厘清形式系统的几个概念

Clearing Some Concepts of Formal System

一致性、可靠性、完全性、不完全性是形式系统的基本概念。在厘清上述概念的基础上,对其间相互关系的梳理使我们明晰了哥德尔完全性定理和不完全性定理的正确含义,以及其成立所需的条件。最后,依据上述分析,指出形式系统存在漏洞和局限性。同时,也看到了形式化方法的弊端和形式化的限度。

Consistent,soundness,completeness,and incompleteness are the basic concepts of formal system.Clearing these notions and relations among them is helpful for us to understand the correct meaning of Gdel′s completeness theorem and Gdel′s incompleteness theorem,as well as the necessary and sufficient condition for both of two theorems.Based on the analysis above,the limitation of the method of formalization and the formal system are discussed.