数学归纳公理与内涵科学分析法

Mathematical Induction Axiom and Scientific Analysing Method of Intension

语句的绝对的、唯一的语义是被其指谓的客观事件。从素朴数学归纳法到皮亚诺数学归纳公理再到基于制约系统Cnd的数论形式系统N的形式公理,是一个历史的发展过程。"从N出发可证明1=0"是种误解。人类把握有限或无限不可逐一列举域不能通过对外延的列举,只能采用内涵科学分析法。

The absolute and sole meaning of a sentence is the objective ovent to which the sentence refers. It is a historical developing process that the original mathematical induction evolves to Peano's mathematical induction Axiom,and then to the Axiom of the Formal system N for the natural numbers based on Lin's entailment logic system Cnd. The saying that 1=0 can be proved on the basis of System N is a misunderstanding. Only by adopting, the scientific analysing method of intension (not by way of the extensional enumeration)can the human master the infinite area or the definite area which cannot be enumerated.