[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.

[naasking]

> 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.

So in your view, anything that is a composite of two or more primitives is by definition "made up".

Therefore, given a standard definition of natural numbers [1], any number except zero is made up?

> Newton's equations are now accepted as an approximation; they are not isomorphic to part of the structure of the noumenon

They are actually, within the domain for which they are valid. General relativity reduces to Newton's equations in the right context.

[1] Nat = Zero | Succ Nat

[blotter_paper]

>So in your view, anything that is a composite of two or more primitives is by definition "made up".

Yes. If we start calling higher order configurations "real" then we have to contend with all of the potentially imaginable subdivisions of the noumenon and either grant them all realness or find some arbitrary criteria upon which to deny some of those subdivisions the property of realness. If we grant that an insect is a real thing then I get to make up a new word, say, "kokirombo," that describes the front two-thirds of a grasshopper combined with the left half of a ladybug, some air, a pinch of grass, and the rear bumper of a 1998 Ford Taurus. You can come up with some arbitrary standard by which your gerrymandering of reality is allowed and mine is not, but there isn't anything that makes your standard more valid than mine. In practice we typically use usefulness as our standard for categorizing things, but dogmatically claiming this as the criteria for realness leads to absurd positions.

>Therefore, given a standard definition of natural numbers [1], any number except zero is made up?

I still haven't necessarily accepted zero as not being made up, but I think your Succ function implicitly depends on one being defined as well.

>They are actually, within the domain for which they are valid.

Strongly disagree. If you believe in quantum mechanics then you believe that things move probabilistically. I'm obviously arguing that every scale except the smallest is made up, but even if we hypothetically accepted the validity of larger scales then we would have to admit that there is an ever-so-vanishingly-small chance that any given cannonball will spontaneously jump three meters to the left thus deviating from it's Newtonian trajectory. The fact that you could launch cannonballs from now until the heat death of the universe without seeing this effect at a scale you would typically notice is inconsequential, Newton's equations are still merely a useful approximation and they are not isomorphic to the behavior of the noumenon.