数学本质的语境论解释

A Contextualist Account of the Nature of Mathematics

"数学本质究竟是什么"是当代数学哲学争论的核心问题之一。对象柏拉图主义认为数学的本质在于研究一些独立的个体对象,结构主义主张数学本质的核心是抽象结构。语境论在阐明传统解释存在缺陷的基础上,运用语境分析对"数学本质"给予了新的解释———在形而上学层面,数学本质是概念;在数学实践层面,数学本质是开放的。更重要的是,如何理解"数学本质"本身就是一个依赖语境的问题。

＂What is the nature of mathematics＂ is one of the central problems in contemporary philosophy of mathematics.Object-Platonism holds that the nature of mathematics regards some independent individual objects as its subject matter.Structuralism argues that the nature of mathematics is Abstract structure.On the basis of illustrating the drawbacks of traditional interpretation,contextualism attempts to give a new account of the nature of mathematics by contextual analysis.It argues that the nature of mathematics is concept in metaphysical sense.And in mathematical practice the nature of mathematics is open-ended.Most importantly,how to understand the nature of mathematics is a context-depended problem.