Re: Halting Problem: What Constitutes Pathological Input

On 5/5/2025 3:54 PM, olcott wrote:

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.
 

In other words, you don't understand what the halting problem is about, because that is EXACTLY the question.
I want to know if any arbitrary algorithm X with input Y will halt when executed directly.  It would be *very* useful to me if I had an algorithm H that could tell me that in *all* possible cases.  If so, I could solve the Goldbach conjecture, among many other unsolved problems.
Does an algorithm H exist that can tell me that or not?