集合论反射原则探析

发布时间：2018-05-11 07:29

本文选题：反射原则 + 集合的迭代概念　；参考：《安徽大学学报(哲学社会科学版)》2015年05期

【摘要】：反射原则作为集合论公理最合理的内在证成方式,被期望经由精确描述"集宇宙V不可定义、不可描述"的思想以力图提供集合论公理的统一解释。但是该原则背后的潜无穷和实无穷观导致如下分歧:逾越Erd錸s基数的大基数公理该不该被视为蕴涵在由反射原则描述的集宇宙V中?通过比较不同视域下的反射原则揭示出,反射原则不是意在描绘潜在的集合迭代概念,而是旨在表达"康托尔意义上作为完成的绝对无穷概念V的超越性"。由此,GRP作为更合理的反射原则为那些逾越Erd錸s基数的大的大基数公理做出内在辩护。
[Abstract]:As the most reasonable way of proving the axiom of set theory, the principle of reflection is expected to provide a unified interpretation of the axiom of set theory by accurately describing the idea of "set universe V is undefinable and undescriptive". But the latent infinity and the real infinity behind the principle lead to the disagreement that the axiom of the large cardinality beyond the Erd rhenium base number should not be regarded as contained in the set universe V described by the reflection principle. By comparing the reflection principles from different perspectives, it is revealed that the reflection principle is not intended to describe the concept of potential set iteration, but to express "transcendence of the absolute infinite concept V in the sense of Cantor". Therefore, as a more reasonable reflection principle, GRP provides an intrinsic justification for the axioms of large cardinality that exceed the base number of Erd rhenium.
【作者单位】：澳门科技大学通识部;
【基金】：国家社会科学基金重大项目(14ZDB014) 中国逻辑学会学术研究项目(13CLQN001) 澳门科技大学研究基金(普通研究项目,0441)
【分类号】：B81-0

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