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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 19:17:08 -0600
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On 3/1/2025 3:58 PM, Richard Damon wrote:
> On 3/1/25 2:58 PM, olcott wrote:
>> On 3/1/2025 2:45 AM, Mikko wrote:
>>> On 2025-02-28 22:04:31 +0000, olcott said:
>>>
>>>> On 2/28/2025 4:04 AM, Mikko wrote:
>>>>> On 2025-02-26 01:33:48 +0000, olcott said:
>>>>>
>>>>>> On 2/25/2025 5:58 PM, Richard Damon wrote:
>>>>>>> On 2/25/25 1:40 PM, olcott wrote:
>>>>>>>> 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:
>>>>>>>>>>>>>>>> On 2/22/2025 9:56 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 2/22/25 1:42 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 2/22/2025 3:25 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>> On 2025-02-22 04:44:35 +0000, olcott said:
>>>>>>>>>>>>>>>>>>>> On 2/21/2025 7:05 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 2/21/25 6:19 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 2/20/2025 2:54 AM, Mikko wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 2025-02-18 03:59:08 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>>>>> 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.
>>>>>>>>
>>>>>>>
>>>>>>> No, only in your faulty logic.
>>>>>>>
>>>>>>> Incomplete means that there are some truths that can't be proven 
>>>>>>> in the system.
>>>>>>>
>>>>>>
>>>>>> That comes from stupidly failing to require {true in the system}
>>>>>> to require {proven in the system}. Fix this one stupid mistake
>>>>>> and all of incompleteness goes away.
>>>>>
>>>>> No, that merely means that "true in the system" is incomplete in some
>>>>> systems (e.g., natural numbers). There are sentences that are true in
>>>>> practical applications of the system but not in the system itself.
>>>>> That is not a defect as it does not prevent useful practical 
>>>>> aplications.
>>>>
>>>> The bottom line here is that expressions that do not have
>>>> a truth-maker are always untrue. Logic screws this up by
>>>> overriding the common meaning of terms with incompatible
>>>> meanings. Provable(common) means has a truth-maker.
>>>
>>> Logic doesn't care about truths and truth makers except in the (usually
>>> uninteresting) special cases where truth makers are found in the logic
>>> itself.
>>>
>>
>> Incompleteness(math) and Undecidability(logic) are
>> artifacts of defining the term provable(math)
>> in a way that is inconsistent with provable(common)
>> {shown to be definitely true by whatever means}.
>>
> 
> Nopw, because shown(common) requires a finite sequence to show to 
> someone, as people can not see all of an infinite sequence
> 

If the Goldbach conjecture is true and there is only
an infinite sequence as its truth-maker then this
infinite sequence <is> its proof(common)
{shown to be definitely true by whatever means}.

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