Some find quantities qualitative:Hobbes' Choice wrote:Maths is just one of the human languages used to discuss and describe the world. Of the range so languages, it is low on ambiguity and low on nuance, and expression. It fails to address qualities, but is all about quantities.
Some find 7 inches more qualitative than 3; Some find 6 ft better than 4.
Sure you can argue that the specific 'units' at issue are in themselves what defines quality. But I think this is just an illusion. A 'vector' for instance, is often defined as a scalar quantity, a linear unit, and some direction. "5 miles [north]", for instance might treat the "miles" and "north" as UNITS of quality, not quantity. But while they seem to be distinctly UNIQUE, these too can be interpreted quantitatively.
"5 miles [north]" may be reinterpreted as " 5 UNITS of an arbitrary agreed upon unit (not in itself 'real') in the arbitrary unit direction arbitrarily assigned of some 'origin' in common, like the North Star, that stays relatively constant."
The arbitrary realities which people agree to as 'units' are themselves determined based on other quantities and units as well. These are also done by the mere ways we observe and negotiate or confer about what we default to be 'real' of our powers of observation.
As such, we "discover" the reality. But the conventions we use to agree among each other to share these are the "invention" aspects and are about assigning those arbitrary 'units' we simply AGREE to conform to. This is what makes numbers appear invented only by perspective.