Full Idea
If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.
Gist of Idea
If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation
Source
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
A Reaction
It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.
Related Idea
Idea 13412 Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]