良莠不齐反驳

On Bad Company Objection

新弗雷格主义是当前较为活跃的数学哲学思潮之一,其主要代表人物莱特和黑尔认为通过二阶逻辑和抽象原则可以在某种意义上证成弗雷格的逻辑主义。但许多学者对抽象原则的合理性提出质疑,其中引起激烈争论的就是良莠不齐反驳。在简要回顾新弗雷格主义和抽象原则的背景基础上,总结良莠不齐反驳的三个重要方面:不一致的抽象原则,例如公理V和序数原则;两两不一致但自身一致的抽象原则,例如奇偶原则和麻烦原则;两两不一致但自身保守的抽象原则,例如分身原则;相应地,莱特和威尔给出了一系列可接受的抽象原则的标准:一致性、保守性、无界性、第二保守性、朴实性、稳定性、平和性等等。

Neo-Fregeanism is one of the most important schools in contemporary philosophy of mathematics.Being the representative figures of Neo-Fregeanism,Crispin Wright and Bob Hale argue that,in some sense,second-order logic and Hume＇s Principle amounts to the establishment of Frege＇s Logicism.However,there are fierce debates,among scholars about whether Abstraction Principle is analytic.One of these debates is Bad Company Objection.We first show the background of Neo-Fregeanism and Abstraction Principle.Then,we summarize three aspects of Bad Company Objection,that is（1） inconsistent Abstraction Principles;（2） consistent but pairwise inconsistent Abstraction Principles,and（3） conservative but pairwise inconsistent Abstraction Principles.Correspondingly,Wright and Weir give a series of standards of acceptable Abstraction Principles： consistency,conservative,unbounded,stability,secondary conservative,modesty,and irenic.