Author’s Response to the Book Review of The Empty and the Full: Is It Possible to Explore the Limit of Language?

Abstract

I want to thank my colleague, Andrea Bréard, for the time she spent reading and commenting. My experience of the editing process was not a pleasant one. There were some communication difficulties meaning that, for instance, I cannot explain why my glossary, which contained 400 terms, was reduced to fewer than 250 terms. I hope that one day I will be given the opportunity to correct this book, to meet my own highest requirements. The purpose of my book is to explore a link between philosophy and mathematics in China and to raise questions of methodology. It is as a philosophy educator, classroom practitioner, and non-mathematician that I write. When Bréard writes that “I could not make up my mind,” this is not the case: I voluntarily chose not to enclose Li Ye’s work within traditional disciplinary divisions. As long as the reader considers the object of study to be “simply” Yigu yanduan益古演段 (Development of Pieces [of Areas] [according to] [the collection] Augmenting the Ancient [knowledge]), this text will indeed come across as of less interest. The text written by Li Ye in 1259 will never be anything but a list of problems concerning the solution of quadratic algebraic equations. Many historians have regarded it as a didactic text to