Is the meaning of this statement independent of the symbols used? Can the meaning be found in nature, outside of our minds, or is it an artifact of our minds or language?
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.
> 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.
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.
> 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.
>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.
