数学循环论证的思考及其价值展望

Thinking and Value Prospect of Mathematical Circular Argument

循环论证的核心问题是推理过程中的逻辑是否严谨.数学证明的过程是否为循环论证,根据不同的标准,有不同的结果.以学科体系、教材体系为标准,得到4种体系下的循环论证:(1)同一教材体系;(2)不同教材体系;(3)同一学科体系;(4)不同学科体系.循环论证所带来的价值有很大的应用前景:能够让知识的学科价值更加充分发挥,能够降低学生负担.未来教材改革应关注:(1)教材改革应兼顾知识的学术逻辑与学生的心理逻辑;(2)教材改革应注重教育逻辑的完善;(3)教材改革可考虑从循环论证根源的剖析上摄取“营养”.

The core problem of circular argument is whether the logic in the reasoning process is rigorous.Whether the process of mathematical proof is a circular argument or not has different results depending on different criteria.The circular argument under the four systems can be obtained taking the discipline system and the textbook system as the standard:(1)the same textbook system;(2)different textbook systems;(3)the same discipline system;(4)different discipline systems.The value brought by circular argument has great application prospects:it can make the disciplinary value of knowledge more fully utilized and reduce the burden on students.This paper puts forward some thoughts for the future reform of textbooks:(1)The reform of teaching materials should take into account the academic logic of knowledge and the psychological logic of students;(2)the reform of teaching materials should focus on the improvement of educational logic;(3)the reform of teaching materials should consider ingesting“nutrition”from the analysis of the root cause of circular argumentation.