Full Idea
Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects.
Gist of Idea
Counting is the assignment of successively larger cardinal numbers to collections
Source
Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5)
Book Reference
-: 'Notre Dame Journal of Formal Logic' [-], p.202
A Reaction
That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality?
Related Ideas
Idea 17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
Idea 17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]