赫尔曼的模态结构主义

Hellman's Modal-structuralism

以消除本体论预设为宗旨,赫尔曼提出了模态结构主义思想,并发展为数学结构主义中极富影响力的理论框架。模态结构主义强调避免对结构或位置进行逐个量化,而是将结构主义建立在某个域以及该域上满足由公理系统给出隐含定义条件之关系的二阶逻辑可能性上。但以二阶逻辑与初始模态事实为基础,导致其理论实际建立在集合论之上,显然与结构主义初衷不符。此外,其对结构的模态中立主义态度,导致无法说明数学的可应用性,难以规避语义学难题。

For the purpose of eliminating the ontological presupposition, Geoffrey Hellman proposed his modal strncturalism. It has developed into an influential systematic theory so far. To avoid quantifying over individual structure or location, modal strncturalism is building up on the second order possibilities of some domains and their appropriate relations （which are given by implicit definitions of the axiom system）. But its presuppositions on second order logic and initial modal facts turn out to be on the basis of set theory, which obviously does not accord with its origi- nal purpose of structuralism. In addition, its modal neutralism results in the inability to illustrate the applicability of mathematics, which is hard to avoid semantic problems.