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Aristote au xixe siècle

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Denis Thouard

L'Aristote logique

The Reception of Aristotle in Poland around 1900

Jan Wolenski

Texte intégral

1. Aristotle in Poland before 1900

1The first testimony of knowledge about Aristotle in Poland goes back to the turn of 12th and 13th centuries, to the chronicle of Wincenty Kadłubek, the Cracow bishop. One of its fragments mentions pupils of Lycofron, a sophist mentioned by Aristotle in his Peri sophistikon elenchon (On Sophistic Refutations). Thus, it appears that some elements of Aristotle’s rhetoric were known in Poland about 1110 (Kadłubek refers to a political dispute from the beginning of 12th century). Logic (as an element of the trivium) was taught in Polish cathedral schools since 11th and 12th centuries. Although the details of the curricula of are not known, it is rather obvious that they were based on the sources accessible in Europe at the time, directly or indirectly influences to the Stagirite. The famous medieval natural scientists Witelo and Theodoric of Opole (both living in Upper Silesia at the end of 13th century) could be regarded as the first Polish Aristotelians.

  • 1 The University of Cracow was the only Polish university until 1571. When Vilna University was foun (...)

2The foundation of Cracow University (1364) became a decisive point for serious academic life in Poland. Strictly speaking, since the university very quickly ceased its activities, its very renewal (1400) brought stabilizing effects for Polish culture. The first influence came from Prague and its university (founded in 1348). This was also the way in which Aristotle came to Poland1. The influence of Prague was very important, but did not last very long. In 15th century, Cracow became an independent centre of study and scholarship. In particular, this concerned studies based on the writings of Aristotle.

  • 2 I give these data after W. Wasik, Sebastian Petrycy z Pilzna i jego epoka. Ze studiow nad dziejami (...)

3Since Aristotle’s philosophy (at first logic, later, the whole of it) was officially declared as the basis of teaching at all faculties in Cracow (including theology, law and medicine), several commentaries on Aristotle were written by professors of the university. About 300 manuscripts devoted to Aristotle (often together with excerpts from his works) have been preserved in Jagiellonian Library (the University Library in Cracow; the name «Jagiellonian University» was adopted in 19th century). Some of them still await analysis. Cracow was also quite an important publishing centre. In the years 1473-1600, 13 editions of Aristotle were published in Cracow2. It is ranked as the sixth place (after Paris–135, Venice–68, Basel–41, Lyon–17 and Frankfurt–18). In the years 1500-1550 (perhaps the best period of Polish culture between 1400 and 1600; the so-called golden period), we note 10 editions (the 4th place, after Paris–44, Basel and Venice–15; in the years 1501-1525 even the 3rd place, after Paris–22 and Venice–15). All editions were in Latin. More specifically the important editions include: Analytica posteriora (1499), De Anima (1512, 1512), Analytica Priora (1520), Physica (1519), Elenchi sophistici (1521), Problemata (1528; a compendium of excerpts from Aristotle together with pseudo-Aristotelian fragments and questions). The first translations of Aristotle (and Pseudo-Aristotle; at that time, some works, for example, Oeconomica were attributed to the Stagirite) into Polish appeared in 1525-1550 (Problemata, Physiognomica). Sebastian Petrycy of Pilzno translated Oeconomica, Politica and Rhetorica into Polish, all in 1601-1625. This structure of translations was common in Europe at that time and displayed the growth of interest in practical philosophy; in general, no work of Aristotle in theoretical philosophy was translated in those days. Poland is to be ranked very highly as far as the matter concerns translations, on with Italy and France (all in 5 translations; Polish translation of Oeconomica was perhaps the first at all).

4The above-mentioned data show that Aristotelianism was fairly well developed in Poland in 1400-1600. Some historians of philosophy even speak about Cracow Aristotelism. Jan of Głogow, Michał of Wrocław, Jakub Gorski and Sebastian Petrycy (mentioned earlier) belong to the most distinguished Polish Aristotelian scholars. Most of them (Jan of Glogow, Michał of Wrocław and Jakub Gorski) worked in logic. In spite of a quite impressive number of commentaries, editions and translations, Cracow Aristotelianism was not particularly original. This is not surprising, if we take into account the fact that scholasticism appeared in Poland much later than in Italy, France or England. When the Risorgimento began to flourish in Europe, Poland still was completely captured by Schoolmen. All main currents of European medieval philosophy were represented in Poland: Thomism, Scottism, via antiqua, via moderna, logica veta, logica nova, etc. This resulted in many mutually crossing points in the works of particular writers; for example, Jan of Stobnica commented on Aristotle’s logic from the point of view of Duns Scotus. Although this variety initiated pluralism, very characteristic of Polish philosophy in its whole history, it could not produce a very original thought. Additionally, Polish studies on Aristotle were base almost exclusively on medieval Latin translations (Aristoteles Latinus); Greek originals were practically unknown. Anyway, the level of Cracow Aristotelianism was certainly lower in its quality and importance than Polish political philosophy at the time (Paulus Vladimirus, Andrzej Frycz-Modrzewski or Polish Brethren).

5The general political crisis of Poland in 1600-1750 was also displayed in the form of Polish philosophy. As far as the matter concerns the Stagirite, we can note only some commentaries to the Organon (for example Samuel of Lublin, Stanislaw Markowski), but these rather served an auxilliary teaching material. After 1625 (until the end of 19th century), no edition or translation of Aristotle appeared in Poland. The Enlightenment, the period in which Polish intellectual life flourished and several attempts to reform the state were undertaken, was anti-scholastic and thereby anti-Aristotelian. Poland lost its independence in 1795 and this fact determined the subsequent development of Polish philosophy. Until the sixties of the 19th century, so-called Polish national philosophy, closely related to German idealism, dominated. It mainly considered the causes of national tragedy and looked for ways of recovering independence. It was very far of Aristotelianism. The only interesting work published in Poland at that time was written by Jan Sniadecki (he was a typical representative of the Enlightenment and its empirical tendency, not romanticism). It was an article «The Content of Aristotle’s and the Past Dialecticians’ Theory of the Syllogism» (1821, published in 1837 as an Appendix to Sniadecki’s, Philosophy of the Human Mind). As it can be expected, this paper, according to the trends of the Enlightenment, was not particularly sympathetic to the Stagirite.

6The situation changed in the eighties of the 19th century. The positivistic movement in Poland (so-called Warsaw positivism) insisted that Poles, including the lower social classes, should be well educated. This postulate resulted in several popular encyclopaedias, textbooks and papers in which Aristotle could not be omitted. His views presented in such a way mostly concerned ethics, poetics and pedagogy. Also new translations were produced, in particular, the Poetics (1887) and The Athenian Constitution (1894). Another impetus came from neo-scholastic philosophy, initiated by the encyclical «Aeterni Patris» of Leo XIII. However, nobody referred to deep studies on Aristotle made in many countries, notably in Germany, but more serious interest came very soon.

2. Three Polish works on the categories and related topics

7In 1895-1910 Polish philosophers published three studies devoted exclusively to Aristotle (I omit a booklet (1896) Aristotle’s Theory of Soul by Z. Uranowicz, which contains nothing interesting, as well as some, earlier and later, PhD dissertations written by Poles in foreign languages, but practically unknown in Poland). They are:

F. Gabryl, O kategoriach Arystotelesa (On Categories of Aristotle), Krakow Polska Akademia Umiejetnosci, 1895;
W. Wasik, Kategorie Arystotelesa pod wzgledem historycznym i systematycznym (Aristotle’s Categories from a Historic and Systematic Point of View), Warszawa E. Wende, 1909;
W. Tatarkiewicz, Die Disposition der aristotelischen Prinzipien, Giessen, A. Töppelman, 1910.

8Father Franciszek Gabryl (1866-1914) was a professor at Jagiellonian University one of the pioneers of neo-scholasticism in Poland. Wiktor Wasik (1883-1963) initiated research on the history of Polish philosophy, in particular, on the early reception of Aristotle in Poland. Władysław Tatarkiewicz (1886-1980), a famous historian of philosophy, in particular of aesthetics, was a professor in Warsaw.

  • 3 A. Trendelenburg, Geschichte der Kategorienlehre, Berlin, Verlag von G. Bethge, 1846; H. Bonitz, « (...)

9The studies of Gabryl and Wasik are closely related. Both concern Aristotle’s Categories. Due to the work of Bonitz, Trendelenburg, Prantl, Prantl and Überweg, it was a favourite topic of historical investigations3. Two topics were considered: (a) are the Categories an original work of Aristotle?; (b) how to interpret the categories? Both Polish authors tried to answer this question. Gabryl defended the originality of the Categories, but Wasik was inclined to treat this work as only partially authentic. As far as the matter concerns the problem of interpretation, Gabryl strongly criticized Trendelenburg’s grammatical hypothesis (the categories are linguistic items) and adopted, due to his involvement in neo-scholasticism, the view that they are modi of being, but Wasik defended its reading as concepts. Additionally, Wasik compared the Aristotelian theory of the categories with Indian philosophy. Contrary to fashionable trends at the time that tried to demonstrate that European philosophy was secondary to or at least much influenced by Indian thought, Wasik defended the originality of Aristotle’s account of the categories. The reviewed works were perhaps not very original, but based on a very solid use of Greek texts and later commentators.

10Tatarkiewicz’s work is his PhD dissertation supervised by Hermann Cohen and Paul Natorp in Marburg. As Tatarkiewicz later reported, Natorp suggested the topic with the following words «Please write something about Aristotle; it can be useful in your country». The traces of Marburgian Neo-Kantianism are obvious in Tatarkiewicz’s book. The author, according to the standards of philosophical research recommended by Cohen and Natorp, did not undertake any historical research. In particular, Tatarkiewicz completely ignored the problem of the authenticity of the Categories. He adopted, also without any discussion, the interpretation of categories as the concepts (another reading was out of question in Marburg) and proposed an abstract system of concepts elaborating Aristotle’s ideas in question. In details, Tatarkiewicz’s approach was not exclusively Neo-Kantian. For example, he did not use any monistic principle to organize the system. Thus, Aristotle appears in this book as a pluralistic thinker. Let me add that Tatarkiewicz changed his view of Aristotle in his later historical writings and interpreted him as a philosopher of common sense.

11It is difficult to assess how much these three writings influenced the subsequent Polish studies on Aristotle. It seems that they were not particularly influential. Certainly, it applies Tatarkiewicz. His work practically not accessible in Poland (it was translated into Polish as a historical peculiarity in 1978). As far as the matter concerns Gabryl and Wasik, it could be that both introduced, at least partially, a pattern of historical investigations with a very serious reference to original sources, later commentaries and secondary literature.

3. Twardowski

  • 4 See J. Wolenski, Logic and Philosophy in the Lvov-Warsaw School, Dordrecht, Kluwer, 1989 for a det (...)

12It is difficult to overestimate the role of Kazimierz Twardowski (1866-1938) in the development of contemporary Polish philosophy. After he becoming (1895) the professor of philosophy at the Lvov University (1895), his task was to create a philosophical school in Poland. Due to his extraordinary teaching abilities, he succeeded in forming a group commonly known as the Lvov-Warsaw School4. Twardowski’s metaphilosophical programme insisted that philosophy should be expressed in a clear manner (he used to say «he who does not speak clearly, does not think clearly») and consist in statements sufficiently justified. According to Twardowski, only philosophy which is methodologically responsible, can be regarded as scientific. These claims favoured logic, semiotic and philosophy of science, other fields of philosophy less. On the other hand, Twardowski and his students, contrary to the Vienna Circle, did nor formulate in advance any criteria that excluded particular philosophical topics from the domain of scientific research. It is true that they were hesitant with respect to so-called great issues concerning being and knowledge, but nothing prevented to being considered them as legitimate. Thus, the Lvov-Warsaw School represented a liberal analytic attitude, at least much more liberal than logical empiricism. Kazimierz Ajdukiewicz (1890-1963), Tadeusz Czezowski (1889-1981), Tadeusz Kotarbinski (1886-1981), Stanislaw Lesniewski (1886-1939) and Jan Łukasiewicz (1876-1957) belong to the first generation of Twardowski’s students.

13This school began its life in Lvov at the end of 19th century. After 1918, when Poland gained its independence, Warsaw became the second centre of Twardowski’s school. Kotarbinvski was appointed as a professor of philosophy at Warsaw University, reopened in 1915. Lesniewski and Łukasiewicz, supported by mathematicians working in set theory and topology, created there Warsaw Logical School, a powerful group of logicians with Alfred Tarski (1901-1983) as perhaps its the most important member. Tarski gave a very remarkable tribute to Twardowski and his role in Polish philosophy:

  • 5 A. Tarski, «[Letter to Otto Neurath, April 24, 1930]», Grazer Philosophische Studien 43 (1992), p. (...)

Almost all researchers, who pursue the philosophy of exact sciences in Poland, are indirectly or directly the disciples of Twardowski, although his own works can hardly be counted within this domain.5

14The Lvov-Warsaw School actively worked until 1939. After World War II, it ended its life due to losses during the war, the emigration many scholars from Poland and the political circumstances that brought Poland into the communist sphere of dominance.

  • 6 Eng. tr. : K. Twardowski, On Content and Object of Presentations, tr. by R. Grossmann, The Hague, (...)

15Twardowski studied with Brentano in Vienna. Brentano insisted that Twardowski should write his Habilitation thesis about the classification of the sciences in Aristotle. However, Twardowski, who earlier received his PhD on the base of a dissertation about Descartes, preferred a more systematic topic (finally, he wrote the book Zur Lehre vom Inhalt und Gegenstand der Vorstellungen for the Habilitation)6 The refusal of Brentano’s proposal, as well as the fact that Twardowski never wrote a paper devoted to Aristotle and his philosophy, was no sign of any disrespect for the Stagirite. As a faithful Brentanist, Twardowski knew Aristotle very well. He perceived Aristotle, through Brentano’s glasses, as a commonsensical realist (as a matter of fact, the mentioned earlier conversion of Tatarkiewicz was made under the influence of Twardowski) and a founder of descriptive psychology. On the other hand, Twardowski, following Brentano, rejected the allogenic theory of judgment (judgment as a composition of presentations) held by Aristotle in favour of an idiogenic one (judgment as a specific primitive mental entity). This led, for instance, to a criticism of the formula veritas est adequatio rei et intellectus as expressing a correspondence (as similarity or something of the sort) between the content of mental acts and the world. Twardowski shared several Aristotelian-like views: absolutism in epistemology and ethics, relying on evidence in particular circumstances as a sufficient basis for judgments and methodological optimism (preserving simple methodological rules is sufficient for a successfully performing science). His metaphilosophical programme recalled Aristotelian attitude to philosophy and science. Twardowski bequeathed his great respect to Aristotle for his students.

4. Łukasiewicz

  • 7 J. Łukasiewicz, Elementy logiki matematycznej (Elements of Mathematical Logic), Warszawa, Nakladem (...)

16Łukasiewicz is certainly the most important Aristotelian scholar that has appeared in Poland. In his lifetime, he published four books of which two are either lecture notes or a small booklet on probability7. Łukasiewicz’s two real books are just on Aristotle:

  • 8 Germ. tr. by J. Barski, Über Satz des Widerspruchs bei Aristoteles, Hildesheim, Olms, Eng. tr. (in (...)

O zasadzie sprzecznośvci u Arystotelesa (On the Pricniple of Contradiction in Aristotle), Krakow, Polska Akademia Umiejetnośvci, 1910;8
Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Oxford, Clarendon Press, 1951 (2nd enlarged ed. 1957).

17Metaphorically speaking, these books became a cramp linking the beginning and the end of Łukasiewicz’s scholarly work. This qualification must be properly understood. In the meantime, Łukasiewicz completed a fundamental wok in mathematical logic, the basic title to his glory. However, his continue interests in Aristotle are remarkable. Łukasiewicz’s respect for Aristotle primarily concerned the Stagirite as the founder and master of formal logic. However, there was also another important factor. Łukasiewicz always thought that the epistemological turn in modern philosophy, which originated with Descartes and Locke, was a great mistake. He preferred the ontological direction of Aristotle and the Schoolmen. In particular, according to Łukasiewicz, modern philosophy corrupted logic by psychologism. Thus, coming back to Aristotle’s philosophy was a way to recover the true stream of thought. Both Łukasiewicz’s of books about Aristotle concern logical matters. Yet the first is logico-philosophical, but the second purely logical, eventually with a little philosophical content.

18Łukasiewicz’s first book was entirely devoted to the principle of contradiction (PC) and its status as a basic law of logic and human thinking. According to Łukasiewicz, history showed that PC was not always considered as obvious; it was sometimes questioned, as in the case of Hegel and even Aristotle himself suggested in some of his remarks that this law required a demonstration. In particular, the Stagirite suggested in the Metaphysics that PC was the foundations of all proofs, but, on the other hand, we find in the Analytics examples of proofs independent of this principle. Thus, the traditional account on which PC is one of the highest rules of human thinking must be regarded as very far from being obvious. This was the general background of Łukasiewicz’s analysis. He began by delineating three different versions of PC:

logical: no proposition can be simultaneously true and false;
ontological: no property can be simultaneously inherent and not inherent to the same object;
psychological: nobody can believe in a judgment and its denial.

19According to his radically anti-psychological position, Łukasiewicz excluded (3) from further considerations. Thus, (1) and (2) remain. Both are logically equivalent. A careful analysis led Łukasiewicz to the following conclusions:

  • 9 L. Couturat, L’Algèbre de la logique, Paris, Gauthier-Villars, 1905.

PC’s logical (or ontological) version is not obvious in itself;
PC, being not obvious, requires a demonstration;
PC is not the simplest logical rule, because the principle of identity is simpler;
PC is neither a sufficient nor a necessary condition for many laws of logic; one might give many examples of logical rules independent of PC;
Łukasiewicz explains (C) by pointing out that from the point of view of mathematical logic (more specifically, the algebra of logic as presented by Louis Couturat9)
PC is not particularly distinguished, it is not an axiom and it appears as a regular theorem of logic;
it is possible to make deductive and inductive inferences without using PC;
PC is not derivable from the definitions of truth and falsity;
one can give a formal proof of PC on the basis of the definition of an object, but such a proof is just formal, not substantial;
we have a puzzling situation, because (a) PC is not demonstrable, and (b) it seems to require a proof;
the puzzle mentioned in (I) can be solved by pointing out that PC, although logically banal and without value as something basic for our thinking, possesses a great significance from the ethical-practical point of view;
the practical-ethical value of PC consists in its role as a device which enables us to preserve the distinction between truths and falsehoods.

20The book On the Principle of Contradiction in Aristotle was the first analysis of Aristotle’s logic (and some points of his philosophy) by means of mathematical logic. Its influence was powerful, although limited only to Poland (the German summary published in reports on Polish Academy of Sciences and Letters in the same year in the book appeared remained practically unknown). Among other things (see below), it initiated a modern approach to Aristotle, his logic and philosophy. In particular, Aristotelian logic was regarded by the pioneers of mathematical logic (Frege, Russell and others) as something not deserving serious investigation. This negative attitude was rejected by Łukasiewicz and other Poles. Ironically, when Natorp with a characteristic feeling of Western superiority (reinforced by a typical ignorance of Neo-Kantians in other philosophical currents) told Tatarkiewicz «Please write something about Aristotle; it can be useful in your country», perhaps the most original study on Aristotle at that time was very advanced.

  • 10 See G. Priest and R. Routley, «First Historical Introduction: A Preliminary History of Paraconsist (...)
  • 11 For the general history of many-valued logic, see (inter alia) J.B. Rosser and A.R. Turquette, Man (...)
  • 12 S. Lesniewski, «O zasadzie wylaczonego srodka» (On the Principle of the Excluded Middle), Przeglad (...)
  • 13 J. Łukasiewicz, «Wyklad pozegnalny, 7 marca 1918» (Farewell Lecture, March 7, 1918), Warszawa 1918 (...)
  • 14 J. Łukasiewicz, «O pojeciu mozliwosci» (On the Concept of Possibility), Ruch Filozoficzny 6 (1920) (...)
  • 15 Rescher (Many-Valued Logic, p. 8) says that «one principal motivating idea of the latter developme (...)
  • 16 Łukasiewicz’s attitude to his first book was later mixed. He mentioned it rather occasionally, lik (...)

21One can ask whether and to what extent the first Łukasiewicz’s first book contributed to his celebrated discovery of many-valued logic. It did, certainly although it is difficult to say how much (on the other hand, some historians see in it, the first attempt toward paraconsistent logic10). The genesis of many-valued logic is a special topic which deserves a separate study, but let me make some remarks as far as the matter was related to Aristotle11. It is well-known that the Stagirite was puzzled by so-called future contingencies, that is, statements about future contingent facts. Are they true or false today, he asked. The same was Łukasiewicz’s the starting point. Also in 1910, Łukasiewicz delivered in Lvov a talk about the principle of the excluded middle (PEM)12. He observed that the unconditional validity of PEM leads to fatalism (this view was later defined as logical determinism). Łukasiewicz ceased his investigations about PC and PEM until 1917. In 1918, he communicated in a public lecture that he had succeded in constructing a three-valued logic13. He called it Non-Aristotelian. More details were given by him in two talks delivered at Polish Philosophical Society in Lvov in 1920; abstract were published in the same year14. They presented three-valued logic formally. However, Łukasiewicz later changed his view concerning many-valued logic as Non-Aristotelian and preferred to call it Non-Chrysippean. His view was that many-valued logic was not concerned with PC or PEM as logical rules, but with the metalogical decision of whether we should accept or reject the principle of bivalence. He thought that Aristotle had doubts about whether the last principle was acceptable, when he considered future contingencies15. On the other hand, Chrysippus and other Stoics recognized bivalence without reservations. Taking these facts into account, we can say that Łukasiewicz’s study on PC in 1910 had no direct link with his main discovery. In particular, the book of 1910 does not contain any non-classical logic, even in outline. However, when he realized that the rejection of one of the most respected principles did not produce any inconsistency, he could proceed much further and ask for a new formal system of logic. Anyway, his discovery of many-valued logic was certainly closely related to his studies on Aristotle16.

  • 17 J. Łukasiewicz, «Z historii logiki zdan» (On the History of the Logic of Propositions), Przeglad F (...)
  • 18 J. Łukasiewicz, «O sylogistyce Arystotelesa» (On Aristotle’s Syllogistic), Sprawozdania Polskiej A (...)
  • 19 See also J. Łukasiewicz, «On a Controversial Problem of Aristotle’s Modal Syllogistic», Dominican (...)

22Łukasiewicz’s returned to Aristotle a second time in his book published in 1951. As I already mentioned, it is a purely logical treatise. As its title suggests, it analyzes Aristotle’s logical system using contemporary formal devices. This pattern was suggested by Łukasiewicz in the 1920’s as a new approach to the history of logic. He had a special vision of the development of formal logic. According to this perspective, formal logic was invented by Aristotle as a logic of terms, then continued by the Stoics as propositional logic (the discovery of the nature of Stoic logic was a great and revolutionary achievement of Łukasiewicz), further developed by the Schoolmen (particularly, William of Ockham), interrupted by a fatal change in modern philosophy (this was one of the reasons for Łukasiewicz’s negative attitude toward Descartes, Locke and Kant) and invented once more by Frege. Thus, it is fully justifiable to look at old masters as the forerunners of our ideas. At first, Łukasiewicz reconstructed Stoic logic as a logic of propositions17. It is not surprising that Łukasiewicz completed his research programme by a detailed exposition of the logical system of Aristotle, his beloved logician and philosopher. Łukasiewicz began to think about this project formal exposition of Aristotle’s logic in the 1920’s. The first results are contained in his lecture notes from 1929 (see above and note 7). Then, he published a paper about syllogistic18. It was a summary of a monograph prepared in Polish. It was destroyed during World War II. The book published in 1951 is a reconstruction of earlier results with extensive additions. The second edition is second edition is enlarged by a treatment of modal syllogistic19.

  • 20 In particular, it concerns modal syllogistic. Łukasiewicz’s interpretation of Aristotle’s modal sy (...)

23I cannot enter here into the details of Łukasiewicz’s reconstruction of Aristotle’s syllogistic20. Let me restrict myself to the following remarks. First, Łukasiewicz treats syllogistic (and similarly, the theory of direct inference) as a formal system of categorical propositions containing general non-empty terms. Thus, singular and empty terms are excluded. Syllogistic is based on propositional logic as the only prior system. The most characteristic feature of Aristotle’s logic is that it forms a specific system independent of predicate logic. Łukasiewicz formulated an axiom system for the whole of traditional logic (that is, logic captured direct as well as indirect inferences with categorical sentences as premises or conclusions). According to his reading, the traditional logic, contrary to the most popular interpretation, consisted of theorems s and rules, and not exclusively of the latter.

  • 21 J. Slupecki, «On Aristotelian Syllogistic», Studia Philosophica 4 (1951), p. 275-300.

The logic of assertoric sentences has the following form. Let the formulas (lower-case letters are term variables) Uab, Iab, Yab, Oab stand for the sentences «every a is b », «no a is b », «some a are b », «some a are not b », respectively. We can also define (the letter N stands for negation) Yab as NIab and Oab as NUab. The axioms are (in Łukasiewicz’s brackets-free notation; the letter C stands for implication): Uaa; Iaa; CKUmbUamUab (the Barbara mode); CKUmbImaIab (the Datisi mode); the rules are: all rules of classical propositional calculus, substitution for term variables, the definitional replacement according to the definitions of Yab and Oab. This machinery is sufficient for proving all valid modes of syllogistic and direct inference. However, it does not provide a decision procedure. In order to solve this problem, Łukasiewicz introduced two special rejection axioms: (the symbol Image means «it is rejected that») ImageCKUcbUabIac; ImageCKOcbOabIac and the usual rejection rules (if an instance of a formula is rejected, than this formula is CKOcbOabIac and the usual rejection rules (if rejected too). However, this was not a complete solution, because some inconclusive forms remained not rejected on this basis. Jerzy Slupecki (1904-1987) (one of Łukasiewicz’s students) found a rule which completed the issue and made the logic of categorical sentences fully decidable21. The rule (roughly speaking) is as follows: if the implications Cxz and Cyz are rejected, then the implication Ckxyz is also rejectable, where the letters x an y stand for Yab or Oab, but z represents Uab, Iab, Ya, Oab or an implication formed from such formulas or their conjunctions.

  • 22 See W. Kneale and M. Kneale, The Development of Logic, Clarendon Press, Oxford, 1962, p. 80-81 foe (...)
  • 23 See J. Corcoran, «Aristotle’s Natural Deduction System» in J. Corcoran (ed.), Ancient Logic and It (...)
  • 24 For Polish works see next section.

24Łukasiewicz claimed that his analysis was a faithful reconstruction of the logical ideas of the Stagirite. He demonstrated this claim by a very careful analysis of the original texts (Łukasiewicz was a great master of Greek; he was very proud that Sir David Ross did not question of any of his translations of Aristotle into English; according to the oral tradition, he discovered Stoic logic while being reviewing a PhD dissertation about Stoic ethics and checking whether the author had correctly translated Greek texts into Polish). However, Łukasiewicz’s reconstruction was also criticized22. There are attempts to introduce empty and singular terms (some examples given by Aristotle himself and especially by the Schoolmen suggest that the latter should be admitted; the empty terms are much more difficult matter). Other interpretations consider traditional logic as a system of natural deduction23. Still another attempt see it as a part of predicate logic or the theory of classes24.

5. Other Polish works on Aristotelian logic

  • 25 It is difficult to say how strong these studies were influenced by Łukasiewicz. However, one can g (...)

25Several other Polish scholars investigated Aristotle’s logical ideas and tried to interpret them via modern logic25. Let me list some of works in the chronological order:

  • 26 Salamucha devoted his PhD thesis (1927; unpublished) to the modal entailment in Aristotle. Łukasie (...)

Jan Sleszynski (1854-1931), O logice tradycyjnej (On Traditional Logic), Krakow, Polskie Towarzystwo Filozoficzne, 1921; Teoria dowodu (Proof Theory), v. 1, Krakow, Nakladem Kolka Matematyczno-Fizycznego U. U. J. 1925). He interpreted Aristotle’s logic as a part of the theory of classes;
Kazimierz Ajdukiewicz, «Zalozenia logiki tradycyjnej» (The Assumptions of Traditional Logic), Przeglad Filozoficzny 29 (1926), p. 200-229). He showed that the whole traditional logic could be embedded into predicate logic, assuming the existence of at least three objects.
Tadeusz Czezowski, Klasyczna nauka o sadzie i wniosku w swietle logiki wspolczesnej (The Classical Theory of Propositions and Conclusions in the Light of Contemporary Logic), Wilno, Ksiegarnia Jozefa Zawadzkiego, 1927). He offered an analysis (not a full reconstruction) of traditional logic in terms of mathematical logic. In particular, he interpreted categorical sentences as combinations of atomic formulas of predicate logic.
Father Jan Salamucha (1903-1944), Pojecie dedukcji u Arystotelesa i Tomasza z Akwinu (The Concept of Deduction in Aristotle and St. Thomas Aquinas), Warszawa, Polskie Towarzystwo Teologiczne, 1930. The book contains an extensive study of the deductive methodology in Aristotle and Thomas Aquinas26.
T. Czezowski, «Arystotelesa logika zdan modalnych» (Aristotle’s Logic of Modal Propositions),Przeglad Filozoficzny 35 (1932), pp. 232-241. This paper presents one of the first treatments of Aristotle’s theory of modal propositions by means of formal logical machinery. In particular, Czezowski pointed out ambiguities in Aristotle’s understanding of possibility.

  • 27 Moreover, Aristotle’s logic was extensively presented in every textbook of logic published in Pola (...)

26It seems that Aristotelian logic in its modern settings was a subject of special courses in Poland. One such courses was given by Kotarbinski in Warsaw in the 1920’s. It is sure that no other country contributed so much as Poland in modern interpretations of Aristotle’s logic in the first half of 20th century27.

6. Classical theory of truth

27Polish philosophers from the Lvov-Warsaw School made fundamental contributions to the theory of truth. In general, they accepted the so-called classical theory of truth (this label was probably invented in Poland) going back to Aristotle. In his Metaphysics, we find two basic passages concerning truth:

1011b: [...] for to say that that which is, is not or that which is not is, is a falsehood; and to say that that which is, is and that which is not is not, is true; so that, also, he who says that a thing is or not will have the truth or be in error.
1027b: Being as truth and not-being as falsity depend on a putting together and a taking apart [...] true judgment affirms when the subject and predicate are in fact combined, denies when they are separated, while the false does the opposite

28The content of Aristotelian definition of truth is often represented by the famous formula of Thomas Aquinas (De Veritate):

Veritas est adequatio intellectus et rei, secundum quod intellectus dicit esse quod est vel non esse quod non est.

29Polish philosophers took Metaphysics 1011b as a key fragment. The definition given in Metaphysics 1027b was not accepted, because it was based on the allogenic theory of judgment. As I already noted, Twardowski, following Brentano, criticized the so-called correspondence theory of truth (typically expressed by Thomas’ adequatio formula) as based a the relation of correspondence. This line of thought was continued by his students, who considered the idea of correspondence between truth-bearers and the world. For example, Kotarbińvski wrote:

  • 28 T. Kotarbinski, Elementy teorii poznania, logiki formalnej i metodologii nauk (Elements of the The (...)

Let us therefore pass to the classical doctrine and ask what is understood by «accordance with reality». The point is not that a true thought should be a good copy or simile of the thing of which we are thinking, as a painted copy or a photograph is. A brief reflection suffices to recognize the metaphorical nature of such a comparison. We shall confine ourselves to the following: «John thinks truly if and only if John thinks that things are so and so, and things in fact are so and so. »28

30Thus, the Aristotelian conception was interpreted in Poland without the notion of correspondence. Even if the word «correspondence» was used, it was considered as a convenient abbreviation, but not as expressing a genuine relation.

31Tarski’s semantic theory of truth is perhaps the most significant philosophical idea coming from Poland. Tarski always stressed his link with Aristotle. The following quotation is particularly clear in this respect:

We should like in our definition to do justice to the intuitions which adhere to the classical Aristotelian conception of truth–intuitions which find their expression in the well-known words of Aristotle’s metaphysics:
To say of what is that it is not, or what is not that it is, is false, while to say of which is that it is, or what is not that it is not, is true.
If we wished to adapt ourselves to modern philosophical terminology, we could perhaps express this conception by means of the familiar formula:
The truth of a sentence consists in its agreement with (or correspondence to) rea- lity.
(For a theory of truth which is to be based upon the later formulation the term «correspondence theory of truth» has been suggested).
[...] if we agreed to speak of the designata of sentences as «states of affairs», we could possibly use for the same purpose the following «phrase » :
A sentence is true if it designates the existing state of affairs.
[...] all these formulations can lead to various misunderstandings, for none of them is sufficiently precise and clear (although this applies much less to the original Aristotelian formulation than to either of the others); at any rate, none of them can be considered a satisfactory definition of truth. It is up to us to look for a more precise expression of our intuitions.

7. Kotarbinski and Lesniewski

  • 29 Reism is expounded in Kotarbinski’s opus magnum quoted in note 24.
  • 30 T. Kotarbinski, Praxiology. An Introduction to the Science of Efficient Action, tr. by O. Wojtasie (...)

32Kotarbinski invented reism, a radically nominalistic ontology understood as a theory of objects29. Of course, it was very far from Aristotle’s metaphysics, being a form of moderate realism; that is, it admitted universals as forms existing in particular substances. However, reism was obviously inspired by Aristotle’s table of categories and can be consider as an attempt to reduce this list to only one, namely material things (the only ousia). Praxiology was another of Kotarbinski’s fields30. He understood it as investigations concerning the effectiveness of actions. Also in this case we have affinities with Aristotle’s idea of practical knowledge and practical wisdom.

33Lesniewski is still another case to be considered in this context. He proposed a complete system of logic as the foundation of all thinking activity. The calculus of names was its second part. It is a theory of the logical constant «is». An interesting remark about the philosophy behind this system was made by Kotarbinski:

  • 31 T. Kotarbinski, Gnosiology, p. 210.

Let it be added that Lesniewski called his system ontology, in conformity with certain terms already used. [...] The term is further justified by the fact that the only specific primitive term which occurs in the axiom of the system in question is «est», or «is», which corresponds to the Greek ἐστί. Now if we want to emphasise that, we may call the system after the appropriate Greek participe, namely ο [ν, which means «being». [...]. It must [...] be admitted that if Aristotelian definition of the supreme theory [...], be interpreted in the spirit of a «general theory of objects», then both the word and its meaning are applicable to the calculus of terms as expounded by Lesniewski.31

34Lesniewski fully agreed with this statement and added:

  • 32 St. Lesniewski, «O podstawach matematyki» (On the Foundations of Mathematics), Przeglad Filozoficz (...)

[...] I used the name «ontology» [...] to characterize the theory I was developing without offence to my ‘linguistic instincts’ because I was formulating in that theory a certain kind of ‘general principles of existence’.32

Final remarks

35Aristotle became the most respected philosopher of the past in Poland, in particular in the Lvov-Warsaw School. This was also documented by a plan of translating of all of his works into Polish. This project was sponsored by the Polish Academy of Science and Letters. The leading Polish philosophers, including Ajdukiewicz, Kotarbinski, Łukasiewicz and Tatarkiewicz agreed to be translators. World War II prevented the executions of this ambitious project; only the Politics was published. Many Polish philosophers accepted various particular Aristotelian-like views. However, it would be incorrect to say that we had to do with a Polish Aristotelianism. It was rather the case that an adherence to a tradition in philosophy originated with Aristotle and saw a deep link between logic and philosophy. An important novelty consisted in linking this tradition with philosophy strongly inspired by mathematical logic, although the Stagirite was also a logical philosopher, of course, of his times.

Notes

1 The University of Cracow was the only Polish university until 1571. When Vilna University was founded; thus, advanced Polish intellectual life can be strongly identified with that of Cracow, at least to the end of 16th century; in fact, Cracow played a dominant role until the turn of 19th and 20th centuries.

2 I give these data after W. Wasik, Sebastian Petrycy z Pilzna i jego epoka. Ze studiow nad dziejami filozofii w Polsce i recepcja Arystotelesa (Sebastian Petrycy of Pilzno and his Epoch. Studies in the History of Philosophy in Poland and the Reception of Aristotle), Warszawa, Kozianski, 1923.

3 A. Trendelenburg, Geschichte der Kategorienlehre, Berlin, Verlag von G. Bethge, 1846; H. Bonitz, «Über die Kategorien Aristoteles», Sitzunsberichte der kaiserlichen Akademie der Wissenschaften in Wien 1853; K. Prantl, Geschichte der Logik in Abendlande, Erster Band, Leipzig 1855; F. Überweg, System der Logik und Geschichte der logischen Lehren, Bonn 1857.

4 See J. Wolenski, Logic and Philosophy in the Lvov-Warsaw School, Dordrecht, Kluwer, 1989 for a detailed history of this school.

5 A. Tarski, «[Letter to Otto Neurath, April 24, 1930]», Grazer Philosophische Studien 43 (1992), p. 21.

6 Eng. tr. : K. Twardowski, On Content and Object of Presentations, tr. by R. Grossmann, The Hague, 1978.

7 J. Łukasiewicz, Elementy logiki matematycznej (Elements of Mathematical Logic), Warszawa, Nakladem Komisji Wydawniczej Kola Matematyczno-Fizycznego Sluchaczow Uniwersytetu Warszawskiego, 1929; Eng. tr. by O. Wojtasiewicz, Oxford, Pergamon Press, 1963; Die logischen Grundlagen der Wahrscheinlichkeitsrechnung, Polska Akademia Umiejetnosci, Krakow 1913; Eng. tr by O. Wojtasiewicz in J. Łukasiewicz, Selected Works, p. 16-63.

8 Germ. tr. by J. Barski, Über Satz des Widerspruchs bei Aristoteles, Hildesheim, Olms, Eng. tr. (in preparation) to be included in J. Łukasiewicz, Collected Works, v. 1, Aldershot, Asgate (Łukasiewicz himself worked on a translation, but he did not finish this work). A brief summary of this work was published in German «Über Satz vom Widerspruch bei Aristoteles», Bulletin International de l’Academie des Sciences de Cracovie, Classe de Philosophie 24 (1910), p. 15-38. It was translated into English by V. Wedin, «On the Principle of Contradiction in Aristotle», The Review of Metaphysics 24 (1971), p. 485-509 and (as «Aristotle on the Law of Contradiction») in J. Barnes, M. Schofield and R. Sorabji (eds.), Articles on Aristotle, v. 3. Metaphysics, London, Duckworth, 1979, p. 50-62. For a closer analysis of Łukasiewicz’s views on the principle of contradiction see T. Kwiatkowski, «Jan Łukasiewicz–A Historian of Logic», Organon 16-17 (1980-1981), p. 169-188; A. Seddon, «The Principle of Contradiction in Metaphysics Gamma », The New Scholasticism LII (1981, p. 191-207; J. Wolenski, «Jan Łukasiewicz und der Satz vom Widerspruch» in N. Öffenberger and M. Skarica (eds.), Beiträge zum Satz von Widerspruch und zur Aristotelische Prädikationstheorie, Hildesheim, Olms, 2000, p. 1-42.

9 L. Couturat, L’Algèbre de la logique, Paris, Gauthier-Villars, 1905.

10 See G. Priest and R. Routley, «First Historical Introduction: A Preliminary History of Paraconsistent and Dialethic Approaches» in G. Priest, R. Routley and J. Norman (eds.), Paraconsistent Logic. Essays on the Inconsistent, München, Philosophia Verlag, 1989, p. 25-29.

11 For the general history of many-valued logic, see (inter alia) J.B. Rosser and A.R. Turquette, Many-Valued Logics, Amsterdam, North-Holland, 1952; A.A. Zinoviev, Philosophical Problems of Many-Valued Logic, Dordrecht, Reidel, 1963; N. Rescher, Many-Valued Logic, McGraw Hill, New York 1967; S. Haack, Philosophy of Logics, Cambridge, Cambridge University Press, 1978; G. Malinowski, Many-Valued Logic, Clarendon Press, Oxford 1993, S. Haack, Deviant Logic. Fuzzy Logic. Beyond the Formalism, Chicago, The Universiyty of Chicago Press, 1996. See also discussionjs in A. Menne and N. Öffenberger (eds.), Modallogik und Mehrhertigkeit, Hildesheim, Olms 1988; N. Öffenberger, Zur Vorgeschichte der mehwertigten Logik in der Antike, Heildesheim, Olms, 1990.

12 S. Lesniewski, «O zasadzie wylaczonego srodka» (On the Principle of the Excluded Middle), Przeglad Filozoficzny 13 (1910), p. 372-373; Eng. tr. by P. Simons and J. Wolenski (with comments by the translators)), History and Philosophy of Logic 8 (1988), p. 67-69.

13 J. Łukasiewicz, «Wyklad pozegnalny, 7 marca 1918» (Farewell Lecture, March 7, 1918), Warszawa 1918; En. tr. by O. Wojtasiewicz in J. Łukasiewicz, Selected Works, p. 84-86.

14 J. Łukasiewicz, «O pojeciu mozliwosci» (On the Concept of Possibility), Ruch Filozoficzny 6 (1920), p. 169-170; «O logice trojwartosciowej», Ruch Filozoficzny 691920), p. 170-171; Eng. tr by H. Hiz in S. McCall (ed.), Polish Logic 1920-1939, Clarendon Press, Oxford, 1967, p. 15-18 and (only the second paper) in J. Łukasiewicz, Selected Work, p. 87-88.

15 Rescher (Many-Valued Logic, p. 8) says that «one principal motivating idea of the latter development of his [that is, Łukasiewicz – J. W.] – vis. the issue of future contingency–is already a major theme» in 1910 book on the principle of contradiction in Aristotle. However, this statement is not correct. On the contrary, this issue is not considered in this book at all.

16 Łukasiewicz’s attitude to his first book was later mixed. He mentioned it rather occasionally, like most his works before the 1920’s. When Łukasiewicz concentrated on hard mathematical logic, he abstained from speaking very much about philosophical matters. Certainly, he considered his On the Principle of Contradiction in Aristotle to be more philosophical than logical. On the other hand, the mentioned fact that he began to translated this book into English could suggest that he recognized its value. It is confirmed by an oral communication of Czeslaw Lejewski who told me that Łukasiewicz considered his first work on Aristotle as valuable.

17 J. Łukasiewicz, «Z historii logiki zdan» (On the History of the Logic of Propositions), Przeglad Filozoficzny 37 (1934), p. 417-437; En. tr. by O. Wojtasiewicz in J. Łukasiewicz, Selected Works, p. 197-212. Heinrich Scholz qualified this paper as the most interesting twenty pages written about the history of logic. See Kwiatkowski’s, «Jan Łukasiewicz – A Historian of Logic» for a general characterization of Łukasiewicz’s writings in the history of logic.

18 J. Łukasiewicz, «O sylogistyce Arystotelesa» (On Aristotle’s Syllogistic), Sprawozdania Polskiej Akademii Umiejetnosci 44 (1939), p. 220-227.

19 See also J. Łukasiewicz, «On a Controversial Problem of Aristotle’s Modal Syllogistic», Dominican Studies VII (1954), p. 114-128.

20 In particular, it concerns modal syllogistic. Łukasiewicz’s interpretation of Aristotle’s modal syllogistic is heavily based on Łukasiewicz’s modal logic. See discussions in S. McCall, Aristotle’s Modal Syllogisms, Amsterdam, North-Holland, 1963; F. Buddensiek, Die Modallogik des Aristoteles in Analytica Priora A, Hildesheim, Olms, 1994; P. Thom, The Logic of Essentialism. An Interpretation of Aristotle’s Modal Syllogistic, Dordrecht, Kluwer, 1996.

21 J. Slupecki, «On Aristotelian Syllogistic», Studia Philosophica 4 (1951), p. 275-300.

22 See W. Kneale and M. Kneale, The Development of Logic, Clarendon Press, Oxford, 1962, p. 80-81 foe a general criticins pointing out that Lukasiewcz departed too much from the ghost of Aristotle’s logic.

23 See J. Corcoran, «Aristotle’s Natural Deduction System» in J. Corcoran (ed.), Ancient Logic and Its Modern Interpretations, Dordrecht, Reidel, 1972, p. 85-131. Other works (a selection): I. M. Bochenski, Ancient Formal Logic, Amsterdam, North-Holland, 1972; G. Patzig, Aristotle’s Theory of Syllogism. A Logico –Philosophical Study of Book of the Prior Analytics, Dordrecht, Reidel, 1968; P. Thom, The Syllogism, München, Philosophia Verlag, 1981.

24 For Polish works see next section.

25 It is difficult to say how strong these studies were influenced by Łukasiewicz. However, one can guess that his work at least created a climate for a considerable interest in the Stagirite.

26 Salamucha devoted his PhD thesis (1927; unpublished) to the modal entailment in Aristotle. Łukasiewicz was one of the examiners.

27 Moreover, Aristotle’s logic was extensively presented in every textbook of logic published in Poland. This concerns elementary textbooks used in secondary schools as well as more advanced ones written for students of universities.

28 T. Kotarbinski, Elementy teorii poznania, logiki formalnej i metodologii nauk (Elements of the Theory of Knowledge, Formal Logic and the Methodology of Science), Lwow, Ossolineum, 1929; Eng. tr. by O. Wojtasiewicz, Gnosiology. The Scientific Approach to the Theory of Knowledge, Oxford, Peganon Press, 1966, p. 106-107.

29 Reism is expounded in Kotarbinski’s opus magnum quoted in note 24.

30 T. Kotarbinski, Praxiology. An Introduction to the Science of Efficient Action, tr. by O. Wojtasiewicz, Oxford, Pergamon Press, 1965.

31 T. Kotarbinski, Gnosiology, p. 210.

32 St. Lesniewski, «O podstawach matematyki» (On the Foundations of Mathematics), Przeglad Filozoficzny 34 (1931); Eng. tr by D. I. Barnett) in St. Lesniewski, Collected Works, Dordrecht, Kluwer, 1992, p. 374 (Note: the translation is not quite faithful to the original, because «ogolne zasady bytu» should be rendered by «general principles of being», not by «general principles of existence»).

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