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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 19:28:51 -0600
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On 3/1/2025 3:58 PM, Richard Damon wrote:
> On 3/1/25 3:17 PM, olcott wrote:
>> 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.
>>
>>
> 
> Except that isn't the case, but just your own unprovable and untrue 
> assuption.
> 

Any expression having no truth-maker is untrue.
Provable(common) means has a truth-maker.

Math simply painted itself in a corner with its own Newspeak.

Newspeak, which is a controlled language of simplified
grammar and limited vocabulary designed to limit a person's
ability for critical thinking.
https://en.wikipedia.org/wiki/Newspeak

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