 Before we examine the powerful consequences that Frege derived from Hume’s Principle, it is worth digressing to describe his attempt to define ‘\(\#F\)’ explicitly and to derive Hume’s Principle from Basic Law V. The idea behind this attempt was the realization that if given any concept \(F\), the notion of equinumerosity can be used to define the second-level concept being a concept G that is equinumerous to F. Frege found a way to collect all of the concepts equinumerous to a given concept \(F\) into a single extension. In Gl §68, he informally took this to be an extension consisting of first-order concepts by stipulating that the number of \(F\)s is the extension of the second-level concept: being a first-level concept equinumerous to F.