The Square of Opposition: Past, Present, and Future

Béziau, Jean-Yves; Vandoulakis, Ioannis M.

doi:10.1007/978-3-030-90823-2_1

Cited by 2 publications

(1 citation statement)

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“…Subalternation in black is an implication, showing for example on the right side that antisymmetry is a particular case of asymmetry, or that the bottom Y corner represents things which are either non-antisymmetric or asymmetric. This hexagon of opposition is an improvement of the square of opposition originally based on some ideas of Aristotle and later on explicitly designed by Apuleius and Boethius (Beziau and Vandoulakis 2022). The hexagon of opposition was mainly promoted in the 2 nd half of the 20 th century by Robert Blanché (1966).…”

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confidence: 99%

Ambiguous Symmetry

Béziau

2022

Symmetry: Art and Science | 12th SIS-Symmetry Congress

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This paper presents, analyses and discusses the notion of ambiguous symmetry through the typical case of human beings, both from the physical and spiritual point of view. We first pre- sent a symmetry hexagon of opposition characterizing what symmetry is by relating it with opposed notions in particular antisymmetry and asymmetry. We then describe and comment the ambiguous symmetry of human beings. We emphasize that there is a contrast between an outside symmetry and an inside asymmetry, for example in the case of the torso. In the case of the hands, the left and right hands look symmetric but the way they work is not. This is related with the left and right parts of the brain which can be seen as a complementary symmetry, similar to the positive and negative inte- gers. We also point out the vertical and horizontal asymmetries of human body and the asymmetry between male and female bodies. Male and female can however be seen as complementary symmet- ric from the point of view of the yin-yang Tao theory. It is a metaphorical way to explain that it makes sense to argue that God is symmetric, and that human being is an image of God.

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confidence: 99%