[blotter_paper]

I wouldn't say that being found in nature means that something is not made up. Issus coleoptratus evolved gears long before humans invented them, yet gears seem purely phenomenal -- I wouldn't expect the noumenon to have anything directly corresponding to gears in it, "gear" is just a useful concept we have that lets us categorize part of an insect or a bicycle (both of which are made up themselves, of course).

There may be discrete math in the noumenon, but I'm not convinced of that. For all I know the noumenon could be dealing in something else entirely, and math might just be a really useful tool we came up with (like classical physics, and probably modern physics). Math is the simplest case you can make, but I don't see a compelling reason to accept it as a given.

[naasking]

> I wouldn't say that being found in nature means that something is not made up.

Then define "made up".

> For all I know the noumenon could be dealing in something else entirely, and math might just be a really useful tool we came up with (like classical physics, and probably modern physics).

Suppose it is merely a useful tool. This tool then necessarily has a structure that's isomorphic to part of the structure of the noumenon, otherwise it wouldn't actually be a useful tool.

Therefore, whatever structure it models is itself mind independent, as I said. The symbols and formalisms we use are interchangeable, but the structure revealed is not.

[blotter_paper]

>Then define "made up".

That which is not a part of base reality. If base reality were operating using the same rules as Conway's game of life then cells would be real, but gliders would be made up. Since Conway's game of life actually runs in a simulation on some computer or another, cells are also made up.

>Suppose it is merely a useful tool. This tool then necessarily has a structure that's isomorphic to part of the structure of the noumenon, otherwise it wouldn't actually be a useful tool.

Newton's equations are now accepted as an approximation; they are not isomorphic to part of the structure of the noumenon, yet remain useful when firing cannons. Myths and legends have been useful in compelling people to wage wars and donate to charities, yet we do not suppose that this usefulness means they are isomorphic to part of the structure of the noumenon.

Perhaps fermions and bosons correspond very closely to real parts of the noumenon, but they could also be a phenomenon which is emergent on top of something else -- as made up as chemistry, biology, psychology, and economics.