Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error

On 4/25/25 12:31 PM, olcott wrote:

On 4/25/2025 3:46 AM, Mikko wrote:

On 2025-04-24 15:11:13 +0000, olcott said:
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On 4/23/2025 3:52 AM, Mikko wrote:

On 2025-04-21 23:52:15 +0000, olcott said:
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Computer Science Professor Eric Hehner PhD
and I all seem to agree that the same view
that Flibble has is the correct view.

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Others can see that their justification is defective and contradicted
by a good proof.
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Some people claim that the unsolvability of the halting problem is
unproven but nobody has solved the problem.

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For the last 22 years I have only been refuting the
conventional Halting Problem proof.

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Trying to refute. You have not shown any defect in that proof of the
theorem. There are other proofs that you don't even try to refute.
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 Not at all. You have simply not been paying enough attention.
 Once we understand that Turing computable functions are only
allowed to derived their outputs by applying finite string
operations to their inputs then my claim about the behavior
of DD that HHH must report on is completely proven.
 

Youy have your words wrong. They are only ABLE to use finite algorithms of finite string operations. The problem they need to solve do not need to be based on that, but on just general mappings of finite strings to finite strings that might not be described by a finite algorithm.
The mapping is computable, *IF* we can find a finite algorith of transformation steps to make that mapping.
You just don't seem to understand that diffence between Requirements and Capability.
Yes, it doesn't make much sense to ask about if we can compute something that we know can not be, but many non-computable problems, like Halting, were first suppoed to be computable, and solutions were looked for, when the, in hind sight obvious, counter example that shows it can't be was found.
In fact, your argument just shows that the problem, as actually stated is impossible to do, but you misuse that to say that means you get to change the question. THAT is a fundamental lie in your logic. The question, "Does the machine+input described by the input halt when run?" is a perfectly valid question. The fact that it turns out that it is impossible to write a program that can do this for all inputs, doesn't make the question suddenly invalid. It says the question is non-computable, and thus no Halt Deciders exist.
This DOES have great impact on much of logic, as a related property of this that exists in any logic system that has the needed propeties of the Natural Numbers having statements that are true but not provable.
This turns out to be an attribute that comes out of the creation of countable infinities which just breaks some of our common notions of how things should work, but end up must being true in those systems.

Actually solving the Halting Problem requires making a computer
program that is literally all knowing about program termination.

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Which is provably impossible.
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