数学与形而上学的起源

Mathematics and the Origin of Metaphysics

哲学的冲动与经历某种“边缘形势”有关,而要使这些冲动形成一门能传承的学问,必依靠某种游戏机制。古希腊的数学是形成西方形而上学传统的关键机制,通过华达哥拉斯而直接影响到巴门尼德和柏拉图,再传至亚里士多德。本文探讨了“数是本原”的具体含义,它的成功与失败之处,以及后来的哲学家们如何吸收与改造它。作者同时提及这种“数形而上学”在今天的新活力。

To integrate philosophical pulses, which relate to certain 'marginal situations' in life, into a sustainable tradition, there must be some game structure or matrix. Math in ancient Greece provided such a key matrix to form a metaphysical tradition in the West, through Pythagoras to Parmenides, Plato, and finally to Aristotle. This paper investigates the real meanings and consequences of Number is the Beginning', i.e., the success and failure of this theme for establishing metaphysics, and how the succeeding philosophers reformed it. Last, the new momentum achieved by this 'metaphysical number' is also mentioned.