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

Vincenzo Ciccarelli

doi:10.5007/1808-1711.2022.e77217

Authors

Vincenzo Ciccarelli Universidade de São Paulo https://orcid.org/0000-0002-8996-9170

DOI:

https://doi.org/10.5007/1808-1711.2022.e77217

Keywords:

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

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.

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