Re: Proof that H(D,D) meets its abort criteria --incorrect question instance--

On 3/20/24 7:05 PM, olcott wrote:

On 3/20/2024 5:53 PM, Richard Damon wrote:

On 3/20/24 4:13 PM, olcott wrote:

On 3/20/2024 2:57 PM, Richard Damon wrote:

On 3/20/24 2:07 PM, olcott wrote:

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Since I defined the term "incorrect question" and I defined the
term "incorrect question instance" I cannot possibly have defined
them incorrectly. These are stipulative definitions.
https://en.wikipedia.org/wiki/Stipulative_definition

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And by stipulating your definition, you havve disconnected it from any other use in the theory, in prticular, just because some question turns out to be an Olcott-Incorrect Question doesn't me it is an improper question to put to a decider to see if it meets its defintion.
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Every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ says Ĥ ⟨Ĥ⟩ halts and fails to halt.
Every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   says Ĥ ⟨Ĥ⟩ does not halt and then halts.
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Every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ that answers YES is wrong.

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Because for THAT H^, the answer is NO
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 "That Ĥ" that you are referring to is not any actual Ĥ at all.
every element of the in finite set Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong
answer because whatever answer it provides is contradicted.
 <snip>

So, you are just admitting you are a LIAR?
Of course it is a specific H^ or nothing you have said makes any sense.
Your "Set" is a pairing of SPECIFIC H with a SPECIFIC H^ built from that H.
So, for each element of that set, which is what matters, there is a correct answer, what ever H (H^) (H^) doesn't say.

 

The question was always "Correct" as it always had a correct answer for all cases.
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 There is never any correct answer for any of these cases: Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩

Of course there is, I just gave it to you for each H that you create.
You are just caught in your lies.

 

All you have done is say that a decider can be considered Olcott-Correct even if it LIES and gives wrong answers, because those cases were just "incorrect question instances" for it.
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 We either change the question or we keep the question the same
and reject the erroneous inputs.

WHY?
YOU are the one trying to come up with an alternate formulation for the problem to try to convince people it might be useful for SOMETHING.
I'm just pointing out the problems with the best I can figure out what you are meaning.
So far, it seems you want to allow deciders to lie if they can't get the right answer.

 

Thus, you have destroyed the ability to gain knowledge by computing, as we can never know if the answer was right unless we can show that the decider did give the right answer, which is an uncomputable problem, so we can never know something we didn't already know the answer to.
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 Actually no one has showed that my abort decider ever gets
the wrong answer. Instead of this the dishonest claim is
made that it always gets the wrong answer.

No, we have shown that ALL the case you have presented, it gets the wrong answer by the definition we agreed upon the other day.
H can abort its simulation and say non-halting if a UTM simulation of the exact same input would be non-halting.

 

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An {incorrect question instance} is any question that has no
correct answer from the one that this question was posed to.

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And, if the "one" that question was posed to, by reason of the "definition" of that "one" just doesn't give the correct answer, are you saying that is enough to make that question instance invalid?
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When the only reason that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ fails to provide a correct
answer is that every answer is contradicted then these incorrect
question instances must be tossed out.
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Excpet that now we can't tell which are those cases.

 If you quit lying about the abort decider being always wrong
we can move on to seeing if there are any counter-examples
that show it is not always right.
 

I am not lying. Show me a case where it WAS right about the ^ input.
Remember, our agreed upon definition of when it can decide to abort.