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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How do simulating termination analyzers work? ---Truth Maker
 Maximalism
Date: Mon, 30 Jun 2025 12:49:20 -0500
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On 6/30/2025 3:14 AM, Mikko wrote:
> On 2025-06-29 14:04:43 +0000, olcott said:
> 
>> On 6/29/2025 3:42 AM, Mikko wrote:
>>> On 2025-06-28 13:28:04 +0000, olcott said:
>>>
>>>> On 6/28/2025 6:47 AM, Mikko wrote:
>>>>> On 2025-06-27 23:35:46 +0000, olcott said:
>>>>>
>>>>>> On 6/26/2025 4:30 AM, Mikko wrote:
>>>>>>> On 2025-06-25 14:33:52 +0000, olcott said:
>>>>>>>
>>>>>>>> On 6/25/2025 1:50 AM, Mikko wrote:
>>>>>>>>> On 2025-06-24 15:00:30 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> A proof is any set of expressions of language that
>>>>>>>>>> correctly concludes that another expression of
>>>>>>>>>> language is definitely true.
>>>>>>>>>
>>>>>>>>> A singlet set of expressions that just states a correct conclusion
>>>>>>>>> satisfy the above definition but does not prove anything. A proof
>>>>>>>>> is something that gives a sufficient reson to believe what 
>>>>>>>>> otherwise
>>>>>>>>> might not be believed.
>>>>>>>>
>>>>>>>> Correct proofs can also depend on the meaning of natural
>>>>>>>> language words.
>>>>>>>
>>>>>>> Yes, and avoid ambiguous expressions or disambiguate them when 
>>>>>>> needed.
>>>>>>>
>>>>>>>> It is typical that formal proofs make sure
>>>>>>>> to totally ignore every aspect of this.
>>>>>>>
>>>>>>> That is the main advantage of formal proofs. But an application
>>>>>>> of a formal proof usually requires natural language to express
>>>>>>> the interpretation.
>>>>>>>
>>>>>>>> An expression of language is proven true when a set of
>>>>>>>> semantic meanings makes it true.
>>>>>>>
>>>>>>> Often it is sufficiently proven if it is observed to be true
>>>>>>> though that of course depends on the qualyty of the obserfation
>>>>>>> and of the quality of the report of the observation.
>>>>>>>
>>>>>>>> To really understand this requires deep understanding of
>>>>>>>> the philosophy of truth, rather than rote memorization
>>>>>>>> of some conventional steps.
>>>>>>>
>>>>>>> Deep understanding is rarely useful. Often it is sufficient to
>>>>>>> understand that what is presented as a proof isn't a proof.
>>>>>>>
>>>>>>>> Two elements that require very deep understanding are
>>>>>>>> (a) truth-makers and (b) truth-bearers.
>>>>>>>> Truthmaker Maximalism says that when there is nothing
>>>>>>>> that makes an expression of language true then this
>>>>>>>> expression is not true.
>>>>>>>
>>>>>>> That is not a useful result as the non-existence is usually
>>>>>>> unobservable and unverifiable.
>>>>>>
>>>>>> Analytical truth has nothing to do with observation
>>>>>> and has everything to do we semantic connections
>>>>>> between expressions of language.
>>>>>
>>>>> Your claims above were about truth in general with no restriction
>>>>> to analytical truths. But if you don't know that a sentence has
>>>>> no truth maker it may be hard to find out.
>>>>>
>>>>>> All of math, computer science and logic is analytic truth.
>>>>>> We don't observe that 5 > 3, it is defined that way.
>>>>>
>>>>> And that includes the non-existence of halt deciders.
>>>>
>>>> *This is only based on false assumptions*
>>>> (a) An *input* can be defined that does the opposite
>>>> of whatever its decider reports. // proven false
>>>
>>> Not an assumption but proven true from definitions.
>>
>> No one ever noticed that it is never an actual
>> *input* that does this.
> 
> That "input" is an input to the halting problem. The input to the
> decider candidate is a representation of input to the halting
> problem. To "do the opposite" refers to what happens if the
> "input" computation is executed. Whether it is actually executed
> is irrelevant.
> 

Yet no directly executed Turing Machine DDD() can be an input
to another Turing Machine HHH making this DDD() outside of the
domain of HHH thus its behavior is irrelevant to the correctness
of HHH(DDD).

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer