Around and Beyond the Square of Opposition by Jean-Yves Béziau

By Jean-Yves Béziau

The speculation of oppositions in accordance with Aristotelian foundations of good judgment has been pictured in a extraordinary sq. diagram which are understood and utilized in lots of alternative ways having repercussions in numerous fields: epistemology, linguistics, arithmetic, sociology, physics. The sq. is usually generalized in different two-dimensional or multi-dimensional gadgets extending in breadth and intensity the unique Aristotelian concept. The sq. of competition from its beginning in antiquity to the current day maintains to exert a profound effect at the improvement of deductive common sense. because 10 years there's a new becoming curiosity for the sq. as a result of fresh discoveries and difficult interpretations. This e-book offers a suite of formerly unpublished papers via excessive point experts at the sq. from world wide.

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Thus, I necessary: “Some men are animals” is true and opposed to O Necessary: “Not all men are 7 Unlike Aristotle, Avicenna does not use the word “contingency” in [14, p. 122]. 26 S. Chatti animals” which is false, and I impossible: “Some men are stones” is false and opposed to O Impossible: “Not all men are stones” which is true. Possible particulars are exemplified by: “Some men are writers” and “Not all men are writers” which are both true. Subcontrariety is then an opposition which makes the propositions never false together but sometimes true together.

233]. In Avicenna’s text, the modal sense is clear as we have seen. Logical Oppositions in Arabic Logic: Avicenna and Averroes 25 modal syllogisms. I. 13, 168)” [21, Sect. 3]. Similar distinctions are made by William of Sherwood, according to the same author [21]. This distribution of truth-values is exactly the same in Avicenna’s (and Al F¯ar¯ab¯ı’s) analysis, as will appear in the following list: A necessary: True E necessary: False A impossible: False E impossible: True A possible: False E possible: False I necessary: True I impossible: False I possible: True O necessary: False O impossible: True O possible: True These truth conditions follow directly from what Avicenna says about the truth-values of the considered propositions [14, p.

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. 17, pp. 102–145. Université de Neuchâtel, Neuchâtel (2004) 42. : The geometry of logical opposition. PhD Thesis, University of Neuchâtel (2009) 43. -Y. Beziau’s method by means of some non-normal modal logics.

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