CAJ | 학술논문

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。
반수결구주의적흥기,수학철학적연구영역발생료범식전환,수학존재적어언건구취대료수학어언적라집분석,성위수학철학발전장대적기본동력여성장원천。결구주의근거불동어언진행수학대상적존재건구,혹자차용수리라집적집합론여모태라집작위어언,혹자돌파분석철학적라집어언광가창조범주론저충본체론어언,종이형성료집합론결구주의、모태결구주의여범주론결구주의。집합론결구주의여모태결구주의성위구통결구주의여수리라집적필요배절,범주론결구주의성위결구주의수학철학적발전방향。
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.