Re: Simulation vs. Execution in the Halting Problem

On 2025-06-04 15:59:10 +0000, olcott said:

On 6/4/2025 2:19 AM, Mikko wrote:

On 2025-06-03 20:00:51 +0000, olcott said:
 

On 6/3/2025 12:59 PM, wij wrote:

On Tue, 2025-06-03 at 16:38 +0100, Mike Terry wrote:

On 03/06/2025 13:45, dbush wrote:

On 6/2/2025 10:58 PM, Mike Terry wrote:

Even if presented with /direct observations/ contradicting his position, PO can (will) just
invent
new magical thinking that only he is smart enough to understand, in order to somehow justify his
busted intuitions.

 My favorite is that the directly executed D(D) doesn't halt even though it looks like it does:
  On 1/24/24 19:18, olcott wrote:
 > The directly executed D(D) reaches a final state and exits normally.
 > BECAUSE ANOTHER ASPECT OF THE SAME COMPUTATION HAS BEEN ABORTED,
 > Thus meeting the correct non-halting criteria if any step of
 > a computation must be aborted to prevent its infinite execution
 > then this computation DOES NOT HALT (even if it looks like it does).

 Right - magical thinking.
 PO simply cannot clearly think through what's going on, due to the multiple levels involved.  In his
head they all become a mush of confustions, but the mystery here is why PO does not /realise/ that
he can't think his way through it?
 When I try something that's beyond me, I soon realise I'm not up to it.  Somehow PO tries, gets into
a total muddle, and concludes "My understanding of this goes beyond that of everybody else, due to
my powers of unrivalved concentration equalled by almost nobody on the planet, and my ability to
eliminate extraneous complexity".  How did PO ever start down this path of delusions?  Not that that
matters one iota... :)
  Mike.

 People seem to keep addressing the logic of the implement of POOH, but it does not matter how
H or D are implemented, because:
 1. POOH is not about the Halting Problem (no logical connection)

 Likewise ZFC was not about what is now called naive set theory.

 To a large extent it is. Both are intended to describe those sets that
were tought to be usefult to think about. But the naive set theory failed
because it is inconsistent. However, ZF excludes some sets that some
people want to consider, e.g., the universal set, Quine's atom. There is
no agreement whether do not satisfy the axiom of choice and its various
consequences should be included or excluded, so both ZF and ZFC are used.

 Quine's atom is nonsense.

No, it is not. It is a set that one can assume to exist or not to exist.

The set of all non-empty sets of non-set elements seems possible.

Some theories may allow that and some may prohibit. For example, in ZFC
there are no non-set elements.
--
Mikko