Skip to main content

The Square of Opposition: Past, Present, and Future

  • Conference paper
  • First Online:
The Exoteric Square of Opposition

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

  • 260 Accesses

Abstract

We first explain the origin and development of the theory of opposition, its generalization to many concepts, and figures of opposition, particularly the hexagon of opposition. We also survey the organization of a series of events on the topic since 2007 in Montreux. We then talk in details about the sixth edition of the world congress on the square emphasizing the fact that it was organized at the Orthodox Academy of Crete. In the third part, we discuss the bright future of the theory.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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. J.-Y.Beziau, D’une caverne à l’autre, MD in Philosophy, supervised by Sarah Kofman, University Paris 1, Panthéon-Sorbonne, 1988.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  4. J.-Y.Beziau, "An Analogical Hexagon", International Journal of Approximate Reasoning , Volume 94, March 2018, Pages 1–17.

    Google Scholar 

  5. J.-Y.Beziau, "The Pyramid of Meaning", in J.Ceuppens, H.Smessaert, J. van Craenenbroeck and G.Vanden Wyngaerd (eds), A Coat of Many Colours - D60, Brussels, 2018.

    Google Scholar 

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

    MATH  Google Scholar 

  7. J.-Y.Beziau and G.Payette (eds), Special Issue on the Square of Opposition, Logica Universalis, Issue 1, Volume 2 (2008).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  10. J.-Y.Beziau and S.Gerogiorgakis (eds), New dimension of the square of Opposition, Philosophia, Munich, 2016

    Google Scholar 

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

    MATH  Google Scholar 

  12. J.-Y.Beziau and R.Giovagnoli (eds), Special Issue on the Square of Opposition. Logica Universalis, Issue 2-3, Volume 10 (2016).

    Google Scholar 

  13. J.-Y.Beziau (ed), special issue on the Square of Opposition, South American Journal of Logic, Volume 3, 2017.

    Google Scholar 

  14. J.-Y.Beziau and J.Lemanski, “The Cretan Square”, Logica Universalis, Issue 1, Volume 14 (2020), pp.1-5.

    Google Scholar 

  15. R.Blanché, “Sur la structuration du tableau des connectifs interpropositionnels binaires”, Journal of Symbolic Logic, 22 (1957), pp.17–18.

    Google Scholar 

  16. R.Blanché, Structures intellectuelles. Essai sur l’organisation systématique des concepts, Vrin, Paris, 1966. Translation in Protuguese: Estruturas intelectuais: ensaio sobre a organização sistemática dos conceitos, Perspectiva, São Paulo, 2012.

    Google Scholar 

  17. C.Chantilly and J.-Y.Beziau, “The Hexagon of Paintings”, South American Journal of Logic, Volume 3, 2017, pp.369-388.

    Google Scholar 

  18. L.Demey and H.Smessaert, “Metalogical decorations of logical diagrams”, Logica Universalis, 10 (2016), pp.233-292.

    Google Scholar 

  19. J. Dupuis (ed.), The Christian Faith in the Doctrinal Documents of the Catholic Church. Alba House, New York, 1962. Including the English translation of Enchiridion symbolorum, definitionum et declarationum de rebus fidei et morum.

    Google Scholar 

  20. D.Jaspers, “Logic and Colour”, Logica Universalis, volume 6 (2012), pp.227–248.

    Google Scholar 

  21. D.Jaspers and P.A.M. Seuren, “The Square of opposition in catholic hands: A chapter in the history of 20th-century logic”, Logique et Analyse, 59 (2016), pp.1-35.

    Google Scholar 

  22. P.McLaughlin & O.Schlaudt, “Kant’s Antinomies of Pure Reason and the ‘Hexagon of Predicate Negation’”, Logica Universalis, volume 14 (2020), pp.51–67.

    Google Scholar 

  23. A.Moretti, The geometry of logical opposition, PhD Thesis, University fo Neuchâtel, 2009.

    Google Scholar 

  24. A.Moretti, “Why the Logical Hexagon?”, Logica Universalis, volume 6 (2012), pp.69–107.

    Google Scholar 

  25. A.Moretti, “Was Lewis Carroll an Amazing Oppositional Geometer?”, History and Philosophy of Logic, 35, (2014), pp.383-409.

    Google Scholar 

  26. F.Nicolas, “The hexagon of opposition in music”, in [8] p.299-320

    Google Scholar 

  27. H.Prade & G.Richard, “From Analogical Proportion to Logical Proportions”, Logica Universalis, volume 7 (2013), pp.441–505.

    Google Scholar 

  28. C.de Ronde, H.Freytes and G.Domenech, “Quantum Mechanics and the Interpretation of the Orthomodular Square of Opposition”, in [8] pp.221-240.

    Google Scholar 

  29. H.Smessaert, “On the 3d visualisation of logical relations”, Logica Universalis, 3 (2009), pp.303-332.

    Google Scholar 

  30. H.Smessaert, “The classical Aristotelian hexagon versus the modern duality hexagon”, Logica Universalis, 6 (2012), pp.171-199.

    Google Scholar 

  31. José-Luis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Lorena Segura-Abad, Kristian Alonso-Stenberg and Hugh Gash, “Mathematical Perspectives on Liar Paradoxes", Logica Universalis, vol.15, issue 3 (2021).

    Google Scholar 

  32. I.M.Vandoulakis and T.Yu Denisova,. “On the Historical Transformations of the Square of Opposition as Semiotic Object”, Logica Universalis 14 (2020), 7-26.

    Article  MathSciNet  MATH  Google Scholar 

  33. I.M.Vandoulakis and D.Nagy (eds), Symmetry and Labyrinth - Proceedings of the 9th Interdisciplinary Symmetry Congress-Festival of the International Society for the Interdisciplinary Study of Symmetry – Crete, Greece, September 9-15, 2013 - With a Forward by Dan Shechtman, 2011 Nobel Prize in Chemistry. Special issue of the Journal of the International Society for the Interdisciplinary Study of Symmetry, 1-4 (2013).

    Google Scholar 

Download references

Acknowledgments

We thank all the participants of SQUARE 2018 and all people who helped to organize it. Special thanks to Dr. Antonis Kalogerakis, responsible for the local organization of the event at the OAC, and Dr. Konstantinos Zorbas, general director of the Orthodox Academy of Crete.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jean-Yves Beziau .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Beziau, JY., Vandoulakis, I. (2022). The Square of Opposition: Past, Present, and Future. In: Beziau, JY., Vandoulakis, I. (eds) The Exoteric Square of Opposition. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-90823-2_1

Download citation

Publish with us

Policies and ethics