I don't think there is a lack of a unifying theoretical framework. Both the turing machine and the lambda calculus are well understood and the foundations of computer science (and are isomorphic to each other).

I think the problem is more that a gap exists between the theoretical framework and practical programming. For example have fun trying to formally verify Javascript code!

Interesting side-note: we are currently unable to prove that there is nothing more powerful than a turing machine, i don't know if its even provable (that smells like something undecidable).

Philosophical nitpick, it's fundamentally impossible to disprove non-existence of an entity.

That may be the border of my english-understanding, but i can prove non-existence of certain things (are they entities?).

Since this is currently my seminar-research topic: In the Zermelo–Fraenkel set theory there is only one Urelement.

I can prove the non-existence of another Urelement not equal to the Urelement.

Since i only care about Zermelo–Fraenkel, i can define Urelemente as things inside the Zermelo–Fraenkel set theory that are not sets themselves but elements of a set. And there is only one element that satisfies this definition. Every other thing is not a Urelement, since it does not satisfy the definition.

I don't understand. Is that the proof?

I don't understand the proof.

If A is an Urelement, and B is an Urelement, ... I don't see a contradiction in A is an element of C, and B is not an element of C?

I mean, I defer to your research, but I do not understand...

My point is really about the impossibility of proving a universal negative. Russell's Teapot is instructive here.

You say it's impossible to prove a universal negative? I'd love to see a proof of that

Hm?

I'm not sure I understand.

I would think that disproving the nonexistence of something would be the same as demonstrating the existence of something. That seems doable, on a sense at least.

And I would think that disproving the existence of something could be done by deriving a contradiction from the assumption that the thing exists. This also seems possible.

I'm guessing I am misunderstanding you in some way. Can you help me understand?

Methinks you had a double-negative too many. Your sentence says it's impossible to prove the existence of something. Unless that's what you had intended, in which case I don't see how that's useful philosophy for this discussion.

You're correct, I mis-typed and it should have been proven the non-existence.