 However, in the development of Gg, Frege didn’t formulate the extensions of second-level concepts. In Gg, extensions do not contain concepts as members but rather objects. So Frege had to find another way to express the explicit definition described in the previous subsection. His technique was to let extensions go proxy for their corresponding concepts. Since a full reconstruction of this technique and the proof of Hume’s Principle in Gg would constitute a digression for the present exposition, we shall describe the details for interested readers in a separate document: 