Full Idea
In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
Gist of Idea
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal
Source
report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
Book Reference
-: 'Notre Dame Journal of Formal Logic' [-], p.194
A Reaction
This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
Related Idea
Idea 17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]