后形而上学的数学实践哲学——从平科克到麦蒂

A Postmetaphysical Approach to Practical Philosophy of Mathematics: from Pincock to Maddy

平科克和麦蒂都是当今数学实践转向潮流的代表人物,综合二者的数学哲学思想,有助于开启一条后形而上学的数学实践哲学路径。一方面,为了与麦蒂反内在主义的立场相兼容,将平科克的数学哲学思想转向语义外在主义,以克服其思想的内在张力;另一方面,在麦蒂数学哲学思想中引入平科克的观念,从而将数学概念(或者理论等)的发展与数学实践的历史关联起来,有助于澄清麦蒂"数学深刻性"之观念。如此诠释的数学实践路径,不再需要承诺任何数学对象的存在,体现着后形而上学的意蕴,符合麦蒂的数学自然主义之初衷。

Stephen Pincock and Penelope Maddy are both representatives of the current trend of mathematical practice. The combination of their mathematical practice thoughts helps to open up a path of "postmetaphysical" philosophy of mathematical practice. On the one hand, in order to be compatible with Maddy′s anti-internalism standpoint, Pincock′s mathematical philosophy was turned to semantic externalism to overcome the internal tension of his thought. On the other hand, the introduction of Pincock′s concept into Maddy′s mathematical philosophy helps to clarify Maddy′s concept of "mathematical depth" by linking the development of mathematical concepts(or theories, etc.) with the history of mathematical practice. Such an approach to mathematical practice, in line with Maddy′s original intention of mathematical naturalism, embodies the implication of postmetaphysics, so we no longer need to commit to the existence of any mathematical object.