数学存在的语言建构——结构主义的研究范式

Language Construction of Mathematical Existence:The Research Paradigm of Structuralism

伴随结构主义的兴起,数学哲学的研究领域发生了范式转换,数学存在的语言建构取代了数学语言的逻辑分析,成为数学哲学发展壮大的基本动力与成长源泉。结构主义根据不同语言进行数学对象的存在建构,或者借用数理逻辑的集合论与模态逻辑作为语言,或者突破分析哲学的逻辑语言框架创造范畴论这种本体论语言,从而形成了集合论结构主义、模态结构主义与范畴论结构主义。集合论结构主义与模态结构主义成为沟通结构主义与数理逻辑的必要环节,范畴论结构主义成为结构主义数学哲学的发展方向。

With the rise of structuralism,paradigm transformation emerges in the field of philosophy of mathematics,replacing the logical analysis of mathematical language.The language construction of mathematical existence has become the basic dynamic of the development of philosophy of mathematics.According to different languages,structuralism constructs mathematical existence,borrowing the languages of set theory and modal logic from mathematical logic,or breaching the logical language framework of analytic philosophy,establishing the ontological language of category theory.Thus different types of mathematical structuralism appear,such as set-theoretic structuralism,modal-structuralism and categorical structuralism.Set-theoretic structuralism and modal-structuralism become the necessary link between structuralism and mathematical logic,whereas categorical structuralism becomes the development direction of philosophy of mathematics.