哲学观下的反演与对称

Inversion Set and Symmetry under the Philosophical Concept

反演集合包含对称性,反演集合与对称破缺有非空交集,但反演集合不等于对称破缺,更不等于不对称性。反演集合的哲学基础是辩证矛盾,对称破缺的哲学基础是逻辑矛盾。在实际应用的一些反演变换分类方法中,许多事物只有在特定的坐标系下才便于分类。家族相似观下的反演与对称,其局部性本质的存在是家族相似性成立的基础。事物的共有本质是事物之间的对称子集,维特根斯坦不是反对本质的存在,而是指出本质只能在有限范围内使用。

The inversion set contains the symmetry. The symmetry breaking and the inversion set have a non-empty intersection. How- ever, neither the symmetry breaking, nor the asymmetry is equal to the inversion set. In this thesis, the author thinks that the philo- sophical basis for inversion set thoughts in mathematics is dialectical contradiction, while the philosophy foundation of symmetry break- ing is the logical contradiction. Then the author discusses the role of symmetric transformation in the classification of the inversion transformation, introducing some classification methods in practical applications, pointing out that many things can only be classified in certain coordinates. Finally the author discusses inversion and symmetry under the family resemblance perspective. He points out that the existence of the local essence is the foundation of family resemblance. The common nature of things is a symmetric subset between things. Ludwig Wittgenstein was not against the existence of essence, but he pointed out that it can only be used in a limited range.