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本文作者认为托姆突变论是奇点理论的新发展、新应用。详细评介了托姆关于奇点在科学研究中的作用 ,奇点对科学定量描述与定性描述之影响的观点。提出奇点的哲学意义在于 :1、奇点是划分两类不同科学的分界线 ;2、表明了局域性科学无法实现传统的非局域性科学的那种精确的定量描述 ;3、能够对奇点附近的各种形态从拓扑同构 (相似 )的意义上进行分类 ,并提供一种整体 (拓扑性质 )看法 ,以及对系统演化轨迹在何处终结给出一种预测
The author of this paper holds that Tom’s sudden change theory is a new development and new application of singularity theory. It gives a detailed review of Thom’s viewpoint on the role of singularities in scientific research and the impact of singularities on the quantitative description and qualitative description of science. The philosophical significance of the proposed singularity lies in: 1. The singularity is the demarcation line that divides the two kinds of different sciences; 2. It shows that locality science can not exactly describe the accurate quantitative description of the traditional non-locality science; Classify the various forms of the singularities in terms of topological isomorphism (similarity) and provide a holistic (topological) view of what the system evolution trajectory ends in giving a prediction