数学工具主义者对弗雷格问题的认识论分析

Mathematical Instrumentalist’s Epistemological Analysis of Frege’s Problem

在数学哲学实在论和反实在论对抗的大背景下,德特勒夫森复活了希尔伯特的有限主义。他把自己的思想称为希尔伯特工具主义,这是一种改良版的实在论。通过对弗雷格问题的解决,我们看到希尔伯特工具主义者是如何既承认抽象对象的存在,又发展出关于抽象对象的认识论。通过在有限思维中加入抽象的元素,他解决了抽象对象存在的问题。通过复制主义策略和证明模式认识论,他解决了认识抽象对象的问题。这种实在论既不同于弗雷格的实在论,也不同于菲尔德的唯名论,它是一种介于实在论和唯名论间的新形式。

In philosophy of mathematics under the background of the debate between realism and anti-realism, Detlefsen has revived the Hilbert’s Finitism. He called this thought Hilbertian instrumentalism. This is a modified realism. Through solving the Frege’s problem and Poincare’s problem, we can see the Hilbertian instrumentalist how both acknowledges the existence of abstract objects and develops the epistemology of abstract objects. By adding the abstract elements to the finitary thinking he solves the problem of existence of abstract objects. By the replicationist strategy he solves the problem of knowing the abstract objects. This realism differs not only with Frege’s realism, but also with Field’s nominalism. It is a new form between traditional realism and nominalism.