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

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

On 23/05/2025 19:37, Keith Thompson wrote:

Ben Bacarisse <ben@bsb.me.uk> writes:

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

[...]

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.

Hmm.  I don't read that the way you do.  Did I miss something?
It assumes that the input is a non-halting computation ("its input
would never halt") and asserts that, in certain circumstances,
his mythical halt decider correctly determines that the input
is non-halting.
When his mythical halt decider correctly determines that its input
doesn't halt, it has made a correct non-halting determination.
It's just a tautology.

>
You're reading it the way most people would, and in the way I said Sipser
would be interpreting the oft-quoted "Sipser quote".  I don't think you've
missed anything particularly.

Maybe it makes less sense out of the context it was posted in.  This was
when he was being less obtuse.  The computation in question only halts
because it is halted by the decider on which it is built.  It is a
halting computation, but according to PO it can reported as not halting
because of what would happen if it were not halted by the decider from
which it is derived.

Subsequent wordings have all been about hiding this.  Just prior to this
wording was the even more explicit claim that non-halting is correct
because of what "would happen if line 15 were commented out".  It's
always been about what would be the correct decision were the
computation not what it actually is.

I suppose Ben quoted PO saying this, because PO /uses/ it to justify that a
particular /halting/ computation will never halt,

He may be doing that now, but he used to use this form of words to
justify why non-halting is the correct result for some halting
computations.  Obviously, to keep people talking he has had to scramble
to get away from what he has said in the past without repudiating it.
No crank likes admit they were ever wrong.

--
Ben.