To count is to count units

Numbers and units are born together. To count something, you have to know:

• what you are counting, and

• when you have counted it. 

In any given count, the things you count are always alike in some sense: apples, bananas, bus rides, dollars.  That remains true even in the most abstract kinds of counting, where the objects may be look very different---even there, the things we count must share some property, however abstract or ad-hoc.  To know what you are counting, you have to be able to distinguish what you are counting from what you are not counting.

You also have to be able to distinguish the things you are counting from each other, or how will you be able to avoid counting the same thing twice, or know when you have finished counting?

In short, things to count have to be alike but also distinct: oranges, marbles, bus rides, dollars, gallons, votes, beats, hours.  In other words, it must have exactly the properties required of a unit.

And this is why, whenever we count, we are are always counting some kind of unit, whether explicit or implicit, whether concrete or abstract.