Abstract
In the paper, Jan Łukasiewicz’s program of the logicization of philosophy is presented and discussed. Łukasiewicz, known mostly for his invention of trivalent logic as well as his achievements in propositional calculus and metalogic, had always been concerned with the methodological condition of philosophy. He finally found “the measure of exactness” in mathematical logic. According to him, only the use of logical tools may provide philosophical investigations with an appropriate level of exactness. He expressed his views most firmly and directly in the paper, “A call for the method of Philosophy” (the translation of this paper is included in an “Appendix”). Łukasiewicz proposed giving philosophical theories the form of axiomatic systems by indicating the primitive terms of their language, selecting suitable axioms, and explicitly determining the applied rules of inference. All the theses of these systems should be consequences of the accepted axioms and confronted with the data of experience and the results of science. Łukasiewicz’s program is presented together with its inspirations and prospects.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
In fact, the idea of this logic had been in development since about 1910 (see Łukasiewicz, 1910). In 1918, in his “Farewell Lecture,” Łukasiewicz announced that he had succeeded in the construction of the first non-Aristotelian system of three-valued logic, which was “as coherent and self-consistent as Aristotle’s logic” and “much richer in laws and formulae” (Łukasiewicz, 1918, p. 86). Two years later, on June 19, 1920, he presented more details in his lecture “On three-valuated logic” (1920).
According to some historians of Polish logic, the idea of parenthesis-free notation was inspired by Leon Chwistek (see, for instance, Woleński (1989), p. 314), but it was Łukasiewicz who developed the rules of parenthesis-free symbolism and applied them in his logical works.
The term “logistyka” (“logistics”) was used by Łukasiewicz and his colleagues interchangeably with the term “mathematical logic” and “symbolic logic” and opposed to “philosophical logic” (by which he meant the inexact, “old” logic developed by philosophers).
Eric Temple Bell’s opinion in 1934 was even stronger, namely that Łukasiewicz’s result is the third of three “outstanding peaks in all the history of deductive reasoning” after Pythagoras defining a proof in the Sixth Century B.C. and Lobachevsky inventing non-Euclidean geometry in 1826 (Bell, 1934, p. 215).
For instance, no comments appear on that matter in the (excellent) papers listed in footnote 1. Certainly, the lack of attention to these matters is caused by the lack of access of English-speaking philosophers to the texts in which Łukasiewicz expresses his metaphilosophical positions. In the Polish literature, the methodological aspect of Łukasiewicz’s views also has not been analysed deeply enough. However, Łukasiewicz’s program is succinctly discussed in Woleński (1989), and extensive fragments of Łukasiewicz’s metaphilosophical papers translated into English are included in Brożek et al. (2021). An English translation of Łukasiewicz’s most crucial metaphilosophical paper (“O metodę w filozofii”) is included in the appendix to this paper.
In its turbulent history, Lvov, founded around 1250, was successively part of: the Principality of Galicia-Volhynia (from its foundation until 1349), Poland (until 1370), Hungary (until 1387), again Poland (until 1772), Austria (until 1918), again Poland (until 1939), and Ukraine (from 1945); in the years of World War II, it was under Russian, German, and again Russian occupation. Poles call it “Lwów,” Austrians—“Lemberg,” and Ukrainians—“L’viv.” Since among the historians of early analytic philosophy, the term “Lvov-Warsaw School” is commonly used, I also refer to Łukasiewicz’s home city as “Lvov.”
In the nineteenth century, the University of Lvov and the Jagiellonian University were the only universities where it was allowed to teach in Polish. Twardowski and all his students that continued his work lectured only in Polish, however their lectures were attended by students of Polish and Ukrainian, as well as Jewish origin.
The content and importance of this “Appendix” is discussed in Trybus and Linsky (2020).
In 1920, Łukasiewicz left university to join the cabinet of Ignacy Jan Paderewski at the ministry of science. Łukasiewicz was also twice elected the president of the University of Warsaw (1922–1923, 1931–1932).
See Łukasiewicz (1920a, 1920b, 1921). The problem of the third logical value had begun to bother Łukasiewicz much earlier—at least as early as 1910. This is evidenced by the following passage from his book, On the Principle of Contradiction in Aristotle: “There must be a moment when logicians begin to consider the mutual relations […] [between Aristotle’s logical laws]. Only then will it be revealed what place the principle of contradiction occupies among other logical laws, what its certainty and value are based on, and to what extent it can be applied; it will then be seen whether this principle is really the highest of all laws and the cornerstone of all our logic, or whether it can be transformed or even omitted to create a system of non-Aristotelian logic, just as a system of non-Euclidean geometry was created by transforming the parallel postulate” (Łukasiewicz, 1910, p. 6). See also above, note 2.
Łukasiewicz’s autobiography is included in Sobociński (1956).
Let us note that Łukasiewicz’s admiration for the 1st volume of Logsiche Untersuchungen was followed with disappointment with the 2nd volume. He wrote, “Although, I agree with Husserl regarding his position concerning the relation between logic and psychology, judging on the basis of the 2nd volume of his Logical Investigations, I can clearly see that Husserl is too deeply rooted in psychology to be able to embark on some bold reform of pure formal logic. I have had the opportunity here [i.e., in Charlottenburg] to learn the main philosophical trends in Germany, and I have found […] that Germany today has no idea what either logic and metaphysics are, or even philosophy in general.” (Łukasiewicz, 1905, p. 469).
Leśniewski and Łukasiewicz strongly influenced each other, although they disagreed on many important matters.
Łukasiewicz wrote, “The apparatus of ideas and problems brought by Twardowski from Vienna to Lvov was extremely barren and poor. There has been constant talk of whether a belief is a psychic phenomenon of a distinct kind or is a combination of concepts; there was always talk of images, presentations, concepts, their content and object, and it was not known whether the analyses conducted were works of psychology, logic, or grammar.” (Łukasiewicz, 1949–1954, p. 65).
With this and other works in this domain (Łukasiewicz, 1906b, 1907, 1909), Łukasiewicz initiated research concerning the processes of reasoning and their logical control, as later continued by many members of the Lvov-Warsaw School (Kazimierz Ajdukiewicz, Janina Hosiasson-Lindenbaum, Tadeusz Kotarbiński, Tadeusz Czeżowski, Jan Salamucha, and others). See also (Jadacki 2003).
See for instance Krajewski (ed.) (2001).
Twardowski lectured on formal logic in the academic year 1899/1900 (“Reformatory aspirations in the field of formal logic”).
It is worth noting that Łukasiewicz explained Twardowski’s aversion to mathematical logic as follows: “Twardowski was not talented, I suppose, in mathematics, and mathematical logic was always alien to him” (Łukasiewicz, 1949–1954, p. 69).
He wrote: “It seems that […] a characteristic feature of […] [Brentano’s] school lays not in psychologism […] but rather formalism and great apriorism, and the dialectic and methodicalness connected with that, worthy of great philosophical masters of the seventeenth century, which characterize the students and supporters of this school. (Łukasiewicz, 1904, p. 468).
The importance of this text is evidenced by Leśniewski’s “autobiographical confession” in his work On the Foundations of Mathematics: “In the year 1911 (still a student) I came across a book by Jan Łukasiewicz about the principle of contradiction in Aristotle. This book, which […] had a considerable influence upon a number of the Polish “philosophers” and the “philosophising” scholars of my generation, became a revelation for me in many respects and for the first time in my life I learned of the existence of symbolic logic.” (Leśniewski, 1927, p. 181).
Łukasiewicz stated: “Compared with these new standards of precision, the exactness of mathematics, previously regarded as an unequaled model, has not held its own. The degree of precision sufficient for the mathematician does not satisfy us any longer. We require that every branch of mathematics should be a correctly constructed deductive system. We want to know the axioms on which each system is based and the rules of inference of which it makes use. We demand that proofs should be carried out in accordance with these rules of inference, that they should be complete and capable of being mechanically checked. We are no longer satisfied with ordinary mathematical deductions, that usually start somewhere “in the middle,” reveal frequent gaps, and constantly appeal to intuition.” (Łukasiewicz, 1922, p. 111).
In particular, in 1925 Łukasiewicz proposed what was essentially a simplification of Nicod’s axiom, that had been formulated in 1918. See Łukasiewicz (1931).
“Anyone who has ever read the treatises of Galileo or the works of Pascal on physics has undoubtedly noticed the great precision and subtlety of thought that these powerful minds were endowed with.
Correct observations of only a few facts were enough for them to create great theories of tremendous generality, and the element of deductive and formal thinking predominated in these theories. They acquired the ability to think in this manner because they received good training in scholastic logic and grew up in an atmosphere where logic was appreciated. How many contemporary naturalists, and even more philosophers, philologists, historians, and sociologists, lack a similar knowledge of logic and the precision of thinking!” (Łukasiewicz, 1910, pp. 182–183).
Łukasiewicz had defended mathematical logic and its methods against attacks from different sides of the philosophical scene in Poland. See Łukasiewicz (1937).
Let us compare Łukasiewicz’s statements with Twardowski’s diagnosis: “The results, appearing as they do in symbolic form, require interpretation. Hence, after performing the operations we may no longer abstract from the fact that the symbols, in the form of which the results of the operations show up, do symbolize something. One must then make the transition from the realm of symbols into the world of the concepts and objects symbolized by them; one must once again turn from the signs to what they mean and designate. Not until we have done this, do we reach the goal which the symbols and the operations performed on them were supposed to make easier to attain — or even make it possible to attain. It follows that in using symbols and operating with them, we must continually reckon as conscientiously as possible with the fact that they play the role of a means intended to lead us to the mentioned goal” (Twardowski, 1921, p. 261).
The reconstructions of these different views as well as comparisons with the approaches of other members of the Warsaw circle can be found in Murawski (2014).
It is worth emphasizing that Łukasiewicz’s negative opinion concerned not only philosophical disciplines: “If mathematics cannot pass the test [of mathematical logic], what shall we say about other disciplines, which have always been less precise and less perfect than mathematics? What a fine target for logical criticism are such natural sciences as physics and chemistry, astronomy and crystallography? How much more imprecision must be inherent in those natural sciences which do not make use of mathematics, such as biology or geology? And how can contemporary philology, psychology, sociology and philosophy defend themselves against precise logical criticism?” (Łukasiewicz, 1916, p. 81).
Łukasiewicz played a crucial role in all three Polish Philosophical Congresses that took place before World War II (Lvov 1923, Warsaw 1927, Cracow 1936).
He stated openly: “I do not reject metaphysics; I do not condemn philosophy. I am not biased in advance against any philosophical trend, but I disapprove of sloppy mental work. And it is probably neither my fault, nor that of logic, that it sharpens criticism and discloses many defects in philosophical speculation. I predict that any person who receives a good training in logic will view these problems in the same way I do” (Łukasiewicz, 1937, p. 242).
“All a priori systems, as soon as they are applied to reality, become hypotheses of natural sciences which have to be verified by facts similarly to how this is done with physical hypotheses. My approach to metaphysics is connected with this opinion” (Łukasiewicz, 1936b, p. 233).
Twardowski’s habilitation, where his theory of objects was presented, as well as Borowski’s thesis (1904) on the concepts could be mentioned here as examples.
Let us quote a significant passage from Łukasiewicz’s paper, “The Principle of Individuation”: “It was in 1921. I was dissatisfied with the inexact description of the copula “is” given by Peano, and with the vague symbol ε of the theory of sets. In the course of a logical discussion I asked Leśniewski what he meant by the expression “a is b”. He replied that he was using it in the sense of everyday life. I was still dissatisfied, for I thought that the copula “is” should be defined, or described by axioms, if taken as primitive term (Łukasiewicz, 1953, p. 77).
About the results of the Cracow Circle, see for instance Tkaczyk (2017).
The list of these works in Poland is presented in the chapter “The Lvov-Warsaw School and its influence upon the Polish Philosophy of the twentieth century” in Jadacki (2009).
These three methods applied in the Lvov-Warsaw School (namely analysis of concepts, paraphrase of statements, and axiomatization of theories) and the dependencies between them are presented in Będkowski et al. (2020).
Łukasiewicz wrote: “In Vienna in 1928, I learned from […] [Schlick] that from the publishing house of J. Springer’s Company in Berlin, called Schriften zur wissenschaftlichen Weltanschaaung, a book by an associate professor of Vienna University, R. Carnap, containing a critique of philosophy from the point of view of mathematical logic, would be issued soon” (Łukasiewicz, 1929, p. 431).
The story has, of course, been partially told. See, for instance, Szaniawski (ed.) (1989).
This text has never been translated into English before. The Polish version was published for the first time in Przegląd Filozoficzny [Philosophical Review], vol. 31 (1928), pp. 3–5. Polish title “O metodę w filozofii” may be translated more directly as “For the Method in Philosophy” but such a translation could be misleading for an English-speaking reader. That is why the term “A call” was added which hopefully reflects Łukasiewicz’s intentions.
References
Ajdukiewicz, K. (1946). O tzw. neopozytywizmie [On so-called neopositivism]. In K. Ajdukiewicz (Ed.), Język i poznanie [Language and cognition] (Vol. II, pp. 7–28). PWN (1965).
Będkowski, M., Brożek, A., Chybińska, A., Ivanyk, S., & Traczykowski, D., et al. (2020). Analysis, paraphrase, axiomatisation. Philosophical methods in the Lvov-Warsaw school. In M. Będkowski (Ed.), Formal and informal methods of philosophy (pp. 56–74). Brill: Leiden.
Bell, E. T. (1934). The search for truth. Allen and Unwin.
Betti, A. (2021). Kazimierz Twardowski. The Stanford encyclopedia of philosophy (Fall 2021 Edition), (Ed. E. N. Zalta). https://plato.stanford.edu/archives/fall2021/entries/twardowski/
Borkowski, L., & Słupecki, J. (1958). The logical works of Jan Łukasiewicz. Studia Logica, 8, 7–56.
Brożek, A. (2018). Interpersonal and intertextual relations in the Lvov-Warsaw School. In A. Drabarek, J. Woleński, & M. Radzki (Eds.), Interdisciplinary investigations into the Lvov-Warsaw school (pp. 87–116). Palgrave & Macmillan.
Brożek, A., Będkowski, M., Chybińska, A., Ivanyk, S., & Traczykowski, D. (2021). Anti-irrationalism. Philosophical methods in the Lvov-Warsaw school. Wydawnicwo Naukowe Semper.
Gabbrielli, M., & Martini, S. (2010). Programming languages: Principles and paradigms. Springer.
Hosiasson-Lindenbaum, J. (1940). On confirmation. Journal of Symbolic Logic, 5(4), 133–148.
Jadacki, J. J. (2003). On reasoning. In J. Jadacki (Ed.), From the viewpoint of the Lvov-Warsaw school (pp. 189–202). Rodopi.
Jadacki, J. J. (2009). Polish analytical philosophy. Studies on its heritage. Wydawnictwo Naukowe Semper.
Jadacki, J. J. (2018). Jan Łukasiewicz: A creator of new ideas in logic and a reinterpreter of its history. In A. Garrido & U. Wybraniec-Skardowska (Eds.), The Lvov-Warsaw school. Past and present (pp. 33–46). Birkhauser.
Krajewski, W. (Ed.). (2001). Polish philosophers of science and nature in the 20th century. Rodopi.
Leśniewski, S. (1927). On the foundations of mathematics. In S. Leśniewski (Ed.), Collected works (Vol. I–II, pp. 174–382). PWN & Kluver Academic Publishers (1992).
Łukasiewicz, J. (1903). O indukcji jako inwersji dedukcji [On induction as an inversion of deduction]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 203–227). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1904). Letter to Kazimierz Twardowski (December 12, 1904). In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 467–468). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1905). Letter to Kazimierz Twardowski (February 6, 1905). In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and Metaphysics] (pp. 468–471). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1906a). Analiza i konstrukcja pojęcia przyczyny [Analysis and construction of the concept of cause]. In J. Łukasiewicz (Ed.), Z zagadnień logiki i filozofii [Problems of logic and philosophy] (pp. 9–62). PWN (1961).
Łukasiewicz, J. (1906b). O dwóch rodzajach wniosków indukcyjnych [On two types of inductive inference]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and Metaphysics] (p. 227). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1907). O wnioskowaniu indukcyjnym [On inductive inference]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (p. 22). Wydawnictwo WFiS, UW (1998).
Łukasiewicz, J. (1908). Zadania i znaczenie ogólnej teorii stosunków. [Tasks and the significance of the general theory of relations] In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 50–52). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1909). O prawdopodobieństwie wniosków indukcyjnych [On the probability of inductive inferences]. In J. Łukasiewicz, Logika i metafizyka [Logic and metaphysics] (p. 231). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1910). O zasadzie sprzeczności u Arystotelesa [On the principle of contradiction in aristotle]. PWN (1987).
Łukasiewicz, J. (1912). O potrzebie założenia instytutu metodologicznego [On the need to establish a methodological institute]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 403–404). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1915). O nauce i filozofii [On science and philosophy]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 33–38). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1916). On the concept of magnitude. In J. Łukasiewicz (Ed.), Selected works (pp. 66–83). North-Holland Publishing Company & PWN (1970).
Łukasiewicz, J. (1918). Farewell Lecture by Professor Jan Łukasiewicz, delivered in the Warsaw University Lecture Hall on March 7, 1918. In S. McCall (Ed.), Polish logic (pp. 84–86). The Clarendon Press (1967).
Łukasiewicz, J. (1920a). On the notion of possibility. In S. McCall (Ed.), Polish logic (pp. 15–16). The Clarendon Press (1967).
Łukasiewicz, J. (1920b). On three-valued logic. In S. McCall (Ed.), Polish logic (pp. 16–18). The Clarendon Press (1967).
Łukasiewicz, J. (1921). Two-valued logic. In J. Łukasiewicz (Ed.), Selected works (pp. 89–109). North-Holland Publishing Company & PWN (1970).
Łukasiewicz, J. (1922). On determinism. In J. Łukasiewicz (Ed.), Selected works (pp. 110–128). North-Holland Publishing Company & PWN (1970).
Łukasiewicz, J. (1924). Kant i filozofia nowożytna [Kant and modern philosophy]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 365–368). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1928). O metodę w filozofii [A call for the method in philosophy]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 41–42). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1929). O znaczeniu i potrzebach logiki matematycznej [On the importance and needs of mathematical logic]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 424–436). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1931). Comments on Nicod’s axiom and on “generalizing deduction”. In Selected works (pp. 179–196). North-Holland Publishing Company – PWN (1970).
Łukasiewicz, J. (1936a). Co dała filozofii współczesna logika matematyczna [What did contemporary logic give to philosophy]. [Discussion.] Przegląd Filozoficzny, XXXIX(4), 326–329.
Łukasiewicz, J. (1936b). Logistics and philosophy. In J. Łukasiewicz (Ed.), Selected works (pp. 218–235). North-Holland Publishing Company & PWN (1970).
Łukasiewicz, J. (1937). In defense of logistics. In J. Łukasiewicz (Ed.), Selected works (pp. 236–249). North-Holland Publishing Company & PWN (1970).
Łukasiewicz, J. (1939). Geneza logiki trójwartościowej [The origins of three-valued logic]. In J. Łukasiewicz (Ed.), Logika i metafizyka [Logic and metaphysics] (pp. 241–245). Wydawnictwo WFiS UW (1998).
Łukasiewicz, J. (1949–1954). Pamiętnik [Diary]. Wydawnictwo Naukowe Semper (2013).
Łukasiewicz, J. (1951). Aristotle’s syllogistic from the standpoint of modern formal logic. Clarendon Press (1957).
Łukasiewicz, J. (1953). The principle of individuation. Proceedings of the Aristotelian Society, 27, 69–82.
Łukasiewicz, J. (1970). Selected works. North-Holland Publishing Company & PWN.
Łukasiewicz, J., & Tarski, A. (1930). Investigations into the sentential calculus. In A. Tarski (Ed.), Logic, semantics, metamathematics. Papers from 1923 to1939 (pp. 38–59). Clarendon Press (1983).
Malinowski, G. (1993). Many-valued logics. Clarendon Press.
Murawski, R. (2014). Philosophy of mathematics and logic in the 1920s and 1930s in Poland. Birkhäuser.
Russell, B. (1903). Principles of mathematics. Routledge (2010).
Rybařiková, Z. (2019). Łukasiewicz and Quine on empirical and a priori sciences. Studia Semiotyczne [Semiotic studies] (Vol. XXXIII, pp. 241–253).
Simons, P. (2020). Jan Łukasiewicz. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Summer 2020 Edition). https://plato.stanford.edu/archives/sum2020/entries/lukasiewicz/
Smith, B. (1988). Kasimir Twardowski. An essay on the borderlines of ontology, psychology, and logic. In Szaniawski (Ed.), The Vienna circle and the Lvov-Warsaw school (pp. 313–373). Kluwer Academic Publishers (1988).
Sobociński, B. (1956). In memoriam Jan Łukasiewicz (1878–1956). Philosophical Studies, 6, 3–49.
Surma, P. (2012). Poglądy filozoficzne Jana Łukasiewicza a logiki wielowartościowe [Philosophical views of Jan Łukasiewicz and many-valued logic]. Wydawnictwo Naukowe Semper.
Szaniawski, K. (Ed.). (1989). The Vienna circle and the Lvov-Warsaw School. Kluwer Academic Publishers.
Szumilewicz-Lachman, I. (1994). Zygmunt Zawirski: His life and work. Kluwer Academic Publishers.
Tarski, A. (1933). The concept of truth in formalized languages. In: A. Tarski (Ed.), Logic, semantics, metamathematics. Papers from 1923 to 1939 (pp. 152–278). Clarendon Press (1983).
Tkaczyk, M. (2017). Cracow circle. Theology in the Lvov-Warsaw school. In A. Brożek, F. Stadler, & J. Woleński (Eds.), The significance of the Lvov-Warsaw school in European Culture. Springer.
Trybus, A., & Linsky, B. (2020). Jan Łukasiewicz. The principle of contradiction and symbolic logic. History and Philosophy of Logic, 41(2), 183–190.
Twardowski, K. (1921). Symbolomania and pragmatophobia. In K. Twardowski (Ed.), On actions, products and other topics in philosophy (pp. 261–270). Rodopi (1999).
Woleński, J. (1989). Logic and philosophy in the Lvov-Warsaw school. Kluwer.
Woleński, J. (2013). The rise of many-valued logic in Poland. In J. Woleński (Ed.), Historico-philosophical essays (Vol. I, pp. 37–50). Copernicus Center Press.
Wybraniec-Skardowska, U. (2018). Introduction. The school: Its genesis, development, and significance. In: U. Wybraniec-Skardowska, & Á. Garrido (Eds.), The Lvov-Warsaw school. Past and present (pp. 3–14). Springer.
Zawirski, Z. (1936–1937). Über die Anwendung der mehrwertigen Logik in der empirischen Wissenschaft. Erkenntnis (vol. VI, pp. 430–435).
Acknowledgements
The paper was prepared as a part of Project No 31H 18 0444 86 supported by the National Program for the Development of Humanities, Poland. The author would like to thank Prof. Jacek Jadacki as well as two anonymous reviewers of “Synthese” for their comments which significantly help to improve the previous versions of the paper.
Funding
This study was funded by Narodowy Program Rozwoju Humanistyki (Poland); Project Number: 31H 18 0444 86.
Author information
Authors and Affiliations
Contributions
Not applicable.
Corresponding author
Ethics declarations
Conflict of interest
The author declares that there is no conflict of interests.
Data availability
Not applicable.
Code availability
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
1.1 Jan Łukasiewicz, "A call for the method in philosophy"
Lecture presented on September 23, 1927, at the 2nd Polish Philosophical Congress in WarsawFootnote 50
Philosophers, even the greatest ones, do not apply the scientific method in creating philosophical systems. The notions they use are predominantly vague and ambiguous; the claims are usually unclear or unjustified; the lines of reasoning are practically always wrong. It is sufficient to recall descartes’ proofs for the existence of God or his definition of substance, spinoza’s pseudo-scientific deductions, leibniz’s fantasies on monads and a pre-established harmony, kant’s critique of pure reason, or the idealistic post-Kantian philosophers’ considerations. All of these philosophical systems are probably significant for the history of human thought; they are often of great aesthetic and ethical value; they even contain some apt observations based on intuition; but they do not have any scientific value at all. This is why philosophy has not only failed to reach some established and commonly accepted truths, as other branches of science have, but it has not even managed to formulate its own main problems strictly.
One of the reasons why philosophy is not scientific seems to be that logic has been neglected by modern philosophers. Rather than perfect this field, passed on to us by ancient philosophers, and intelligently cultivated in the Middle Ages, modern philosophers, with only the exception of leibniz, have directed their attention at obscure and unproductive topics concerning the “theory of cognition.” “Philosophical” logic, that is, the logic which is practiced by philosophers, is in a state of dire decline. One has the impression that philosophers have chosen the path of least resistance, as speculation does not require as much mental effort as the study of logic in the scientific sense. Subsequently, two negative results for philosophy follow from neglecting logic: firstly, philosophers who are ignorant of logic do not follow the requirements of scientific accuracy in their works, or to put it simply, cannot think logically; secondly, as is the case with Kant, they often base their philosophical views on erroneous logical theories.
The logic created by mathematicians has opened our eyes to the uselessness of philosophical speculation by establishing a new measure of scientific exactness, far exceeding any past measure of exactness. Therefore, as in kant’s times, there arises a need to reform philosophy; not a reform in the name of some vague “criticism” and in the spirit of a non-scientific “theory of cognition,” but a reform in the name of science and in the spirit of mathematical logic. Future scientific philosophy must be built from the very beginning, from the foundations. Beginning from the foundations means having made an overview of philosophical problems, selecting only those which can be formulated clearly, and rejecting all others. Mathematical logic is useful in this preparatory work, as it has established the meaning of many expressions used in philosophy. The next step is to attempt to solve those philosophical problems that can be formulated clearly. Again, the best method to use towards achieving this goal seems to be that of mathematical logic: the deductive, axiomatic method. One has to rely on sentences, intuitively clear and as certain as possible, and these sentences ought to be accepted as axioms. Expressions whose meaning can be explained comprehensively through examples should be selected as primitive, or non-definable, notions. Care should be taken to ensure that there are as few axioms and primitive notions as possible, and they should all be listed carefully. All other notions must be unconditionally defined based on primitive notions and all other theses must be unconditionally proved based on axioms, as well as by the use of the rules of inference that have been adopted in logic. The results obtained in this way should be constantly compared with the data from intuition and experience, as well as with the results of other sciences, especially the natural sciences. If there are inconsistencies, the system should be perfected by formulating new axioms and selecting new primitive notions. Contact with reality should be constantly ensured in order not to create mythological entities like platonic ideals and kantian things-in-themselves, but rather to understand the essence and structure of the real world in which we live and act, the world which we want to somehow transform into a better and more perfect one.
For now, one should act in this task as if nothing had been done in philosophy so far. Any return to aristotle, leibniz, or kant will not only be of no use but will cause harm. We should avoid succumbing to the pressure of famous names and assuming bad thinking habits. When the axiomatic method, applied to philosophy, has rendered results, there will be time to return to the past and look for the initial traces of the new achievements in the history of philosophy. The work set out for future scientific philosophers is immense anyway. It can only be managed by much more powerful minds than those that have hitherto appeared on the Earth.
Rights and permissions
About this article
Cite this article
Brożek, A. Jan Łukasiewicz’s program of the logicization of philosophy: its genesis, content and realizations. Synthese 200, 199 (2022). https://doi.org/10.1007/s11229-022-03699-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11229-022-03699-7