a more complete illustration of his scientific involvement, I have made up my mind to present his biographical data below. This is important because it allows me to show – in the form of a critical analysis – many of his achievements and stages of the research carried out by him.
From the biography of Zygmunt Zawirski
Zygmunt Michał Zawirski was born on September 29, 1882 in Podolia in Berezowica Mała next to Zbaraż and died on April 2 in Końskie23. He was a son of Józef and Kamila Zawirska. Zygmunt Zawirski was a better than average learner24 in the 3rd Gymnasium in Lvov from 1893 till 1901. From 1901 till 1906 he studied at the Philosophical Faculty of Jan Kazimierz University in Lvov, his mentor being Professor Kazimierz Twardowski (1866–1938). During his studies he also attended other lectures delivered, among others, by Mścisław Wartenberg (1868–1938) on issues concerning metaphysics after Kant and Witold Rubczyński (1864–1938) on history of Greek philosophy. He also studied mathematics, physics and philosophy in Berlin (1910) and in Paris (1910). During his Berlin studies he attended the lectures delivered by Carl Stumpf, Georg Simmel and Alois Adolf Riehl.
In 1904 Zygmunt Zawirski became one of the founder members of the Polish Philosophical Society, originally founded by Kazimierz Twardowski in Lvov. He was granted the PhD degree in philosophy in July 1906 on the basis of his work entitled O modalności sądów, which was written under Professor Twardowski’s supervision. Zawirski belonged to the ←25 | 26→first generation of Twardowski’s students. Therefore, he is recognized by historians of philosophy as a co-founder of the famous The Lvov-Warsaw School (LWS).
After his graduation, he first (up till Septemebr 1906) began to work in the 4th Gymnasium25 in Lvov: since 1907 commenced his career as a teacher of philosophy, mathematics and physics in Gymnasium no.2 in Rzeszów. In January 1911, having completed his studies in Berlin and Paris, he started teaching in Gymnasium no.3 in Lvov. He also started to cooperate with a journal titled “Ruch Filozoficzny” and wrote many reports on books and reviews appearing in renowned French and German philosophical magazines such as “Revue Philosophique de la France et de L’étrange”, “Revue de Métaphysique et de Moral” and “Archiv für Geschichte der Philosophie”. Apart from his reporting activities, he participated actively in the meetings of the Polish Philosophical Society in Lvov, presenting many papers developed in the form of scientific articles or more advanced writings. Zawirski achieved the first prize in the 3rd competition of “Przegląd Filozoficzny” in 1912 on the basis of his work entitled Przyczynowość a stosunek funkcjonalny. Studium z zakresu teorii poznania. In this work he demonstrated that it is impossible to reduce completely the notion of causality to the notion of functionality.
The period of the World War I resulted in a one-year-long gap in the scientific activity of Polish researchers. At that time Zawirski had left Lvov and returned in 1915 only to intensify his scientific activity. The subject of his interest included the following problems: hypothesis of constant returns of all-matters, inductive metaphysics, relations between metaphysics and science, detailed issues from logic and their significance in mathematical and natural research. The research conducted by him had an impact on the development of his opinions that were later expressed in the paper entitled Refleksja filozoficzna nad teorią względności (1920), and the following treaties: Relatywizm filozoficzny i fizykalna teoria względności (1921) and Metoda aksjomatyczna a przyrodoznawstwo (1923), which were the ←26 | 27→products of earlier written, but unpublished, writings such as O stosunku metafizyki do nauki (1919) and Nauka i metafizyka (1920).
Since 1922, till 1928, he used to be lecturing at Politechnika Lwowska, leading courses in logic, logic basis of mathematics as well as the courses dealing with natural history, theory of deduction, history of philosophy and psychology. One year later he also started delivering lectures at the National School of Pedagogy, improving his educational experience and skills as an academic teacher. He combined his didactic with his scientific activity.
During the 1st Polish Philosophical Convention (Lvov 1923), so as to share the research he used to carry out as well as the results concerning the implementation of axiomatic method applied in the history of nature, he presented a paper entitled Współczesne próby aksjomatyzacji przyrodoznawstwa matematycznego i ich znaczenie filozoficzne. In the same year he wrote a thesis entitled Metoda aksjomatyczna a przyrodoznawstwo and presented it to Władysław Heinrich (1869–1957). This work became the basis to initiate the proceedings for the qualification as a university professor at the Jagiellonian University, which was completed in 1924 with the defence of his postdoctoral thesis entitled The Relations between Many-valued Logic and Probability Calculus (A Habilitation Lecture).
In the period between 1928 and 1936, Zawirski began to cooperate with the University of Poznań. Professor Władysław Mieczysław Kozłowski (1858–1935) had retired and Zawirski was appointed a lecturer for the courses in the theory and methodology of sciences at the Humanistic Faculty; since August 1, 1929, he began his work as an associate professor at the Faculty of Mathematics and the History of Science. The classes led by Zawirski had a good reputation among students. He was interested in students’ access to the basic philosophical works which were the subjects of his lectures and seminars. Then, he gathered valuable literature in his department, which was destroyed by the Nazis during the World War II. During his seminars, his students read such seminal works as Hume’s Badania dotyczące rozumu ludzkiego [Research Concerning Human Mind] or Hilbert’s Theoretische Logik. During his lectures, Zawirski focused on the philosophical problems of the history of nature, basic problems of mathematics, issues of epistemology as well as the theory of classes and oncoming relations.←27 | 28→
Zawirski got in close touch with his master, Kazimierz Twardowski, in the period of his activity at the University of Poznań. He used to send him his reports and/or reviews of books for the periodical “Ruch Filozoficzny” edited by Twardowski. He also gave lectures during the meetings of the Poznań Society of Friends of Sciences, which were later summarized in the PTPN Summaries. He participated in the 7th International Congress of Philosophers in September 1930 in Oxford where he presented his paper entitled On Indeterminism in Quantum Physics, published in the PTF Visitor’s Book (1931).
The period of work for the University of Poznań is the most important stage in his scientific life. His work entitled L’évolution de la notion du temps was awarded the first and very prestigious prize in the Rignan’s competition in 1933, announced by the Italian magazine “Scientia”. This report was published only in 1936 by the Publishing House of the Polish Academy of Skills and Sciences, but earlier it had been summarized in the magazine “Scientia”. His work was not translated into Polish in 1936. Therefore, its Polish summary entitled Rozwój pojęcia czasu was published in “Kwartalnik Filozoficzny” in the same year.
Zawirski was nominated as a full professor in 1934. He stayed two years more at the Faculty of Mathematics and Natural Sciences where he was the Dean and the Chair of the Department of Theory and Methodological Sciences, being an active member of scientific life internationally. He participated in the 8th International Philosophical Congress in Prague (1934) and presented a paper entitled Znaczenie logiki wielowartościowej dla poznania i związki jej z rachunkiem prawdopodobieństwa. He also participated in the 9th Congress in Paris in 1934 and presented a paper entitled O stosunku logiki wielowartościowej do rachunku prawdopodobieństwa. In the same year he welcomed members of the International Convention of Thomistic Philosophy held in Poznań instead of absent Michał Sobecki, the President of the Poznań Philosophical Society. Zawirski also participated in the 1st (Paris, 1935) and the 2nd (Kopenhagen, 1936) Congress of Scientific Philosophy where he presented a paper entitled O zastosowaniach logiki wielowartościowej w przyrodoznawstwie. He participated in the 3rd Polish Philosophical Convention in Cracow in 1936, where he presented a paper entitled W sprawie syntezy naukowej.←28 | 29→
Nearby the end of his scientific work at the University in Poznań, he was awarded an honorary doctorate by the University of Poznań and the Faculty of Mathematics and Natural Sciences on November 12, 1936 and accepted it on November 18, 1936 from President Ignacy Mościcki.
He was asked by Władysław Heinrich in 1935 to chair the faculty after Tadeusz Grabowski (1869–1940). Zawirski accepted it and as a full professor he started his work since January 1, 1937 at the Philosophical Faculty. Later, after its division, he worked at the Faculty of Mathematics and Natural Sciences. In the period between 1938 and 1939 as well as between 1945 and 1946 he was the Dean of this Faculty.
He took over the editorial office of the “Kwartalnik Filozoficzny” after Władysław Heinrich in 1936. In the period between 1938 and 1945, he was the President of Cracow Philosophical Society and gave papers entitled, among others, O działalności naukowej prof. Kazimierza Twardowskiego (1938) and Materializm dialektyczny a logika matematyczna (1947). He gave two lectures at the University in Bucharest in 1938 entitled Science and Philosophy and On the Notion of Time. In the period between 1938 and 1941 he worked on Słownik filozoficzny, following the model presented in Schmidt’s Taschenbuch der Begriff und Denker (1934) and Thormeyer’s Teubners kleine Fachwӧrterbücher – 1930. Unfortunately, the censorship stopped the printing of the dictionary copies in 1948. A manuscript of this dictionary survived in the Polish Academy of Sciences Archives and only some terms were published in “Przegląd Filozoficzny – Nowa Seria” (1993).
The Nazis pacifist action “Sonderaktion Krakau” against the Polish researchers and scientists took place on November 6, 1939. Zawirski was outside Cracow on this very day and due to it he barely avoided transportation to the Nazi concentration camp in Sachsenhausen. During the World War II he participated in the clandestine academic teaching. After World War II he was a full professor at the Jagiellonian University. He was appointed a chairperson of the Cracow Philosophical Society since 1945.
Zawirski was very active in the scientific life in the period between 1945 and 1948. At that time his works were published as the result of his long standing research. Some of them were, for example: Geneza i rozwój logiki intuicjonistycznej (1946), O współczesnych kierunkach filozofii (1947). When traveling to Zakopane to take part in the Philosophical Conference ←29 | 30→in winter 1947, a luggage with two manuscripts: O metodzie naukowej and manuscript of Patristic Monography26 were stolen from him.
Zawirski prepared a written speech for the 10th International Philosophical Congress in Amsterdam in 1948, but unfortunately he did not manage to present it. First of all the works of the manuscript reconstruction, and the work undertaken that year, overstrained his organism, moving toward an unexpected catastrophe. Zawirski died suddenly at his son Kazimierz’s home in Końskie.
Zygmunt Zawirski by his didactic and scientific work inspired many Polish logicians and philosophers. The following students, among others, wrote their diploma works under his guidance or worked in these fields: Józef Maria Bocheński (1902–1995), Andrzej Grzegorczyk (1922–2014), Zygmunt Spira (1911–1942?) and Roman Suszko (1919–1979) and he was closest to the last two ones.
Admittedly, Józef Bocheński, listed above, did not write any work under Zawirski’s supervision. However, being a student in Gymnasium no. 4 in Lvov, before he graduated from it in 1910, he had participated in Zawirski’s maths lessons. Bocheński describes Zawirski in Wspomnienia as a passionate teacher, who can be easily put into contemplative reflections. It can be assumed that Bocheński’s interests into mathematics and logics were born during Zawirski’s lessons. The second student, mentioned above, Andrzej Grzegorczyk, studied at clandestine classes at the University of Warsaw. He completed his studies in 1945 at the Jagiellonian University achieving an MA degree in philosophy and defending his work on Leśniewski’s ontology and Kotarbiński’s reizm under Zawirski’s supervision. However, in the following years, in the period between 1946 and 1948, Grzegorczyk was Władysław Tatarkiewicz’s assistant and secretary of “Przegląd Filozoficzny”.
Zygmunt Spira was interested in the natural history sciences, methodology and metaphysics. As a twenty-year-old student of the Jagiellonian ←30 | 31→University, he wrote a letter to Albert Einstein in 1931, asking him about the relations between the theory of relativity and some of Berkeley’s and Kant’s concepts. When answering the question, Einstein explained that the notion of relativity got the physical meanings only when, after one’s having sought philosophical inspirations, one could find them in Leibniz’s or Mach’s works. Spira wrote his PhD dissertation at the Faculty of Philosophy at the Jagiellonian University under Zawirski’s supervision. He published his first article entitled Mechanistyka ewolucyjna Kanta w świetle jego przedkrytycznej metafizyki in “Kwartalnik Filozoficzny” 14(1937). He was interested in methodology and theory of learning presented in Carl Popper’s work titled Logik der Forschung. A result of the research done by Spira was a work entitled Uwagi nad metodologią i teorią poznania Poppera unpublished during his life time. The first part of this work was published in 1946 in “Kwartalnik Filozoficzny”. The second part vanished in the backstreets of the Cracow ghetto in 1942. Spira was a well-promising philosopher; however, the events of World War II made him share the fate of the Cracow Jews – he found himself in the ghetto where he died.
Roman Suszko is one of the most outstanding professionals of Polish logics. He began his studies in Poznań in 1937 and completed them at the clandestine classes in Cracow in 1945 under the direction of Zygmunt Zawirski. He wrote his MA work entitled Dorobek logiki polskiej on logics, and became Zawirski’s youngest assistant running Zawirski’s designed seminars in philosophy at the Jagiellonian University. He arrived in Poznań in 1946 and worked for the Department of Theory and Methodology of Sciences led at that time by Kazimierz Ajdukiewicz. He gave lectures on mathematical logics. He defended his PhD work in 1948 based on the systems of axioms and the theory of definitions written under the supervision of Ajdukiewicz and published in “Kwartalnik Filozoficzny” in a series of two papers. The first one was entitled O analitycznych aksjomatach i logicznych regułach and the second one had the title Z teorii definicji (both parts, when translated into English, appeared in the book entitled: On Analytical Axioms and Logical Principles. From Theory of Definition published by Polskie Towarzystwo Przyjaciół Nauk, Poznań 1949). In this dissertation he offered a general theory of definitions for elementary systems. He also defended his post-doctoral thesis entitled Canonic axiomatic system, which appeared in “Studia Philosophica” 4(1949/1950) in 1951.←31 | 32→
He has worked at the Faculty of Philosophy at the University of Warsaw where he achieved a degree of associate professor in 1959. His important scientific achievements include works from such areas as the theory of models and the theory of consequences, which appeared in the volume entitled Sentential Logics (1958), and which had an impact on the development of the paradigm that created one’s possibility to enter the realm of metalogic. He was one of the first logicians in the world who used the theory of models to investigate problems beyond mathematics. Suszko used this theory in the analysis of the development of cognition and the formal logics used in this research named diachronic formal logics.
The most important Suszko’s achievement was the form of logics developed by him, later named non-Fregean Logic. The logic is a generalization of the classical logics. Its particular example is the classical calculation of sentences and predicates, valued completion of Łukasiewicz’s logics and some modal logics. Considering its extensionality and dual value, it should be stated that non-Fregean logics is the weakest one, while the classical logics is the strongest one.
* * *
Zawirski left behind a rich philosophical heritage, which until now have not been fully critically examined. Without undertaking such a maximal task, I will only pay attention to his attempts to develop scientific metaphysics, referring to the results of scientific research obtained in the first half of the 20th century, which remains a valid and important contribution to the understanding of the natural reality we are surrounded by.←32 | 33→
23 Zygmunt’s father, Józef Zawirski (actually Jan Gieysztor-Buchowiecki) after the collapse of January Uprising hid himself under the assumed name in the Austria-Hungarian Part of the partitioned country. Zygmunt’s mother née Strońska got married to Józef Zawirski in 1869. They had 10 children. Zygmunt was their seventh child. Zygmunt’s nephew was Jerzy Kalinowski (1916–2000), a professor of philosophy at the Catholic University in Lublin.
24 See: Michał Sepioło: Zygmunt Zawirski (1882–1948). Bibliografia, in: Zygmunt Zawirski, O stosunku metafizyki do nauki, (Warszawa: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego, 2003), pp. 253–265.
25 A gymnasium was at that time a type of school with a strong emphasis on academic learning, and providing advanced secondary education.
26 Roman Ingarden in the work Wspomnienia o prof. Zawirskim (1948) wrote that the author managed to reconstruct his stolen works.
Zawirski was interested in the development of natural sciences and modern mathematics. While trying to answer the questions stated and/or the philosophical matters discussed at that time, he has left many original works in some ways connected to one of these theories. In his numerous works, Zawirski presented new philosophical implications derived from these theories.
The axiomatization of deductive theory is the last stage of its development27. The axiomatic method does not increase the content of theory. For deductive reasoning, it is completely out-of-question whether what you deduce from is something obvious or not. Whether or not a given assertion is an axiom is determined by whether it can be proved by other existing axioms. Deductive reasoning based on principles which often obviously contradict one another may turn out to be an extremely important scientific achievement, as evidenced by the existence of non-Euclidean geometries28. It is also ←33 | 34→not unusual that science often deviates from the ordinary meaning of colloquial speech, creating its own language and its own symbolism.29 According to Zawirski, some extreme formalizations of deductive theories may lead to absurdity, when it is demanded not only to forget what the individual symbols mean and remember only about the rules of the existing counting procedures, but also when it is declared that the symbols we operate have no meaning. In such situations, we have to do with misunderstandings, because by appropriate selection of axioms we create a certain type of objects that we deal with in a given deductive theory, and the meaning of the symbols we use each time boils down to existing axiomatic relations30.
Understanding the essence of the axiomatic method in the theory of deduction can be expressed in three important areas of its application. First of all, the set of basic concepts and principles must be complete, which means that it cannot lack anything that would be needed to derive theorems of the theory and at the same time there cannot be anything that would have an effect on the theorems of a given theory. Only the set of axioms with the basic concepts introduced in them should define the subject of a given deductive theory. Second, the axioms do not have to be obvious; on the contrary, they can express something incompatible with the segment of obviousness. Thirdly, the terms or symbols we use do not have to have an understandable intuitive sense31.←34 | 35→
According to Zawirski, the axiomatic method leads to the demarcation of the formal and logical side of cognition from the overall epistemological basis. The use of the axiomatic method is not strictly connected either with the obviousness of the adopted principles or with the intuitive meaning of the terms used. In Zawirski’s opinion32, the use of the axiomatic method is not at the same time a symptom of disregarding the intuitive sources of our cognition, without which science would not have arisen at all. What’s more, the results that this method leads to cannot be affected by some epistemological issues, such as the nature of the courts of mathematics.
The axiomatization of deductive theories brings definite benefits33. One of them is the search for an arrangement of axioms, which remains related to the search for those properties of objects on which the deductive theory really rests. These searches lead to a deeper penetration into the essence of a given theory. Another advantage of using the axiomatic method remains its role as an economic measure in our thinking34. The axiomatic method makes it possible to transfer whole theories from one domain to another, if both these theories have the same group of axioms. We save the time needed to carry out the evidence of the theorems of the second theory35. Moreover, axioms of a certain deductive theory can be used to obtain the axioms of a new theory, or by rejecting certain axioms, thus creating more general theories, or by denying certain axioms and introducing in their place axioms contrary to the first. An example of the first type can be projection geometry in relation to metric geometry, and an example of the second type – non-Euclidean geometries originating from Euclidean geometry36.←35 | 36→
The axiomatic method can be used as a reliable heuristic agent in scientific research. An example of this can be the introduction of completely new concepts to the theory of deduction. Instead of looking for a set of axioms and concepts that are already ready for a given theory, one can look for new concepts that satisfy certain conditions, i.e. adopted axioms.
At the beginning of the 20th century, it became obvious that some of the natural sciences constitute the area of applied mathematics. If the methods of mathematical research are deepened by their axiomatization, it has to affect the natural sciences themselves. The axiomatic method, as Zawirski notes, is applicable to natural research, for which it is not indifferent what a reason is, or how to observe phenomena. The observation concerns an accurate quantitative measurement, and the reason is nothing more than an expression of certain solid quantitative relations between facts. The laws of nature, that express constant relationships of consequences and contemporaneity, must be checked if only they contain hypothetical elements. In addition, we strive to ensure that the laws of nature can be linked to a system free of contradictions, giving the opportunity to develop a unified scientific theory. In the natural sciences, therefore, attempts are made to link newly observed facts with existing ones.
Zawirski assumes that the inductive method of empirical sciences, constituting an inversion of deduction used by mathematics, has significance only for heuresis. In the natural sciences, we create a systematic system of acquired messages, which is based on a deductive course, as illustrated by a concrete empirical theory, in which general laws result in specific laws, and from them specific applications of them. It should be noted that physics, being the basis for mathematical natural science, uses seductive methods of its departments, although its laws have been acquired through the inductive method. The laws of physics can be expressed in mathematical symbols and usually take the form of differential equations. Mathematical symbols can be assigned to certain specific meanings, certain observed phenomena or certain quantities that can be measured. The same applies to the use of geometry in natural science. We apply this geometry, which is the geometry of a given area of reality, and as such must also be included in the natural sciences37.←36 | 37→
Due to the fact that physics is not a closed science, and its development is not free of certain surprises, its axiomatization may be subject to constant changes. Each time the mathematical symbols of physics must be selected so that some empirical data can be subordinated to them, but this never interferes with the attempts of axiomatization of physics. By penetrating deeper and deeper into the accepted axioms, we gain an ever-more comprehensive understanding of the essence of scientific thinking and we are better aware of the unity of our knowledge.
Physics axioms, for many representatives of this science, can be considered sufficient to capture all physical phenomena, but they certainly cannot be regarded as a complete elaboration of the axioms of natural science. The change of the axioms of mathematical natural science proceeds in parallel with the development of theoretical physics and with the history of efforts to obtain the largest number of deduction-based detailed laws explaining natural phenomena and draw from them sets of the simplest ever rules, logically ordered and transparent38.
The proper philosophical problem arises at the stage of axiomatization of natural science, where, apart from the axioms of physics, in which particular expressions applied to the experience are associated with mathematical symbols and, additionally, when the conditions and bases on which the use of these symbols for experience are to be based. According to Zawirski, it was assumed that the laws of logic and mathematical analysis exist alongside the general principles of cognition, which natural research must follow and on which only the application of mathematics to natural science can be based. Search for the so-called constitutive principles of mathematical natural science was one of the main goals of Kant’s critique of pure reason. Immanuel Kant subjected the study to a sustainable framework, the principles on which all natural laws must be based. The research itself was based on the assumption that the distinguished constitutive principles must be obvious, intuitively certain and refer to the necessity of thought. Consequently, constitutive principles must be such a priori rules, which further nature research cannot in any way violate. Kant included to ←37 | 38→the constitutive principles of natural sciences the assumptions about the Euclidean character of space and the absolute character of time, the lapse of which remained independent of the reference system. The emerging new axioms of natural science, transform Kantian aprioristic forms as the fundamental concepts of natural science. Naturally, the dynamic principles of natural science are also subject to change; and, together with them, the fundamental concept of the principle of causality39 closely connected with the concept of time40.
At the beginning of the 20th century, physicists were aware of the great transformations regarding the understanding of space, time and matter, but they were not able to cope with the problem of the relation of physics to geometry. Physics for Hilbert and Weyl, thanks to the axiomatic method, becomes a kind of geometry. The adoption of such an understanding of physics requires explanation, since it cannot be reduced only to an unambiguous assignment of the experience of certain mathematical symbols to the facts, which for Moritz Schlick is already a sufficient account of the essence of natural cognition41. In turn, for Albert Einstein and Max Born, the transformations in physics are regarded as evidence of a change in geometry into natural sciences.
In the natural science, there was a dispute over whether physics became geometry or geometry became physics42. According to Zawirski, the existing ←38 | 39→dissimilarity of physics and geometry can be reconciled with each other, despite the existing difference between their objects and the methods used there43. Geometry constructs its objects, regardless of the concrete reality, and justifies its claims by deduction. In turn, physics deals with data subjects found in experience and formulates laws mostly by induction. However, when we strive to build a unified theory of a certain group of physical phenomena, the difference in the method used disappears44. At the moment of creating the theory, the rights acquired in the way of experience can be justified by deduction, and unless they can be deduced from previously accepted assertions, then they must be accepted in a given theory as axioms. The above case concerns only the stage of systematization, not heuretics, where the significant difference between physics and geometry is still not questioned. In physics, theorems can occur only because they correspond to certain facts of the experiment, despite the fact that they cannot be related to any previously known laws. In geometry, however, as generally in mathematics, although certain ideas of laws can be born under the influence of experience45, then such ideas cannot be introduced as geometrical assertions until they can be derived from the previously proven theorems.
According to Zawirski, the axiomatization of natural science is not an easy matter. After all, you cannot arbitrarily construct objects of physics, which are known to us only on the basis of descriptive features. According to Zawirski, we tend to assign univocally defined mathematical symbols to the objects of physics46. However, we act in such a way that first we consider the simplest, most typical and idealized phenomena and analyze the behavior of properly constructed objects only in terms of features strictly ←39 | 40→defined in a given section of physics, abstracting from other features. In this way, the analysis starts with the phenomenon of motion, and therefore the mechanics obtained the status of a strict science very early. Then, taking mechanics analysis as a pattern, similar results were obtained in other branches of physics, and so, among other things, Maxwell’s mathematical theory was created. In some cases, when attempts were made to combine several branches of physics into one theory, hypothetical factors were often referred to, specifying in advance their ownership and attitude to the characteristics of objects, or data assumed to be found in the description. This was the case in the case of the explanation of thermal phenomena by the movement of molecular particles in the kinetic theory of matter, or the reduction of light phenomena to electromagnetic phenomena. After completing these partial works, one could strive to create a unified scientific theory. However, as one can never have a guarantee that we will know all the properties of objects and their relations, and all possible ways of behaving in any conditions, therefore theoretical systematization is presented as a never-ending task, and thus the axiomatics to which such systematization leads, cannot have the character of eternal and inviolable truths47. Each time, in a system of mathematical laws created in the above manner, abstracted from the physical phenomena to which they can be assigned, we obtain the appropriate section of pure mathematics.
An important problem that attracted the attention of physicists was the geometry-based arrangement (“geometrization”) of physics. The use of the name “geometrization of physics” remains justified by the need to treat the time coordinate in relation to spatial coordinates, which means that the concept of change is subject to geometrical treatment. It also turned out that the components of the metric tensor, determining the metric relations in the Riemannian four-dimensional continuum, turned out to be identical to the components of the gravitational potential. This means that not only spatio-temporal relations, but also dynamic relations can be treated in a geometric way. In the laws of physics, apart from the physical meaning of the respective symbols, we obtain the representation of relations in a kind of ←40 | 41→four-dimensional continuum. It is worth noting that in differential geometry the same symbols were operated much earlier before it was noticed that they may also have physical meaning; later they were only identified with the components of gravitational potential.
Not only is it justified to talk about the geometry of physics, but also about treating geometry in a sense as a empirical science modeled on physics48. Geometry, only in the sense of researching the spatial properties of bodies, should be included in the natural sciences. The laws of geometry understood in this way must pass as a component of physics. There is close formal communication between the laws of body geometry and the laws of physics49. In Einstein’s theory of gravity, the laws of body geometry cannot be strictly separated from the laws of physics. In this theory, mathematical laws expressing the metric of space, and laws expressing the nature of the gravitational field are the same50. In isolation from the physical meaning of the symbols used in Einstein’s theory, the laws of geometry become nothing more than a branch of pure mathematics. According to Zawirski, if the laws of geometry are called laws of physics or laws of natural science, it is only because they are constructed so that natural phenomena can be unambiguously assigned to them. On the other hand, without natural research, ←41 | 42→we would never be able to choose the right geometry so that it would be suited to the sought-after, proper interpretation. The laws of axiomatically constructed geometry are at the same time the branch of natural sciences. Therefore, geometry becoming a natural science is a science in which laws are selected so as to express real relations in the existing world. However, claiming that physics is a science modeled on geometry, means that its laws, despite empirical origin, can be linked to axiomatically constructed deductive theory51.
Zawirski notes that the contemporary axioms of physical theories replace the old, intuitive and certain axioms with the ones, where the spatial continuum depends on the time continuum on the one hand and on the masses disposed in it on the other. Zawirski, while not undermining the importance of intuitive sources of our cognition in the form of obvious principles, without which the emergence of mathematics and physics would be impossible, notes, however, that the results we reach using the axiomatic method are the further consequence of the path we follow in cognition of reality, where common sense criteria often fail.
According to Zawirski, the axiomatic method, which was only sporadically used in philosophy, should be significantly acquired for the purpose of philosophical reflection on reality, similarly to the research in natural science. Thanks to this, natural science is enriched with the possibility of using the axiomatic method in its research.
According to Zawirski, nature remains the subject of natural science insofar as there is a specific material of empirical data that we obtain either by direct observation or by means of an account, in accordance with accepted axioms and based on measurements made52. Zawirski claims that the problem of the applicability of the set of axioms to the data of experience does not exist in the form in which it existed for Immanuel Kant, ←42 | 43→who selected axioms, so that empirical reality would apply to them. Kant accepted that forms of phenomena are something that our mind considers necessary, common and obvious. These forms are therefore subjective and therefore the universe considered in these forms is only a phenomenon. As Zawirski notes, the existence of the thing in itself is an assumption adopted by Kant, which he could not prove, but could not reject either. According to Zawirski, the space-time forms of phenomena, instead of becoming obvious to our mind, are mysterious to the mind and seem accidental to it. Therefore, there is no need to consider our mind as a co-creator of nature. The reality with which we are dealing, remains independent from a subject, not only as to its existence, but also as to its essence, which manifests itself in certain formal schemes.
Zawirski, however, does not consider, for example, that absolute realism should be attributed to the space-time continuum of general relativity theory, just as the quasi-spherical form of the world does not have such a reality, because the geometrical interpretation is obtained by appropriate mathematical formulas only by assigning empirical facts or results of certain measurements, and without this empirical content, mathematical formulas do not necessarily deserve their geometrical interpretation.
By rejecting apriorism and its phenomenalistic consequences in the Kantian sense, Zawirski does not reject the phenomenalistic consequences that contemporary physics comes to, regardless of philosophical considerations. The phenomenality of physics boils down to the claim that none of the attributes of material objects, including those of shape or body mass, can be attributed to existence in isolation from the conditions, in which an object reveals certain characteristics.
Some of the features revealed by objects can be included in such a general mathematical form that does not undergo any changes. Any mathematical form treated independently of these features, i.e. aspects of nature, can be given a different interpretation. However, the form that is the result of agreeing on all possible aspects of nature, presents itself as one of the possible constructions to which the sensual aspects of nature apply by accident, because this form does not seem to be of the shape necessary for the mind. Such a mathematical form, as long as it finds its reference to the adopted set of axioms in the field of natural sciences, should be regarded as something in which the nature of absolute reality ←43 | 44→is manifested53. The absolute reality can be treated here as an assumption adopted in many systems of natural philosophy which concerns one and the same world. All efforts of Copernicus, Galileo and Newton went in the same direction to capture this one, independent from our senses, reality. According to Zawirski, any allegations raised against such a determined striving to capture reality ultimately amount to misunderstandings54.
If the set of axioms is treated as a kind of symbolic definition of absolute reality by enumerating symbols of essential features, then the formal-logical system of assertions resulting from axioms can be considered as symbols of derivatives of this absolute reality. Derivative symbols are symbols of everything that results from the nature of absolute reality, as indicated by symbols of axioms. The admission of absolute reality is attested by existing specific laws, which on the one hand result from accepted axioms, and on the other hand do not depend on their empirical interpretation. Therefore, without paying attention to the intuitive meaning of symbols used to formulate axioms, the axiomatic method of mathematics shows us how to build a deductive diagram of the whole theory of natural science.
Zawirski notes that natural cognition does not exclude the possibility of possession by objects experienced sensually, apart from the properties available to measurements, properties that cannot be determined experimentally. In addition, natural cognition does not exclude the possibility of the existence of knowledge, and even remains indifferent to this knowledge, whether there is a completely different, separate world outside the world of sense objects, whose logical and formal order is reflected in the accepted axioms of natural science55. The existence of a reality that goes beyond the world of sensory objects, however, does not remain indifferent to minds prone to metaphysical speculation. The metaphysical search is directed ←44 | 45→toward the knowledge of the essence of being, and the sensual world often plays the role of a means leading to the discovery of the supersensitive world. The use of the axiomatic method in natural science indicates the possibility of building such a metaphysics that is based on experience and at the same time can preserve the nature of deductive theory.
For Zawirski, the application of the axiomatic method to solve metaphysical problems is the implementation of the old metaphysics’ search, to bring the whole reality out of one or several of the highest principles. The principles adopted in metaphysics would be presented to the human mind in such a way that all the rich and varied content of the cognized reality can be deduced from them. However, the axiomatic method applied in natural science does not lead to the knowledge of the real essence of this reality, but it only gives the possibility of symbolic recognition of it. The axiomatic method makes it possible to develop a certain closed view of the world without resolving issues that have been subject to metaphysical disputes. Based on the subject of positivized natural sciences, we obtain that the axioms of this natural science do not exclude a different interpretation of them. On the other hand, how to find this “right” interpretation is always a matter of a given metaphysical system.
If two different theories have a strict dependence in formal and logical terms, both can be reduced to a common way of treating them. Assuming that there is a certain commonality of their logical-formal side between the sensual world and the post-emergent world, it means that the given order of the one side corresponds to the specific order of the other one. According to Zawirski, in this situation, all metaphysical issues boil down to the content of the logical-formal schemes of the natural order, in order to be able to read from them the laws of the extrasensory world56.
Zygmunt Zawirski points out that every attempt to apply the axiomatic method to metaphysical cognition is usually supported on quite any assumption. In particular, he refers to the use of the axiomatic method in developing a scholarly picture of the world by Schlick and Eddington. For Schlick, cognition consists in assigning specific objects to the appropriate mathematical symbols, used in the axiomatic method, regardless of ←45 | 46→whether these objects are the so-called phenomena, or things in themselves. According to Schlick, if, apart from the phenomena available for our cognition, there are things in themselves then, while making an attempt to know the phenomena, we also know things in themselves, because “the sign of the sign is after all the sign of the thing marked”57. Zawirski disagrees with such a view, believing that assigning objects to symbols each time produces a concrete cognition, expressed in sentences with a certain meaning. If we use symbols for phenomena, we always get a specific content that we associate with specific symbols. On the other hand, because specific things are rich in content, the use of symbols to mark them does not deprive us of any interpretation58.
Eddington, in the work Space, Time and Gravitation59, points out that the concepts of new physical theories are treated first as axiomatic defined symbols, and only then we assign a particular sense to them60. According to Eddington, objects or physical phenomena, in addition to the mathematical form that can be attributed to them, have a deeper meaning. On closer familiarization through experience, objects turn out to be complexes of some of the simplest elements that cannot be defined. Each time, by building complex concepts from these indefinite elements, we bring something that is undefined to these concepts. In this way, we come to a series of concepts that are defined in form, but are not defined as to the content, and which we use to explain all properties of matter. As an example, you can enter the concept of a point-event. Initially, such a “point event” is considered to be the name of something that cannot be determined in ordinary speech, the name signifying a certain moment in a certain place of space. We realize that the “point event” is something that is outside the realm of human reason. In turn, the set of point events begins to be called the world. Then, to express that this world is four-dimensional, one should first notice the ←46 | 47→ordering of its elements, and this requires the use of the concept of interval, which, as the author notes, does not have to be treated as the equivalent of the real relationship between each of the two neighboring point events, but as something lying beyond the ability of our understanding. Finally, Eddington, arriving at the basic equations of the gravitational field without matter and with matter, allows himself to his own interpretation, in which he does not treat matter as a factor disturbing the gravitational field, but vice versa – he interprets the field disorder as matter61.
In Eddington’s interpretations of formal patterns, one can feel certain metaphysical tendencies that are very clearly related to the interpretation of the physiological processes of our brain. But does matter adopted in relativity by the coefficient gμν explain the processes of our thinking? Probably not. The coefficient gμν, like the interval mentioned above, contains an undefined element, defined in form, but not specified in content. The matter of the brain in its physical aspect is only a form, but the reality of the brain contains a certain content. Therefore, one cannot expect the form to be sufficient to explain this content62.
Zawirski, citing Schlick and Eddington, argues that the axiomatization of natural science can be used for metaphysical speculation. However, although he does not attach much importance to such attempts to use the axiomatic method for metaphysical purposes, he does not deny the validity of such attempts63. In terms of accepted physical theories, formulated mathematically, individual physics sections can be reduced to their common, mathematical treatment; in this way, for example, a vector algebra was created, allowing for the treatment of all directional quantities like force, speed or acceleration. The appropriate mathematical operations performed on vectors led physicists to formulate consecutive concepts such as gradient, potential or rotation. Further mathematical operations allowed to detect some invariant forms obtained from vector quantities and in this way a tensor account was created. It turns out that the search for mathematical laws of nature is a search for certain invariant forms.←47 | 48→
In physics, the same mathematical symbols subjected to an appropriate interpretation allow to define its individual sections. Metaphysical speculation in relation to the entirety of mathematical natural science attempts to behave similarly, but one should consider whether there is a key to the metaphysical interpretation of the basic concepts and principles of natural science. The applied axiomatic method in mathematical natural science can be used to more fully understand the existence of reality independent of our consciousness. There are, however, some reservations about this project, if we remain only in the area of knowledge in the field of physics. One should agree with Zawirski that due to the ignorance of the proper interpretation of these laws of nature, the mathematical form and the mathematical meaning of this form are of no interest to the physicist. Physical knowledge does not reveal absolute reality to us, it indicates it at most, and this is not the subject of physicists’ knowledge. The mathematical form of the laws of nature determines the subject of physics as much as it is possible to assign to it some sensual or sensory elements, which can be reached through the performed account. Sensory phenomena are not a starting point in the knowledge of the laws of nature, but they provide specific content to the mathematical forms of the laws of nature.
It should be noted that Zawirski accepts two assumptions on which the possibility of using the axiomatic method for metaphysical issues is based. The first assumption concerns the existence of a reality independent of the human mind, and the second assumption is that not all metaphysical problems can be solved through a different interpretation of the laws of the phenomenal world.
Against Zawirski’s acceptance of the existence of a reality independent of the mind, one can raise a charge of unlawful ontologies of concepts and violation of the intuitive meaning of names. The charge of formation of hypothetical notions remains valid, as long as it concerns those metaphysicists who, based on a simple analysis of concepts, without paying attention to experience, created any images of reality, while treating the concept of existence equally with other concepts at the same time. The solution to the problem of reality is also difficult when we develop conceptual constructions to interpret specific facts of the experience. The constructions we use have only a conventional value, they are only a useful fiction that ←48 | 49→we use for a specific cognitive purpose. However, the use of conceptual constructions leads to the breakdown of the unity of reality into the multitude of worlds. Zawirski notes that one cannot treat existence as a feature of any whatsoever concept, nor can one treat the notion of being as a qualitative sense inherent in sense qualities. In no way can it also be treated as a given quality64.
In various philosophical systems, a different emphasis on the acceptance of the existence of external objects can be observed. At this point, one should ask the question whether in the sense of the existence of these objects we leave the intuitive meaning of the word “existence”, or can the intuitive meaning of this word be maintained? For example, Berkeley’s immaterialism is a departure from common sense, but also representatives of positivism, proclaiming the slogan of returning to naive realism, as well as representatives of metaphysical realism, advocating for the existence of the extrasensory world, change the intuitive sense of the word “existence”. None of the positions mentioned retains some original, intuitive meaning of the word “existence”.
Analyzing the problem of existence, one can recall the concept of Zawirski regarding the existence of absolute reality, which is a good justification of how the axiomatic method can be used to study metaphysical problems. Actually, a physicist considers as real only what can be measured. Undoubtedly, this is a symptom of their healthy scientific instinct, without which physics would lose the proper sense of learning about nature. The physicist also realizes that the results of his/her measurements in different conditions fall differently. In this way, the physicist creates the concept of the existence of relative features relative to a given system, but at the same time assumes the existence of properties independent of any system. The latter is achieved through an account based on the axiomatic method. According to Zawirski, both objects with variable features and certain unchanging forms, which can be achieved mathematically, have their deeper base in the sphere of absolute reality. A physicist who each time, on the basis of his/her professional knowledge, makes judgments about the dependence of the object of research on the whole of the cognized being, should ←49 | 50→not forget about the existence of absolute reality, although the concept does not belong to physical concepts65.
The second assumption, which Zawirski accepts regarding the applicability of the axiomatic method to metaphysical problems, boils down to the fact that not all metaphysical problems can be resolved by a different interpretation of the laws of the phenomenal world. In addition to the subject of mathematical natural science, the psychological world, the world of spiritual life, remains.
Zawirski assumes the existence of a reality independent of the human mind. This reality indicates the existence of absolute reality, the existence of a deeper unity of the world. Due to the fact that all of the properties and relations of the learned objects remain relative; the clearer, according to Zawirski, is the need to adopt a reality independent of the subjective and relative manifestations of the objects learned for the human mind. Otherwise, one would have to accept an infinite multitude of subjective worlds and one could not explain where the source the possibility of unambiguously assigning specific, subjective data to a specific object and on the basis of adjudging on the identity of an object comes from. The invariant form of the laws of nature indicates a real unity of the world. While not accepting the invariant nature of natural laws, which in the light of modern knowledge becomes impossible, the world would be strange and incomprehensible.
It must be said that the question still remains whether contemporary mathematical natural sciences reveal to us the nature of absolute reality. According to Zawirski, physical knowledge does not present absolute reality to us, but it indicates it at most. Both the objects with relative traits and invariant laws belonging to the world of phenomena must have their deeper base in the sphere of absolute reality.
Zawirski was interested in the development of natural sciences and, first of all, the theory of relativity and quantum mechanics. Constantly trying to answer the questions stated and the philosophical matters discussed at that time, he has left many original works linked with these theories. Zawirski ←50 | 51→presented new philosophical implications derived from these theories in his numerous works and their impact on wider understanding of reality.
At the beginning of the 20th century, while conducting a research on the nature of time, space and cosmology, Zawirski was interested in the philosophical principles and implications linked with the general theory of relativity. Not much time behind, as it was only five years after Albert Einstein had presented his theory, Zawirski published his paper entitled Refleksje filozoficzne nad teorią względności which appeared in “Przegląd Filozoficzny” in 192066. Not only did he notice crucial importance of Einstein’s theory, but also made an attempt to explain the existence of absolute necessity to eliminate a number of philosophical premises out of science, especially the ones which had been accepted earlier by a number of physical theories and kept functioning in the notion of absolute time, space and movement. Zawirski paid close attention to, as well as followed the development of research undertaken within Einstein’s theory. Such an approach is evidenced by his numerous reviews of books on this theory published at that time (10 reviews in total). However, first of all, it is evidenced by his work entitled Relatywizm filozoficzny a fizykalna teoria względności67 published in 1921 in Lvov, as well as three smaller studies on this matter entitled respectively Rzecz o ‘obronie absolutu’68, Czas i przestrzeń w przedstawieniu wielkich filozofów69 and Fizykalna teoria względności a relatywizm filozoficzny70 having published them in the same year in Słowo Polskie.←51 | 52→
One of the first issues that did not directly relate to the philosophy of nature raised by Zawirski was a hypothesis on the so-called eternal returns of the worlds. He published a series of three papers on these matters in Kwartalnik Filozoficzny in the period between 1927 and 1928. He had already thought these problems over, studied them and was ready for the publication of the issues for the last fifteen years. The first drafted versions were presented on the May 27 and June 24, 1911 at the meetings of Polish Philosophical Society in Lvov, as well as during the Convention of Polish Medicals and Naturalists in Cracow in the same year.
Zawirski came back to this motive of “eternal returns” in his main work entitled L’évolution de la notion du temps, which was published in 193671. His work is still worth considering due to the clear and deepened presentation of history linked with the notion of time; it starts with the Pythagoreans and ends with the modern philosophical concepts of his time, including the claims of H. Bergson and E. Husserl, and the latest relativists and researchers in quantum physics. L’évolution de la notion du temps is still a work worth reading and studying by anybody interested in philosophy.
Zawirski’s most important achievements circulated around a number of issues related with time. He wrote many papers dealing with time and two books which we shall discuss later. The first book, Wieczne powroty światów. Badania historczno-krytyczne nad doktryną ‘wiecznego powrotu’, was published in Cracow in 192772. In this work, the issues of eternal return, involving a rather odd theory, were awakened in his mind as a profound interest in the problem of time which, as if shaped in the form of enigma, became his focus of investigation almost since.
Human curiosity about the eternal return of the world could be observed as vividly awakened in the earliest stages of culture. We have often to do is to think about the mystery of the past, the future and the present. The past has already ceased to exist but the future has not arrived yet. In addition, the only way present remains is a point of contact between the past and the ←52 | 53→future. This problem can be found in the ancient philosophy and the ancient books, the Bible included. Many thinkers were fascinated by the mystery of time; it is enough to mention Anaximander, Plato, Aristotle, Augustine, Thomas Aquinas to Pascal, Leibniz and Bergson where the problem of time could be found to remain the center of philosophical and scientific discussions. In Wieczne powroty światów, Zawirski deals with the theory of eternal universe and the idea of cyclic time. Following Zawirski’s concepts, it means that after a relatively long period, the universe returns to its initial point and from this point its old order is re-shifted, so as to begin a new history which is identical with the previous one. Zawirski’s book consists of two parts. The first one is highly instructive and of the historical character. The second part is a critical analysis of the theory of cyclical time, adopting the issues observed in the light of contemporary science.
In Modern Times, we can observe that the discussion about the idea of returns was particularly favorable due to the laws of mechanics. These laws are recognized as symmetrical to the direction of time – all the phenomena may run from past to future and from future to past. Kant was also an adherent of the laws of mechanics and the theory of returns, which can be found in his work titled Allgemeine Naturgeschichte and Theorie des Himmels (1755). Other adherents of the idea of returns were: the author of a discourse L’Eternité par les Astres, Auguste Blanqui (1805–1885)73, and Friedrich Nietzsche, the author of the seminal work Also sprach Zarathustra74. The idea of eternal return, as approached form the point of view of the direction of time was observed to be prevailing in science almost until the mid-19th century.
The situation radically changed in the second half of the 19th century, when in 1824 Nicolas L. Sadi Carnot discovered the Second Law of Thermodynamics. In the seventies of the 19th century Rudolf Clausius presented thermodynamic trans-formations, where thermal energy got transformed into mechanical work, currently known as the so-called law of ←53 | 54→the increase of entropy. It means that, after we have applied the Second Law of Thermodynamics to the entire universe observed as an isolated system, the universe itself moves toward the state of maximum entropy, i.e. to thermal death. Zawirski, who clearly leans toward the cycles of time, extensively analyzed the theory of universal thermal death and drew a conclusion from the extrapolation of the second law. He began with the arguments which undermined the validity of universal thermal death (found in the philosophical approaches of Ernst Mach, Henri Poincaré and Ludwig Boltzmann).
The strongest arguments against the theory of the thermal death of the universe were suggested by Poincaré and Boltzmann. Poincaré, in the work Le Mécanisme et l’Expérience (1893), wrote that our observations can appear to be incompatible with mechanics and thus unable to formulate the differences between irreversible and reversible phenomena. Irreversible phenomena possess a relatively long period of return to the preceding state, while the time of return in respect to the reversible phenomena is relatively short. The time of all observation is too short, so our conclusions about the thermal death of the universe can be simply short-sighted. At the same time, Boltzmann suggests a statistical formulation of the second law and suggests an equal probability of all possible micro-states. This Boltzmann’s idea of fluctuation connects the reversibility of the phenomena in the entire universe with the irreversibility of processes within the fluctuation range.
An experimental confirmation of the statistical interpretation of the second law was found within the micro-system. Marian Smoluchowski assumes that, where the number of particles is relatively small, that anti-entropy processes can be observed most easily. Up till now, the statistical character of the second law of thermodynamics had been confirmed experimentally by Böhi, Chaudesaigues, Dąbrowski, Perrin, Seddig, Svedberg and Zangger. Zawirski, on the basis of Poincaré’s, Boltzmann’s and Smoluchowski’s theorems, adopts the concepts of quasi-return phenomena. In this way Zawirski, in Wieczne powroty światów, accepts the theory of eternal return of the universe only because it cannot be denied with complete certainty75.←54 | 55→
Ten years after 1927, Zawirski decided to publish his new work titled Rozwój pojęcia czasu. It appeared to be his opus magnum. In an international competition under the auspices of Italian Scientia Zawirski was awarded the First Prize for it. No other publication known at that time was so up-to-date as Zawirski’s book. Up till 1936, we knew only about Duhem’s Le temps selon les philosophes hellènes76 that was devoted to the ancient period only; Werner Gent’s Die Philosophie des Raumes und der Zeit77 included the period from Aristotle to the end of the 17th century, whereas Baumann’s Die Lehren von Raum, Zeit und Mathematik78 ends with Hume.
Zawirski’s book contains the development of the idea of time up to the latest period and discusses the problems of time in relativistic physics and quantum mechanics. This work is semantically clear but its style is characteristic of the mental formation to which Zawirski belongs as a faithful disciple of Kazimierz Twardowski. Rozwój pojęcia czasu consists of two parts. The first contains the history of theories from the ancient philosophy up to Zawirski’s period of time. The second one is critical in nature and devoted to the analysis of some aporias of the notion of time. We will confine ourselves to a very short review of these aporias.
The first group of aporias contains all the questions connected with problem of absolute time and – connected with that – the a priori or a posteriori elements naturally contained within the idea of time. Zawirski’s answers to these problems are as follows: “[…] all the elements of the idea of time are of empirical origin, but the idea of time is nonetheless the product of our mental activity, because our mind’s attitude in the formation of this idea cannot be a solely passive and receptive one. […] We reject the a priori idea as a blind and mysterious force which weighs heavily upon us, just as did the fatum of the Ancients. Such a conception of the a priori has nothing in common with science or with philosophy of science. It is ←55 | 56→the great merit of Husserl to have modified the sense of Kant’s a priori, by limiting it to the consciousness of what is necessary and essential in the structure of an object. However, when penetrating the essence of objects, Husserl fell into the errors of the old metaphysics. Discrimination as to what is essential to, or accidental in, an object may change with the progress of science and, according to our opinion, it depends solely upon the definition of an object, which can also vary with experience. The point is that all a priori truths undergo a limitation of their application. Phenomenological investigations can in no way settle the problem of the reality of an object, or of its origin. The progress of sciences gives us the respective warning. It is from this point of view that the phenomenological axiomatization of time should be considered”79.
The second group of aporias concerns the question of the psychological origin of the idea of time and relation between intuitive and physical time. This part includes the critique of Bergson and discusses the role of memory in the formation of the idea of time, temporal illusions and the relation between ideas such as the temporal order, the interval and the instant80.
The third group of aporias concerns the problems raised by modern physics. All these aporias belong to the problem of the uniformity of the temporal flow and all those questions created by the theory of relativity. Zawirski concluded that metrical time and physical time are not identical notions. He concentrated upon these problems which led to two opposed orientations. One of them considers the ideas of the uniformity of time and the one of simultaneity as completely relative and conventional, while the other defends their intuitive and absolute character. Zawirski admitted that intuitionism found itself in a more difficult position after the advent of the theory of relativity. He does not exclude it, and indeed shall try to assume an intermediary position which takes into account the results of modern physics while not neglecting the data of intuition.←56 | 57→
The truth is that the axioms are often used in modern theories. We can formulate a series or propositions wherein we find the primitive terms of the constructed theory, connected to each other by means of logical terms. The primitive terms are defined implicitly by the role they play in these axioms or primitive propositions. We know that this method of defining issues implicitly has been used by Peano, who defined the notion of the integer in this way by means of five axioms and three primitive terms, but it was Hilbert who applied this method to geometry. Zawirski, making an attempt to provide this third group of aporias an end, focused his attention upon the attempts of such philosophers like Carnap and Whitehead, for example, who sought to axiomatize the science of time. Carnap gives several examples of the application of the axiomatic method to the topology of space-time, according to the theory of relativity; whereas Whitehead adopts axiomatizing as the basis of his theory, not the points of the universe, but the natural elements which are the events, and constructs the geometry of the events81.
The last group of aporias is devoted to problems of continuity, of the infinity of time and of its irreversibility. Zawirski has decisively solved none of these problems, since the state of modern science did not permit it. He said that the problem of continuity could be distinguished in future but now the result of quantum physics renders the mathematical continuity of time unverifiable; nevertheless, the intuitive notion of continuity should be maintained as different forms of atomism of time are not verifiable. The problem of the infinity and irreversibility of time provides the occasion for considering the value of the second law of thermodynamics and of other laws of physics. He suspected that by far modern physics did not reveal new possibilities which could be able to resolve the problem of determining the conditions and the direction of change82.
Zawirski developed many methodological problems such as causality, determinism, axiomatic method and experimentum crucis. He investigated ←57 | 58→problems of casual relation from various perspectives during all his scientific research. He was certain about the importance of this principle for scientific research. In his work entitled Przyczynowość a stosunek funkcjonalny83, published in Lvov in 1912, he demonstrated that the notions of “casual relation” and “functional relation” differ in terms of content. As casual relation is a real relation, considering the influence and time relations between reasons and consequences, it cannot be replaced with functional relation. In his paper entitled Teoria kwantów a zasada przyczynowości84 from 1930, he presented an opinion clearly polemical to Heisenberg’s theory claiming that the principle of uncertainty proves the falsity of the principle of causality.
Zawirski paid attention to any signal of philosophical thinking outside the borders of his mother country. He reacted violently to the methodological research included in Karl R. Popper’s work entitled Logik der Forschung. Zur Erkenntnisheorie der modernen Naturwissenschaft, published in Vienna in 1934. Zawirski criticized Popper’s falsificationism, which claimed that lack of agreement between some law and one of recognized and elementary opinions can be regarded as a sufficient reason for the rejection of this law. Zawirski notices that a single empirical law hardly ever is tested as perceived separately from the other laws. The whole system of opinions or theories is either tested or invalidated. Moreover, the number of laws and independent hypotheses becomes constantly smaller and smaller during such a test. Then, each general empirical task “becomes itself responsible” for the whole system to which it belongs. In this way, development of real sciences constitutes a continuation of the theory, which fight with each other and modify themselves constantly85.
In an interesting paper Doniosłość badań logicznych i semantycznych dla teorii fizyki współczesnej86 Zawirski was rather critical with Popper’s ←58 | 59→concept of falsibility as the most important criterion of a scientific aspect in a theory, but he agrees with Popper as to the rejection of induction to be recognized as an appropriate method in science. Zawirski also states that there exists asymmetry in falsification on the one hand and verification on the other. The falsification of a theory is a proof, based on modus tollendo ponens that the theory is false, but empirical verification of a theory does not prove that the theory is a true one. Notwithstanding, Zawirski in his paper is openly critical to Popper’s analysis and he expresses some arguments. Zawirski claims that induction and deduction are indispensable for science. Induction is important when a law or a theory is formulated in statu nascendi, but deduction plays its part during the processes aimed at testing any of them. He also states that falsification, like verification, is never of final character. We never test a singular theory, but always a group of theories or laws. We never know which theory has exactly been recognized as false, because falsification and verification are based on protocol sentences which do not form bottom of the rock. The protocol sentences depend on a number of factors: of theoretical, methodological or linguistic character. Summarizing, Zawirski concludes that “[…] a falsification by way of an experiment or an observation has the same relative character as verification […] so we shall find that between them no apparent asymmetry can exist”87.
A problem of testing hypotheses in empirical sciences was also undertaken by Zawirski in the paper entitled Uwagi o metodzie nauk przyrodniczych88. In a way similar to Popper’s, Zawirski assumes that we derive consequences ←59 | 60→out of the accepted hypothesis. Then, we make an attempt to test it whether it agrees with the facts concerned with it. The hypothesis is found as correct when there is an agreement between the facts directly observed and the conclusions derived out of it. If there is found some form of disagreement, the hypothesis should be rejected due to its invalidation. In this paper, Zawirski does not mention the name of Popper, but still criticizes his concept of falsification and impossibility to achieve experimentum crucis. Currently, it can be stated that what he criticized was the so-called naive Popper’s falsificationism.
Zawirski agrees with asymmetry to possibly appear between positive and negative result when testing a hypothesis. A question whether the negative result is to be considered as more serious than the positive one remained a problem for him. It is clear for Zawirski that the positive result still does not prove rightness of the particular hypothesis because it can always be changed in a minute; whereas, at the same time, the negative result does not always lead toward a complete withdrawal of the hypothesis. Invalidation of the hypothesis might be a decisive moment only when none of the notions describing an experiment remained unchanged. Every single change of meaning in the terms used leads to another undertaking of the particular hypothesis, in spite of the fact that it was invalidated. The example of such a situation can be earlier rejected by means of wave-particle theory of light that came out after Foucault’s experiments and was later introduced with the help of the theory of quantum. A similar situation occurs in the experiments related to experimentum crucis and instantia crucis when we select the one which includes some newly-revealed fact out of two competing hypotheses or theories.
Zawirski notices an analogy between a verification of the particular hypothesis and acceptance of the one out of two competing hypotheses. As long as we expect a positive or negative answer in the first case, the positive answer linked with one of the hypotheses in the second case is simultaneously the negative answer for the other one. In the situation of experimentum crucis it rarely occurs that two competing hypotheses were of the opposite opinions. There are usually more complicated hypotheses. Therefore, logical conjunctions of sentences whose negation is their alternatives are often checked, Popper does not notice it in his concept of falsification. Zawirski agrees here with Duhem for whom experimentum ←60 | 61→crucis has never invalidated one isolated hypothesis but only the whole theory full of linked tasks.
The comments presented above refer only to the theoretical testing of hypothesis. In practice, the situation does not look to be complicated so much. Each theory, apart from the formulated laws, also includes numerous defined terms, as well as a number of agreements. The simplest way of testing a hypothesis is usually selected. However, more complicated cases occur and may trigger “[…] a revolution in science”. “The cases occur when it is difficult to select which way is surely the simplest”89. Such a situation occurred during the development of the theory of relativity and quantum mechanics, when a number of negative experiences increased constantly together with the one of supporting hypotheses which explained these experiences. After some time, the edifice of classical physics had to be reconstructed, which appeared to be the best solution in this difficult situation90.
After the end of the 19th and the beginning of the 20th centuries, the classical logic of Aristotle represented a small fraction of modern logics, whose basic part was the one of sentential calculus. The development of logic enabled the work of Aristotle to be understood better and more profoundly. The discovery of the structure and function of deductive systems was an inspiration for further impressive development of logic.
Jan Łukasiewicz devoted many years to study Aristotle’s syllogisms. He started his studies on this problem with the publication of his monograph On the Principle of Contradiction in Aristotle. In this book, Łukasiewicz ←61 | 62→represented the first sustained questioning of the assumptions of traditional Aristotelian logic. The results of these studies were presented at the session of the Department of History and Philosophy of the Polish Academy of Sciences and Letters in 1939. Łukasiewicz demonstrated that Aristotle’s syllogism is a deductive system constructed by the axiomatic method. He completed this system and accurately defined its theorems by using the modern formal method. His studies of Aristotle’s original texts also made possible to discover new problems in the domain of modal sentences and the possibility of attributing a different value to some such sentences (Cf. On three-valued logic, 1920; Two-valued logic, 1921). He wrote about it in more detail in Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic (1951).
Zawirski followed the debate about a possibility of attributing a different value to sentences. In 1914 he published O modalności sądów91 where he critically analyzed the said discussion of the modality of judgments starting his analysis from the ancient philosophers up to the ideas observed in the time of Sigwart’s, Windelband’s, Wundt’s, Twardowski’s and Husserl’s philosophical activity. In this work Zawirski presents his own point of view, strongly speaking in favor of the two-valued logic. When Jan Łukasiewicz formulated the three-valued logics, where – in addition to true (1) and false (0) values, he introduced a third value (1/2) – Zawirski took part in the discussion of Łukasiewicz’s bold new idea by publishing a series of papers in this field of logic. He was interested in the possibility of using the idea of manyvalue logic for solving numerous difficulties which appeared alongside the development of quantum mechanics and mathematics. Zawirski sees that Łukasiewicz’s idea makes it possible to eliminate certain logical antinomies, and he believes that this idea is a better one for removing the said antinomies than Russell’s theory of types.
The indeterminism of quantum mechanics appears to supply a field of applicability to the new logic, i.e. many-valued logic. In 1920, while discussing the notions of modality and, in particular, possibility, Jan Łukasiewicz introduced the third value in his first published paper titled On the Concept of Possibility. This paper was based on a talk given by him ←62 | 63→on June 5, 1920 in Lvov. Two weeks later, a second talk given by him (also in Lvov) was more transparently titled On Three-valued Logic.
Zawirski pointed at two potential uses of many-valued logic in 1932 in the paper entitled Les logiques nouvelles et le champ de leur application which appeared in “Revue de Métaphysique et de Morale”92. The first one focused on the link between the theory of probability and many-valued logic. The second one focused on the use of Łukasiewicz’s three-valued logic in the analysis of wave-particle duality. Nevertheless, Zawirski admitted that this attempt was too early. In further works, Zawirski spoke in favor of the use of the theory of probability in the description of quantum phenomena. He stated that various degrees of probability can be assigned to such quantities of feedback as time, energy, position and momentum elemental particles.
Zawirski sees that three-valued logic provides better understanding of the complementary theory in micro-physics but he also notices the difficulties in the application of the notions of three-value logic to modern physics. The difficulties that are found in this application are compared with the traditional way of handling marks that are mainly associated with compound sentences. One problem that is concerned is that the negation of a sentence with a logical value of ½ can also obtain the same value of ½. Some other problem concerns the postulate of correspondence observed in the requirement that any later theories ought to be recognized as corresponding to the earlier theories. It means that the equations of the later theory should pass into equations of the earlier theory in the limited cases. In this time, scientists used to be convinced that this principle of correspondence provided a kind of guarantee that nothing will be lost from what is valuable in the achievement of the development of science. At the same time, this principle makes it possible to conduct a critical analysis from a new point of view. Zawirski writes that some time ago scientists simply adopted this postulate which was assumed to be intuitively certain, but now one ought to admit that such a new principle would be valid93.←63 | 64→
Zawirski produces a table for the implication p ⊃ q in Łukasiewicz’s logic and Brouwer’s logic (Tab. 1.)
Tab. 1: Implication in Łukasiewicz’s logic and Brouwer’s logic
One can see from the table (cf. position 8) that although ½ in Łukasiewicz’s logic is possible, it turns to be false in Brouwer’s logic. In intuitionist logic, when the antecedent has a higher value than the consequent, the implication is false. The same notion is observed in the traditional logic. So we can see that Brouwer’s logic comes nearer to the traditional one. There are no propositions that the two-valued logic ought to reject the intuitionist logic as being false. The situations appears to be different in Łukasiewicz’s logic, the law of negation of the equivalence of two contradictory sentences ~(p ≡ ~p), for p = 1/2 and ~p = 1/2, is false but in Brouwer-Heyting’s logic this law continues to be true94.
Łukasiewicz’s logic had only three values and these were not enough for the interpretation of probabilistic laws observed in quantum mechanics, so Zawirski tries to form its alterations and works out his own variant of a many-valued logic which is to fulfill this interpretation. Zawirski deals with this problem in two works: Znaczenie logiki wielowartościowej dla poznania i związki jej z rachunkiem prawdopodobieństwa (1934)95 and Stosunek logiki wielowartościowej do rachunku prawdopodobieństwa ←64 | 65→(1934)96. He sees that as any connection of logic and probability calculus is impossible a priori, so he introduces new logical factors. He has increased the number of logical operators of the sum and of the product in such a way that only logical value corresponds to each of these factors; this can be, for example, the logic of five values, symbolized by the series of numbers 0, ¼, 2/4, ¾, 1. In this logic the different formulae of the sum are justified by the difference in the order in which the true propositions follow the false propositions in these classes. If the values of the arguments v(p)=2/4 and v(q)=2/4, the corresponding classes, containing two true propositions for four true or false ones, can have the form: p=(0,0,1,1), q=(0,0,1,1) or else p=(1,1,0,0), q=(0,0,1,1), or p=(0,0,1,1), q=(1,0,1,0). The logical sum p^q as a number of two-valued logical sums was formed by joining the first members of the first series with the first member of the second series, so in the first case p^q=(0^0, 0^0, 1^1, 1^1)=(0,0,1,1), the value of this sum will be 2/497. Zawirski’s results were presented at the Prague Conference in 1934 and at the First International Congress of Scientific Philosophy in Paris in 1935. During this Congress Hans Reichenbach, independently of Zawirski, spoke about the logic of probability. There are differences between Zawirski’s and Reichenbach’s conceptions of the calculus of probability and many-valued logic. Reinchenbach interpreted the probability calculus as a kind of generalized logic. At the same time, Zawirski underlined the importance of the notion of a parallelism between the formulae of the calculus of probability and Łukasiewicz’s and Post’s many-valued logic.
In 1938 Zawirski published Doniosłość badań logicznych i semantycznych dla teorii fizyki współczesnej98. In this paper, Zawirski analyzes the relationship between logic and science. The new developments in the field of deductive systems are of high importance for the understanding of the theories in science, but it is the new theories in physics, such as the theory ←65 | 66→of relativity and quantum mechanics, that contribute to the development of logico-semantical investigations. When Zawirski analyzed the status of physical theories, he concluded that they are based on both arithmetic and logic. Furthermore, the developments in many-valued and intuitionistic logic give rise to some important problems. In addition, the development of many-valued logic and intuitionistic logic leads to the emergence of certain problems relating to the legitimacy of applying the excluded measure rule or the existence of undecidable sentences in properly rich formal systems, which Kurt Gödel pointed out. 99.
The scientific interests of Zawirski were also linked with more general problems of truth and being. The point of departure for his interests were the profound cognition of classical metaphysics and natural sciences within which more and more often the problems that previously had been reserved for philosophers only, were undertaken.
In the first decades of the 20th century, Zawirski witnessed an argument and a dispute concerned with the role of natural sciences in the development of general outlook on life. He noticed that both the metaphysicians and the opponents of metaphysics that took part in the said debate expressed a need to develop a scientific outlook on life. This fact made him ponder over a possibility to design metaphysics based on experience. He realized very quickly that metaphysics understood in this way would not be able to completely replace classical metaphysics perceived as scientia entis. It would not have been balanced only with the synthesis of natural sciences admitted by positivists. However, considering the mutual struggle of the most opposite reasoning movements, he undertook an attempt to develop a middle path leading toward the formation of the scientific metaphysics – both critical and open when using the results of the empirical experience. Zawirski presented his first ideas on the relations between metaphysics and science during a lecture given on May 5, 1917. His lecture, entitled O stosunku ←66 | 67→metafizyki do nauki, was presented at the meeting of the Philosophical Society in Lvov100.
The issue concerning the relations between metaphysics and science on the one hand and possibilities of developing a general theory that would embrace the notion of reality dominated in Zawirski’s research till 1923 when he published his post-doctoral thesis entitled Metoda aksjomatyczna a przyrodoznawstwo. The work was a summary of the research conducted earlier that focused on the possibility of axiomatization of metaphysical systems. Before 1923 Zawirski had also written two more works that discussed the said issues, entitled O stosunki metafizyki do nauki (1919)101 and Nauka i metafizyka (1920). Both works remained in the manuscript form and only in the period between 1995 and 1996 Nauka i metafizyka was published in the periodical “Filozofia Nauki”102. Then, the second work O stosunku metafizyki do nauki waited for its publication till 2003.
Reflecting on an important ontological issue regarding the relationship between the sensual and extrasensory world, Zawirski developed the concept of three worlds. A sensual world that is given to us directly in the sensual experience and guarantees a permanent opportunity to experience sensory perceptions (we may call it the permanent possibility of sensation). This is a world that I would call – following Zawirski – a “mental world”, the one that guarantees the permanent possibility of feelings. This world contains a permanent opportunity to experience and feel sentient beings; ←67 | 68→this is the world of subjective experiences. In turn, the objective world is to some extent an imposed part of the subjective worlds.
Knowledge of the objective world is dealt with by the natural sciences, in this way providing more and more accurate messages about it, as well as more and more powerful tools for action to transform the world of sensory experiences and the real transformation of contemporary cultures. According to Zawirski, success in transforming our lives and providing powerful tools of action is primarily owed by the objective world to the fact that “theories and hypotheses submit to the constant control of experience; for each dispute, he (i.e. Zawirski) tries to detect any experimentum crucis that would tip the scales of victory in favor of one of the rival hypotheses; as soon as new facts become known, he improves his theories and in this way, thanks to the arduous work of tens and hundreds of minds, he constantly moves his work”103.
It should be agreed with Zawirski that until today in natural science the issue of the essence of the objective world is still unresolved. Indeed, this unresolved issue continues to this day, some scholars point to the issue of mathematics of nature pointing to the objective nature of the world of mathematics (e.g. M. Heller, R. Penrose), others point to the objective existence of the field of rationality (e.g. J. Życiński), yet others strongly accept the original nature of God (Whitehead) or the so-called objective world 3 (K. Popper), etc.
Zawirski, however, approximates the understanding of the objective world he has selected to honor; in this way, for example, he draws the reader’s attention onto the problem of apriority of the axioms of logic; he analyzes this issue by referring to the views presented by, among others, B. Russell and I. Kant. According to Russell, the axioms of logic exist independently of the human mind; they are endowed with an ideal, timeless and eternal being. In this case, we are dealing with a platonizing view, according to which Zawirski describes the objects of the objective world as entia rationi, which do not mean to reveal either potentiality or timeliness. Each transition from the potential to the current state occurs ←68 | 69→only in the mind of the subject, as presented by Kant in the construction process.
Zawirski attempts to develop his own position, which would be somewhere between Russell’s and Kant’s. He speculates how the Platonic view of entia rationis can be reconciled with the idea of Kant, who conditions the apriority of knowledge with the forms of the mind. While reflecting on this issue, he believes that, for example, the Pythagorean Theorem did not change because it was formulated as a law, which means that the fact that the human mind knows the geometry’s judgments does not affect the shape of these judgments. This, in turn, means that we do not establish the laws of geometry, but discover what occurs “in the womb of the All-Eternal” as an eternal opportunity. The world of eternal opportunity in the form of entia rationis is an infinite multitude of possibilities, of which only the selected ones are updated in the world of existence, described by Zawirski as entia naturea104.
- ISBN (PDF)
- ISBN (ePUB)
- ISBN (MOBI)
- ISBN (Book)
- Publication date
- 2019 (April)
- philosophy of nature ontological structure of reality axiomatization of mathematical natural science Polish philosophy three-valued logic quantum mechanics
- Berlin, Bern, Bruxelles, New York, Oxford, Warszawa, Wien, 2019. 164 pp., 1 table