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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 17:22:24 +0200
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On 2025-03-01 20:17:04 +0000, olcott said:

> On 3/1/2025 2:52 AM, Mikko wrote:
>> On 2025-02-28 14:30:44 +0000, Richard Damon said:
>> 
>>> On 2/27/25 11:02 PM, olcott wrote:
>>>> On 2/27/2025 7:00 PM, Richard Damon wrote:
>>>>> On 2/27/25 9:46 AM, olcott wrote:
>>>>>> On 2/27/2025 6:45 AM, Richard Damon wrote:
>>>>>>> On 2/26/25 11:24 PM, olcott wrote:
>>>>>>>> On 2/26/2025 9:59 PM, Richard Damon wrote:
>>>>>>>>> On 2/26/25 8:39 PM, olcott wrote:
>>>>>>>>>> On 2/26/2025 10:03 AM, joes wrote:
>>>>>>>>>>> Am Wed, 26 Feb 2025 08:34:47 -0600 schrieb olcott:
>>>>>>>>>>>> On 2/26/2025 6:18 AM, joes wrote:
>>>>>>>>>>>>> Am Tue, 25 Feb 2025 12:40:04 -0600 schrieb olcott:
>>>>>>>>>>>>>> On 2/25/2025 12:15 PM, joes wrote:
>>>>>>>>>>>>>>> Am Mon, 24 Feb 2025 20:02:49 -0600 schrieb olcott:
>>>>>>>>>>>>>>>> On 2/24/2025 6:12 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 2/24/25 6:11 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 2/24/2025 6:27 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 2/23/25 11:39 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 2/23/2025 8:50 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/23/25 1:08 PM, olcott wrote:
>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>> Sure I do.
>>>>>>>>>>>>>>>>>>> A Systems is semantically sound if every statement that can be
>>>>>>>>>>>>>>>>>>> proven is actually true by the systems semantics,
>>>>>>>>>>>>>>>>>> That is very good.
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>> in other words, the system doesn't allow the proving of a false
>>>>>>>>>>>>>>>>>>> statement.
>>>>>>>>>>>>>>>>>> That is not too bad yet ignores that some expressions might not
>>>>>>>>>>>>>>>>>> have any truth value.
>>>>>>>>>>>>>>>>> Which has nothing to do with "soundness".
>>>>>>>>>>>>>>>> When any system assumes that every expression is true or false and
>>>>>>>>>>>>>>>> is capable of encoding expressions that are neither IT IS STUPIDLY
>>>>>>>>>>>>>>>> WRONG.
>>>>>>>>>>>>>>> In honour of Gödel this is usually called "incomplete".
>>>>>>>>>>>>>> Where "incomplete" has always been an idiom for stupid wrong.
>>>>>>>>>>>>> Your understanding of logic is incomplete.
>>>>>>>>>>> Which is to say, stupidly wrong.
>>>>>>>>>>> 
>>>>>>>>>>>> The screwed up notion of "incomplete" is anchored in the stupid idea
>>>>>>>>>>>> that {true in the system} is not required to be {provable in the
>>>>>>>>>>>> system}.
>>>>>>>>>>> You are about a century behind on the foundations of mathematics.
>>>>>>>>>>> 
>>>>>>>>>>>> Any expression of language that can only be verified as true on the
>>>>>>>>>>>> basis of other expressions of language either has a semantic connection
>>>>>>>>>>>> truthmaker to these other expressions or IT IS SIMPLY NOT TRUE.
>>>>>>>>>>> I.e. its negation is true.
>>>>>>>>>>> 
>>>>>>>>>> 
>>>>>>>>>> WTF is the truth value of the negation of nonsense?
>>>>>>>>>> The Liar Paradox has ALWAYS simply been nonsense.
>>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> But we aren't negating "nonsense", we are negating the actual valid 
>>>>>>>>> truth value out of the Truth Primative.
>>>>>>>>> 
>>>>>>>>> You don't seem to understand that the DEFINITION of what a truth 
>>>>>>>>> primative is requires that True(Nonsense) be false, not "nonsense".
>>>>>>>>> 
>>>>>>>> 
>>>>>>>>   True("lkekngnkerkn") == false
>>>>>>>> False("lkekngnkerkn") == false
>>>>>>>> 
>>>>>>> 
>>>>>>> But ~True("lkekngnkerkn") == true.
>>>>>>> 
>>>>>> 
>>>>>> Yes
>>>>>> 
>>>>>>> so if we can define that lkekngnkerkn is ~True(lkekngnkerkn) then we 
>>>>>>> have a problem.
>>>>>>> f
>>>>>> 
>>>>>> We are not defining gibberish as anything.
>>>>>> Gibberish evaluates as ~True because it is gibberish.
>>>>> 
>>>>> But you are trying to define LP := !True(LP) as gibberish.
>>>>> 
>>>> 
>>>> Prolog already knows that it <is> gibberish.
>>> 
>>> Because, like you, Prolog can't handle the needed logic.
>>> 
>>>> 
>>>> It has an infinite cycle in the directed graph of its
>>>> evaluation sequence.
>>> 
>>> But infinite cycles are not prohibited in logic systems that support 
>>> the properties of the Natural Numbers. The MUST allow them or you can't 
>>> HAVE the Natural Numbers.
>>> 
>>>> 
>>>> See Page 3 for Prolog
>>>> https://www.researchgate.net/ 
>>>> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence 
>>>> 
>>>> 
>>> 
>>> Just shows your stupidity, thinking that all logic is just primitive, 
>>> and not understanding what the Godel sentence actually is. Your mind 
>>> seems to have blocked out the actual sentence presented earlier because 
>>> you know you don't understand it, so you think it must be gibberisn, 
>>> but it is you mind that is gibberish.
>>> 
>>> You didn't give it the ACTUAL Godel sentence, just the simplified 
>>> interpretation of it. The problem is that the actual Godel sentence 
>>> can't be expressed in Prolog, as it uses 2nd order logic operations, 
>>> which Prolog doesn't handle.
>> 
>> There is a (long) sentence of first order logic that can be used as a Gödel
>> sentence in a first order proof that the first oder Peano arithmetic is
>> incomplete. Prolog can handle that sentence (e.g., as a list of characters)
>> if the implementation has sufficiently memory.
> 
> When unprovable always mean untrue then incompleteness
> cannot possibly exist.

True as "unprovable" never always means 'untrue'. What is true is not
untrue even when unprovable.

Nevertheless, the connection to incompleteness is not there.
Incompleteness exists because it is possible to construct an incomplete
theory.

-- 
Mikko