数学说明及其哲学使命

Mathematical Explanation and Its Philosophical Missions

与科学说明相比,数学说明在数学哲学中长期遭到忽视。蒯因提出的不可或缺性论证、爱因斯坦-维格纳之谜以及数学哲学对数学实践的日趋重视,使数学说明重返哲学议程。数学自身内部对说明的需求和自然现象的数学说明都表明,数学不仅求真,而且寻求说明。哲学的使命就是要建立数学说明的相应标准、机制和模型,为数学决策提供建议,并推进对数学的本性、数学与世界及科学之关联的理解,为数学与科学统一的哲学解释搭建通道。

Compared with scientific explanation, mathematical explanation has received only scant attention. W.V. Quine＇s Indispensability Argument, Einstein - Wigner＇s puzzle and along with the increasing attention to mathematical practice in the philosophy of mathematics has made mathematical explanation return into the agenda of philosophy. Both the requirement for explanation within mathematics and mathematical explanation of natural phenomena indicate that mathematics not only tries to find the truth but also seeks to do explanations. The missions it brings to philosophy are to build the corresponding criteria, mechanisms and models of mathematical explanations so that it can give advice for mathematicians＇making decision, promote our understand- ing the nature of mathematics, connections between mathematics and the world, and science as well, and also build a path to the unified philosophical account for mathematics and science.