Predicative vs. Impredicative Abstraction

According to Frege and many of his followers, there is no “metaphysical distance” between the two sides of an acceptable abstraction principle. How should this attractive idea be understood? An analysis is developed in terms of the existence of a translation from the language concerned with the relevant abstract objects to a language not committed to such objects, such that this translation maps one side of the abstraction principle to the other. Next, two different notions of predicativity are distinguished: one pertaining to the background higher-order logic, and another associated with the abstraction principle itself. Finally, it is shown that only abstraction which is predicative in the latter sense satisfies our explication of the attractive idea about no “metaphysical distance”. This provides a reason to favor a conception of abstraction which is predicative in this sense.