For a number like 2 to exist, the implication is that there are two things in the universe that can be exactly equal.
I'm not convinced. You are defining the number 2 as a material cardinal, and then coupling the existence of the number 2 to the existence of two completely identical material objects. But why would the existence of those objects give rise to the existence of the number 2?
Can't I similarly define that the number 2 is a materialized ordinal, and simply count the revolutions of a moving object, and state that the number 2 is instantiated by observing the periodicity of a single material object?
I'm not convinced. You are defining the number 2 as a material cardinal, and then coupling the existence of the number 2 to the existence of two completely identical material objects. But why would the existence of those objects give rise to the existence of the number 2?
Can't I similarly define that the number 2 is a materialized ordinal, and simply count the revolutions of a moving object, and state that the number 2 is instantiated by observing the periodicity of a single material object?