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Is Logic Exceptional?

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Logic in Question

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

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Abstract

We examine in which sense logic can be considered as exceptional. We start by emphasizing the difference between Logic as reasoning and logic as the science of reasoning, an essential distinction to launch the discussion. We then investigate if reasoning itself can be seen as exceptional, in particular an exceptional feature of human beings, and next if the science of reasoning can be regarded as exceptional. This study is further extended on the one hand by discussing the relativity and universality of logic and on the other hand by stressing the dialectical interaction between logic and metalogic, the interdisciplinary and transdisciplinary character of logic.

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Bibliography

  1. J.-Y.Beziau, “Universal logic”, in Logica’94 - Proceedings of the 8th International Symposium, T.Childers & O.Majer (eds), Prague, 1994, pp.73-93.

    Google Scholar 

  2. J.-Y.Beziau, “Théorie législative de la négation pure”, Logique et Analyse, 147-148 (1994), pp.209-225.

    Google Scholar 

  3. J.-Y.Beziau, “New light on the square of oppositions and its nameless corner”, Logical Investigations, 10, (2003), pp.218-232.

    Google Scholar 

  4. J.-Y.Beziau, “Logic is not logic”, Abstracta 6 (2010), pp.73-102.

    Google Scholar 

  5. J.-Y.Beziau, “What is a logic? - Towards axiomatic emptiness", Logical Investigations, 16 (2010), pp.272-279.

    Google Scholar 

  6. J.-Y.Beziau, “Rougier: Logique et Métaphyisque”, in P.Zordan (ed) Proceedings of the 4th World Confrence on Metaphysics, Dykinson, 2011, pp.464-472.

    Google Scholar 

  7. J.-Y.Beziau, “The power of the hexagon”, Logica Universalis, vol.6 (2012), pp.1-43.

    Google Scholar 

  8. J.-Y.Beziau, “The new rising of the square of opposition”, in J.-Y.Béziau and D.Jacquette (eds), Around and Beyond the Square of Opposition, Birkhäuser, Basel, 2012, pp.6-24.

    Google Scholar 

  9. J.-Y.Beziau, “Three Sisters : Philosophy, Mathematics and Logic”, in N.Nabais and O.Pombo (ed), O lugar da Filosofia da Ciência na nova Universidade de Lisboa, University of Lisbonne, 2013, pp.271--291.

    Google Scholar 

  10. J.-Y.Beziau, “The relativity and universality of logic”, Synthese - Special Issue Istvan Németi 70th Birthday, 192 (2015), pp. 1939-1954.

    MathSciNet  MATH  Google Scholar 

  11. J.-Y.Beziau, “Being Aware of Rational Animals”, in G.Dodig-Crnkovic and R.Giovagnoli (eds), Representation and Reality in Humans, Other Living Organisms and Intelligent Machines, Springer International Publishing, Cham, 2017, pp.319-331.

    Google Scholar 

  12. J.-Y.Beziau, "The Lvov-Warsaw School: A True Mythology", in Ángel Garrido and Urszula Wybraniec-Skardowska (eds), The Lvov-Warsaw School. Past and Present, Birkhäuser, Basel, 2018, pp.779-815.

    Google Scholar 

  13. J.-Y.Beziau, “Is the Principle of Contradiction a Consequence of x 2 = x?”, Logica Universalis, vol.12 (2018), pp.55-81.

    Google Scholar 

  14. J.-Y.Beziau, “Metalogic, Schopenhauer and Universal Logic” in J.Lemanski (ed), Language, Logic, and Mathematics in Schopenhauer, Birkhäuser, Basel, 2020, pp.207-257.

    Google Scholar 

  15. J.-Y.Beziau, “The Mystery of the Fifth Logical Notion (Alice in the Wonderful Land of Logical Notions)”, Studia Humana, 9 (2020), pp.19-36.

    Google Scholar 

  16. J.-Y.Beziau, “Logical structures from a model-theoretical viewpoint ” in A.Costa-Leite (ed), Abstract Consequence and Logics - Essays in Honor of Edelcio G. de Souza , College Publications, London, 2020. pp.21-34.

    Google Scholar 

  17. J.-Y.Beziau, “What is an axiom?” in A. da Barros and D.Krause (eds), A True Polymath - A Tribute to Francisco Antonio Doria, College Publications, London, 2020, p.122-142.

    Google Scholar 

  18. J.-Y.Beziau, “Is there an axiom for everything?” in O.Passon and C.Benzmüller (eds), Wider den Reduktionismus -- Ausgewählte Beiträge zum Kurt Gödel Preis 2019, Springer Spektrum, Springer Nature Switzerland, Cham, 2021, pp.103-117, pp.103-117

    Google Scholar 

  19. J.-Y.Beziau, “Turnstile Figures of Opposition” in J.-Y.Beziau and I.Vandoulakis (eds), The Exoteric Square of Opposition, Birkhäuser, Basel, 2022, pp.225-240.

    Google Scholar 

  20. J.-Y. Beziau and G.Basti (eds), The square of opposition, a cornerstone of thought, Birkhäuser, Basel, 2016.

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  22. J.-Y. Beziau and G.Payette (eds), The square of opposition - A general framework for cognition, Peter Lang, Bern, 2012.

    Google Scholar 

  23. J.-Y.Beziau and S.Read (eds), Special issue of History and Philosophy of Logic on the square of opposition, 4 (2014).

    Google Scholar 

  24. G.Birkhoff, “Universal algebra”, in Rota, G.-C. and Oliveira, J. S. (eds.), Selected Papers on Algebra and Topology by Garret Birkhoff, Birkhäuser, Basel, 1977, pp. 111-115.

    Google Scholar 

  25. R.Blanché, Structures intellectuelles. Essai sur l’organisation systématique des concepts, Vrin, Paris, 1966.

    Google Scholar 

  26. G.Boole, An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities, Macmillan, London, 1854.

    Book  MATH  Google Scholar 

  27. M.E.Boole, Philosophy and Fun of Algebra, C.W.Daniel, London, 1909.

    Google Scholar 

  28. N.Bourbaki, Eléments de mathématique, 11 volumes, Hermann and Others Publishers, Paris, 1939-2016. The English translation has been published by various publishers. It is currently published by Springer.

    Google Scholar 

  29. W.Colón, P.Chitnis, J.P.Collins, J.Hicks, T.Chan and J.S. Tornow, “Chemical biology at the US National Science Foundation”, Nature Chemical Biology, volume 4, number 9, pp.511-514

    Google Scholar 

  30. W.S.Cooper, The evoltuion of reason – Logic as a branch of biology, Cambridge University Press, Cambirdge, 2001.

    Book  Google Scholar 

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

    Google Scholar 

  32. J.Dieudonné, Pour l'honneur de l'esprit humain. Les mathématiques aujourd'hui, Hachette, Paris, 1987.

    MATH  Google Scholar 

  33. V.Glivenko, Théorie générale des structures, Hermann, Paris, 1938

    MATH  Google Scholar 

  34. D.Hilbert. Die logischen Grundlagen der Mathematik, Mathematische Annalen, 88 (1923), pp.151–165.

    Google Scholar 

  35. O.T.Hjortland, “Anti-exceptionalism about logic”, Philosophical Studies, 174 (2017), pp.631–658.

    Google Scholar 

  36. S. Lesniewski, "Grundzüge eines neuen Systems der Grundlagen der Mathematik", Fundamenta Mathematicae, 14: 1-81.

    Google Scholar 

  37. A.Lindenbaum and A.Tarski, “Über die Beschränktheit der Ausdrucksmittel deduktiver Theorien”, in Ergebnisse eines mathematischen Kolloquiums, fasc. 7, 1934–1935, pp. 15–22.

    Google Scholar 

  38. B.Nicolescu, “Moving Worldviews - Reshaping sciences, policies and practices for endogenous sustainable development”, COMPAS Editions, Holland, 2006, edited by Bertus Haverkort and Coen Reijntjes, p. 142-166.

    Google Scholar 

  39. J.Piaget, Traité de logique, Armand Colin, 1949.

    MATH  Google Scholar 

  40. D.Rabouin, “Interpretations of Leibniz’s Mathesis Universalis at the Beginning of the XXth Century”, in Krömer R., Chin-Drian Y. (eds) New Essays on Leibniz Reception.. Springer, Basel, 2012. pp. 187-201

    Chapter  Google Scholar 

  41. D.Rabouin, Mathesis universalis – L’idée de "mathématique universelle" d'Aristote à Descartes, Paris, PUF, coll. Epiméthée, 2009,

    Book  Google Scholar 

  42. L.Rougier, Les paralogismes du rationalisme, Félix Alcan, Paris 1920.

    MATH  Google Scholar 

  43. L.Rougier, “The relativity of logic”, Philosophy and Phenomenological Research”, 2, 1941, pp. 137-158. Reprinted in J.-Y.Beziau (ed), Universal Logic : An Anthology, Birkhäuser, Basel, 2012 with a prestentation by M.Marion.

    Google Scholar 

  44. L.Rougier, Le traité de la connaissance, Gauthiers-Villars, Paris 1955.

    MATH  Google Scholar 

  45. M.Serfati, La revolution symbolique. La constitution de l’écriture symbolique mathématique, Petra, Paris, 2005.

    MATH  Google Scholar 

  46. A.Tarksi. “Remarques sur les notions fondamentales de la méthodologie des mathématiques”, Annales de la Société Polonaise de Mathématiques, 7 (1929), pp.270-272. English tanslation by R.Purdy and J.Zygmunt in J.-Y.Beziau (ed), Universal Logic : An Anthology, Birkhäuser, Basel, 2012., pp.67-68.

    Google Scholar 

  47. A.Tarksi. “Contributions to the theory of models. I, II, III”, Indigationes Mathematicae, 16 (1954), pp.572-581, pp.582-588, vol.17 (1955), pp.56-64.

    Google Scholar 

  48. A.Tarksi, “Truh and proof”, Scientific American, 1969, pp.63-77.

    Google Scholar 

  49. A.Tarksi, “What are logical notions?” (edited by J.Corcoran), History and Philosophy of Logic, 7 (1986), pp.143-154.

    Google Scholar 

  50. A.N.Whitehead and B.Russell, Principia Mathematica, Cambridge University Press, Cambridge, 1910-1913.

    MATH  Google Scholar 

  51. J.-Y.Beziau, “Disentangling Contradiction from Contrariety via Incompatibility”, Logica Universalis, vol.10 (2016), pp. 157-170.

    Google Scholar 

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Author information

Authors and Affiliations

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

    Jean-Yves Béziau

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  1. Jean-Yves Béziau
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Correspondence to Jean-Yves Béziau .

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Editors and Affiliations

  1. Philosophy, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Jean-Yves Béziau

  2. Mathematics, Sorbonne University, Paris, France

    Jean-Pierre Desclés

  3. Ragnar Nurkse Department of Innovation and Governance, Tallinn University of Technology, Tallinn, Estonia

    Amirouche Moktefi

  4. Laboratory of Sciences and Techniques of Information, Communication and Knowledge, University of Western Brittany, Brest, France

    Anca Christine Pascu

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Béziau, JY. (2022). Is Logic Exceptional?. In: Béziau, JY., Desclés, JP., Moktefi, A., Pascu, A.C. (eds) Logic in Question. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-94452-0_14

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