Re: ZFC solution to incorrect questions: reject them --discourse context --

On 3/17/24 10:08 PM, olcott wrote:

On 3/17/2024 7:26 PM, immibis wrote:

On 18/03/24 00:35, olcott wrote:

On 3/17/2024 3:02 PM, Richard Damon wrote:

On 3/17/24 10:13 AM, olcott wrote:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
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When posed to each entity (Carol/Ĥ.H) their respective question (a)/(b):
(a) Can Carol correctly answer “no” to this [yes/no] question?
(b) Does Ĥ ⟨Ĥ⟩ halt?
lacks a correct answer because this answer is contradicted.
*Incorrect questions do not lack answers they lack correct answers*
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*THIS CANNOT BE CORRECTLY IGNORED*
*The discourse context of who is asked is the determining factor*
*of whether the very same answer to the same word-for-word question*
*is correct or incorrect*
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But the question, "Does the machine this input describes Halt when run?" doesn't depend on who you ask. (Unless your input isn't actually a Computation)
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Your "Carol" question is about Carol being able to answer, so it naturally depend on Carol.
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THe Halting Question doesn't mention the decider in any way, so doesn't.
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Yes, the particular question include a copy of one decider, but that doesn't refer to that decider in any specific way, so doesn't make the question change.

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The question is the same: Does Ĥ ⟨Ĥ⟩ halt?
The answer is the same (assuming a simulating halt decider): YES.
For H1 ⟨Ĥ⟩ ⟨Ĥ⟩ this answer is CORRECT  // waits for more execution traces
For H ⟨Ĥ⟩ ⟨Ĥ⟩ this answer is INCORRECT

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Wrong, it's correct in both cases because Ĥ ⟨Ĥ⟩ halts in all cases.
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H1 correctly determines that it need not abort its simulation thus returns 1
H has the inductive basis to know that it must abort its simulation thus returns 0

And what is that "Inductive basis" that allows H to give the wrong answer?
Remember, H is the algorithm that it is, and not the algorithm it is not, so an H that identifies itself must include in its argument that what it is looking at will do whatever it does.

 

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Thus the same question has a different meaning depending on who is asked.
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