为什么布尔巴基运动会衰落?——布尔巴基结构主义范式的视域盲区及其祛蔽

Why Bourbaki’s Movement was Faded?:The Horizon Blind Area of Paradigm of Bourbaki’s Structurism and Its Elimination

20世纪30年代之后,布尔巴基结构主义运动开始崭露头角并迅猛发展,成为20世纪纯粹数学发展的一种重要范式。结构主义范式的一个突出和本质特征就是对结构视角的固守。虽然采用结构的视角对于认识纯粹数学的知识特征是十分有效的,但这不意味着结构的视角就是唯一的和万能的。结构视角有其难以掩饰的盲区,这就是非结构或难以结构化的数学对象与系统。而对非结构的数学对象与系统的研究恰恰是20世纪后半叶以来壮丽的数学与科学知识创新图景中一个突出和显著的特点。只有突破"结构性"的框架与教条,祛蔽结构主义视域的盲区,克服其知识的内在局限性,结构主义的范式悖谬性才能得以消弭并有可能获得新的生机。

Since the 1930s, the structurism of Bourbaki has begun to develop rapidly and gradually become one of the most important paradigms of pure mathematics of 20th century. The prominent and essence feature of structuralist paradigm is to stick to the structural perspective. Although the structural perspective is effective for the understanding of knowledge characters of pure mathematics, it does not mean the structural perspective is the only and all-powerful. The structural perspective has its obvious fade zone, i.e. non-structure or unstructured mathematical objects and systems. A significant feature of mathematics and science innovations since the second half of 20th century is the study on the non-structured objects and systems. The paradigm paradox of structurism could be eliminated and regain vitality only if the framework and doctrine of structurality have been broken through, its dead zone has been unconcealed and its inherent limitation has been overcome.