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

On 2025-05-23 05:25:30 +0000, olcott said:

On 5/22/2025 8:24 PM, Mike Terry wrote:

On 22/05/2025 06:41, Richard Heathfield wrote:

On 22/05/2025 06:23, Keith Thompson wrote:

Richard Heathfield <rjh@cpax.org.uk> writes:

On 22/05/2025 00:14, olcott wrote:

On 5/21/2025 6:11 PM, Richard Heathfield wrote:

[...]

Turing proved that what you're asking is impossible.
 

That is not what he proved.

 Then you'll be able to write a universal termination analyser that can
correctly report for any program and any input whether it halts. Good
luck with that.

 Not necessarily.

 Of course not. But I'm just reflecting. He seemed to think that my inability to write the kind of program Turing envisaged (an inability that I readily concede) is evidence for his argument. Well, what's sauce for the goose is sauce for the gander.
 

Even if olcott had refuted the proofs of the
insolvability of the Halting Problem -- or even if he had proved
that a universal halt decider is possible

 And we both know what we both think of that idea.
 

-- that doesn't imply
that he or anyone else would be able to write one.

 Indeed.
 

I've never been entirely clear on what olcott is claiming.

 Nor I. Mike Terry seems to have a pretty good handle on it, but no matter how clearly he explains it to me my eyes glaze over and I start to snore.

 Hey, it's the way I tell 'em!
 Here's what the tabloids might have said about it, if it had made the front pages when the story broke:
   COMPUTER BOFFIN IS TURING IN HIS GRAVE!
   An Internet crank claims to have refuted Linz HP proof by creating a
  Halt Decider that CORRECTLY decides its own "impossible input"!
  The computing world is underwhelmed.
 Better?  (Appologies for the headline, it's the best I could come up with.)
 Mike.
 

 When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

That is not a valid sentence: there is an subordinate clause and two
main clauses but nothing that combines the main clauses to an overall
meaning.
--
Mikko