曲面上向量场微分运算理性重构与经典表述的逻辑证伪
Logic falsification about the classical differential expression of vector field on a curved surface and its rational reconstruction
本文从一切有意义数学表述必须遵循的“逻辑自洽性”原则出发，指出“不变性”微分算子必须和必然蕴含的“客观性”基础，重新为2维曲面上向量场的微分运算构建符合逻辑的形式表述。进而在此基础之上，指出相关的经典表述充其量不过是某种特例下才可能存在“单称性”陈述，一旦将这个“条件存在”的陈述普遍化，整个陈述系统必然陷入“约定论”引起的逻辑紊乱之中，从而为整个现代微分几何得以存在的基础提供了一次“逻辑证伪”。
Based upon the logic self-consistence principle every significant mathematical expression must obey, this paper points out that any invariant differential operator should possess the material foundation belonging to it-self and provides a formal expression consistent in logic for the differential operation defined in the 2-dim curved surface. And this paper consequently points out that the related classical result could be regarded as a ‘singular statement’ at most and, in case used as a universal truth, it should fall into confusion in logic. Then, all of these actually supply a time of falsification on the foundation for the modern differential geometry to exist.
杨本洛
数学
张量，形式不变性，客观性基础，微分算子，梯度，曲面，向量场，逻辑重构，证伪
tensor formal invariance objective foundation differential operator gradient curved surface vector field logic reconstruction falsification
杨本洛.曲面上向量场微分运算理性重构与经典表述的逻辑证伪[EB/OL].(2007-01-18)[2025-08-18].http://www.paper.edu.cn/releasepaper/content/200701-230.点此复制
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