There’s a difference between an existence proof and a constructive proof. We can talk about existence proofs for, “Here’s what happens when we hook a magical Halting Oracle to a Turing Machine and run certain programs.” We do not have any constructive proof of how a Halting Oracle would behave.
Just because you can say, “Imagine we had a thing with these properties” doesn’t mean you know how to build such a thing.
There’s a difference between an existence proof and a constructive proof. We can talk about existence proofs for, “Here’s what happens when we hook a magical Halting Oracle to a Turing Machine and run certain programs.” We do not have any constructive proof of how a Halting Oracle would behave.
Just because you can say, “Imagine we had a thing with these properties” doesn’t mean you know how to build such a thing.