The Square of Opposition: A Cornerstone of Thought

Chapter

Abstract

We first describe how after having started in Montreux, Switzerland in 2007, the congress on the square of opposition moved to the American University of Beirut in Lebanon in 2012 after a stop at the University Pasquale Paoli in Corsica in 2010. We then describe the square congress at the Pontifical Lateran University in the Vatican in 2014 and the resulting publications.

Keywords

Fuzzy logic Interdisciplinarity Intuitionistic logic Modal logic Paraconsistent logic Square of opposition Syllogistic 

Mathematics Subject Classification (2000)

Primary 00B25; Secondary 00A66 03A05 03B22 03B45; 03B53 

References

  1. 1.
    J.R.B. Arenhart, Liberating paraconsistency from contradiction. Log. Univers. 9, 523–544 (2015)CrossRefGoogle Scholar
  2. 2.
    C. Benzmüller, B.W. Paleo, The ontological modal collapse as a collapse of the square of opposition, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  3. 3.
    J.-Y. Beziau (ed.), Special issue of Logica Universalis dedicated to the hexagon of opposition. Log. Univers. 6 (1–2) (2012)Google Scholar
  4. 4.
    J.-Y. Beziau, Logical autobiography 50, in The Road to Universal Logic: Festschrift for the 50th Birthday of Jean-Yves Béziau, vol. II, ed. by A. Koslow, A. Buchsbaum (Birkhäuser, Basel, 2015), pp. 19–104CrossRefGoogle Scholar
  5. 5.
    J.-Y. Beziau, Round squares are no contradictions, in New Directions in Paraconsistent Logic, ed. by J.-Y. Beziau, M. Chakraborty, S. Dutta (Springer, New Delhi, 2015), pp. 39–55CrossRefGoogle Scholar
  6. 6.
    J.-Y. Beziau, Disentangling contradiction from contrariety via incompatibility. Log. Univers. 10, 157–171 (2016)CrossRefGoogle Scholar
  7. 7.
    J.-Y. Beziau, There is no cube of opposition, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  8. 8.
    J.-Y. Beziau, G. Basti (eds.), The Square of Opposition, A Cornerstone of Thought (Birkhäuser, Basel, 2016)Google Scholar
  9. 9.
    J.-Y. Beziau, S. Gerogiorgakis (eds.), New Dimension of the Square of Opposition (Philosophia, Munich, 2016)Google Scholar
  10. 10.
    J.-Y. Beziau, R. Giovagnoli (eds.), Special Issue on the square of opposition. Log. Univers. 10 (2–3) (2016)Google Scholar
  11. 11.
    J.-Y. Beziau, D. Jacquette (eds.), Around and Beyond the Square of Opposition (Birkhäuser, Basel, 2012)Google Scholar
  12. 12.
    J.-Y. Beziau, G. Payette (eds.), Special Issue on the square of opposition. Log. Univers. 2 (1) (2008)Google Scholar
  13. 13.
    J.-Y. Beziau, G. Payette (eds.), The Square of Opposition - A General Framework for Cognition (Peter Lang, Bern, 2012)Google Scholar
  14. 14.
    J.-Y. Beziau, S. Read (eds.), Special issue of History and Philosophy of Logic on the square of opposition. 35 (2014)Google Scholar
  15. 15.
    A. Bobenrieth, The many faces of inconsistency, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  16. 16.
    W. Carnielli, Groups, not squares: exorcizing a fetish, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  17. 17.
    F. Cavaliere, Iconic and dynamic models to represent “distinctive” predicates: the octagonal prism and the complex tetrahedron of opposition, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  18. 18.
    M. Correia, The proto-exposition of Aristotelian categorical logic, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  19. 19.
    E. dal Covolo, Welcome address to the participants of the IV international congress on: the square of opposition, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  20. 20.
    A. Drago, From Aristotle’s square of opposition to the “tri-unity’s concordance: Cusanus non-classical arguing”, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  21. 21.
    S.B. Fink, Why care beyond the square? Classical and extended shapes of oppositions in their application to “introspective disputes”, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  22. 22.
    J.D. García-Cruz, From the square to octahedra, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  23. 23.
    R. Giovagnoli, P. Larrey, Aristotle, frege and “second nature”, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  24. 24.
    S. Johnstone, The modal octagon and John Buridan’s modal ontology, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  25. 25.
    B. Kumova, Symmetric properties of the syllogistic system inherited from the square of opposition, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  26. 26.
    F. Lepage, A square of oppositions in intuitionistic logic with strong negation. Log. Univers., 10, 327–338 (2016)CrossRefGoogle Scholar
  27. 27.
    G.-J. Lokhorst, Fuzzy Eubouliatic logic: A fuzzy version of Anderson’s logic of prudence, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  28. 28.
    P. Murinová, V. Novák, Syllogisms and 5-Square of opposition with intermediate quantifiers in fuzzy natural logic. Log. Univers. 10, 339–358 (2016)CrossRefGoogle Scholar
  29. 29.
    J. Piaget, L’épistémologie des relations interdisciplinaires, in L’interdisciplinarité: Problèmes d’enseignement et de recherche, Centre pour la Recherche et l’Innovation dans l’Enseignement, ed. by L. Apostel, G. Berger, A. Briggs, G. Michaud (Organisation de Coopération et de développement économique, Paris, 1972)Google Scholar
  30. 30.
    J. Raclavský, Two standard and two modal squares of opposition, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  31. 31.
    S. Robert, J. Brisson, The Klein group, squares of opposition and the explanation of fallacies in reasoning. Log. Univers., 10, 377–392 (2016)CrossRefGoogle Scholar
  32. 32.
    F. Schang, An arithmetization of logical oppositions, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  33. 33.
    H. Smessaert, L. Demey, The unreasonable effectiveness of bitstrings in logical geometry, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  34. 34.
    J. Vidal-Rosset, The exact intuitionistic meaning of the square of opposition, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar
  35. 35.
    P. Weingartner, The square of opposition interpreted with a decidable modal logic, in The Square of Opposition: A Cornerstone of Thought, ed. by J.-Y. Beziau, G. Basti (Birkhäuser, Basel, 2016). doi:10.1007/978-3-319-45062-9Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Brazilian Research CouncilUniversity of BrazilRio de JaneiroBrazil
  2. 2.Pontifical Lateran UniversityRomeItaly

Personalised recommendations