在数学与哲学之间——分形理论的哲学启示

分形理论是当今非线性科学前沿学科之一 ,与哲学有着不可分割的联系。从哲学层面看 ,分形理论将事物局部与整体辩证关系的研究定量化 ,成为对事物“由表及里”、“见微知著”的认识工具 ,并力图找出不规则中的一定规则 ,不确定性中的某种确定性。把这一点提高到哲学上来认识 ,分形理论以事物的自相似性为基础 ,包含着一种新兴的观察现象、接近现实的成分 ,形成了一种对事物不是与他物比较而是自比的反身认识的新视角 ,是一种“就事物论事物”的认识新途径。

Between mathematics and philosophy The philosophical enlightenment of the fractal theory

Fractal theory, as one of the frontier subjects in non-linear science, is closely related with philosophy. From the view of philosophy, fractal theory quantizes the study of the relation between the part and the whole, and can be used as a tool to understand the interior of matters. It tries to find out regularities from irregularities, certainties from uncertainties. Based on the self-contained similarities of the matters, this theory offers new ways to observe the phenomenon and approach the facts and forms a new angel of knowing matters by self-comparing rather than by comparing with others.