“exist"? I would hardly use such words in this frame of reference.
I'm saying that “identities” are a fuzzy human “You know it when you see it, and different men see it differently.” category that is bereft of any definition that can be objectively measured and reasoned about, and that what I just said is a trivial and obvious conclusion.
They “exist” in the same way that borders between different oceans exist, arbitrarily drawn, and different people will think differently as to where they lie.
If you wish to call that an “existence”, then be my guest, though many others would præfer to not call it such. — ironically the border between “existence” and “nonexistence” is of a similar quality.
> Do triangles exist? Is the definition of triangle "bereft of any definition that can be objectively measured"?
Certainly not, the definition of a triangle is quite a rigorously defined mathematical construct.
> Is the Ship of Theseus fundamentally different than a triangle, or is it merely a difference of degree?
It is not a difference of quantity but quality. A triangle is an objectively defined, mathematical concept; identities are as I said “You know it when you see it, and different men see it differently.”. — you will not find many mathematicians disagreeing on what is, and is not a triangle.
Another fundamental difference is that a triangle is an abstract reasoning tool, not an empirical one, and no mathematician would suggest that real life objects are, or are not, triangles.
> Ask any random human to define some extremely complex mathematical entity, and you'll get various fuzzy answers.
A lay human being with no mathematical understanding perhaps, but all of these entities have been defined rigorously in mathematical terms.
> Does that mean complex math doesn't really exist?
You were the one who speaks in such terms as “existence”. I will not have you put words in my mouth.
All I said is that one has an objective, rigorous definition such that you will find that every single educated man in the field agrees on what is, and what is not a triangle, such that a machine proof assistant can be fed this definition, and verify machine-level proofs that reason about them, and that the other lacks this such that you find that nigh any man, expert or not, has a different definition of what constitutes the identity of a physical object, and where a new object starts.
The fact that borders exist doesn’t imply that there are different centers of power. In fact, for most of history borders were notoriously ill-defined.
But power in practice does not adhere to how different parties arbitrarily define where borders lie.
Most of nations of the world officially define Crimea to be within the Ukrainian border, but it is the Russian government who wields the actual, practical power there.
It took a rather long time for many countries to stop defining mainland China as falling within the power of the R.O.C. government, despite the R.O.C. wielding no practical power there any more, and the R.O.C. still defines mainland China as falling within it's power.
If “borders” of nations were defined descriptively based on sovereign entities having control over them, then they would certainly be more useful, but, this would also assume a simplified world where it is easy to decide what powerbase is sovereign, and what powerbase binarily has control over what surface of the planet; it is often not so simple and often multiple parties vie for control over a single area, and whether a powerbase be sovereign is not so easy to simply answer.
If the law is observed broken once, that is a falsification of the entire theory.
And I assume you live in a rather peaceful area if you think powers adheres to borders. In many parts of the world governments have a harm time enforcing their law upon fringe areas where effective anarchy is quite common. — the picture is certainly not as simple as you paint it.
I'm saying that “identities” are a fuzzy human “You know it when you see it, and different men see it differently.” category that is bereft of any definition that can be objectively measured and reasoned about, and that what I just said is a trivial and obvious conclusion.
They “exist” in the same way that borders between different oceans exist, arbitrarily drawn, and different people will think differently as to where they lie.
If you wish to call that an “existence”, then be my guest, though many others would præfer to not call it such. — ironically the border between “existence” and “nonexistence” is of a similar quality.