Dr Swamidass:
I am puzzled by why you say oracles are logically impossible.
First, let me be very clear that I am not questioning your demonstrations that Turing machines cannot be used to implement oracles.
But for me, something is logically possible if we can reason consistently about it.
Of course, Turing himself invented oracles to help him reason about uncomputability. Scott Aaronson has a nice summary of his work in section 3 of this course excerpt.
Since then, the philosopher Jack Copeland and many others have explored oracles through his concept of hypercomputation. I’ve linked the Wikipedia article. It cites many papers on the topic.
So it seems to me that it is possible to reason consistently about oracles and hypercomputation, and therefore it is fair to say oracles are logically possible.
Are they physically possible in our universe? The SEP article on Computation in Physical Systems briefly considers that issue. It claims there is a slight possibility that they might be: “Relativistic hypercomputers exploit the properties of a special kind of spacetime called Malament-Hogarth spacetime, which is physically possible in the sense of constituting a solution to Einstein’s field equations for General Relativity. … The first question is whether our spacetime is Malament-Hogarth. The answer is currently unknown. Even if our spacetime is not Malament-Hogarth globally, it might still contain regions that have the Malament-Hogarth property locally.”