Mozi’s Square of Opposition and Logemes as New Logical Approach

The first logical treatise in Chinese was written by Mozi and entitled the Dialectical Chapters (Mòbiàn). In this work we cannot detect a single logical system, but it contains many valuable logemes (logical fragments that are consistent). In particular, we find a non-Aristotelian square of opposition in which the existential quantifier is understood in the narrow sense as some and only some. We remember that Aristotle treats the existential quantifier in a broad sense as some, or perhaps all. Mozi was the first logician who proposed considering logic not as a single system, but as a set of different logemes, realized on some partially ordered sets (posets). This is a semantic approach to logic, which was then further developed in the Chinese school of names. In this paper, I logically formalize this approach, proposing to use simplicial complexes from topology as logical diagrams. The point is that these complexes uniquely represent finite posets up to homeomorphisms. Therefore, within the framework of simplicial complexes we can consider different logemes realized on different finite posets at once.