论数学结构主义对元数学对象的解释

On the Interpretation of Meta-Mathematical Objects byMathematical Structuralism

关于元数学对象在结构主义数学哲学中的地位,成为近年来数学哲学争论的焦点问题之一。当代著名数学哲学家C·帕森斯认为,元数学对象只是个体独立的准具体对象,不会形成某种结构,那么结构主义对元数学对象的解释就是不成立的。与C·帕森斯的观点相反,S·弗里德里希认为元数学研究的对象事实上是表示数学结构的形式符号,故数学结构主义可以应用于元数学对象。从“形式符号”的观点出发,根据数学对象的同一性标准,可以得出:元数学本身具有结构主义特性。因此,用数学结构主义对元数学对象进行解释是成立的。

Regarding the status of meta-mathematical objects in structural philosophy of mathematics, it has become the focus of the debate in recent years. C. Parsons, a famous contemporary mathematics philosopher argues that meta-mathematics objects are only quasi-specific objects, while quasi-concrete objects are independent of individuals. There is no structure that will be formed. Thus structuralism cannot be established when explaining meta-mathematics. Contrary to C. Parsons s point of view, S. Friedrich believes that the object of meta-mathematics research is a formal symbol that represents a mathematical structure. Therefore, mathematical structuralism can be applied to meta-mathematical objects. From the point of view of “formal symbols”, according to the criterion of the identity of mathematical objects, it can be concluded that meta-mathematics itself has the characteristics of structuralism. So mathematical structuralism can explain the objects of meta-mathematics.