By Jean-Yves Béziau

The speculation of oppositions in line with Aristotelian foundations of good judgment has been pictured in a remarkable sq. diagram that are understood and utilized in lots of other ways having repercussions in quite a few 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 idea. The sq. of competition from its beginning in antiquity to the current day maintains to exert a profound effect at the improvement of deductive good judgment. considering 10 years there's a new transforming into curiosity for the sq. as a result of fresh discoveries and difficult interpretations. This booklet provides a suite of formerly unpublished papers via excessive point experts at the sq. from worldwide.

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Triangular logic. The Philosophers’ Magazine 44, 83–88 (2009) 36. : A system of modal logic. J. Comput. Syst. 1, 111–149 (1953) 37. : 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.

Furthermore, he did not consider subalternation as an opposition which makes his figure different from a closed hexagon. But Averroes’ position about the notion of opposition itself is different from both Avicenna’s and Aristotle’s ones. For in Aristotle’s view, the notion of opposition is meant to be incompatibility since he admits only contradiction and contrariety while in Avicenna’s view, the opposition is defined by the difference in truth-values but there are different oppositions which are more or less strong depending on the number of propositions involved.

In the same vein, the sentence “Stones are sick” does not contradict “Stones are healthy” but it does contradict “Stones are not sick” [12, p. 258], because the first two sentences are false while the last one is true. But the notion of opposition is more general than contradiction, contrariety or correlation. It can be seen as a genus that includes several species [12, p. 245]. How can we apply this to the different kinds of propositions that are expressed by singular, quantified or non quantified sentences?

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