Re: Halting Problem: What Constitutes Pathological Input

On 5/6/25 11:36 AM, olcott wrote:

On 5/6/2025 4:47 AM, Mikko wrote:

On 2025-05-05 19:54:55 +0000, olcott said:
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On 5/5/2025 2:49 PM, dbush wrote:

On 5/5/2025 3:38 PM, olcott wrote:

On 5/5/2025 2:23 PM, Richard Heathfield wrote:

On 05/05/2025 20:20, olcott wrote:

Is "halts" the correct answer for H to return?  NO
Is "does not halt" the correct answer for H to return?  NO
Both Boolean return values are the wrong answer

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Or to put it another way, the answer is undecidable, QED.
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See? You got there in the end.
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Is this sentence true or false: "What time is it?"
is also "undecidable" because it is not a proposition
having a truth value.
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Is this sentence true or false: "This sentence is untrue."
is also "undecidable" because it is not a semantically sound
proposition having a truth value.
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Can Carol correctly answer “no” to this (yes/no) question?
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Both Yes and No are the wrong answer proving that
the question is incorrect when the context of who
is asked is understood to be a linguistically required
aspect of the full meaning of the question.

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And "does algorthm X with input Y halt when executed directly" has a single well defined answer.
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That is not even the actual question.
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Does the finite string input DD to HHH specify
a computation that halts? No it does not.

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That question is a category error. The halting question is not about
finite strings but about computations.
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 HHH must compute the mapping from its finite string
of x86 code input to the actual behavior that this
finite string input specifies.

Right, it needs to, but doesn't.
It is just a FACT that the actual behavior of the input DD is to Halt.
The fact that HHH INCORRECTLY stops its emulation, means it is not a correct emulator, and thus doesn't know the answer it needs to give to be correct.
It MUST (to be correct) do what it CAN'T, and so it is INCORRECT.

 The same thing goes for TM's
H must compute the mapping from the finite string
TM source-code input to the behavior that this TM
source-code specifies.
 

Right, it MUST to be correct, but it can't, so it is incorrect.
You don't seem to understand the difference between requirements and abilites, just like you don't understand the difference between Truth and Knowledge, because you are fundamentally ignorant of the basics of the field.