@BestGirlGrace Quantity, together with all the emergent properties thereof, is a natural phenomenon and is therefore discovered. Tools operating on those properties, such as notation and terminology, are arbitrary attempts to describe those phenomena and are therefore invented.

Is mathematics the study of quantity, or is it the study of tools for characterizing quantity? A student of anything learns both the tools themselves and that which the tools manipulate.

@fool

Quantity is most decidedly not a natural phenomenon.

This is because quantity is a product of Type.
Type, e.g. "a horse" is a human invention along the lines of metaphor.

In reality, every four-legged hoof-haver is a unique being, and certainly not some "exemplar" of some "type".

Without Types, there is nothing to count. Everything is unique. 1 is the only number, and that too is superfluous.

@BestGirlGrace

@androcat Quantity is evident elsewhere than in what our models abstractly deem countable. Distance, for instance. To the extent that this one and that other one are not the same one (and if we can meaningflly speak of uniqueness, then we can on that same basis also speak of distinction), then some distance separates them, and that distance has quantity.

(@BestGirlGrace if this continues should we refrain from tagging you?)