Models of Reasoning in Ancient China

Imagine for a moment that you are given the opportunity of a trip to the ancient state of Qi (齊) in a suitably reliable time machine. Your destination is the famous Jixia (稷下) academy, which was founded during the reign of the King Wei of Qi (齊威王, 356–321 B.C.). When you arrive, the halls will be full of scholars debating such topics as the importance of ritual lǐ (禮), how to determine what is right yì (義), the relationship between names míng (名) and objects/reality shí(實), and of course, human nature xìng (性). 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 must be appreciated.