摘要
认识论问题是数学柏拉图主义面临的主要难题。回应它的进路有两种:一是为人类认知主体与抽象对象之间寻找某种联系,如哥德尔的数学直觉学说;二是为数学提供一种免接触的认识论,如新弗雷格主义、全面柏拉图主义等。但从自然主义的观点看,这两种进路都隐含深刻的困难,因为自然主义下的认识论问题不是单纯的证成问题,它更主要地是认知机制问题。特别地,它要求回答相关性问题,即说明人类大脑中的数学概念如何能与抽象对象相关联,而不只是大脑的想象。
The epistemological problem is the main problem faced by mathematical Platonism.There are roughly two ways for a Platonist to approach the problem:one is to find some connections between the human cognitive subject and abstract objects,such as G9 del’s theory of mathematical intuition;the other is to provide a no-contact epistemology for mathematics,such as neo-Fregeanism and full-blooded Platonism.However,from a naturalistic point of view,both of the two approaches have serious difficulties,because the epistemological problem is not purely about justification,but also about cognitive mechanism.In particular,it requires an answer to the aboutness problem,i.e.,explaining that how a mathematical concept in the brain can be about some abstract objects rather than a mere imagination of the brain.
作者
高坤
GAO Kun(Research Center for Philosophy of Science and Technology,Shanxi University,Taiyuan 030006,China)
出处
《自然辩证法研究》
CSSCI
北大核心
2021年第8期109-114,共6页
Studies in Dialectics of Nature
关键词
数学柏拉图主义
认识论问题
免接触认识论
相关性
mathematical Platonism
the epistemological problem
no-contact epistemology
aboutness
