Is there a definition of the relationship between real quantities and the numbers we relate to them, generally we use 'numbers' as mathematical objects with a 'proper' nouns, but we associate them with a unit to give a quantity like '5 apples' or '5 metres'. We use numbers like adjectives, which suggests we could define the numbers as a 'state' of quantity.
The issue with this becomes that the 'object' nature of numbers means that we can differentiate between a number as a real or natural. The number '2' that is an element of the real numbers is technically a different object to the number '2' as a natural number. The question arises, when we use a statement such as 'there are two apples', which '2' are we using?
If there are different object we can call '2', we cannot have them as states of quantity, as the same 'state of quantity' can be represented by two different numbers.
In particular if we consider numbers as a level of quantity or state then each quantity can 'instantiate' the number, however if the numbers are distinct from the state of quantity then we struggle with whether a quantity can be a physical token of it.
How do we relate numbers and quantity, especially when giving them in natural language?