关于数学哲学的新思考

Some New Viewpoints and Topics for Research in Philosophy of Mathematics

本文以计算机软件 ,程序语言等作类比 ,提出数学命题是一种“概念实在”,以阐明数学对象的本体论地位 ;并根据自然科学只能基于现有的数学理论而建构这一事实 ,对数学在自然科学中的超前性和有效性作出了新的解释 .同时 ,本文勾划了一种新的数学哲学的轮廓 ,它以数学中引入新结构 ,提出猜想等创造性活动为课题 ,以数学史材料研究为方法 ,以探求数学发展的内在统一性为目的 .

By analyzing the ontological characteristics of a class of abstract entities such as software or programming language, mathematical propositions are suggested to belong to the same form of existence——″conceptual entity″. Then, based on the fact that (natural) scientists have no other way to express and exchange their viewpoints and theories than PRESNT mathematical knowledge, a new explanation for the potent application of mathematics to natural science is suggested. The outlines of a new philosophy of mathematics that focuses on such highly creative mathematical activities as introducing new mathematical structure and advancing conjectures, takes historical studies as its methodology and aims at prusuing unity in the development of mathematics, are also advanced.