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From: dbush <dbush.mobile@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Sun, 2 Mar 2025 12:00:50 -0500
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On 3/2/2025 11:53 AM, olcott wrote:
> 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
>>>>>>> to touch their own head by adding the requirement
>>>>>>> that they must touch their own head without ever
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