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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: Sun, 2 Mar 2025 10:53:40 -0600
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On 3/2/2025 10:28 AM, dbush wrote:
> On 3/2/2025 11:02 AM, olcott wrote:
>> On 3/2/2025 9:23 AM, dbush wrote:
>>> On 3/1/2025 11:46 PM, olcott wrote:
>>>> On 3/1/2025 7:27 PM, Richard Damon wrote:
>>>>> On 3/1/25 8:22 PM, olcott wrote:
>>>>>> 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.
>>>>>
>>>>> And "Shown" requires finite.
>>>>>
>>>>> Please show me an infinite proof.
>>>>>
>>>>> Try to do it. That might be your task if Gehenna.
>>>>>
>>>>>>
>>>>>> We could say that it is totally impossible for anyone
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