论无理数的哲学意义——基于柏拉图和胡塞尔的研究

The Philosophical Meaning of Irrational Number: A Finding Based upon the Thinking Paths of Plato and Husserl

无理数的出现瓦解了毕达哥拉斯把算术、几何学与宇宙论锻造在一起的统一性,推动了柏拉图将数字本身与计数对象分离开来,发现了有形对象在某种程度上的非存在性以及无形对象在某种程度上的存在性,进而提出可感世界与可知世界、意见与真理相互区别的"分离学说"。可以说,无理数直接引发了柏拉图所谓的"灵魂转向"。无独有偶,无理数的出现打碎了数学博士出身的胡塞尔企图从心理主义出发理解计数过程和重建算术学科的理想,迫使胡塞尔承认包括数在内的一般对象相对于具体对象的分离性和在先性特征,从而提出现象学还原理论,而还原其实正是现代版的灵魂转向。

The emergence of irrational number disintegrates the unity between arithmetic,geometry and cosmology forged by Pythagoras,and induces Plato to distinct the number itself from the object counted,so as to discover,to some extent,the nonexistence of visible objects and the existence of invisible objects,and to put forward the theory of separating the sensible world from the intellectual one,thus named as [WTBX]doxa[WTBZ]and [WTBX]alethia. [WTBZ]It can be said that the irrational number gives rise to Plato's 'soul turning'. The emergence of irrational number also breaks up the Ideal of E. Husserl,who,as a mathematical doctor,seeks to understand the process of counting number and re-establish the subject of arithmetic,which makes Husserl recognize such characters as the separable and the precedent of general objects,including numbers related to concrete objects,so as to come up with a theory of phenomenological reduction,which is actually the soul turning in modern sense.