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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Wed, 26 Feb 2025 07:33:09 -0500
Organization: i2pn2 (i2pn.org)
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On 2/26/25 12:02 AM, olcott wrote:
> 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.

And there is not an issue with getting the answer to that particular 
problem. Note, it isn't the decider that defines the value of the 
expression, it is the problem statement that the instance is from.

For instance, for a Halt Decider, the question is does the program the 
input represent Halt when it is run, and that ALWAYS has an answer, so 
that instance is "decidable". We may not know the answer, but it has 
one, and since non-halting can't always be finitely determinable, we 
find we can't compute the answer.

For instance, the halting of DD is NOT "undecidable", as HHH1 was able 
to simulate it to the end, showing it halts. The HHH you have provided 
just has a "bug" in it that misunderstands the nature of HHH.

You are just showing that you fundamentally are ignorant of important 
aspects of the field, and too stupid to see that error.

> 
>> You seem to have a fundamental problem with the meaning of the words, 
>> likely because you can't handle the needed abstractions.
>>
>> Of course, since you don't understand what a "program" is, you never 
>> were on a good track.
> 
>