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

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

Do you understand why this question has no correct answer?
The question is: >>>Is this sentence true: "This sentence is not true." ???<<< — PL Olcott

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

In other words you do not understand that it is an incorrect question. — PL Olcott

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

PL Olcott. ok. Next. — Banno

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

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

The Halting Problem is:

INPUT: A string P and a string I. We will think of P as a program.

OUTPUT: 1, if P halts on I, and 0 if P goes into an infinite loop on I.

Theorem (Turing circa 1940): There is no program to solve the Halting Problem.

Proof: Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem, Halt(P, I) returns True if and only P halts on I. The given this program for the Halting Problem, we could construct the following string/code Z:

Program (String x)
If Halt(x, x) then
Loop Forever
Else Halt.
End.

Consider what happens when the program Z is run with input Z
Case 1: Program Z halts on input Z. Hence, by the correctness of the Halt program, Halt returns true on input Z, Z. Hence, program Z loops forever on input Z. Contradiction.

Case 1: Program Z loops forever on input Z. Hence, by the correctness of the Halt program, Halt returns false on input Z, Z. Hence, program Z halts on input Z. Contradiction.

End Proof. — Prof Kirk Pruhs

• Assume there is a program Halt
• Show that Halt leads to a contradiction
• Conclude that there can be no program such as Halt

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

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

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

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

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

"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 }

↪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

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

SO, Z?

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

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

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