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

On 4/25/2025 11:54 AM, Richard Damon wrote:

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.
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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.
 

There are no finite string operations that can
be applied to the input to HHH(DD) that derive
the behavior of of the directly executed DD thus
DD is forbidden from reporting on this behavior.
It is forbidden for the same reason that
int sum(int x, int y) { return x + y; }
sum(3,2) IS NOT ALLOWED TO REPORT ON THE SUM OF 5 + 7.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer