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By Jean-Yves Béziau

The idea of oppositions in accordance with Aristotelian foundations of common sense has been pictured in a awesome sq. diagram which might be understood and utilized in lots of other ways having repercussions in a number of fields: epistemology, linguistics, arithmetic, sociology, physics. The sq. is also 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 maintains to exert a profound effect at the improvement of deductive common sense. due to the fact that 10 years there's a new transforming into curiosity for the sq. as a result of fresh discoveries and hard interpretations. This ebook offers a suite of formerly unpublished papers by means of excessive point experts at the sq. from around the world.

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Extra resources for Around and Beyond the Square of Opposition

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The necessity, possibility or impossibility is internal and is not expressed by a specific word. As an example of a necessary proposition, Avicenna gives the following: “Every man is an animal”, this proposition is necessary because of the fact that being an animal is an essential attribute of men. The example corresponding to an impossible proposition is the following: “No man is a stone” [14] which expresses the fact that “stone” cannot be a feature of the subject “man”. This sentence expresses an impossible proposition because Avicenna defines material impossibility in this way: it is “what is permanent and whose affirmation is necessarily false” [14, p.

If this is so, then E has an import as well as A. Therefore if the disjunction is inclusive, ‘E or O’ will be equivalent to O. e. ‘A or I but not both’ and ‘E or O but not both’, the indefinites remain also ambiguous and different from the quantified propositions. However, this creates other problems which we will consider in our last part. Anyway the figure is more complex then Aristotle’s and Avicenna’s ones since we could also add the singular propositions which are explicitly included by Averroes into the class of opposed propositions and construct a new kind of hexagon where the new line is horizontal.

When we add negations, the universal negative is expressed by “No A is B” and the particular negative by “Not all A are B”. As in the Aristotelian tradition, Avicenna considers that the universal negative (E) and the particular affirmative (I) on the one side, and the universal affirmative (A) and the particular negative (O) on the other are contradictories, that is, they never share the same truth-value. But what is added is the subdivision of these quantified propositions into three kinds which are: Necessary, Impossible and Possible.

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