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

• Autor(a) principal: Ciccarelli, Vincenzo
• Data de Publicação: 2022
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Principia (Florianópolis. Online)
• Texto Completo: https://periodicos.ufsc.br/index.php/principia/article/view/77217
• topic: Abstraction principles; Basic Law V; content recarving; higher-order logic

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.