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Łukasiewicz’s concept of logic and anti-psychologism

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Abstract

In the nineteenth century, philosophy was at a crossroads. While the natural and technical sciences were developing in an unprecedented fashion, philosophy seemed to be stalled. Inspired by the progress of the natural sciences, many philosophers attempted to make such progress in philosophy and make philosophy a truly scientific discipline. This effort was also reflected in the philosophy of the Lvov-Warsaw school. While its founder, Kazimierz Twardowski, following his teacher Franz Brentano, promoted psychology as a method of scientific philosophy, one of his first students, Jan Łukasiewicz, was convinced that mathematical logic was such a method. To use mathematical logic as a tool, Łukasiewicz had to, however, argue convincingly that logic is an independent science and hence is not a part of psychology, i.e., arguing for anti-psychologism in logic. He initially adopted the arguments provided by Husserl, then celebrated as a proponent of anti-psychologism, and Frege’s views. When Łukasiewicz developed, however, his systems of many-valued logic, he denied almost all the principles that characterise Husserl and Frege’s anti-psychologism, i.e., the objectivity of the laws of logic, the existence of apodictic propositions, and the distinction between a priori and empirical sciences. He was, however, a proponent of anti-psychologism up to the end of his life. The aim of my paper is to introduce Łukasiewicz’s unique concept of anti-psychologism that significantly affected the views of mathematical logic in the Lvov-Warsaw School, and the views of his colleagues which helped him develop the concept.

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Notes

  1. The addition ‘in logic’ is important as there could also be psychologism (or anti-psychologism) in other philosophical disciplines. (see e.g. Kusch, 1995, p. 105). The terms psychologism and anti-psychologism mean psychologism in logic and anti-psychologism in logic, respectively in this paper.

  2. At the beginning of his academic career, Łukasiewicz spent some time in Berlin contributing to experiments that took part at the Institute of Philosophy. He proposed in his letters to Twardowski that he could cooperate in a similar institute at the University of Lvov (see Łukasiewicz, 1905/1998, pp. 470–471). It was at the time when he already denied psychologism in logic. It seems therefore that he was not entirely sceptical about psychology, although, he aimed to lessen its position in philosophy. Łukasiewicz (1927/1998, pp. 41–42) later, however, explicitly acknowledged mathematical logic as the only method of scientific philosophy.

  3. Łukasiewicz (1953) knew and appreciated the work of another proponent of anti-psychologism, Bernard Bolzano. There is no evidence, however, that Łukasiewicz considered Bolzano’s views on psychologism in logic, unlike Husserl (1900/2001, pp. 142–143) who directly expressed his gratitude to Bolzano.

  4. In Łukasiewicz’s (1907/1961) paper, the precise formulation of arguments slightly differs. Namely, he formulated them as:

    the laws of logic are not grounded in laws of psychology.

    the laws of logic have a different content than the laws of psychology.

    logic as a science does not concern correct reasoning but truth and falsehood.

    logical terms differ from psychological terms.

    In my formulation, I merged the first two and pointed out another distinction which was important to Łukasiewicz’s formulation of anti-psychologism later. All four points will be developed in further chapters.

  5. Surma (2012, pp. 64–65) pointed out this issue out in his book but did not go into detail as to how Łukasiewicz’s views on psychologism changed.

  6. Claiming this, Łukasiewicz clearly followed Husserl (1900/2001, p. 47) and also Frege (1893/1964, p. 13).

  7. Using the term ‘proposition’ here, it has to be pointed out that the term is used without any philosophical connotation, i.e., it by no means meant the Fregean propositions that are placed in the third realm. Łukasiewicz and several of his colleagues from the Lvov-Warsaw School opposed the introduction of these entities in logic. The term ‘zdanie’ which would correspond to the English word ‘sentence’, is used in Polish. The term ‘sentence’ has a slightly different meaning in English, however, and cannot be used in logic. This issue is further discussed in the fifth chapter of my paper.

  8. The psychological law of contradiction is false, as Łukasiewicz (1910/1987, pp. 33–35) later emphasized in his book. In the book, Łukasiewicz (1910/1987, p. 9–13) also identified a third meaning of the law of contradiction, namely an ontological one. Its formulation is ‘no object can have and lack a property at the same time’.

  9. It is important to stress that this empirical research concerns by no means psychology. Łukasiewicz (1922/1961) favoured in this respect physics. He did not express clearly, however, which new findings of physics could undermine laws of logic. In contrast, his colleague Tarski (1987, pp. 31–32) and also Quine (1951, p. 40) clearly mentioned quantum mechanics as a possible refutation of certain laws of logic.

  10. Paradoxically, it is also a period when intensional systems of logic began to flourish.

  11. Łukasiewicz did not describe these abstract objects among which he listed cause nor did he intend to do so. Woleński (1989, pp. 54–55) argues that the best candidate for such objects might be certain Platonistic entities, as they are not placed in human minds either in time or in space.

  12. To differentiate his approach from the psychological one, Łukasiewicz (1906/1961, p. 49) pointed out that he did not ascribe the properties to the objects of thoughts but to the judgements.

  13. For instance, if electricity is passing through a thin platinum wire (the cause), the wire gets warm (the effect). The fact, that electricity is passing through the wire, implies that the wire gets warm. However, the sole fact that the wire gets warm does not imply the cause, as there might be other causes that affect the wire. In contrast, when the wire is not warm (e.g., the effect is missing), it is the case that electricity is not passing through it (see Łukasiewicz 1906/1961, pp. 26–28).

  14. Łukasiewicz (1910/1987, pp. 13–14) was aware that Meinong also differentiated between two meanings of the term ‘judgement’. Meinong identifies the judgements in the logical meaning with his ‘Objectives’. However, Łukasiewicz’s judgements in the logical meaning are not entirely equal to ‘Objectives’, since Łukasiewicz (1910/1987, p. 14) described them as: “Objectives expressed in words or other symbols”.

  15. The change of terms in clearly visible in the new Polish version of the paper, where both editions are compared (see Łukasiewicz, 1912/1970). The translator of the English version of the paper seemingly translated the first version of the paper (see Łukasiewicz, 1912/1970).

  16. It is important, however, to point out that Łukasiewicz was not a nominalist.

Bibliography

  • Betti, A. (2006). The Strange Case of Savonarola and the Painted Fish: On the Bolzanization of Polish Thought. In A. Chrudzimski, & D. Łukasiewicz (Eds.), Actions, Products and Things: Brentano and Polish Philosophy (pp. 55–81). Frankfurt: Ontos Verlag. https://doi.org/10.1515/9783110325706.55

    Chapter  Google Scholar 

  • Frege, G. (1893/1964). Grundgesetze der Arithmetik. Jena: Pohle; English The Basic Laws of Arithmetic: Exposition of the System. Berkeley: University of California Press

    Google Scholar 

  • Husserl, E. (1900/2001). Logische Untersuchungen. Erster Teil: Prolegomena zur reinen Logik. vol. 1. Halle: Niemayer; English Husserl, E. Logical Investigations, J. Findlay (trans.) London and New York: Routledge

  • Kleszcz, R. (2009). L’antipsychologisme en logique. Twardowski et Łukasiewicz. In A. Horecka (Ed.), Logic, Methodology and Philosophy of Science at Warsaw University (5 vol., pp. 163–170). Semper: Warsaw

    Google Scholar 

  • Koj, L. (1977). Logika a psychologia. W siedemdziesięciolecie referatu Jana Łukasiewicza. Studia Filozoficzne, 6, 21–26

    Google Scholar 

  • Kotarbiński, T. (1929/1961). Elementy teorii poznania, logiki formalnej i metodologii nauk. Lviv: Zakład Narowowy im. Ossolińskich – Wydawnictwo; repr. Wrocław: Zakład Narowowy im. Ossolińskich – Wydawnictwo

  • Kusch, M. (2005). Psychologism: A Case Study in the Sociology of Philosophical Knowledge. London: Routledge

    Book  Google Scholar 

  • Leśniewski, S., Surma, S. J., & Srzednicki, J. T. J. (1927–31/1992). J. D. Barnett, and V. F. Rickey (eds.) O podstawach matematyki. Przegląd Filozoficzny, 30(2–3), 164–206, 31(2–3), 261–299, 32(1), 60–101, 33(1–2), 77–105, 34(2–3), 142–170; English S. Leśniewski. On the Foundations of Mathematics. In S. Leśniewski, Collected Works I. (pp. 174–382). Surma, S. J., Srzednicki, J. T. J., J. D. Barnett, and V. F. Rickey (eds.), Dordrecht: Kluwer Academic Publishers

  • Łukasiewicz, J. L. (1904/1998a). Z Korespondencji z Kazimierzem Twardowskim 17.05. 1904. In J. L. Łukasiewicz. Logika i metafizyka (pp. 459–460). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1904/1998b). Teza Husserla o stosunku logiki do psychologii. Przegląd Filozoficzny, 7(4), 476–477; repr. In J. L. Łukasiewicz. Logika i metafizyka (pp. 341–342). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1905/1998). Z Korespondencji z Kazimierzem Twardowskim 06.02. 1905. In J. L. Łukasiewicz. Logika i metafizyka (pp. 468–471). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (Ed.). (1906/1961). Analiza i konstrukcja pojęcia przyczyny. Przegląd Filozoficzny, 9(2), 105–179; repr. In J. L. Łukasiewicz. Z zagadnień logiki i filozofii: Pisma wybrane. (pp. 9–62). Słupecki (ed.), Warsaw: Państwowe wydawnictwo naukowe

  • Łukasiewicz, J. L. (Ed.). (1907/1961). Logika a psychologia. Przegląd Filozoficzny, 10(4), 489–491; repr. J. L. Łukasiewicz. Z zagadnień logiki i filozofii: Pisma wybrane. (pp. 63–65). Słupecki (ed.), Warsaw: Państwowe wydawnictwo naukowe

  • Łukasiewicz, J. L. (1910/1987). O zasadzie sprzeczności u Arystotelesa, Studium krytyczne. Cracow: Polska Akademia Umiejętności; repr. Woleński J (ed.), Warsaw: Państwowe wydawnictwo naukowe

  • Łukasiewicz, J. L. (1912/1998). O twórczości w nauce. In: Księga pamiątkowa ku uczczeniu 250-tej rocznicy założenia Uniwersytetu Lwowskiego przez króla Jana Kazimierza r. 1661. Lviv: Uniwersytet Lwowski.; repr. In J. L. Łukasiewicz. Logika i metafizyka (pp. 9–33). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1912/1970). O twórczości w nauce. In: Księga pamiątkowa ku uczczeniu 250-tej rocznicy założenia Uniwersytetu Lwowskiego przez króla Jana Kazimierza r. 1661. Lviv: Uniwersytet Lwowski.; English J. L. Łukasiewicz. Creative Elements in Science. In L. Borkowski (ed.), Selected Works (pp. 1–15). Amsterdam, Warsaw: North-Holland Publishing Company – Polish Scientific Publisher

  • Łukasiewicz, J. L. (1920/1998). O przedmiocie logiki. Tydzień Polski, 1(33), 16; repr. In J. L. Łukasiewicz. Logika i metafizyka (p. 57). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1922/1961). O determinizmie. Rector’s lecture delivered at the University of Warsaw at the Inauguration of the academic year 1922/1923.; English J. L. Łukasiewicz. On Determinism. In L. Borkowski (ed.), Selected Works (pp. 110–128). Amsterdam, Warsaw: North-Holland Publishing Company –Polish Scientific Publisher

  • Łukasiewicz, J. L. (1924/1998). Kant i filozofia nowożytna. In J. L. Łukasiewicz. Logika i metafizyka (pp. 365–368). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1927/1998). O metodę w filozofii. Przegląd Filozoficzny, 31(1–2), 3–5; print In J. L. Łukasiewicz. Logika i metafizyka (pp. 41–42). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1929/1966). Elementy Logiki Matematycznej. Authorised textbook. Warsaw: Komisja Wydawnicza Koła Matematyczno-Fizycznego Słuchaczów Uniwersytetu Warszawskiego; English. Łukasiewicz, J. L. Elements of Mathematical Logic. Warsaw: PWN-Polish Scientific Publisher

  • Łukasiewicz, J. L. (1929/1988). O rozumowaniu w naukach przyrodniczych. In: Łukasiewicz, J. L. (1929) Elementy Logiki Matematycznej. Authorised textbook. Warsaw: Komisja Wydawnicza Koła Matematyczno-Fizycznego Słuchaczów Uniwersytetu Warszawskiego; repr. Studia Filozoficzne, 270(5), 124–126

  • Łukasiewicz, J. L. (1936/1970). Logistyka i filozofia. Przegląd Filozoficzny, 39(2), 115–131; English J. L. Łukasiewicz. Logistic and Philosophy. In L. Borkowski (ed.), Selected Works (pp. 218–235). Amsterdam, Warsaw: North-Holland Publishing Company – Polish Scientific Publisher

  • Łukasiewicz, J. L. (Ed.). (1937/1970). W obronie logistyki, In: Myśl katolicka wobec logiki współczesnej. Poznań: Studia Gnesnesia, 15, 12–26, 159–165; English J. L. Łukasiewicz. In Defense of Logistic. In L. Borkowski (ed.), Selected Works (pp. 236–249). Amsterdam, Warsaw: North-Holland Publishing Company – Polish Scientific Publisher

  • Łukasiewicz, J. L. (1947/1998). Z Korespondencji z J. M. Bocheńskim 7. 10. 1947. In J. L. Łukasiewicz. Logika i metafizyka (pp. 523–524). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1949-1954/2013). Pamiętnik, manuscript stored in the archive of the University of Warsaw; print J. J. Jadacki, P. Surma (eds.), Warsaw: Semper

  • Łukasiewicz, J. L. (1953). Łukasiewicz to Prior 2. 5. 1953, unpublished manuscript stored in Bodleian Library in Oxford, Box 4

  • Łukasiewicz, J. L. (Ed.). (1953/1970). A System of Modal Logic. The Journal of Computing Systems, 1(3), 111–149; repr. In L. Borkowski (ed.), Selected Works (pp. 352–390). Amsterdam, Warsaw: North-Holland Publishing Company – Polish Scientific Publisher

  • Łukasiewicz, J. L. (Ed.). (1954/1970). Arithmetic and Modal Logic. The Journal of Computing Systems, 1(4), 213–219; repr. In L. Borkowski (ed.), Selected Works (pp. 391–400). Amsterdam, Warsaw: North-Holland Publishing Company – Polish Scientific Publisher

  • Łukasiewicz, J. L. (1954/1998). On a Controversial Problem of Aristotle’s Modal Syllogistic. Dominican Studies, 7, 114–128, repr. J. L. Łukasiewicz O pewnym spornym problemie arystotelesowskiej sylogistyki modalnej. In J. L. Łukasiewicz. Logika i metafizyka (pp. 252–265). J. J. Jadacki (red.). Warsaw: Wydział Filozofii i Socjologii Uniwersytetu Warszawskiego

  • Łukasiewicz, J. L. (1957). Aristotle’s Syllogistic: From the Standpoint of Modern Formal Logic. 2nd edition. Oxford: Clarendon Press

  • Miszczyński, R. (2008). Antypsychologizm i formalizm Jana Łukasiewicza. Prace Naukowe Akademii im. Jana Długosza w Częstochowie. Filozofia, 5, 37–47

  • Quine, W. V. O. (1951). Main Trends in Recent Philosophy: Two Dogmas of Empiricism. The Philosophical Review, 60(1), 20–43. https://doi.org/10.2307/2181906

    Article  Google Scholar 

  • Rojszczak, A. (2005). In J. Woleński (Ed.), From the Act of Judging to the Sentence: The Problem of Truth Bearers from Bolzano to Tarski. Dordrecht: Springer

    Chapter  Google Scholar 

  • Simons, P. (2020). Jan Łukasiewicz. In The Stanford Encyclopedia of Philosophy (Summer 2020 Edition). E. N. Zalta (ed.), Available at: <https://plato.stanford.edu/archives/sum2020/entries/lukasiewicz/>. [Accessed 1 March 2021]

  • Surma, P. (2012). Poglądy filozoficzne Jana Łukasiewicza a logiki wielowartościowe. Warsaw: Semper

    Google Scholar 

  • Tarski, A. (1987). A Philosophical Letter of Alfred Tarski. M. White (ed.). The Journal of Philosophy, 84(1), 28–32. https://doi.org/10.2307/2027134

  • Woleński, J. (1989). Logic and Philosophy in the Lvov-Warsaw School. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-94-009-2581-6

    Book  Google Scholar 

  • Woleński, J. (1999). Mathematical Logic in Poland 1900–1939 People, Circles, Institutions, Ideas. In J. Woleński (Ed.), Essays in the History of Logic and Logical Philosophy (pp. 59–84). Cracow: Jagiellonian University Press

    Google Scholar 

  • Woleński, J. (2003). Psychologism and Metalogic. Synthese, 137, 179–193. https://doi.org/10.1023/A:1026291203636

    Article  Google Scholar 

  • Woleński, J., & Binder, T. (1991). Kazimerz Twardowski: Selbstdarstellung. Grazer Philosophische Studien, 39(1), 1–26. https://doi.org/10.1163/18756735-90000458

    Article  Google Scholar 

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Acknowledgements

Previous versions of the text have been presented at the Philosophical Workshop of the Lvov-Warsaw School Research Center at the University of Warsaw and the Sixteenth International Congress on Logic, Methodology, and Philosophy of Science and Technology in Prague. I am grateful to the audiences at these events for their comments. My colleagues from Tadeusz Ciecierski’s research group and my colleague from Palacký University in Olomouc, Martina Číhalová, reviewed previous versions of the text and suggested several important improvements. I would like to thank them from the bottom of my heart. I am also obliged to unknown reviewers of this paper for their suggestions. The work on this paper was supported by the project “JG_2020_005 Times, Events, and Logical Specification” of Palacký University Olomouc, the Czech Republic.

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I began, therefore, my war with psychology, which, as it seems to me, does not completely justly occupy a so dominant position in philosophy (Łukasiewicz, 1904/1998a, p. 460)

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Rybaříková, Z. Łukasiewicz’s concept of logic and anti-psychologism. Synthese 200, 103 (2022). https://doi.org/10.1007/s11229-022-03479-3

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