摘要
众所周知,哥德尔是一位实在论者。然而,他在构造主义数学方面也有着精深的研究和重要的工作。例如,哥德尔的否定性翻译和《辩证法》翻译。这些方法在现今的数理逻辑研究,尤其是证明论中有广泛的应用。而本文关心的是这些工作在数学基础和数学哲学方面的价值。我们将介绍、整理哥德尔的这些成果,并试图将它们编制成一幅围剿直觉主义的布阵图。我们也会讨论其中的薄弱之处,并由此碰触哥德尔哲学中一些挣扎而神秘的地方:绝对证明、概念理论和心物关系。
Kurt Godel is a well-known realist. However, he also had some remarkable works on constructive mathematics, e.g. the G6del＇s Negative Translation and Dialectica In- terpretation. These methodologies are fruitful in today＇s proof theory. However, we are mostly interested in their foundational or philosophical consequences. We will introduce these achievements, and try to reorganise them as an intended arrangement against in- tuitionism. We will also discuss its weakness, and then touch the most tangled part of G6del＇s philosophy： the concept of absolute proof, the theory of concept, and the issues on mind and body.
出处
《逻辑学研究》
CSSCI
2014年第3期12-29,共18页
Studies in Logic
基金
教育部人文社会科学研究青年项目--"当代集合论哲学及其对数学基础研究的影响"(13YJCZH226)
复旦大学新进青年教师科研起步项目
复旦大学青年教师科研能力提升项目资助
