Ok, I wrote a long reply trying to figure out what exactly 2 is for him in terms of modern set theory notation, but I got really muddled. German’s not my mother-tongue/the pdf isn’t searchable, and when he says “Anzahl”/“Zahl” I’m never sure if he’s talking about size or abstract property, and would have to read a lot more of the book to figure out!

[but naively: in §76 “n folgt in der natürlichen Zahlenreihe unmittelbar auf m.” is defined as “es giebt einen Begriff F und einen unter ihn fallenden Gegenstand x der Art, dass die Anzahl, welche dem Begriffe F zukommt, n ist, und dass die Anzahl, welche dem Begriffe ““unter F fallend aber nicht gleich x” zukommt, m ist””. “ is ‘n follows directly after m’ is defined as: there’s a preposition F and an object satisfying F such that the number of objects satisfying F is n and the number of objects satisfying “satisfying F but not x” is m. This really looks von Neumann like!]

He also talks about numbers in §56 (but Zahlen, not Anzahlen)...with the problem of deciding in Julius Caesar is an (ordinal?) number or not, or whether anything has Julius Caesar as a number.

[there’s also an english translation here http://www.naturalthinker.net/trl/texts/Frege,Gottlob/Frege,... but honestly it’s not much easier there :P ]

ALL of this is confusing with what wikipedia says on the matter of defining natural number “Gottlob Frege and Bertrand Russell each proposed defining a natural number n as the collection of all sets with n elements.” - which may also be the case, but lacks a citation alas. https://en.wikipedia.org/wiki/Set-theoretic_definition_of_na...

I don’t know if I have it in me to straighten this all out (that is, to RTFM).