罗素的数学逻辑主义思想研究

【作者】 陈志美；

【导师】 胡泽洪；

【作者基本信息】 华南师范大学 ， 逻辑学， 2002， 硕士

【摘要】 本文对伟大的数学家和逻辑学家伯特兰·罗素的数学逻辑主义思想进行了研究和探讨。 在前言中，简要地介绍了罗素的数学逻辑主义思想，认为它除了“将数学还原为逻辑”这一观点外，还包括了解决罗素悖论的工作。 第一章介绍了罗素形成数学逻辑主义思想的历史背景及其提出数学逻辑主义论题的情况。认为罗素形成数学逻辑主义思想的历史背景在于他对数学基础建立在数学理论的“算术化”的不满。他认为，数学的基础应是逻辑，从而提出他的数学逻辑主义论题：数学与逻辑等同，全部数学可以化归为逻辑。 第二章详细介绍了罗素对其数学逻辑主义论题的证明。罗素在弗雷格研究的基础上，提出逻辑类型论来解决罗素悖论，以非集合论理论为基础，以无穷公理和选择公理为前提，利用逻辑概念定义数学概念，并构造系统，通过逻辑演绎法从逻辑公理推导数学定理。 第三章对罗素的数学逻辑主义思想作出评论。认为罗素的数学逻辑主义因为没有实现从纯逻辑出发、将数学化归为逻辑的目标，因而是失败的。失败原因主要是由罗素本人哲学思想的错误决定的。但这种失败只是部分失败，其成功之处在于，罗素的数学逻辑主义研究对数理逻辑的发展作出了重要的贡献。更多还原

【Abstract】 This thesis makes an exposition of the mathematics logicism thought of Russell ,the great mathematician and logician in phytogeny of logic.In preface, Russell’s mathematics logicism is introduced in brief. It is thought to be include not only the idea of mathematics can be deoxidized to logic, but also the work of settle Russell’ paradox.In chapter one, it gives a historical introduction to Russell’ mathematics logicism and introduces how Russell put forward his idea. As a mathematician, Russell is critical of arithmetization of mathematics theory underlying the basic of mathematics. In Russell’s opinion, logic should be the foundation of mathematics. Then he put forward his topic that mathematics is the same as logic and it can be deoxidized to logic.In chapter two, how Russell proved his topic of mathematics logicism is introduced in detail. On the base of Frege’s study, Russell put forward the theory of types to settle Russell’s paradox. On the base of non-set, Russell brought forward axiom of infinity and axiom of option as the premises and built a system. He tried to defined the non-negative integer in logic terms and derive the theorems of arithmetic from the laws of logic by deductive method.In chapter three, the author makes a comment on Russell’s mathematics logicism. She thinks it impossible for Russell to deoxidize mathematics to logic because he couldn’t derive arithmetic from purely logic laws. In this meaning, we can say that Russell’s trying is failed. Russell’s failure is mainly due to his mistakes in his philosophical ideas. But it is not a whole failure. Russell’ contribution lies in his study of mathematics logicism promoting the development of mathematics logic.更多还原