@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
you are Bertrand Russell and I claim my note which is deemed equivalent to (but not the same as) 5 units of currency

@fool @BestGirlGrace

@ASprinkleofSage

I'll get your unique currencies to you as soon as I discover which ones were intended.

This may take a while.

@fool @BestGirlGrace

@ASprinkleofSage

You're confusing convention and ontology.

I am specifically pointing out that over the course of history we have invented types and countability and other such conventions.

And now, we have things that really only make sense on the basis of those types.

They are dependent on those inventions.

But they aren't real things as such.

@fool @BestGirlGrace