弗雷格关于数的本体论研究

发布时间：2017-12-27 09:15

本文关键词：弗雷格关于数的本体论研究　出处：《河北大学》2015年硕士论文　论文类型：学位论文

【摘要】：德国数学家弗雷格于1879年创立了一阶逻辑系统,并借助该系统进行了数学基础的研究。他关于数的本体论研究包括两个方面:一是反驳传统的关于数的本体论观点,二是从一阶逻辑的角度出发揭示数的本质。弗雷格的批判主要在于:反对把数看做一种物理现象,反对把数看做心理活动的产物,以及反对把数看做客观对象的一种性质。弗雷格对于数概念的分析方式,是运用一阶逻辑的方法进行语言分析。他通过对数词在语句中的使用进行讨论,明确了“数的给出包含着对一个概念的表达”。通过概念和对象层面的讨论,弗雷格确定了每一个个别的数都是一个对象。在明确了数的性质后,弗雷格将属于“与自身不相等”这一概念的数定义为0,从而确定了自然数序列的起点。他随后定义了“紧跟”,作为自然数数列的后继规则。借助这样的起点和后继规则,弗雷格推出了整个自然数序列。弗雷格的这些工作最终因遭遇罗素悖论而陷入困境。晚年弗雷格对自己早年关于数的本体论的观点进行反思,试图重新建立一个算术基础的研究体系,但最终没有成功。弗雷格关于数的本体论研究对于一阶逻辑和数学基础,都产生了重大的影响。
[Abstract]:German mathematician Frege founded the first order logic system in 1879, and carried out the research on the basis of the system with the aid of the system. His ontological research on numbers includes two aspects: one is to refute the traditional view of number ontology, and the two is to reveal the essence of numbers from the perspective of first-order logic. Frege's criticism mainly lies in his opposition to counting as a physical phenomenon, opposing the number as a product of mental activities, and opposing the nature of number as a guest object. Frege's analysis of the number of concepts is to use the method of first order logic to carry out the language analysis. By discussing the use of logarithmic words in statements, he made it clear that "the given number is contained in the expression of a concept." Through the discussion of conceptual and object levels, Frege determined that each individual number is an object. After defining the nature of the number, Frege defines the number of the concept of "unequal to itself" as 0, thus determining the starting point of the sequence of natural numbers. He then defines "heel" as the successor rule of the number of natural numbers. With the help of such starting points and following rules, Frege introduced the whole sequence of natural numbers. Frege's work was in the end because of the Russell paradox. In his late years, Frege reconsidered his early views on the ontology of numbers, trying to reestablish an arithmetic basis, but eventually failed. Frege's research on the ontology of numbers has a great influence on the first - order logic and the mathematical basis.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O156

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