哥德尔定理:对卢卡斯-彭罗斯论证的新辨析  

Gdel's Theorem:Analysis of the Lucas-Penrose Argument

作　　者：刘大为[1] LIU Da - wei(Department of Philosophy, Hunan Normal University, Changsha 410081, China)

机构地区：[1]湖南师范大学公共管理学院哲学系,长沙410081

出　　处：《科学技术哲学研究》2017年第4期25-30,共6页Studies in Philosophy of Science and Technology

摘　　要：卢卡斯和彭罗斯先后论述,利用哥德尔不完全性定理可以得出人心胜过机器(图灵机),心灵是不可计算的,现在这被统称为卢卡斯-彭罗斯论证。卢卡斯-彭罗斯论证中最主要的焦点就在于所谓的"一致性或健全性前提",卢卡斯和彭罗斯坚持回应各种质疑,认为可以知道我们(心灵)是一致的。事实上,卢卡斯-彭罗斯论证需要加上一些理想化的假设,尤其应该对彭罗斯论证中"F是健全的"这一断言予以澄清和补充。费弗曼指出彭罗斯论证的疏忽,试图调和机械论和反机械论的完全对立,并提出开放模式的公理系统表示心灵的数学能力。由对数学实践的分析阐述费弗曼论证存在不足之处后,在借鉴卢卡斯-彭罗斯论证和费弗曼论证的基础上,考虑数学理解力和环境的重要性,尝试提出基于完全开放的数学形式系统的心灵模型。Lucas and Penrose argue that according to Godel＇ s incompleteness theorems the human mind surpasses a Turing machine and the mind is noncomputable, and these are known as the Lucas-Penrose argument. The Lucas- Penrose argument invokes intense and long-lasting disputes until today. Many opponents query the premise of con- sistency or soundness, whereas Lucas and Penrose reply that we can know we are consistent. In fact the Lucas-Penrose argument needs some idealized assumptions. This paper clarifies and supplements statements about ＂F is sound＂ in Penrose＇ s argument. Feferman＇ s argument tries to straddle the division of mechanism and anti-mechanism. In reference to the Lucas-Penrose argument and Feferman＇ s argument, we emphasize the importance of mathematical understanding and environment. Moreover, we put forward a new model representing the mathematical capacities of the mind, which is based on a fully open-ended mathematical formal system.

关 键 词：哥德尔不完全性定理 卢卡斯-彭罗斯论证 心灵与机器 一致性 开放形式系统 

分 类 号：N02[自然科学总论—科学技术哲学]