Full Idea
Learning number words in the right order is counting 'intransitively'; using them as measures of sets is counting 'transitively'. ..It seems possible for someone to learn the former without learning the latter.
Gist of Idea
We can count intransitively (reciting numbers) without understanding transitive counting of items
Source
Paul Benacerraf (What Numbers Could Not Be [1965], I)
Book Reference
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.274
A Reaction
Scruton's nice question (Idea 3907) is whether you could be said to understand numbers if you could only count intransitively. I would have thought such a state contained no understanding at all of numbers. Benacerraf agrees.
Related Idea
Idea 3907 Could you be intellectually acquainted with numbers, but unable to count objects? [Scruton]