哥德尔纲领的实现能支持数学实在论吗?

Can the Realization of G?del’s Program Support Mathematical Realism?

哥德尔纲领是由哥德尔提出的一个旨在解决集合论独立性问题的研究方略,它对最近半个世纪的集合论研究产生了巨大的影响。当代集合论的一些最新成果显示,这个纲领有可能面临一个完美的实现。很多人认为,这将有力地支持数学实在论。但更深入的分析表明,哥德尔纲领的真正基础是集合的迭代概念,而非实在论;并且,集合的迭代概念以及践行哥德尔纲领所使用的外在的公理辩护方法,实际上与实在论的立场有潜在的冲突,反倒与反实在论的图景更为契合。

G?del’s Program is a research program proposed by G?del to solve independent problems of set theory.It had a great influence on the set theoretic research in the last half century.In particular,some of the latest results in contemporary set theory show that this program is getting close to an perfect realization.Many people think that this will strongly support mathematical realism.However,a deeper analysis suggests that the real foundation of G?del’s Program is the iterative conception of sets,rather than realism;moreover,the iterative conception of sets and the extrinsic method for defending axioms used in the implementation of the program are actually in potential conflict with the position of realism,but fit the antirealistic picture much better.