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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth
Date: Mon, 3 Mar 2025 17:25:02 +0200
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On 2025-03-01 20:20:17 +0000, olcott said:

> 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.

No, it is not.

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

That is not a "halting problem instance" but a "computation".

-- 
Mikko