On the Asymmetry Between the Four Corners of the Square

As is well known, the three first corners of the square of opposition, i.e. A, E, and I, are expressed by single words, in English, French and other Indo-European languages, whether the square is quantified, modal, temporal, or deontic, while O is expressed by two words, and is not lexicalized. This has given rise to the following question: why is the O corner always expressed in a complex way in these languages? Why isn’t it lexicalized? Some people such as Laurence Horn, for instance, provide solutions based on the meaning of O and its intimate link with I, which makes it more complex than E and justifies the asymmetry. However, in Arabic, there is no asymmetry, given that the two negatives are expressed by groups of words, while the affirmatives are expressed by single words. This feature gives rise to a different problem, related rather to the E corner, which can be raised as follows: Given that E is as complex as O, being negative and quantified, why is it expressed in the Indo-European languages by a single word rather than a group of words? In this paper, I answer this question by making use of Saussure’s Course in General Linguistics, and by applying the concepts of agglutination and analogy, introduced by Saussure in this text, to the expressions corresponding to the corners of the quantified, modal, temporal and deontic squares of oppositions. This relativizes the singularity of O, and confirms the arbitrariness of the sign by showing the differences of functioning between these various languages.

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