I think only a mod can change the subject of a topic, so it is safe.
So yes, just be more careful when selecting your logically impossible thing, because so far none of them has qualified. Then, having found some suitable impossible requirement, in order to make your point in the subject line, you need to come up with a scenario that lists it as a requirement. That was also missing in the OP. So let's say for argument sake that a square circle (suitably defined) is impossible. What argument would plausibly list that as a requirement? — noAxioms

On the surface of the Earth, imagine drawing squares centered on the North Pole with increasing length sides until the sides coincide with the circle of the equator. As ↪noAxioms said ,what can be done is all about unstated presumptions. — magritte

Not logically impossible. — noAxioms

Are you referring to Squaring the circle? Are you sure about your opening statement? — jgill

↪PL Olcott I think you have some interesting stuff here, but you haven't demonstrated an error on Gödel or Turing. — Banno

↪PL Olcott If you would show that a well-accepted and well-understood part of logic is in error, you will need a good deal of strong, formal argument to carry your case. — Banno

..and so on. I don't think it's just me. — Banno

My conclusion is that you're unable to present your thesis in a manner that is sufficiently clear to be evaluated. — Banno

↪PL Olcott All I'm asking is where Carol's question occurs.
Sure, show me in C. — Banno

SO, Z?

It shouldn't be this hard. I'm just checking that I've understood your point. — Banno

↪PL Olcott Your claim is that some equivalent of Carol's question occurs in the halting program proof. It's not unreasonable to ask you to show where it occurs. — Banno

That Carol's question contradicts every yes/no answer that Carol can provide <is> isomorphic to input D to decider H that does that opposite of whatever Boolean value that H returns. — PL Olcott

"Will Program Z loop forever if fed itself as input?"
— Banno — Banno

// The following is written in C
//
01 typedef int (*ptr)(); // pointer to int function
02 int H(ptr x, ptr y) // uses x86 emulator to simulate its input
03
04 int D(ptr x)
05 {
06   int Halt_Status = H(x, x);
07   if (Halt_Status)
08     HERE: goto HERE;
09   return Halt_Status;
10 }

Your question occurs in Z, not in H. Z is problematic, but Z is also a consequence of H, hence H is problematic. — Banno

Have a think on it again. You have shown that Z is problematic. Sure, it is. That's what shows that H is impossible. — Banno

It is equally a logical impossible for any CAD system to correctly draw a square circle. The inability to do the logically impossible never places any actual limits on anyone of anything. — PL Olcott

So sure, "the inability of a halt decider to correctly provide the halt status of an input that does the opposite of whatever halt status is provided does not place any actual limit on computation." But the impossibility of writing the program Halt does. — Banno

First and most obvious question is where in this the thing you called the "isomorphism from Carol's question to the halting problem proof counter- example template" is located. It's not there. But we can add it: "Will Program Z loop forever if fed itself as input?" — Banno

PL Olcott. ok. Next.
— Banno — PL Olcott

↪PL Olcott I think you are wasting my time. — Banno

PL Olcott. ok. Next. — Banno

Well, no. I’m pointing out that you only have a problem here if you restrict yourself to yes/no with no revision. — Banno

But that's not right - you've been given several correct answers. — Banno

So an {epistemological antinomies} (why the curly brackets?) is, for example, the liar. Where is there an example of the Liar being used in a diagonalization? What might that look like? OR do you mean something else? — Banno

Here's where we are up to: can you explain how you reject diagonalisation for Gödel but not for Cantor? Or do you reject Cantor's argument, too? — Banno

↪PL Olcott I don't see this conversation progressing. — Banno

↪PL Olcott Well, we've dealt with that already, and as ↪Antony Nickles showed, it's problematic for you to insist on a yes or no answer. — Banno

Also, "This sentence is not true" is not a question. — Banno

And further the liar does not play a role in the issue at hand, Gödel incompleteness and Halting. — Banno

a question is not the sort of thing that is apt to contradiction. — Banno

After all, what I said above is the case; that is the reason for the halting problem. One way to treat this is as a reductio, showing that your approach has problems. — Banno

The reason that the halting problem persists is that the number of possible Turing machines is not enumerable; but any Turing machine designed to check for a halt can only check at most an enumerable number of Turing machines. It therefore cannot check if every Turing machine will halt. — Banno

PL Olcott That post doesn't tell me anything. — Banno

↪PL Olcott You seem to me to be doing no more than recursive assertion. It is because it is because it is because... — Banno

Do you also reject the uncountability of the reals? — Banno

You would presumably, for consistency's sake, say the same for Turing Machines, — Banno

Well, no. He carefully shows why G is unprovable. — Banno

As long as you acknowledge that, again, the “solution set” is YOUR requirement, not revealing anything but the answer you dictate. What you have imposed as “correct” suppresses any other interpretation and thus only has one set of answers. — Antony Nickles

Exactly. That's what I attempted to explain to PL Olcott, but it is impossible to agree with him, because according to his point, there will always be an incorrect answer because the question is 'posed' to Carol. It seems that poor Carol is guilty of everything regarding this tricky dilemma! — javi2541997

Carol does not need to be “indicating… an incorrect answer”, she could be indicating there IS NO sense of correctness in this “question” — Antony Nickles

G is not a deduction in F. That would be silly.

Rather, Gödel shows using arithmatization and the diagonalization that the structure of F is such that there must be WFF such as G. He's not using the deductive power of F to prove that G is unprovable. — Banno

But there is no proof of G in F. That's the point of G. — Banno

Gödel does not prove in F that some statement in F is not provable. — Banno

...We are therefore confronted with a proposition which asserts its own unprovability. 15 ... (Gödel 1931:43-44) — PL Olcott