In logic, Aristotelian diagrams are almost always assumed to be closed under negation, and are thus highly symmetric in nature. In linguistics, by contrast, these diagrams are used to study lexicalization, which is notoriously not closed under negation, thus yielding more asymmetric diagrams. This paper studies the interplay between logical symmetry and linguistic asymmetry in Aristotelian diagrams. I discuss two major symmetric Aristotelian diagrams, viz. the square and the hexagon of opposition, and show how linguistic considerations yield various asymmetric versions of these diagrams. I then discuss a pentagon of opposition, which occupies an uneasy position between the square and the hexagon. Although this pentagon belongs neither to the symmetric realm of logic nor to the asymmetric realm of linguistics, it occurs several times in the literature. The oldest known occurrence can be found in the cosmological work of the 14th-century author Nicole Oresme.

中文翻译：

---

Oresme 的 Livre du Ciel et du Monde 的 Square 和 Hexagon 之间

在逻辑中，亚里士多德的图几乎总是假设在否定下是封闭的，因此本质上是高度对称的。相比之下，在语言学中，这些图用于研究词汇化，众所周知，词汇化不是在否定下封闭的，因此会产生更多的不对称图。本文研究了亚里士多德图中逻辑对称性和语言不对称性之间的相互作用。我讨论了两个主要的对称亚里士多德图，即。对立的正方形和六边形，并展示语言上的考虑如何产生这些图表的各种不对称版本。然后我讨论了一个对立的五边形，它在正方形和六边形之间占据了一个不安的位置。虽然这个五边形既不属于逻辑的对称领域，也不属于语言学的不对称领域，它在文献中多次出现。已知最古老的事件可以在 14 世纪作家 Nicole Oresme 的宇宙学著作中找到。