Some New Viewpoints and Topics for Research in Philosophy of Mathematics
Qian Jiang · Shuxue de shijian yu renshi · 2000
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.