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 impressive sq. diagram which are understood and utilized in lots of other ways having repercussions in a number of fields: epistemology, linguistics, arithmetic, sociology, physics. The sq. is usually generalized in different two-dimensional or multi-dimensional items extending in breadth and intensity the unique Aristotelian thought. The sq. of competition from its foundation in antiquity to the current day maintains to exert a profound influence at the improvement of deductive common sense. on the grounds that 10 years there's a new becoming curiosity for the sq. because of contemporary discoveries and tough interpretations. This publication offers a set of formerly unpublished papers via excessive point experts at the sq. from around the world.

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Other contradictories are the quantified propositions which never share the same truth value “in all matters” [9, p. 92]. These are A and O on the one side and E and I on the other. To illustrate this, he gives the following example: “All men are white” and “Not all men are white”. Then we have the contraries which are the two universal propositions and do not share the same truth value “in the Necessary and the Impossible” [9, p. 92] but are both false when they are Possible. The examples given are the following: “Every man is white”, “No man is white” which are both false.

The distribution that Avicenna presents corresponds to the truth cases of these different operators, which shows that his characterization of the oppositions does not differ from the classical one but is more precise in that it determines exactly the cases of truth and falsity of the propositions. We could then define opposition by distinguishing between a complete opposition and partial oppositions in the following way: Logical Oppositions in Arabic Logic: Avicenna and Averroes 33 (I) Two propositions are opposed completely if and only if: (1) They have the same subject and the same predicate but one of them is affirmative and the other is negative (2) They never share the same truth-value whatever matter they have (II) Two propositions are partially opposed if and only if: (1) They have the same subject and the same predicate but one of them may deny the other (2) They do not share the same truth-value in one or two matters This distinction between the two kinds of oppositions is justified by the fact that Avicenna considers contradiction as the most important opposition and that he says that the opposition is “a genus which could be divided into species” [12, p.

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.

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