数学哲学:20世纪末的回顾与展望

Philosophy of Mathematics: Review and Prospect at the End of the 20th Century

一、数学哲学研究的黄金时代从1890年到1940年的这50年被称为是“数学哲学研究的黄金时代”。在这一时期中,数学基础问题取代传统的数学本体论问题和认识论问题成为数学哲学研究的中心问题,一些著名的学者,如弗雷格(G.Freg e)、罗素(B.Russell)、布劳维尔(L.E.J.Bro uw er)和希尔伯特(D.Hilbert)等,更围绕基础问题进行了系统和深入的研究,从而发展起了逻辑主义、直觉主义和形式主义等具有广泛和深远影响的数学哲学理论。

This paper offers a general survey of the modern studies of the philosophy of mathematics.It not only concerns the main features of the foundational studies and different paradigms in the recent researches in this field,but also confirms that it is now undergone a revolution,which can be seen as the radical changes of the central problem,the methodology,the basic positions for research,and the basic view of mathematics.