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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention
Date: Sat, 20 Jul 2024 11:42:16 +0300
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On 2024-07-19 13:48:49 +0000, olcott said:

> On 7/19/2024 2:30 AM, Mikko wrote:
>> On 2024-07-18 13:36:53 +0000, olcott said:
>> 
>>> On 7/18/2024 2:55 AM, Mikko wrote:
>>>> On 2024-07-17 13:14:43 +0000, olcott said:
>>>> 
>>>>> On 7/17/2024 2:08 AM, Mikko wrote:
>>>>>> On 2024-07-16 14:46:40 +0000, olcott said:
>>>>>> 
>>>>>>> On 7/16/2024 2:18 AM, Mikko wrote:
>>>>>>>> On 2024-07-15 13:32:27 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> On 7/15/2024 2:57 AM, Mikko wrote:
>>>>>>>>>> On 2024-07-14 14:48:05 +0000, olcott said:
>>>>>>>>>> 
>>>>>>>>>>> On 7/14/2024 3:49 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-07-13 12:18:27 +0000, olcott said:
>>>>>>>>>>> 
>>>>>>>>>>> When the source of your disagreement is your own ignorance
>>>>>>>>>>> then your disagreement has no actual basis.
>>>>>>>>>>> 
>>>>>>>>>>> *You can comprehend this is a truism or fail to*
>>>>>>>>>>> *comprehend it disagreement is necessarily incorrect*
>>>>>>>>>>> Any input that must be aborted to prevent the non
>>>>>>>>>>> termination of HHH necessarily specifies non-halting
>>>>>>>>>>> behavior or it would never need to be aborted.
>>>>>>>>>>> 
>>>>>>>>>>> Disagreeing with the above is analogous to disagreeing
>>>>>>>>>>> with arithmetic.
>>>>>>>>>> 
>>>>>>>>>> A lame analogy. A better one is: 2 + 3 = 5 is a proven theorem just
>>>>>>>>>> like the uncomputability of halting is.
>>>>>>>>> 
>>>>>>>>> The uncomputability of halting is only proven when the problem
>>>>>>>>> is framed this way: HHH is required to report on the behavior
>>>>>>>>> of an input that was defined to do exactly the opposite of
>>>>>>>>> whatever DDD reports.
>>>>>>>> 
>>>>>>>> No, it is proven about the halting problem as that problem is.
>>>>>>> 
>>>>>>> Which is simply a logical impossibility
>>>>>> 
>>>>>> Yes, a halting decider is a logical impossibility, as can be and has
>>>>>> been proven.
>>>>> 
>>>>> If it is a logical impossibility then it places no
>>>>> actual limit on computation otherwise we would have
>>>>> "the CAD problem" of the logical impossibility of making
>>>>> a CAD system that correctly draws a square circle.
>>>> 
>>>> A logical impossibility does place a limit on computation.
>>>> Otherwise it would be possible to build a CAD system that
>>>> can correctly draw a square circle.
>>> 
>>> Of the set of possible things TM's can do them all.
>> 
>> Depends on the meanings of "possible" and "thing". Of things other than
>> computation no TM can do any. A Turing machine can determine whether
>> a sentence of Presburger arithmetic is provable but no Turing machine
>> can determine whether a sentence of Peano arithmetic is provable.
> 
> Some undecidable expressions are only undecidable because
> they are self contradictory. In other words they are undecidable
> because there is something wrong with them.

Being self-contradictory is a semantic property. Being uncdecidable is
independent of any semantics. An arithmetic sentence is always about
numbers, not about sentences. A proof is about sentences, not about
numbers.

> The Liar Paradox: "This sentence is not true"

cannot be said in the language of Peano arithmetic.

-- 
Mikko