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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: Fri, 28 Feb 2025 16:04:31 -0600
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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.



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