论何物为数——弗雷格数学本体论研究析论

On What is Number——A Brief Discussion on Frege’s Mathematical Ontology

在《算术基础》中,弗雷格研究了数的本体论问题。他以其所创立的一阶逻辑为工具,反驳了经典作家将数视为某种物理对象、属性或主观创造的观点,并借助对自然语言的分析解释了数的本质,指出数的给出包含着对一个概念的表达;继而从技术的角度定义了数0和紧跟关系,在此基础上形成了自然数的定义。弗雷格所使用的驳论和立论,都有很强的方法论动机,而这种方法论既是数学的,又是哲学的。因此,弗雷格关于数的本体论研究,不仅有数学上的意义,而且有哲学上的价值。

In foundations of Arithmetic,Frege studied the ontological problem of numbers. He founded the first order logic as a tool to refute classical writers＇ views,including seeing the number as objects,some physical properties or subjective creation and by means of analysis of natural language he explained the nature of the number,and the content of a statement of number is an assertion about a concept; then from the technical point he showed the definition of the number 0 and after,which formed the definition of natural numbers. Frege used the debate and argument,there is a strong motivation method,and this method is not only on mathematics,and philosophy. Therefore,its ontological research on numbers is not only mathematical,but also philosophical.