On 4/27/2026 4:22 AM, Mikko wrote:If your best argument is an ad-hominem fallacy you have nothingOn 26/04/2026 16:22, olcott wrote:Until you become a PTS expert your critique ofOn 4/26/2026 3:09 AM, Mikko wrote:>On 25/04/2026 15:25, olcott wrote:>>>>>> That does not help if it is not known whether such sequence ofOn 4/25/2026 3:20 AM, Mikko wrote:>>inference steps exists.>
It does help for the halting problem counter-example input
and it does help for the 1931 Incompleteness Theorem. Both
of these are ruled ungrounded rather than undecidable.
The halting problem counter-example is grounded. One of the following
statements is true per the definition of "halting decider":
- The proposed decider accepts the counter-example.
- The proposed decider rejects the counter-example.
- The proposed decider is not a halting decider.
It is not necessary to know which one is true. Each one is sufficient
to infer that the propsed decider is not a halting decider.
>
Whether a halting oracle is possible is another problem. Accordint to
the CHurch-Turing thesis it isn't but there is no known proof.
>
typedef int (*ptr)();
int HHH(ptr P);
>
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
>
int main()
{
HHH(DD);
}
>
Proof theoretic halt prover HHH is fully operational
code since 2022 can correctly rejects its input DD
as lacking a well-founded justification tree.
Which is not quite correct. The input should be rejected as incomplete
(unless the exact meaning of HHH is a part of the input language).
my work is like a carpenter trying to provide
medical advice on the basis of carpentry skills.
worth of notice to say about the halting problem.
--
Mikko
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