Skip to main content

Russian Origins of Non-Classical Logics

  • Chapter
  • First Online:
Modern Logic 1850-1950, East and West

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

This paper reviews the conditions under which non-classical logic was historically promoted in Russia. It identifies those Russian scholars who, beginning in the second part of the nineteenth and in the turn of twentieth century, contributed most to the formation and development of non-classical logic along with the socio-cultural milieu crucial to the birth of non-classical (non-Aristotelian) ideas.

Dedicated to Dr Irving Anellis, whose God-given talent in the field of history of logic is highly appreciated by his Soviet/Russian colleagues.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. C. Eisele, The New Elements of Mathematics by Charles S. Peirce, in Men and Institutions in American Mathematics, ed. by J.D. Tarwater, J.T. White, J.D. Miller (Lubbock, Texas Tech University Press, 1976), pp. 111–122

    Google Scholar 

  2. Carus, Paul (ed.), The nature of logical and mathematical thought. Monist XX(1), 33–75 (1910)

    Google Scholar 

  3. C.S. Peirce (P.C.), Non-Aristotelian logic. Monist XX(1), 158–159 (1910)

    Google Scholar 

  4. E.Y. Bakhmutskaya, About early works related to the foundations of mathematics of S.O. Shatunovsky. Historico-Math. Stud. 16, 207–218 (1965) (in Russian)

    Google Scholar 

  5. E.A. Sidorenko, Ideas of non-monotonic and paraconsistent logic in the works of P. Florensky. Log. Investig. 4, 290–303 (1997) (in Russian)

    MathSciNet  Google Scholar 

  6. B.V. Birukov, B.M. Shuranov, Russian neo-Kantians: on the verge of paraconsistency idea, in Modern Logic: Problems of Theory, History, and Applications (St.-Petersburg University press, 1996), pp. 125–127 (in Russian)

    Google Scholar 

  7. V.A. Bazhanov, Nicolai A. Vasiliev (Nauka., Moscow, 1988) (in Russian)

    Google Scholar 

  8. V.A. Bazhanov, N.A. Vasiliev and his Imaginary Logic: The Revival of One Forgotten Idea (Kanon, Moscow, 2009) (in Russian)

    Google Scholar 

  9. V.A. Bazhanov, The Origins and Emergence of Non-Classical Logic in Russia (nineteenth century until the turn of the twentieth century), in Zwischen traditioneller und moderner Logik. Nichtklassiche Ansatze (Mentis-Verlag, Paderborn, 2001), pp. 205–217

    Google Scholar 

  10. A.I. Mal’tsev, Selected works, vol. 1 (Nauka, Moscow, 1976) (in Russian)

    MATH  Google Scholar 

  11. A. Fraenkel, Y. Bar–Hillel, Foundations of Set Theory (North-Holland Publ.Co., Amsterdam, 1958)

    MATH  Google Scholar 

  12. R. Feys, Modal Logics (E. Nauwelaerts, Louvain, 1965)

    MATH  Google Scholar 

  13. A.I. Arruda, in A Survey of Paraconsistent Logic, ed. by A.I. Arruda, R. Chuaquai, N.C.A. Da Costa. Mathematical logic in Latin America (Amsterdam, N.Y., Oxford, North-Holland, 1980), pp. 1–41

    Google Scholar 

  14. V.A. Bazhanov, The scholar and the “wolfhound era”: The fate of Ivan E. Orlov’s ideas in logic, philosophy, and science. Sci. Context 16, 535–550 (2003)

    Article  Google Scholar 

  15. V.M. Popov, The Decidability of Relevant Logic System RAO, in Modal and Intensional Logics (Institute of Philosophy, Moscow, 1978), pp. 115–119 (in Russian)

    Google Scholar 

  16. K. Došen, The first axiomatization of relevant logic. J. Philos. Log. 21, 339–356 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  17. S.N. Artemov, Personal letter to author (2003)

    Google Scholar 

  18. E. Alves, The first axiomatization of paraconsistent logic. Bull. Section Log. 21, 19–20 (1992)

    MathSciNet  MATH  Google Scholar 

  19. N.C.A. Da Costa, J.-Y. Beziau, O.S. Bueno, Aspects of paraconsistent logic. Bull. IGPL 3(4), 597–614 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgment

The author is grateful to M. Fuller for valuable suggestions, which enabled him to improve this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Valentin A. Bazhanov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Bazhanov, V.A. (2016). Russian Origins of Non-Classical Logics. In: Abeles, F., Fuller, M. (eds) Modern Logic 1850-1950, East and West. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-24756-4_10

Download citation

Publish with us

Policies and ethics