后现代:一个观照数学哲学的新视阈——数学哲学的范式分期与“后现代数学”的数学教育前瞻

Postmodern:A New Perspective on Surveying the Philosophy of Mathematics——The Rebuild of Historical Division of Paradigm about Philosophy of Mathematics and the Prospect of Mathematics Education in“Postmodern Mathematics”

后现代主义者对现代性思想体系、知识范型和方法论纲在多个维度上的解构与批判有着其内在的历史、逻辑与现实合理性.后现代思想对于数学这样独特的知识型有着怎样的启示和价值,是一个有待探究的哲学课题.在数学哲学研究中,范式的分期问题一直为学界所忽视.既有的叙事模式大多沿用数学史或哲学史的研究路线,致使数学哲学史的研究在涉及与分期有关的课题时陷入难以突破和视角散焦的状态.借鉴后现代的理论、立场和视角,追索数学知识嬗变与哲学思辨的轨迹,可以获得一个有别于传统数学史和哲学史叙事方式的新的范式分期.其中,“后现代数学”在对现代性数学的超越中获得了自我确认,凸显了其在数学哲学范式上的革命性、转换性、连续性和整体性以及对于未来数学教育的一种前瞻.

Postmodernist’s deconstruction and critique of the modernity ideology system,knowledge paradigms,and methodological outlines in multiple dimensions have their inherent historical,logical,and realistic rationality.What kind of inspiration and value does the postmodern thought has for such a unique type of knowledge as mathematics is a philosophical topic to be explored.In the study of mathematical philosophy,the question of historical division about the paradigm has always been neglected by the researchers.Most of the existing narrative modes follow the research route of the history of mathematics or philosophy,which makes the research of the history of mathematical philosophy difficult to break through and the perspective is out of focus when it comes to topics related to the historical division.Drawing on postmodern theories,standpoints,and perspectives,tracing the evolution of mathematical knowledge and the trajectory of philosophical speculation,a new paradigm periodization can be obtained which is different from the traditional narrative mode of history of mathematics and history of philosophy.Postmodern mathematics confirms itself in the process of transcendence of modern mathematics and the basic features of this new concept highlight the revolutionary,transformational,continuous,and holistic characteristics of the paradigm of philosophy of mathematics and prospects for future mathematics education.