对欧几里德几何体系之可能世界的考察--以纯粹演绎的观点为基础

莱布尼兹的可能世界与现实或存在的关系,是在限定的"必然的实体中"讨论的.而演绎逻辑是从真前提到真结论之间具有必然性的,欧几里德几何原本所追求的正是这种必然性,他试图从有限的公理逻辑地推出所有定理;但是其前提并不充分,因而其所谓定理构成的可能世界具有虚幻性或非逻辑性.后来,希尔伯特在公理系统的不矛盾性和独立性中提出一种给已知系统找到其可能的实现的方法,不过它只有相对的意义,而哥德尔的否定性结果表明,欧几里德几何的可能世界有很多逻辑无法深入的地方.

Examination of the possible world in Europead's geometrical system based on pure deduction

Labniz's view of the relationship between the possible world and reality or existence is discussed in the definite "certain entity ".However,due to the inadequate precondition of the inference from finite axiom to all theoroms,there is transience and illogicality in the formation of Europead's theorom.Later,only relative meaning is found in Hilbert's possible solution to the logically and independence in the axiomatic system,and the negative result of Godel suggests that many things in Europead's possible world cannot be analyzed by logic.