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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How do simulating termination analyzers work? ---Truth Maker
 Maximalism
Date: Sun, 29 Jun 2025 09:04:43 -0500
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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.

>> (b) Turing machines can take directly executing Turing
>> machines as *inputs* // false by definition
> 
> Not assumend and not relevant to halting problem.
> 

Only directly executing Turing Machines *not inputs*
can do the opposite of whatever the decider decides.

When HHH(DDD) returns 0 then when called by a directly
executed DDD() this DDD() does the opposite.

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

When Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ rejects its input and transitions
to Ĥ.qn then the directly executed Ĥ ⟨Ĥ⟩ does the opposite.

It is never the case that any input to a TM does the
opposite of whatever its decider decides.

>> A Turing machine partial halt decider computes the
>> mapping from a finite string input to the behavior
>> that this finite string actually specifies.
>>
>> A Turing machine partial halt decider never computes the
>> mapping from the direct execution of any other Turing
>> machine because direct executions are not finite string
>> inputs.
> 
> A partial halt decider is permitted to compute nothing for some
> inputs but if it does compute and answer the answer must agree
> with the direct execution (if there is a direct execution to
> compare).
> 

No Turing Machine can possibly compute the mapping
from anything besides its actual finite string inputs.
Expecting otherwise it like expecting your pickup
truck to bake you a cake.

>>>>> None of which affects the truth that
>>>>>
>>>>>>> A set of expressions is not sufficiently organized to count as a
>>>>>>> proof. The conclusion of the proor is its last sentence and in a
>>>>>>> set there is no last one.
> 


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