Abstract logic of oppositions

Fabien Schang

DOI: http://dx.doi.org/10.12775/LLP.2012.019


A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.


INRC Group; negation; opposite; opposition; proto-negation

Full Text:



Aristotle, Categories.

Aristotle, Metaphysics.

Aristotle, On Interpretation.

Aristotle, Prior Analytics.

Belnap, N.D., “A useful four-valued logic”, pages 8–37 in: Modern uses of multiple-valued logic, G. Epstein and J. Dumm (eds.), D. Reidel Publishing Company, Dordrecht, 1977.

Béziau, J.-Y., “New light on the square of opposition and its nameless corner”, Logical Investigations 10 (2003): 218–233.

Blanché, R., “Sur l’opposition des concepts”, Theoria 19 (1953): 89–130.

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

Bocheński, J.M., Formale Logik, Freiburg-München, 1956.

Bochvar, D.A., “On a three-valued calculs and its application to analysis of paradoxes of classical extended functional calculus”, Matematičceskij Sbornik 4 (1938): 287–308.

Chatti, S., & F.Schang, “A cube to save the square”, submitted.

Czeżowski, T., “On certain peculiarities of singular propositions”, Mind 64, 255 (1955): 392–395.

Hughes, G.E., “The modal logic of John Buridan”, pages 93–111 in: Atti del Convegno internazionale di storia della logica: le teorie delle modalitŕ, Editrice Cooperativa Libraria Universitaria Editrice, Bologna, 1989.

Keynes, J.N., Studies and Exercises in Formal Logic, Macmillan and Co., London, 1884.

Kleene, S., Introduction to Metamathematics, North-Holland Publishing Co. and P. Noordhoff N.V., Amsterdam and Groningen, 1952.

Łukasiewicz, J., “O logice trójwartościowej”, Ruch Filozoficzny 5 (1920), 170–171.

Marcos, J., “Opposition from the viewpoint of universal logic”, talk presented at the 3rdWorkshop N.O.T., University of Nice, 22–23 June 2010.

Moretti, A., “The geometry of logical opposition”, University of Neuchâtel, 2009.

Pellissier, R., “‘Setting’ n-opposition”, Logica Universalis 2 (2008), 235–262.

Piaget, J., Traité de logique (essai de logistique opératoire), Armand Colin, 1972 (1sted. 1949).

Plato, Sophist.

Priest, G., “The logic of paradox”, Journal of Philosophical Logic 8 (1979): 219–241.

Schang, F., “Questions and answers about oppositions”, pages 283–314 in: New Perspectives on the Square of Opposition, J.-Y. Béziau and G. Payette (eds.), Peter Lang, Bern, 2011.

Schang, F., “Two Indian dialectical logics: saptabha˙ ng¯ı and catus.kot.i”, Journal of the Indian Council of Philosophical Research 27 (2011): 45–75.

Schang, F., “Relative charity”, Revista Brasileira de Filosofia 233 (2009): 159–172.

Sion, A., Future Logic, Geneva, 1996.

Skura, T., “A refutation theory”, Logica Universalis 3 (2009): 239–302.

Słupecki, J., “The theory of rejected propositions”, Studia Logica 29, 1 (1971): 75–115.

Smessaert, H., “On the 3D Visualisation of logical relations”, Logica Universalis 3 (2009): 212–231.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism