康德数学的构造理论

Kant's Theory of Mathematical Construction

康德数学的构造理论使得数学通过纯直观直接地构造概念和判断。纯直观作为第三者,之所以能进行构造,是知性、想像力和感性共同作用的结果。知性提供的直观的公理指出直观都是定量,想像力通过图型将定量形象化,并构造出结果。纯直观在此过程中产生出数学概念。具体而言,算术和几何学的构造分四步进行,首先产生出概念,其次将概念形象化,再次提取同质单位,最后得出结果。这项研究可以为创造性发挥提供基础,并为更好地理解批判哲学体系提供指引。

Mathematics directly constructs concepts and propositions by the pure intuition due to Kant＇s theory of mathematical construction. That the pure intuition,as the third thing,can construct them is the result of combined action of the understanding and the imagination and the sense. Axioms of intuition provided by the understanding advance that all intuitions are extensive magnitudes. The imagination puts these magnitudes into images and constructs the result by the schema. The pure intuition produces mathematical concepts in the constructive process. Specifically,the construction of arithmetic and geometry is divided into four steps： firstly,concepts are produced; secondly,they are put into images; thirdly,homogeneous units are extracted; and finally,the result is constructed. This paper may provide the base for the creative interpretation and the conduct for understanding the whole critical philosophy better.