自然主义与数学本体论问题

Naturalism and The Ontological Problem of Mathematics

自然主义提供了思考数学本体论问题的一个重要进路,比如蒯因的不可或缺性论证就是一个典范。但不可或缺性论证有很多缺陷,于是蒯因之后的很多自然主义者试图对数学本体论问题做出新的自然主义回答,其中就包括伯吉斯和罗森的数学-自然主义论证和叶峰的物理主义论证。然而,精细的分析表明,这两个论证也是有问题的:前者隐含了关于常识和数学专家意见的一些错误假设,后者则在论证过程中忽略了关于物理对象的一个关键的区分。

Naturalism provides an important approach to ontological issues about mathematics, for which Quine＇s Indispensability argument is a paradigmatic example. But the Indispensability argument is severely defected, thus many naturalists after Quine seek for new answers to mathematical ontology, among which are Burgess and Rosen＇s Mathematical-naturalistic argument and Feng Ye＇s Physicalistic argument. However, a careful examination shows that both of the two arguments are problematic, the former relies on some mistaken presuppositions about the common sense and expert mathematician opinions, and the latter ignores a critical distinction about physical objects in the course of the argument.