By Jean-Yves Béziau
The speculation of oppositions according to Aristotelian foundations of common sense has been pictured in a outstanding sq. diagram which are understood and utilized in lots of other ways having repercussions in a variety of fields: epistemology, linguistics, arithmetic, sociology, physics. The sq. can be generalized in different two-dimensional or multi-dimensional gadgets extending in breadth and intensity the unique Aristotelian thought. The sq. of competition from its starting place in antiquity to the current day keeps to exert a profound influence at the improvement of deductive good judgment. on the grounds that 10 years there's a new transforming into curiosity for the sq. as a result of fresh discoveries and not easy interpretations. This e-book provides a set of formerly unpublished papers by way of excessive point experts at the sq. from around the world.
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Extra info for Around and Beyond the Square of Opposition
Logical extensions of Aristotle’s square. Logica Univers. 2, 167–187 (2008) 38. : On Beziau’s logic Z. Logic Log. Philos. 18, 305–320 (2008) 39. : Nearly every normal modal logic is paranormal. Log. Anal. 48, 279–300 (2005) The New Rising of the Square of Opposition 19 40. : Modality and paraconsistency. , Behounek, L. ) The Logica Yearbook 2004, pp. 213–222. Filosofia, Prague (2005) 41. : Geometry of modalities? Yes: through n-opposition theory. , Facchini, A. ) Aspects of Universal Logic. Travaux de logique, vol.
He does not even use the word “Tad¯akhul” which was used by Avicenna and so known by the Arabic logicians. This shows that he probably does not consider subalternation as an opposition or else that he did not want to adopt Avicenna’s views but rather to return to Aristotle’s ones (even if it is with some modifications) and probably to Al F¯ar¯ab¯ı’s opinions, since Al F¯ar¯ab¯ı admits exactly the same kinds of oppositions: contradiction, contrariety and subcontrariety and differs from Averroes only in his treatment of the indefinites which, according to him, are subcontrary.
S5 is a paraconsistent logic and so is first-order classical logic. Log. Investig. 9, 301– 309 (2002) 10. : New light on the square of oppositions and its nameless corner. Log. Investig. 10, 218–232 (2003) 11. : Paraconsistent logic from a modal viewpoint. J. Appl. Log. 3, 7–14 (2005) 12. : The paraconsistent logic Z—a possible solution to Jaskowski’s problem. Logic Log. Philos. 15, 99–111 (2006) 13. : Paraconsistent logic! (A reply to Salter). Sorites 17, 17–26 (2006) 14. : Adventures in the paraconsistent jungle.
Around and Beyond the Square of Opposition by Jean-Yves Béziau