, Volume 192, Issue 7, pp 1939–1954 | Cite as

The relativity and universality of logic

  • Jean-Yves BeziauEmail author


After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we discuss the emergence of universal logic as a general theory of logical systems, making comparison with universal algebra and the project of mathesis universalis. In a third part we critically present three lines of research connected to universal logic: logical pluralism, non-classical logics and cognitive science.


Logic Universality of logic Relativity of logic Universal logic Universal algebra Mathesis universalis Characteristica universalis Logical pluralism Non-classical logics Paraconsistent logic Cognitive science 



Thanks to anonymous referees and all the people with whom I have been discussing these ideas over the years.


  1. Bazhanov, V. A. (1990). The fate of one forgotten idea: N.A.Vasiliev and his imaginary logic. Studies in Soviet Thought, 39(3–4), 333–334.CrossRefGoogle Scholar
  2. Beall, J. C., & Restall, G. (2000). Logical pluralism. Australasian Journal of Philosophy, 78(4), 475–493.CrossRefGoogle Scholar
  3. Beall, J. C., & Restall, G. (2006). Logical pluralism. Oxford: Clarendon.Google Scholar
  4. Beziau, J.-Y. (1994). Universal logic. In T. Childers & O. Majer (Eds.), Logica’94–Proceedings of the 8th international symposium (pp. 73–93). Prague.Google Scholar
  5. Beziau, J.-Y. (1995). Recherches sur la Logique Universelle. PhD Thesis, Department of Mathematics, University Denis Diderot, Paris.Google Scholar
  6. Beziau, J.-Y. (2000). What is paraconsistent logic? In D. Batens, et al. (Eds.), Frontiers of paraconsistent logic (pp. 95–111). Baldock: Research Studies Press.Google Scholar
  7. Beziau, J.-Y. (2001). From paraconsistent to universal logic. Sorites, 12, 5–32.Google Scholar
  8. Beziau, J.-Y. (2006a). The paraconsistent logic Z—A possible solution to Jaskowski’s problem. Logic and Logical Philosophy, 15, 99–111.CrossRefGoogle Scholar
  9. Beziau, J.-Y. (2006b). 13 questions about universal logic. Bulletin of the Section of Logic, 35, 133–150.Google Scholar
  10. Beziau, J.-Y. (2010a). Logic is not logic. Abstracta, 6, 73–102.Google Scholar
  11. Beziau, J.-Y. (2010b). What is a logic? Towards axiomatic emptiness. Logical Investigations, 16, 272–279.Google Scholar
  12. Beziau, J.-Y. (Ed.). (2012a). Paralogics and the theory of valuation. In Universal logic: An Anthology - From Paul Hertz to Dov Gabbay (pp. 361–372). Birkhäuser, Basel.Google Scholar
  13. Beziau, J.-Y. (2012b). The power of the hexagon. Logica Universalis, 6, 1–43.CrossRefGoogle Scholar
  14. Beziau, J.-Y. (Ed.). (2012). Universal logic, an anthology–From Paul Hertz to Dov Gabbay. Basel: Birkhäuser.Google Scholar
  15. Beziau, J.-Y., & Buchsbaum, A. (2013). Let us be antilogical: Anti-classical logic as a logic. In A. Moktefi, A. Moretti, & F. Schang (Eds.), Let us be logical. London: College Publications.Google Scholar
  16. Beziau, J.-Y., & Jacquette, D. (2012). Around and beyond the square of opposition. Basel: Birkhäuser.CrossRefGoogle Scholar
  17. Beziau, J.-Y., & Payette, G. (2012). The square of opposition—A general framework for cognition. Bern: Peter Lang.Google Scholar
  18. Birkhoff, G. (1946). Universal algebra. In Comptes Rendus (Ed.), du Premier Congrès Canadien de Mathématiques (pp. 310–326). Toronto: University of Toronto Press.Google Scholar
  19. Birkhoff, G. (1987). Universal algebra. In G.-C. Rota & J. S. Oliveira (Eds.), Selected papers on algebra and topology by Garret Birkhoff (pp. 111–115). Basel: Birkhäuser.Google Scholar
  20. Blanché, R. (1966). Structures intellectuelles. Essai sur l’organisation systématique des concepts. Paris: Vrin.Google Scholar
  21. Bourbaki, N. (1948). L’architecture des mathématiques—La mathématique ou les mathématiques. In F. le Lionnais (Ed), Les grands courants de la pensée mathématique, Cahier du Sud (pp. 35–47); translated as “The Architecture of Mathematics”, American Mathematical Monthly, 57, 221–232, 1950.Google Scholar
  22. Carnap, R. (1934). Logische Syntax der Sprache. Vienna: Springer, translated in English as The logical syntax of language. London: Kegan Paul, 1937.CrossRefGoogle Scholar
  23. Couturat, L. (1901). La Logique de Leibniz–D’après des documents inédits. Paris: Félix Alcan.Google Scholar
  24. da Costa, N. C. A., & Beziau, J.-Y. (1994a). Théorie de la valuation. Logique et Analyse, 145–146, 95–117.Google Scholar
  25. da Costa, N. C. A., & Beziau, J.-Y. (1994b). La théorie de la valuation en question. Proceedings of the XI Latin American symposium on mathematical logic (Part 2) (pp. 95–104). Bahia Blanca: Universidad Nacional del Sur.Google Scholar
  26. da Costa, N. C. A., Beziau, J.-Y., & Bueno, O. A. S. (1995). Paraconsistent logic in a historical perspective. Logique et Analyse, 150–152, 111–125.Google Scholar
  27. Descartes, R. (1628). Regulae ad directionem ingenii (Rules for the direction of mind), published in Amsterdam, 1701.Google Scholar
  28. Descartes, R. (1637). Discours de la méthode (Discourse on the method), Leyde.Google Scholar
  29. Destousches, J.-L. (1948). Cours de logique et philosophie générale. Paris: Centre de document universitaire, Fournier & Constane.Google Scholar
  30. Feferman, S., & Feferman, A. B. (2004). Tarski: Life and logic. Cambridge: Cambridge University Press.Google Scholar
  31. Février, P. (1937). Les relations d’incertitude d’Heisenberg et la logique. In Travaux du IXème Congrès International de Philosophie (Vol. VI, pp. 88–94). Paris: Hermann.Google Scholar
  32. Fitting, M. (1992). Preface. Journal of Logic and Computation, 2(6), 783–785.CrossRefGoogle Scholar
  33. Gentzen, G. (1934–1935). Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39(2), 176–210, 39(3): 405–431.Google Scholar
  34. Gödel, K. (1932). Zum intuitionistischen Aussagenkalkül. Akademie der Wissenschaften in Wien, Mathematisch-natuirwissenschaft Klasse, 64, 65–66.Google Scholar
  35. Gödel, K. (1933). Zur intuitionistischen Arithmetik und Zahlentheorie. Ergebnisse eines mathematischen Kolloquiums, 4, 34–38.Google Scholar
  36. Gödel, K. (1949). An example of a new type of cosmological solution of Einstein’s field equations of gravitation. Review of Modern Physics, 21(3), 447–450.CrossRefGoogle Scholar
  37. Grothendieck, A. (1974). La nouvelle église universelle. Pourquoi les mathmématiques (pp. 11–35). Paris: UGE.Google Scholar
  38. Henkin, L., Suppes, P. & A. Tarski (eds.). (1958). The axiomatic method with special reference to geometry and physics. Proceedings of an international symposium held at the University of California, Berkeley, December 16, 1957–January 4, 1958 (pp. 291–307). Amsterdam: North-Holland.Google Scholar
  39. Kauppi, R. (1980). Mathesis universalis. In J. Ritter & K. Gründer (Eds.), Historisches Worterbuch der Philosophie (Vol. 5, pp. 937–938). Basel and Stuttgart: Schwabe.Google Scholar
  40. Marion, M. (2012). Louis Rougier on the relativity of logic—An early defence of logical pluralism. In Béziau.Google Scholar
  41. Miller, G. A. (2003). The cognitive revolution: A historical perspective. Trends in Cognitive Sciences, 7, 141–143.CrossRefGoogle Scholar
  42. Moschovakis, J. R. (2009). The logic of Brouwer and Heyting. In D. M. Gabbay & J. Woods (Eds.), Handbook of the history of logic (Vol. 5). Amsterdam: Elsevier.Google Scholar
  43. Piaget, J. (1950). Introduction à l’épistémologie génétique. Paris: PUF. Translated as Genetic epistemology, Columbia University Press, New York, 1968.Google Scholar
  44. Post, E. (1921). Introduction to a general theory of elementary propositions. American Journal of Mathematics, 13, 163–185.CrossRefGoogle Scholar
  45. Riche, J. (2007). From universal algebra to universal logic. In J. Y. Beziau & A. Costa-Leite (Eds.), Perspectives on universal logic (pp. 3–39). Monza: Polimetrica.Google Scholar
  46. Rota, G.-C. (1997). Indiscrete thoughts. Basel: Birkhäuser.CrossRefGoogle Scholar
  47. Rougier, L. (1941). The relativity of logic. Philosophy and Phenomenological Research, 2, 137–158, reprinted in (Béziau 2012).CrossRefGoogle Scholar
  48. Rougier, L. (1955). Traité de la connaissance. Paris: Gauthiers-Villars.Google Scholar
  49. Rougier, L. (1977). Le conflit du christianisme primitif et de la civilisation antique. Paris: Copernic.Google Scholar
  50. Sokal, A. (1996). A physicist experiments with cultural studies. Lingua Franca, 62–64.Google Scholar
  51. Sokal, A., & Bricmont, J. (1997). Impostures intellectuelles. Paris: Odile Jacob. Translated as Fashionable nonsense, Picador, New York, 1998.Google Scholar
  52. Suppes, P. (2002). Representation and invariance of scientific structures. Stanford: CSLI.Google Scholar
  53. Suszko, R., & (with Brown, D.J.). (1973). Abstract logic. Dissertationes Mathematicae, 102, 43–52.Google Scholar
  54. Sylvester, J. J. (1884). Lectures on the principles of universal algebra. American Journal of Mathematics, 6, 270–286.CrossRefGoogle Scholar
  55. Tarski, A. (1928). Remarques sur les notions fondamentales de la méthodologie des mathématiques. In Annales de la Société Polonaise de Mathématique) (Vol. 7, pp. 270–272), translated as “Remarks on Fundamental Concepts of the Methodology of Mathematics” In (Beziau ed 2012).Google Scholar
  56. Tarski, A. (1936). 0 logice matematycznej i metodzie dedukcyjnej, Ksiaznica-Atlas, Lwów and Warsaw (English translation; we refer here to the 4th edition by Jan Tarski: Introduction to logic and to the methodology of the deductive sciences (p. 1994). Oxford: OUP.Google Scholar
  57. Tarski, A. (1937). Sur la méthode déductive. In Travaux du IXe Congrès International de Philosophie (Vol. VI, pp. 95–103). Paris: Hermann.Google Scholar
  58. van Stigt, W. P. (1990). Brouwer’s intuitionism. Amsterdam: North Holland.Google Scholar
  59. Weil, A. (1991). Souvenirs d’apprentissage. Basel: Birkhäuser; translated as The apprenticeship of a mathematician, Basel: Birkhäuser.Google Scholar
  60. Whitehead, A. N. (1898). A treatise of universal algebra. Cambridge: Cambridge University Press.Google Scholar
  61. Whitehead, A. N., & Russell, B. (1910–1913). Principia Mathematica. Cambridge: Cambridge University Press.Google Scholar
  62. Zürn, M. (2000). Vom Nationalstaat lernen, Das zivilisatorische Hexagon in der Weltinnenpolitik. In U. Menzel (Ed.), University PressVom Ewigen Frieden und vom Wohlstand der Nationen (pp. 21–25). Frankfurt.Google Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhilosophyFederal University of Rio de Janeiro, Brazilian Research Council, Brazilian Academy of PhilosophyRio de JaneiroBrazil

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