摘要
哥德尔不完全性定理可以表述为没有机械定理证明机器(或程序)能够只证明全部真的数学命题。它不仅仅是一个确定的逻辑定理,还对数学真理的本性以及人心与机器的关系等哲学问题有着深远的影响。本文从两个角度讨论哥德尔与人工智能的关系:第一部分从哥德尔不完全性定理出发,以此为工具来考察“人心胜过机器”反机械论中著名的“卢卡斯—彭罗斯论证”以及“哥德尔析取式论证”;第二部分则集中讨论哥德尔对图灵关于机械程序分析的看似不一致的评论,一方面他毫无保留地赞成图灵关于机械程序的分析,但是另一方面他又断言图灵的分析中包含一个“哲学错误”,这个错误会导致图灵的分析为“人心无法超出机械程序”提供证据。最后从科尔纳对哥德尔式反机械论的最新研究以及当代人工智能在数学定理发现与证明方面的最新进展对哥德尔与人工智能的讨论做一些评论与展望。
Gödel’s incompleteness theorem can be formulated as that no machinal theorem-prover(or procedure)can prove all and only true mathematical propositions.It is not only a definite logical theorem,but also has significant implications for philosophical problems such as the nature of mathematical truth and the relation between human mind and machine.This paper discusses the relationship between Gödel and artificial intelligence from two perspectives.The first part starts from Gödel’s incompleteness theorem and uses it as a framework to investigate the famous Lucas-Penrose argument and Gödel’s disjunctive argument for the anti-mechanic theory that“the human mind surpasses the machine”.The second part focuses on Gödel’s seemingly inconsistent remark on Turing’s analysis of mechanical procedure.On the one hand Gödel approves without reservation of Turing’s analysis of mechanical procedure,but on the other hand he claims that Turing analysis contains a"philosophical error"that would give credence to the thesis that human mind cannot surpass mechanic procedure.Finally,some comments and prospects are made on the discussion of Gödel and artificial intelligence in light of Peter Koellner’s latest logical research on Gödelian anti-mechanic argument and the latest progress of contemporary artificial intelligence in the area of discovery and proof of mathematical theorems.
作者
陈龙
Chen Long(School of Philosophy,Beijing Normal University,Beijing 100875,China)
出处
《科学．经济．社会》
2022年第3期28-37,共10页
Science Economy Society
关键词
哥德尔
人工智能
反机械论
人工直觉
Gödel
artificial intelligence
anti-mechanism
artificial intuition
