不可超越的无穷：关于直谓性和后继公理的关系

本文首先将新弗雷格主义的发展划分为三个阶段：（1）弗雷格算术（由二阶逻辑和休谟原则构成的理论）的一致性和对于二阶皮亚诺算术公理的可推出性的证明,（2）对休谟原则和二阶逻辑的哲学辩护与反驳,（3）对休谟原则和二阶逻辑进行限制,并证明其一致性和可推出性。然后着重介绍：（1）直谓二阶逻辑和公理V的一致性,（2）直谓二阶逻辑和休谟原则不能推出皮亚诺算术的后继公理。这说明一致性和可推出性在弗雷格系统的直谓片段中不可兼得。最后在直观上做出简单的分析。

Unattainable Infinite:The Relation between Predicativity and Successor Axiom

This paper first divides the development of Neo-Freganism into three stages:(1) Frege Arithmetic,the theory consisting of second-order logic and Hume's Principle,is consistent,and Peano Arithmetic is derivable from Frege Arithmetic;(2)There are philosophical debates about Hume's Principle and second-order logic;(3)Many scholars make restrictions on Hume's Principle and second-order logic,and show the consistency and derivability of the resulting theories.Then,this paper shows:(1)predicative secondorder logi...