从希尔伯特规划到数学的地图

希尔伯特规划的原初目的是为无穷数学辩护,然而为哥德尔不完全性定理所挫。反推数学的根本目标是为数学命题找寻能够证明它的下限公理,而其中相当一部分工作可以看作为对希尔伯特规划的部分实现。本文在梳理有关工作的基础上试图为希尔伯特规划提供一个新的视角,即在绕开哲学负担之后,希尔伯特规划或许可以推进为为数学绘制地图。

From Hilbert’s Program to Map of Mathematics

The orginal purpose of Hilbert’s program is to defend the validity of infinite mathematics.But it was think that it is failure due to the attack of the G?del’s incompleteness theorem.A large part of achievement of the Reverse mathematics,which try to discover the appropriate axioms for proving particular theorems,could looked as partial realization of Hilbert’s program.Base on relevent references,I propose a new understanding of the Hilbert’s program: we might could extend it to a program of acquiring the map of whole mathematics.