Re: Analysis of Flibble’s Latest: Detecting vs. Simulating Infinite Recursion ZFC

On 21/05/2025 06:23, olcott wrote:

On 5/20/2025 9:15 PM, Richard Damon wrote:

On 5/20/25 3:10 PM, Mr Flibble wrote:

<snip>

Conclusion: ----------- Flibble sharpens his argument by
clarifying that SHDs are not required to simulate infinite
execution. They are expected to *detect* infinite behavior
structurally and respond in finite time. This keeps them
within the bounds of what a decider must be and
strengthens the philosophical coherence of his
redefinition of the Halting Problem.

>
But you can't "redefine" the Halting Problem and then say you have answered the Halting Problem.

 Do you mean like how ZFC resolved Russell's
Paradox thus converting "set theory" into "naive set theory"?

No, because there is no paradox in the Halting Problem. A proof by contradiction is not a paradox.
A better parallel would be Cantor's proof that there are uncountably many real numbers, or Euclid's proof that there is no largest prime. Both of these proofs make a single assumption and then derive a contradiction, thus showing that the assumption must be false. No paradoxes need apply.
In the Halting Problem's case, the assumption is that a UNIVERSAL algorithm exists for determining whether any arbitrary program halts when applied to given arbitrary input. The argument derives a contradiction showing the assumption to be false.
Whatever you think your HHH determines, we know from Turing that it doesn't determine it for arbitrary programs with arbitrary input. It therefore has no bearing whatsoever on the Halting Problem.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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