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“抽象的数学世界存在吗”是当代数学本体论领域持久争论的两大核心问题之一。实在论主张数学为我们描述了一种抽象的实在世界;反实在论则认为数学仅仅是一种有用的虚构和方便的工具而已。语境论在阐明传统解释存在缺陷的基础上,对数学的实在性问题给出了新的说明。以作为世界观的语境论为基点,得出:抽象的数学世界不存在,数学是表征而非描述物质世界。
“The existence of an abstract mathematical world ” is one of the two core issues of the lasting debate in the field of contemporary mathematical ontology. Realism argues that mathematics describes an abstract real world for us; anti-realism holds that mathematics is merely a useful fictional and handy tool. On the basis of clarifying the defects of the traditional interpretation, the context theory gives a new explanation of the real problem of mathematics. Based on the contextualism as a world view, we conclude that the abstract mathematical world does not exist and that mathematics represents rather than describes the physical world.