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.

But such is absent here.

Cheers.

Ok.
What I am saying is much the same as you received elsewhere:

As a theoretical computer scientist, I can confirm that nothing in this paper shows anything about Turing's proof to be erroneous. Indeed, it is not a work of mathematics or theoretical computer science at all (due to lack of formality) and judt vaguely discusses some general points about objective and subjective specifications, nothing of which is relevant for the halting problem or the proof of its unsolvability. Also, notice that "This statement is not true" is not a statement that can even be formulated in first-order arithmetic or any standard logical system Turing or Church were concerned with. Indeed, Tarski's theorem on the undefinability of the truth predicate shows that statements of this type cannot even be formulated in these systems, so it is meaningless to discuss their formal validity or "truth" since they do not even exist formally. — Gutsfeld

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

I give up.

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

All I'm asking is where Carol's question occurs.
Sure, show me in C.

This is pointless.

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.

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.

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

IS this the equivalent of Carol's question? If not, what is?

Your last few replies do not seem to be addressed to my point.

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

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

You've moved back from Gödel to the halting problem. Ok.

So check this out:

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

This is a reductio argument:

• 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?"

Will Program Z loop forever if fed itself as input? The argument shows that we can't have an answer to that question. But that's exactly the point that shows that a program such as Halt cannot be written.

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.

The argument is not that Z is impossible, but that H is.

there are an infinite number of infinities. — an-salad

Cantor beat you to it.

I think you are wasting my time.

. ok. Next.

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.

Go on. But be brief. You seem to be repeating yourself yet again.

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.

I can't work out what that means.

So {epistemological antinomies} (why the curly brackets?) are, 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?

I've answered that.

...as ↪Antony Nickles showed, it's problematic for you to insist on a yes or no answer. But there are various ways of dealing with the liar. You earlier went with claiming that it was not a proposition, not eligible for a truth value, Another approach might be to drop bivalence, after Kripke. OR one could go with the revision theory of truth. — 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?

I don't see this conversation progressing.

Well, we've dealt with that already, and as showed, it's problematic for you to insist on a yes or no answer. But there are various ways of dealing with the liar. You earlier went with claiming that it was not a proposition, not eligible for a truth value, Another approach might be to drop bivalence, after Kripke. OR one could go with the revision theory of truth.

Also, "This sentence is not true" is not a question. So I'm unclear as to how your reply addresses the point that a question is not apt to contradiction.

And further the liar does not play a role in the issue at hand, Gödel incompleteness and Halting. The sentence of interest is not "This sentence is not true" but "this sentence is not provable".

So again, for consistency, mustn't you also reject Cantor's Diagonal argument as well? — Banno

Well?

When I stopped tolerating infinite digression it ceased. — PL Olcott

So again, for consistency, mustn't you also reject Cantor's Diagonal argument as well?

...a self-contradictory thus incorrect question... — PL Olcott

There are issues here as well, since a question is not the sort of thing that is apt to contradiction. A pair of statements can contradict; some statements can contradict themselves; but questions that are infelicitous are "inappropriate" or "ill-founded" or some such rather than contradictory.

Austin would have a field day.

Perhaps this indicates that there is a problem with the approach you have taken.

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.

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.

That post doesn't tell me anything.

You seem to me to be doing no more than recursive assertion. It is because it is because it is because...

The "Why" you are after is simply that there are more WFF, more Turing Machines and more Markov algorithms than can be counted.

Cheers.

it abstracts away WHY. — PL Olcott

An odd view.

You would presumably, for consistency's sake, say the same for Turing Machines, Lambda calculus, and Markov Algorithms; each of which have similar issues. Do you also reject the uncountability of the reals?

If so, we might leave this conversation here.

while carefully hiding WHY G is unprovable in F. — PL Olcott

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

You have Carol not playing the game. I wouldn't play , either. Fair call.

...to prove there is no proof G in F requires a sequence of
inference steps that prove that they themselves do not exist. — PL Olcott

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.

Hmm.

To be sure, G is a statement in F (is that what you are saying?)

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

The arithmatization of F - the assigning of Gödel numbers - does not take place within the language F. Rather it is about the language F.

"This sentence is not true." is not a truth bearer and thus cannot be true
or false. — PL Olcott

Good. I must have misread you previously.

When an expression of language G asserts that it is not provable in F
G := (F ⊬ G) then to be proven in F requires a sequence of inference
steps in F. — PL Olcott

Sure. Apart from some difficulty in your saying G is a language. I take it you mean the statement G?

Since we are proving that G is unprovable in F then these steps must
prove that they themselves do not exist — PL Olcott

Unclear.

Gödel does not prove in F that some statement in F is not provable. Rather he numbers all the provable statements on F, the shows via a diagonal argument that there is a statement G that is not amongst them and yet is true in F.

Absolute nothingness is impossible, but it would not be impossible if it were not for the existence of something.

All you've succeeded in doing is making the grammatical point that if there is something then there is not nothing.

Writing "absolute" in front of "nothing" only serves to obfuscate.

Mmm. I'm just attempting to help bring out your usage. So for you, (p & ~p) is a contradiction, and false, but also for you, (this sentence is not true) is a self-contradiction, and also false. Is that right?

I hope not, and that I've misunderstood, because (this sentence is not true) cannot be false.

But now I'm also not following your rendering of Gödel.

Self-reference itself is not problematic. So, for instance the following sentence is true and self-referential. This sentence contains five words. Hence, further, "This statement is not provable in F" may be self-referential but true.

Sure, nice. So whereabouts in such a coding are we going to see the equivalent of (p & ~p)? Where's the demonstration?

perhaps that is not as clear as you seem to think. My guess is that a much more formal account is needed. The problem is that “self” is ambiguous.

Again, the result is not a simple (p & -p).

I saw that earlier. Problem is that a self contradiction is something of the form (p & -p); and it’s clear the halting problem is not of this sort.

So presumably you mean something else by”self contradiction”, but it is unclear to me what that might be.

Sure. What's unclear to me is what it is you think this tells us about the halting problem.

The original article seems to be

https://www.cs.toronto.edu/~hehner/OSS.pdf?fbclid=IwAR2uE4I_faeh_MPXAom8fl7FyTtwqi_Ll7VjxSqabll6zjGQ2kCJMDOz9wI

The supposed outcome is that no computer program A can say what another computer program B will do when B does the opposite of whatever A says

But what if A just prints "B will do the opposite of whatever I say it will do"?

So I'm unconvinced.

Are you conflating irrational with inscrutable? — frank

Well, no, I'm saying even if your goal is to be rational, there are situations that do not have a rational response. Even if, or perhaps because, you understand the motivation of the folk involved, there need be no reasonable choice. But nevertheless, one can be obligated to do something (When you are in the Chaotic quarter of the Cynefin Framework).

Sometimes there is not only no best choice, but no reason for preferring one option over another.

But that's a different issue to whether we should be rational. Perhaps we should pick one issue here. I suggest the former is closer to the issue of the OP?

Why is it immoral to bomb workers in armaments factories? — RogueAI

Check out what Anscombe says about innocence, and the sleeping soldiers example, in Mr Truman's Degree.

Destroying a city involves the murder of innocents.