公理与假说异同论——兼论数学科学与教育的特殊性

On similarities and differences of axiom and hypothesis

以历史上经典案例为证,阐述公理与假说在定义与应用中的异同,指出它们虽然都是科学发展的理论基础,起着对不同学科理论创建的奠基作用,但在初期二者命题设立的基础、内容接受的对象和理论发展的方式上有本质差异,并由此导致数学科学与数学教育有别于其他学科分支特殊性的表现,以及公理作为科学数学化趋势标志的原因.

By taking the examples of the historical classical case, this paper elaborates the similarities and differences in the definition and application of the axiom and hypothesis. In particular, it points out that although they are both the rationale of the development of the science and play a fundamental role in the founding of the theory of different displines, the two have the essential difference in their foundation of the establishment of the proposition, their content, their object and their ways of development in early days. It causes the manifestation of the particularity which distinguishes the sciences and education of mathematics from other sciences, as well as it is the reason that the axiom symbols the tendency of mathematical sciences.