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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Fri, 6 Jun 2025 11:57:14 +0300
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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