The bad company objection and the extensionality of Frege’s logic

Abstract

According to the Bad Company objection, the fact that Frege’s infamous Ba-sic Law V instantiates the general definitional pattern of higher-order abs-traction principles is a good reason to doubt the soundness of this sort of de-finitions. In this paper I argue against this objection by showing that the defi-nitional pattern of abstraction principles – as extrapolated from §64 of Frege’s Grundlagen– includes an additional requirement (which I call the spe-cificity condition) that is not satisfied by the Basic Law V while is satisfied by other higher-order abstractions such as Hume’s Principle. I also show that the failure of this additional requirement in the case of Basic Law V is engende-red by an essential feature of Frege’s conception of logic and thus that Frege himself should not have regarded the Basic Law V as a definition by abstraction.