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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sat, 1 Mar 2025 14:20:17 -0600
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On 3/1/2025 3:01 AM, Mikko wrote:
> On 2025-02-28 23:47:11 +0000, olcott said:
> 
>> On 2/28/2025 4:59 AM, Mikko wrote:
>>> On 2025-02-26 05:02:13 +0000, olcott said:
>>>
>>>> On 2/25/2025 10:21 PM, Richard Damon wrote:
>>>>> On 2/25/25 4:10 PM, olcott wrote:
>>>>>> On 2/25/2025 9:35 AM, Mikko wrote:
>>>>>>> On 2025-02-24 21:44:10 +0000, olcott said:
>>>>>>>
>>>>>>>> On 2/24/2025 2:58 AM, Mikko wrote:
>>>>>>>>> On 2025-02-22 18:42:44 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 2/22/2025 3:25 AM, Mikko wrote:
>>>>>>>>>>> On 2025-02-22 04:44:35 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> On 2/21/2025 7:05 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 2/21/25 6:19 PM, olcott wrote:
>>>>>>>>>>>>>> On 2/20/2025 2:54 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 2025-02-18 03:59:08 +0000, olcott said:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>>>> Tarski anchored his whole proof in the Liar Paradox.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> By showing that given the necessary prerequisites, The 
>>>>>>>>>>>>> equivalent of the Liar Paradox was a statement that the 
>>>>>>>>>>>>> Truth Predicate had to be able to handle, which it can't.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> It can be easily handled as ~True(LP) & ~True(~LP), Tarski just
>>>>>>>>>>>> didn't think it through.
>>>>>>>>>>>
>>>>>>>>>>> No, it can't. Tarski requires that True be a predicate, i.e, 
>>>>>>>>>>> a truth
>>>>>>>>>>> valued function of one term.
>>>>>>>>>>
>>>>>>>>>> It does not matter a whit what the Hell his misconceptions
>>>>>>>>>> required.
>>>>>>>>>
>>>>>>>>> It is not required by any misconception. It is required by the
>>>>>>>>> meanings of the words and symbols, in particular "predicare"
>>>>>>>>> and "~".
>>>>>>>>
>>>>>>>> That none of modern logic can handle expressions
>>>>>>>> that are not truth bearers is their error and
>>>>>>>> short-coming.
>>>>>>>
>>>>>>> Why should any logic permit formulas that are not truth-bearers?
>>>>>>> (Of course, term expressions are not truth-bearers.)
>>>>>>>
>>>>>>
>>>>>> Undecidable expressions are only undecidable because they
>>>>>> are not truth bearers. Logic ignores this and faults the
>>>>>> system and not the expression
>>>>>>
>>>>>
>>>>> Nope. And "expressions" are not "undecidable", but "Problems" are.
>>>>>
>>>>
>>>> A specific problem instance is a single finite string expression input
>>>> to a specific decider.
>>>
>>> No, it is not. The decider is no way a part of a specific problem
>>> instance unless it is a part of that finite string expression.
>>
>> Is the term decider/input pair over your head?
> 
> No, only an idiot could think so.
> 
>> A unique finite string of integers combined
>> with a specific decider is a SPECIFIC PROBLEM INSTANCE.
> 
> No, it is not. It is a computation.
> 
>> A decider is itself a unique finite string of integer
>> values for any 100% specific system of Turing Machine
>> descriptions.
> 
> No, it is not. A decider is a Turing (or similar) machine that for
> every valid input either accepts or rejects. It can be encoded as
> a unique finite string of integer values but usually other ways of
> presentation are better.
> 
>>> That a specific problem instance is a single finite string expression
>>> is true about formal problems but usually not about practical problems.
>>
>> Like how to get your wife to quit yelling at you?
> 
> Yes, for example.
> 

The halting problem is one arbitrary machine applied to
all possible inputs.

A halting problem instance is one specific machine applied
to one unique finite string.

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