By Jean-Yves Béziau
The idea of oppositions in accordance with Aristotelian foundations of common sense has been pictured in a remarkable 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 idea. The sq. of competition from its foundation in antiquity to the current day maintains to exert a profound effect at the improvement of deductive good judgment. considering the fact that 10 years there's a new starting to be curiosity for the sq. as a result of contemporary discoveries and hard interpretations. This e-book provides a suite of formerly unpublished papers by way of excessive point experts at the sq. from worldwide.
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Additional info for Around and Beyond the Square of Opposition
Br Logical Oppositions in Arabic Logic: Avicenna and Averroes Saloua Chatti Abstract In this paper, I examine Avicenna’s and Averroes’ theories of opposition and compare them with Aristotle’s. I will show that although they are close to Aristotle in many aspects, their analysis of logical oppositions differs from Aristotle’s by its semantic character, and their conceptions of opposition are different from each other and from Aristotle’s conception. Following Al F¯ar¯ab¯ı, they distinguish between propositions by means of what they call their “matter” modalities, which are determined by the meanings of the propositions.
How can we apply this to the different kinds of propositions that are expressed by singular, quantified or non quantified sentences? To answer this question let us see what Avicenna says in al-‘Ib¯ara. e. e. Universal and Particular propositions. We have to notice here that Avicenna uses a specific term to indicate the presence of a quantification. The quantifier is expressed by the word ‘s¯ur’ [14, p. 52] and 1 Wilfrid Hodges in [19, p. 2 This word ‘s¯ur’ is also used by Al F¯ar¯ab¯ı in al-Qawl fi al-‘Ib¯ar¯a, for instance.
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. 17, pp. 102–145. Université de Neuchâtel, Neuchâtel (2004) 42.
Around and Beyond the Square of Opposition by Jean-Yves Béziau