数学认知中的具身进路及其哲学观初探

An Embodied Approach to Mathematical Cognition and Its Philosophical View

数学认知中基于认知语言学的具身进路认为,数学是人基于天生的简单算术能力,通过概念隐喻以及概念混合等源于日常实践的基本认知机制,把日常身体实践经验中的推理结构以及物质世界的空间逻辑结构映射到抽象的概念域而形成的。该理论持有一种自然主义的反实在论,其核心在于把数学对象以及数学思想看作一种认知的过程而不是抽象的实体,这种认知过程与包含身体在内的物质世界的某些结构和过程同构。

An embodied approach to mathematical cognition points out that mathematics is based on the natural ability of simple arithmetic,i.e.,through conceptual metaphor and conceptual blending,which are derived from the basic cognitive mechanism of daily practice,mapping the reasoning structure of daily physical practice experience and the spatial logical structure of the material world to abstract domain.This theory holds a naturalistic anti-realism,the core of which is to regard mathematics as a cognitive process rather than an abstract entity.Furthermore,the process is isomorphic to some structures and processes in the physical world.