One, Numbers and Language in Liu Hui’s Commentary to the Nine Chapters on Mathematical Procedures

In this article, I compare passages from the works of the Neo-Daoist philosopher Wang Bi 王弼 and the mathematician Liu Hui 劉徽 about the generation of one and numbers. I argue that despite the differences between these thinkers, their accounts are both informed by a concern for language and metaphysics. For both of these authors, the word “one” does not refer to any specific thing, but is employed to designate something which might also be called otherwise. This can be seen as a speech act through which numbers are created. There is no single unified way in which numbers are generated from one. Instead, there are multiple different ways in which one and numbers can be related to each other. This becomes especially clear for Liu Hui. I argue that, to him, the word “one” can, among other things, be used for a counting unit, the word itself, or the act of taking something as one. All these different ways of thinking are related to each other and together constitute a sophisticated and multi-faceted concept of one.