Grundlagen §64: an alternative strategy to account for second-order abstraction

Abstract

A famous passage in Section 64 of Frege’s Grundlagen may be seen as a justification for the truth of abstraction principles. The justification is grounded in the procedure of content recarving which Frege describes in the passage. In this paper I argue that Frege’s procedure of content recarving while possibly correct in the case of first-order equivalence relations is insufficient to grant the truth of second-order abstractions. Moreover, I propose a possible way of justifying second-order abstractions by referring to the operation of content recarving and I show that the proposal relies to a certain extent on the Basic Law V. Therefore, if we are to justify the truth of second-order abstractions by invoking the content recarving procedure we are committed to a special status of some instances of the Basic Law V and thus to a special status of extensions of concepts as abstract objects.

Keywords

• Abstraction principles
• Basic Law V
• content recarving
• higher-order logic