V. Losev: Logic and/or Dialectics. Discontinuity of Numerical Sets as a Form of Expression of Personal Being: Losev, Luzin, Florensky

Aim. This article was brought into being by the attempt to analyze the recent publication of A. F. Losev’s works on the classification of various types of formal logical knowledge and their creative commentary of V. P. Troitsky. The task is to determine the significance of the Losev’s logical thought and the place of the above-mentioned Losev’s text in the history of the overall logical research.

Methodology. The procedure for the study of the historical and philosophical phenomenon – logical research in the USSR in the 1920–1940s – is based on the following scientific methods: historical, hermeneutic, nomothetic, ideographic, synchronic, diachronic, as well as the method of comparative analysis.

Results. The result of the study was a clearer, more detailed definition of the phenomenon of logical research in the period the 1920–1940s in the overall picture of the history of philosophy of the USSR.

Research implications. This work is one of the first studies of the formation of logical thought in the USSR during the designated historical period. Within the framework of the study, different aspects of logical knowledge that have not been studied to date are problematized and special ways of their nowadays actualization are proposed.

1. Anisov A. M., Malyukova O. V., Demina L. A. Stanovlenie otechestvennoj logiki: diskursy i sud’by [Formation of Domestic Logic: Discourses and Fates]. Moscow, RG-Press Publ., 2021. 672 p.

2. Asmus V. F. Logika [Logics]. Moscow, State Publishing House of Political Literature, 1947. 388 p.

3. Biryukov B. V. Trudnye vremena filosofii. Kn. 1: Otechestvennaya istoricheskaya, filosofskaya i logicheskaya mysl’ v predvoennye, voennye i pervye poslevoennye gody [Hard Times for Philosophy. V. 1: Domestic Historical, Philosophical, and Logical Thought in the Prewar, War, and First Postwar Years]. Moscow, KomKniga Publ., 2019. 244 p.

4. Biryukov B. V. Trudnye vremena filosofii. Otechestvennye logika, istoriya i filosofiya v poslednie stalinskie gody. Ch. 2.: Ideologicheskie kampanii 1948–1950 godov. Logicheskoe i psihologicheskoe. Bogoborcheskaya sovetskaya filosofiya. Problemy russkogo nacional’nogo soznaniya [Hard Times for Philosophy. Domestic Logic, History, and Philosophy in the Last Stalin Years. Part 2: Ideological Campaigns of the 1948– 1950s. Logical and Psychological. God-fighting Soviet Philosophy. Problems of Russian National Consciousness]. Moscow, LIBROKOM Publ., 2009. 192 p.

5. Vasil’ev N. A. [Logic and Metalogic]. In: Logos. 1912–1913 gg. Kn. 1 i 2 [Logos. 1912–1913. Book 1 and 2]. Moscow, Musaget Publ., 1913, pp. 53–81.

6. Gogotishvili L. A. Nepryamoe govorenie [Indirect Speaking]. Moscow, Yazyki slavyanskih kul’tur Publ., 2006. 720 p.

7. Dietzgen J. Letters on Logic. Especially Democratic-Proletarian Logic (Rus. ed.: Dauge P. G., ed. Pis’ma o logike. Special’no-demokraticheski-proletarskaya logika. Moscow, Librokom Publ., 2010. 144 p.).

8. Kaku M. Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension (Rus. ed.: Sapcina U. V., transl. Giperprostranstvo. Nauchnaya odisseya cherez parallel’nye miry, dyry vo vremeni i desyatoe izmerenie. Moscow, Al’pina non-fikshn Publ., 2024. 660 p.).

9. Kaku M. Physics of the Impossible: A Scientific Exploration into the World of Phasers, Force Fields, Teleportation, and Time Travel (Rus. ed.: Lisova N., transl. Fizika nevozmozhnogo. Moscow, Al’pina nonfikshn Publ., 2024. 586 p.).

10. Kolesnichenko Yu. V. Lichnost’ v russkoj filosofii 1920–1930-h godov: biografiya idei [Personality in Russian Philosophy of the 1920–1930s: Biography of an Idea]. Moscow, Enciklopedist-MAKSIMUM Publ., 2018. 416 p.

11. Kol’man E. Uchebnik logiki [Textbook of Logic]. Moscow, OGIZ Publ., Gospolitizdat Publ., 1942. 175 p.

12. Kol’man E. Ya. Predmet i metod sovremennoj matematiki [Subject and Method of Modern Mathematics]. Moscow, State Socio-Economic Publ., 1936. 315 p.

13. Korsakov S. N. [From the History of the Revival of Logic in the USSR in 1941–1946. Part I]. In: Logicheskie issledovaniya [Logical Studies], 2015, vol. 21, no. 2, pp. 145–169.

14. Losev A. F. Dialekticheskie osnovy matematiki [Dialectical Foundations of Mathematics]. Moscow, Academia Publ., 2013. 800 p.

15. Losev A. F. [Methods of Modern Logic]. In: Russkaya filosofiya [Russian Philosophy], 2023, no. 2 (6), pp. 59–85.

16. Motroshilova N. V. [“Imaginary Logic” by N. A. Vasiliev and the Contribution of V. A. Smirnov to Its Research]. In: Filosofiya nauki [Philosophy of Science], 1998, no. 4, pp. 192–201.

17. Rubinshtejn S. L. [Study of the Problem of Method (dissertation for the degree of Doctor of Philosophy. 1914. University of Marburg. Germany)]. In: Transcendental’nyj zhurnal [Transcendental Journal], 2021, vol. 2, iss. 3. Available at: https://transcendental.su/S271326680018222-4-1 (accessed: 26.05.2024). DOI: 10.18254/S271326680018222-4

18. Sedyh O. M. [The Role of Mathematics in P. A. Florensky’s Theory of Culture]. In: Chelovek – kul’tura – obshchestvo. Aktual’nye problemy filosofskih, politologicheskih i religiovedcheskih issledovanij. T. 2 [Man – Culture – Society. Actual Problems of Philosophical, Political and Religious Studies. Vol. 2]. Moscow, Sovremennye tetradi Publ., 2002, pp. 273–276.

19. Sinkevich G. I. [Moscow Mathematicians and Philosophers of the First Third of the 20th Century: Descriptive Set Theory and the Problem of Naming]. In: Genealogiya cennostej v russkoj filosofii Serebryanogo veka: sbornik nauchnyh trudov [Genealogy of Values in Russian Philosophy of the Silver Age: Collection of Scientific Papers]. St. Petersburg, St. Petersburg State University of Economics Publ., 2013, pp. 444–456.

20. Smirnov A. V. Vsechelovecheskoe vs obshchechelovecheskoe [Panhuman vs Universal]. Moscow, Sandra Publ., YASK Publ., 2019. 216 p.

21. Smirnov A. V., Solondaev V. K. Processual’naya logika [Procedural Logic]. Moscow, Sandra Publ., 2019. 150 p.

22. Troicky V. P. [On A. F. Losev’s Assessment of Logical Methods]. In: Russkaya filosofiya [Russian Philosophy], 2023, no. 2 (6), pp. 55–58.

23. Snigireva T. A., Podchinenov A. V., eds. Fenomen zateksta [The Phenomenon of the Behind the Text]. Ekaterinburg, Ural University Publ., St. Petersburg, Publ., Aletejya Publ., 2023. 532 p.

24. Florensky P. A. [Introduction to the Dissertation “The Idea of Discontinuity as an Element of Worldview” (1900–1903)]. In: Istoriko-matematicheskie issledovaniya. Vyp. XXX [Historical and Mathematical Research. Issue XXX]. Moscow, Nauka Publ., 1986, pp. 159–177.

25. Florensky P. A. [Pythagorean Numbers]. In: Florensky P. A. Sochineniya. T. 2 [Works. Vol. 2]. Moscow, Mysl’ Publ., 1996, pp. 632–646.

26. Yurkevich E. N. [Characteristics of Volume in Hermeneutic Logic]. In: Uchyonye zapiski Tavricheskogo nacional’nogo universiteta im. V. I. Vernadskogo. Seriya: Filosofiya. Kul’turologiya. Politologiya. Sociologiya [Scientific Notes of the Tauride National University. V. I. Vernadsky. Series: Philosophy. Culturology. Political science. Sociology], 2011, vol. 24 (63), no. 1, pp. 287–294.

27. Kolman E. Logika. Praha, 1947. 184 p.