Good question, but I think there might be a difference. Suppose, in a galaxy far, far away, there are aliens. They probably don't have the concept of unicorns. However, they probably have discovered numbers, pi, Pythagoras theorem, e^(i pi) + 1 = 0, etc.
So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status?
We can only be confident of that if they're in this universe. Also, this is only a conjecture. It's just something some of us imagine would be true. You can't elevate such an idea to the level of empirical data.
So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status?
Unicorns. Kirin. Narwhals. Rhinos. So you have two independent origins in culture for such a creature, plus two appearances of something similar in nature. Does that confer it some sort of elevated ontological status?
It's not at all clear that the cultural constructs are independent of each other or real world creatures. Particularly in the Western case, some of the earliest Greek accounts of the unicorn as well as Marco Polo’s account confirming its existence and difference from the contemporary evolution of the image stem from the distant East (from the European perspective) and clearly are describing a rhinoceros. They are also very similar to accounts of the Kirin.
Rather: if we have a notion of something and statements about it in every universe, then it must exist. However, come to think of it, that's bonkers.
Still, it's remarkable that mathematics allows us to make reproducible true statements about fictional objects.
What would happen to your epistemology if every alien civilization has unicorns but some lack π?
I knew it, Unicorns are real!!11!
I am not sure I can conceive of aliens that don't have pi (how can they have cylindrical rockets?).
Anyway, maybe we should let the professionals deal with this.
https://plato.stanford.edu/entries/platonism-mathematics/
https://plato.stanford.edu/entries/intuitionism/
https://plato.stanford.edu/entries/mathphil-indis/
We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe".
(For starters, what is the definition of "unicorn"? If it's just a horse with a horn, then such a thing is plausible with genetic engineering in our universe.) As we endow the unicorn with additional properties, then it becomes less and less clear that there exists a universe where such a thing can exists other than as an imaginary being. If the concept of a unicorn could be axiomatized, then it could constitute a universe.
> Or, math is also a number of simplified alternate views of reality.
Well, that's the math that we do; not the math that we (possibly) are.
Indeed. The current better known attempts at a "unicorn universe" have problems with power scaling and the square-cube law. https://www.reddit.com/r/mylittlepony/comments/mrs81/accordi...
Do you have a good definition of what constitutes a "well-developed" universe?
An easy definition would be one where everyone agrees on the exact mechanics and sequence of states. The fibonacci sequence is well-developed: it has an exact definition that every competent simulator can simulate the same way. If I say my favorite number is the 1000th item in the sequence (starting with 0, 1, 1 as items #1, #2, #3), then everyone can calculate the 1000th item the same way.
If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that. There's no unambiguous rules for how the unicorn universe is calculated. Everyone has a different "unicorn universe" in their heads, and each of those universes operates on our own mind's whims rather than any rules we can describe to each other.
Homo sapiens has this issue with this universe. Even if you subset that group to just scientists, there are still differences of opinion.
How is it any different than believing that unicorns exist as physical objects, just in their own universe?
What we call "physical existence" could...just be "math all the way down".
Or, math is also a number of simplified alternate views of reality of varying degrees of "applicability." (Where "applicability" has to do with predictive power over reality.)