Some Criteria for Acceptable Abstraction

where the variables α and β range over entities of some sort, and where ∼ is an equivalence relation on this sort of entity. Frege’s inconsistent Basic Law V shows that not every such principle is acceptable. A variety of criteria for acceptable abstraction have been proposed.1 In this note I analyze the logical relations between some of the proposed criteria, in particular conservativeness, irenicity, and stability. I answer some technical questions thrown open by the discovery of errors in the proofs of some crucial theorems in a deservedly influential study of these issues [Weir, 2003]. No attempt will be made in this note to assess the plausibility of the suggested criteria.2