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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 17:15:20 +0200
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On 2025-03-02 01:22:12 +0000, olcott said:

> On 3/1/2025 3:58 PM, Richard Damon wrote:
>> On 2/28/25 6:57 PM, olcott wrote:
>>> On 2/28/2025 8:30 AM, Richard Damon wrote:
>>>> 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.
>>>> 
>>>> Of course, since your mind can't handle them either, you can't understand that.
>>> 
>>> Carefully study the Clocksin and Mellish on page 3 knucklehead.
>>> Read and reread the yellow highlighted text until you totally get it.
>>> 
>> 
>> Right, Neither G nor ~G are provable in F.
>> 
> 
> Provable(common)
> {shown to be definitely true by whatever means}
> is the only relevant notion of provable.

The Common Language term for that is not "provable" but "proven".

-- 
Mikko