從懷德海“數學之善”反思數學文化

Cultural Reflection on Mathematics

10.7065/MRPC.200706.0131

蔡仲(Zhong Cai)

歐幾里得理性 ； 科學危機 ； 善 ； Euclidean reason ； Science Crisis ； the Good ； the Evil

哲學與文化

34卷6期（2007 / 06 / 01）

131 - 141

繁體中文

歐幾里得理性與審美直覺位於人類智力的兩個極端。西方文化偏重於前者，偏重於理智性和概念性的知識分析以求得公理化的理解。然而，這種理解使西方科學文化陷入一種悖論：一方面，科學把自然的一切物質運動歸結在普遍有效的數學公式的演繹系統中，加深了對自然的真理性的認識，並產生巨大的生產能力；另一方面，這種抽象性必然意味著科學把自然理解為一種沉寂的，無色彩的運動中的物質世界，導致了(1)機械論的出現；(2)科學喪失生活的意義；(3)科學文化和人文文化的分裂和對抗；(4)中西文化的隔閡。科學要擺脫危機，必須走出歐幾里得的堡壘，走向生活，走向審美直覺，到廣闊的和富有歷史文化感的歷程哲學中去汲取營養。

The Euclidean reason and aesthetic intuition stand in two poles of human intelligence. The Westerners are good at analyzing knowledge with logic and conceptual apparatus in order to arrive at the formalized comprehending of the world. However, the logical and conceptual analysis pushes the science culture to a dilemma. On the one hand, science makes all kinds of material motion appear as working in the way governed by formalized mathematics system and shows this kind of formalization as common effective to all kinds of motion. The formalization and abstraction of the material world really make human being endowed with the powerful capability to understand and rein the world. On the other hand, however, according to Whitehead, understanding and reining way based on formalism deprive human of intuition for evaluating and perceiving the meaning of the concrete living world, kill the aptitudes rooted in humanity and drive human being to live in a categorized world which is against human nature. As a result, the dilemma leads science to plunge in crisis. Thus, if we who live in this scientific culture want to avoid this crisis, we must go out the Euclidean fortress, to go straight forward to the lively world and real life, to restore our aesthetics intuition, and to take our nourishment from process philosophy.

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