数学虚构主义与不完全性问题

Mathematical Fictionalisms and The Incompleteness Problem

数学虚构主义在当代数学哲学中是一支影响很大的反实在论。这篇文章讨论的虚构主义主要是启发性的虚构主义、算子(或元)-虚构主义、对象-虚构主义和比喻性的-虚构主义。这几种虚构主义都面临着不完全性的问题,虚构主义者对此提出了不同的回应。这篇文章在指出这些回应不成功的基础上,提出一种新的解决不完全性问题策略:释义性办法,就不完全问题,对各种形式的虚构主义提出一个统一的辩护。

Mathematical fictionalism is one of the most influential anti-realisms in contemporary philosophy of mathematics. Of the various kinds of fictionalisms on the current philosophical market, Hermeneutic Fictionalism （which contains Operator （or Meta-） Fictionalism, Object-Fictionalism and Figurative Fictioalism） is one which will be discussed in this paper. According to many philosophers, those three kinds of fictionalism are all susceptible to incompleteness problems, against which many fictionalists have made a lot of defenses and responses. According to my argument, all of those defenses are unsatisfying. The paper attempts to propose a new solution to the incompleteness problem, the paraphrase strategy, and give a uniform defense for all these kinds of ficionalism.