Traditional Chinese Logic And Mathematics

Logic in science is closely related with mathematics, but in the history of Chinese mathematics and Chinese Logic, few scholars were dedicated to the study of "traditional Chinese mathematics and its own Logic". As a consequence, basic problems have not been solved yet. For example, does the traditional Chinese mathematics have its own Logic? If so, what is it? What is the major type of inference in such Logic? How does the Logic of traditional Chinese mathematics influence the follow-up development? It is the commencement of this Dissertation to consider these problems. The so-called Chinese Logic refers to ancient Chinese Logic. In other words, it is the traditional Chinese Logic which was not influenced from the western Logic composed mainly by Aristotelian Logic. The main components of Chinese Logic is "MING"(名),"CI"(辞),"SHUO"(说), and the way of inference is TUILEI in the Chinese Logic. Traditional Chinese mathematics means the part of Chinese mathematics established before the input of western mathematics into China at the end of MING Dynasty (16th century), and the part of Chinese mathematics from then to the beginning of 20th century. It mainly experienced five stages and formed a particular system of thought, i.e. the beginning, the stage of theory formation, the slow development and gaining ground of mathematics, the enrichment of theory, and the stage of declining and transformation. In QIN-HAN Dynasties traditional Chinese mathematics'logical methods and logical thoughts accommodated the standpoints and methods of Mohist Logic. The idea and method of TUILEI in Mohist Logic was used extensively by QIN-HAN mathematics so that the particular Logic—using the type to match the type—was primarily set up. In the SANGUO-LIANGJIN-NANBEICHAO Dynasties traditional Chinese mathematics not only theoretically came to an unprecedented high degree, but also methodologically came to the highest level. In particular, the Logic which represents the backbone and main body of mathematics methodology arrived its summit, and the way of inference, i.e., TUILEI based upon "type matching type"was established as the major way of inference in the traditional Chinese mathematics. In SONGYUAN Dynasties traditional Chinese mathematics accomplished the last climax of development —not only in the important breakthroughs in thought and the theory of mathematics, but also in the significant innovations in methods and ways of thinking. It consists of the transform of inheriting from the TUILEI in traditional Chinese mathematics to the deductive mode or the machine-thinking mode, which can be seen from either QINJIUSHAO's work, or JIAXIAN's or ZHUSHIJIE's work. All in all, on the one hand, the Chinese Logic produced deep and positive influences on Chinese traditional mathematics, and the thought and method in Chinese Logic pushed the traditional Chinese mathematics to keep on developing; On the other hand, traditional Chinese mathematics became Logic of its own, whose way of inference is TUILEI until SONGYUAN Dynasties. In fact, the deductive TUILEI had already arrived to the very high level in LIUHUI's times, and in the SONGYUAN Dynasties, seeing from QINJIUSHAO's work, the mathematics thought and reason had already started to have axiom characteristics. In MING Dynasties Chinese mathematic lagged behind the world, which was resulted not from the mathematics itself, but from other social factors: poor economy, social turbulence, the masses without means to live, feudalist economy, and the Policy that government officials were elected from the test on BAGU directly obstructed the development of traditional Chinese mathematics. The supposition that the development of traditional Chinese mathematics in MING Dynasty was refrained by traditional Chinese way of thinking is worth doubting. Chinese Logic was not the factor baffling the development of traditional Chinese mathematics, and the Logic of traditional Chinese mathematics of its own was not the reason for its development restriction.