反映原理作为大基数内在辩护的不可行性

Infeasibility of Reflection Principles as Intrinsic Justifications for Large Cardinals

本文主要研究使用反映原理对大基数进行内在(intrinsic)辩护。目前大基数的辩护主要分为两种:外在(extrinsic)辩护和内在辩护。外在辩护从丰富性和实用性角度出发,但其无法解释为什么集合论学家格外看重大基数公理,同时也难以令实在论者满意:实在论者希望提供基于集合概念本质的辩护。因此一些学者提出了一系列的内在辩护。本文基于实在论的立场考察现有的内在辩护,讨论了内在辩护的典型:通过反映原理和它的各类变种进行的辩护,得出的结论是:现有的使用反映原理对大基数进行内在辩护方案都无法令人信服。

This article investigates the intrinsic justifications for large cardinal axioms by reflection principles.There are currently two main types of justifications for large cardinal axioms:the extrinsic justifications and the intrinsic justifications.The extrinsic justifications,from the point of view of richness and utility in mathematical practice,do not explain the importance of large cardinals axioms in contemporary set theory,nor do they satisfy the Platonist:the Platonist wishes to provide some justifications based on the nature of the conception of the set.Therefore some authors provided a sequeLnce of intrinsic justifications for large cardinal axioms.This article examines the existing intrinsic justifications based on a Platonism position.I have mainly discussed the archetype of intrinsic justification:the justification by reflection principle and its various variants.It concludes that none of the existing intrinsic justifications by reflection principles are satisfactory.