On Bad Company Objection

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.