The Logic of Mohist Reasonings; Leis and Structured Sorts

It is well-known that some Mohist reasonings of the final portion of the Xiao qu 〈小取〉 are paradoxical: “a robber is a man, but to kill a robber is not to kill a man”. In this paper, we analyze and formalize the different groups of Mohist reasonings using concepts of contemporary western logic: classes, sorts, structured sorts as they appear in the mathematical theory of categories. We solve those paradoxes by using sorts and more generally arrive at the conclusion that those reasonings are based on structured sorts, a notion which, in our opinion, is fundamental to clarify the notion of lei (類).