Scale property

A scale property or cardinal property is a shared property of all properties in some collection. For example, the numbers one, two, three, and four all have the scale properties of "being numbers" and "being less than five".

Interpreting sets as properties, a scale property (of a set A) is a subset of every element in the set. One uses them to collect or quantify over sets (i.e. other properties).

As sets are extensional by definition...

Can we use scale properties to classify properties generally?