Mathematical Structuralism
Mathematical Structuralism
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数学结构主义
DOI：
10.1017/9781108582933
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S. Shapiro
中科院分区：
文献类型：
--
作者：
G. Hellman;S. Shapiro
目前的工作是对阐述数学结构主义的五个框架或观点的系统研究，其核心思想是数学主要关注从对象的本质中抽象出来的相互关系。前两种理论，集合论和范畴论，是在数学内部产生的。在揭示了一些问题之后，《元素》考虑了逻辑学家和数学哲学家制定的三个进一步的观点：自成一体，将结构视为抽象共相；模态，消除结构作为对象，以支持自由接受的逻辑可能性；最后，模态集论，一种集合论和模态观点的综合。
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.