Models of Reasoning in Ancient China

Abstract

The aim of this paper is exploratory: to propose a few models of the central concepts of classical Chinese philosophy, with the modest aim of indicating, in rough terms, how the techniques of modern logic may be applied to matters of ancient concern. We do not claim that any of the ideas presented here give a correct or faithful account of their subject matter. They are models, that is all. Some may ultimately prove useful; others will have to be discarded along the way. We hope only to demonstrate the kind of application of modern techniques that we believe to be generally useful. By ‘modern logic’ we do not mean the predicate calculus or set theory or any one symbolic system, classical or non-classical. Instead, we draw on the spirit of research in modern logic, especially those parts of logic commonly termed ‘philosophical’ or ‘applied’. That is a spirit of ‘anything goes,’ in which problems and conundrums are approached on their own terms, without ideological bias towards any one system or set of techniques. Imagine for a moment that you are given the opportunity of a trip to the ancient state of 齊 Qí in a suitably reliable time machine. Your destination is the famous 稷下 Jìxìa academy. When you arrive, the halls will be full of scholars debating such topics as the importance of 禮 lĭ (ritual), how to determine what is 義 yì (right), the relationship between 名 míng (names) and 實 shí (reality), and of course, the nature of 性 xìng (human nature). Equipped with the tools of modern logic, you set out to make sense of these debates in the best way you can. One approach would be to start a school of logic, teaching the predicate calculus and set theory, in the hope that once the light of 21st century reason has been shed on the dark corners of the hall, many mysteries and sources of confusion would just evaporate. This may not be the best strategy. One immediate problem is that these tools were developed in the 19th and 20th centuries to deal with problems in the philosophy of mathematics. For that, they are very well suited. Of course, they have gone on to find application in a much broader arena. But first and foremost, they are tools for reasoning about mathematical objects, timeless and discrete numbers, whose properties are more-or-less determinate, and about which the largest mystery concerns the treatment of infinity. No matter how much faith one has in the power of logic, the difficulty of showing the application of these techniques to the ancient debates, which are mostly concerned with the time-bound, vague, indeterminate and finite affairs of humankind, must be appreciated. Our approach will be different. To be sure, an understanding of our techniques depends on the same educational background as other parts of mathematical logic. But we will try to model the subject matter of the ancient debates directly, using only what is needed when it is needed, without presupposing the possibility of a translation or interpretation of the models back into something more standard, even though it is almost certain that such a possibility could eventually be realized.