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

Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:

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.)

And the big picture is that this can be done because false is the
correct halting decision for some halting computations.  He has said
this explicitly (as I have posted before) but he has also explained it
in words:

| When-so-ever a halt decider correctly determines that its input would
| never halt unless forced to halt by this halt decider this halt
| decider has made a correct not-halting determination.

Or perhaps you prefer this explanation from 2023:

| (1) A return value of 1 from H(D,D) means the input to H(D,D) has halted
|
| (2) A return value of 0 from H(D,D) has been redefined to mean
|     (a) D does not halt
|     (b) D has been defined to do the opposite of whatever Boolean value
|         that H returns.

All very clear.  Of course (2)(b) is undeciable in general.

--
Ben.