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The relativity and universality of logic

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Abstract

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.

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Notes

  1. Rougier was close to the Vienna Circle, helping to promote it. His paper “ The relativity of logic ” (1941) has been recently re-edited in the Anthology of Universal Logic with comments by Mathieu Marion (2012).

References

  • 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.

    Article  Google Scholar 

  • Beall, J. C., & Restall, G. (2000). Logical pluralism. Australasian Journal of Philosophy, 78(4), 475–493.

    Article  Google Scholar 

  • Beall, J. C., & Restall, G. (2006). Logical pluralism. Oxford: Clarendon.

    Google Scholar 

  • Beziau, J.-Y. (1994). Universal logic. In T. Childers & O. Majer (Eds.), Logica’94–Proceedings of the 8th international symposium (pp. 73–93). Prague.

  • Beziau, J.-Y. (1995). Recherches sur la Logique Universelle. PhD Thesis, Department of Mathematics, University Denis Diderot, Paris.

  • 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 

  • Beziau, J.-Y. (2001). From paraconsistent to universal logic. Sorites, 12, 5–32.

    Google Scholar 

  • Beziau, J.-Y. (2006a). The paraconsistent logic Z—A possible solution to Jaskowski’s problem. Logic and Logical Philosophy, 15, 99–111.

    Article  Google Scholar 

  • Beziau, J.-Y. (2006b). 13 questions about universal logic. Bulletin of the Section of Logic, 35, 133–150.

    Google Scholar 

  • Beziau, J.-Y. (2010a). Logic is not logic. Abstracta, 6, 73–102.

    Google Scholar 

  • Beziau, J.-Y. (2010b). What is a logic? Towards axiomatic emptiness. Logical Investigations, 16, 272–279.

    Google Scholar 

  • 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.

  • Beziau, J.-Y. (2012b). The power of the hexagon. Logica Universalis, 6, 1–43.

    Article  Google Scholar 

  • Beziau, J.-Y. (Ed.). (2012). Universal logic, an anthology–From Paul Hertz to Dov Gabbay. Basel: Birkhäuser.

  • 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 

  • Beziau, J.-Y., & Jacquette, D. (2012). Around and beyond the square of opposition. Basel: Birkhäuser.

    Book  Google Scholar 

  • Beziau, J.-Y., & Payette, G. (2012). The square of opposition—A general framework for cognition. Bern: Peter Lang.

    Google Scholar 

  • 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 

  • 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 

  • Blanché, R. (1966). Structures intellectuelles. Essai sur l’organisation systématique des concepts. Paris: Vrin.

    Google Scholar 

  • 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.

  • Carnap, R. (1934). Logische Syntax der Sprache. Vienna: Springer, translated in English as The logical syntax of language. London: Kegan Paul, 1937.

    Book  Google Scholar 

  • Couturat, L. (1901). La Logique de Leibniz–D’après des documents inédits. Paris: Félix Alcan.

    Google Scholar 

  • da Costa, N. C. A., & Beziau, J.-Y. (1994a). Théorie de la valuation. Logique et Analyse, 145–146, 95–117.

    Google Scholar 

  • 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 

  • 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 

  • Descartes, R. (1628). Regulae ad directionem ingenii (Rules for the direction of mind), published in Amsterdam, 1701.

  • Descartes, R. (1637). Discours de la méthode (Discourse on the method), Leyde.

  • Destousches, J.-L. (1948). Cours de logique et philosophie générale. Paris: Centre de document universitaire, Fournier & Constane.

    Google Scholar 

  • Feferman, S., & Feferman, A. B. (2004). Tarski: Life and logic. Cambridge: Cambridge University Press.

    Google Scholar 

  • 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.

  • Fitting, M. (1992). Preface. Journal of Logic and Computation, 2(6), 783–785.

    Article  Google Scholar 

  • Gentzen, G. (1934–1935). Untersuchungen über das logische Schließen. Mathematische Zeitschrift, 39(2), 176–210, 39(3): 405–431.

    Google Scholar 

  • Gödel, K. (1932). Zum intuitionistischen Aussagenkalkül. Akademie der Wissenschaften in Wien, Mathematisch-natuirwissenschaft Klasse, 64, 65–66.

  • Gödel, K. (1933). Zur intuitionistischen Arithmetik und Zahlentheorie. Ergebnisse eines mathematischen Kolloquiums, 4, 34–38.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Grothendieck, A. (1974). La nouvelle église universelle. Pourquoi les mathmématiques (pp. 11–35). Paris: UGE.

    Google Scholar 

  • 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.

  • 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 

  • Marion, M. (2012). Louis Rougier on the relativity of logic—An early defence of logical pluralism. In Béziau.

  • Miller, G. A. (2003). The cognitive revolution: A historical perspective. Trends in Cognitive Sciences, 7, 141–143.

    Article  Google Scholar 

  • 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 

  • Piaget, J. (1950). Introduction à l’épistémologie génétique. Paris: PUF. Translated as Genetic epistemology, Columbia University Press, New York, 1968.

  • Post, E. (1921). Introduction to a general theory of elementary propositions. American Journal of Mathematics, 13, 163–185.

    Article  Google Scholar 

  • 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 

  • Rota, G.-C. (1997). Indiscrete thoughts. Basel: Birkhäuser.

    Book  Google Scholar 

  • Rougier, L. (1941). The relativity of logic. Philosophy and Phenomenological Research, 2, 137–158, reprinted in (Béziau 2012).

    Article  Google Scholar 

  • Rougier, L. (1955). Traité de la connaissance. Paris: Gauthiers-Villars.

    Google Scholar 

  • Rougier, L. (1977). Le conflit du christianisme primitif et de la civilisation antique. Paris: Copernic.

    Google Scholar 

  • Sokal, A. (1996). A physicist experiments with cultural studies. Lingua Franca, 62–64.

  • Sokal, A., & Bricmont, J. (1997). Impostures intellectuelles. Paris: Odile Jacob. Translated as Fashionable nonsense, Picador, New York, 1998.

  • Suppes, P. (2002). Representation and invariance of scientific structures. Stanford: CSLI.

    Google Scholar 

  • Suszko, R., & (with Brown, D.J.). (1973). Abstract logic. Dissertationes Mathematicae, 102, 43–52.

    Google Scholar 

  • Sylvester, J. J. (1884). Lectures on the principles of universal algebra. American Journal of Mathematics, 6, 270–286.

    Article  Google Scholar 

  • 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).

  • 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.

  • Tarski, A. (1937). Sur la méthode déductive. In Travaux du IXe Congrès International de Philosophie (Vol. VI, pp. 95–103). Paris: Hermann.

  • van Stigt, W. P. (1990). Brouwer’s intuitionism. Amsterdam: North Holland.

    Google Scholar 

  • Weil, A. (1991). Souvenirs d’apprentissage. Basel: Birkhäuser; translated as The apprenticeship of a mathematician, Basel: Birkhäuser.

  • Whitehead, A. N. (1898). A treatise of universal algebra. Cambridge: Cambridge University Press.

    Google Scholar 

  • Whitehead, A. N., & Russell, B. (1910–1913). Principia Mathematica. Cambridge: Cambridge University Press.

  • 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.

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Acknowledgments

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

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  1. Department of Philosophy, Federal University of Rio de Janeiro, Brazilian Research Council, Brazilian Academy of Philosophy, Rio de Janeiro, Brazil

    Jean-Yves Beziau

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  1. Jean-Yves Beziau
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Correspondence to Jean-Yves Beziau.

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Dedicated to Istvan Németi for his 70th birthday.

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Beziau, JY. The relativity and universality of logic. Synthese 192, 1939–1954 (2015). https://doi.org/10.1007/s11229-014-0419-0

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