Full Idea
Roughly, Frege's picture of counting is this. When we count something, we determine what number belongs to a given concept.
Gist of Idea
Frege says counting is determining what number belongs to a given concept
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §54) by Kathrin Koslicki - Isolation and Non-arbitrary Division 2.1
Book Reference
-: 'Synthese' [-], p.405
A Reaction
If the concept were 'herd of sheep' that would need a context before there could be a fixed number. You can count until you get bored, like counting stars to get to sleep. 'Count off 20 sheep' has the number before the counting starts.
Related Idea
Idea 17429 Frege says only concepts which isolate and avoid arbitrary division can give units [Frege, by Koslicki]