 Though the formal representation could be taken further, if we expand the definitions of \(\mathit{Precedes}^*\), \(\#F\), and \(\#[\lambda u \: Fu \amp u \!\neq\! z]\), enough has been said to pose the question: why think that by deriving the formal representation from more fundamental principles, Frege has derived the arithmetic law that no natural number precedes Zero?  This question is tackled in some detail in in the early part of Blanchette 2012, which investigates Frege’s understanding of conceptual analysis. Her answer (Chapter 4) is that the formal representation of the arithmetic law has to be (self-evidently) logically equivalent to a good analysis of the original. If it is, then notwithstanding Frege’s failed reduction of numbers to extensions, a derivation of the formal representation from more general logical laws of the kind represented in his system would have in fact achieved the goal of reducing arithmetic to logic. The reader is directed to her work for discussion of this important point.