 In terms of the example used at the end of the previous subsection, this informal definition identifies the number of the concept author of Principia Mathematica as the extension consisting of all and only those first-level concepts that are equinumerous to this concept; this extension has both \([\lambda x \, Axp]\) and \([\lambda x \, 1\lt x\lt 4]\) as members. Frege in fact identifies the cardinal number 2 with this extension, for it contains all and only those concepts under which two objects fall. Similarly, Frege identifies the cardinal number 0 with the extension consisting of all those first-level concepts under which no object falls; this extension would include such concepts as unicorn, centaur, prime number between 3 and 5, etc. Frege’s insight here inspired Russell to develop a somewhat similar definition in his work, and it is now common to see references to the so-called “Frege-Russell definition of the cardinal numbers” as classes of equinumerous concepts or  sets.[8]  Of course, this explicit definition of ‘the number of \( F\)s’ stands or falls with a coherent conception of ‘extension’. We know that Basic Law V does not offer such a coherent conception. 