戴德金与皮亚诺关于算术基础的研究

Dedekind and Peano's study on the foundations of arithmetic

戴德金与皮亚诺都是在分析算术化背景下进行算术基础研究的数学家。通过文献考证与理论分析的方法,对他们的研究工作进行比较,得到的结果如下:戴德金和皮亚诺研究目的不同;戴德金的工作体现出一般化的特点,皮亚诺更加重视逻辑符号的系统化。由于戴德金的研究表述过于抽象复杂,而皮亚诺的研究使用了现代逻辑符号,更易为人们所接受,易于理解,所以,至今关于自然数的公理还被大多数人称为皮亚诺公理。

Dedekind and Peano are mathematicians who study the foundations of arithmetic. Based on the back- ground Analysis and theory analysis of the Arithmetization. Their study on the foundations of arithmetic are com- pared, which concludes that their study aims differ, Dedekind＇s study embodies generalization characteristics, Peano＇s study further attaches systematism of logic symbol. People are more likely to accept and understand Peano＇ s work because Dedekind＇s statements are too abstract and Peano＇s research uses the modem logic symbols. So, up to the present the Axioms of natural number are called Peano＇s axioms by most people.