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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception
Date: Fri, 31 Jan 2025 20:52:49 -0500
Organization: i2pn2 (i2pn.org)
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On 1/31/25 12:42 PM, olcott wrote:
> On 1/31/2025 10:08 AM, Richard Damon wrote:
>> On 1/31/25 10:20 AM, olcott wrote:
>>> On 1/31/2025 8:49 AM, Richard Damon wrote:
>>>> On 1/30/25 8:24 PM, olcott wrote:
>>>>> On 1/30/2025 7:06 PM, Richard Damon wrote:
>>>>>> On 1/30/25 6:10 PM, olcott wrote:
>>>>>>> Within the entire body of analytical truth any expression of 
>>>>>>> language that has no sequence of formalized semantic deductive 
>>>>>>> inference steps from the formalized semantic foundational truths 
>>>>>>> of this system are simply untrue in this system. (Isomorphic to 
>>>>>>> provable from axioms).
>>>>>>>
>>>>>>> In other words when any expression of language of any system 
>>>>>>> (formal or informal) has no semantic connection to its semantic 
>>>>>>> meaning in this system then this expression is simply nonsense in 
>>>>>>> this system. "This sentence is untrue" is Boolean nonsense.
>>>>>>>
>>>>>>> Copyright PL Olcott 2016 through 2025.
>>>>>>>
>>>>>>
>>>>>> Except that isn't what incompleteness says.
>>>>>>
>>>>>> Incompleteness is about the existance of statements which are 
>>>>>> TRUE, because there is a sequence of formal semantic deduction 
>>>>>> that reaches the statement, abet an infinite one, but there is no 
>>>>>> finite sequnce of formal semantic deduction to form a proof.
>>>>>>
>>>>>
>>>>> That might be correct. If it is correct then all then
>>>>> all that it is really saying is that math is incomplete
>>>>> because some key pieces were intentionally left out.
>>>>
>>>> What was left out?
>>>>
>>>
>>> If there exists no contiguous sequence of semantic deductive inference
>>> steps from the basic facts of a system establishing that the semantic 
>>> meaning of this expression has a value of Boolean true in this system 
>>> then this expression is simply not true in this system even if it may be
>>> true in other more expressive systems.
>>>
>>> The system is incomplete in the artificially contrivance way of
>>> deliberately defined system to be insufficiently expressive.
>>>
>>
>> And what about the fact that ther *IS* a contiguos sequence, infinite 
>> in length, that makes the statement true that you don't understand.
>>
> 
> "Incomplete" means that there is no contiguous sequence of inference
> steps within the expressiveness of this specific formal system.
> 

No, "Incomplete" means that there is some true statement that can not be 
proven.

That means that there exist some statement whose only semantic chain of 
inference is infinite, and not finite.

Where do you get your definition from? I suspect it is from the lies of 
your mind.