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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: Thu, 27 Feb 2025 22:02:00 -0600
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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.

It has an infinite cycle in the directed graph of its
evaluation sequence.

See Page 3 for Prolog
https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence 


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