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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception
 [CORRECTION]
Date: Mon, 3 Feb 2025 14:41:19 -0600
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On 2/1/2025 12:23 PM, Richard Damon wrote:
> On 2/1/25 1:10 PM, olcott wrote:
>> On 2/1/2025 7:56 AM, Richard Damon wrote:
>>> On 1/31/25 10:43 PM, olcott wrote:
>>>> On 1/31/2025 7:52 PM, Richard Damon wrote:
>>>>> 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.
>>>>>
>>>>
>>>> Within empirical truth this is possible.
>>>> Within analytical truth this is impossible.
>>>
>>> No, you only think it is impossible, becuase you don't know what you 
>>> are talking about.
>>>
>>>>
>>>> Unless there is a semantic connection with
>>>> a truthmaker to what makes the expression
>>>> true IS IS NOT TRUE.
>>>
>>> Right, and that can be an INFINITE series of connection, which thus 
>>> don't form a proof.
>>>
>>
>> It does make a {proof} within the foundational base meaning
>> of the term {proof} even though it may not meet the idiomatic
>> term-of-the-art meaning from math. The generic notion of {Truth}
>> itself is only defined in terms of base meanings. When math
>> diverges from this it is no longer talking about actual truth.
>>
>>
> 
> The "foundational base meaning" of a proof in Formal Logic is a FINITE 
> series.
> 

True[0] cannot possibly exist for any expression of language that
is only made true by a semantic connection to its truthmaker
WITHOUT SUCH A CONNECTION.

This makes the notion of provable[math] essentially a misnomer
because it attempts to override and supersede the most basic
foundation of the notion of truth itself.

> I know of no standard theory of logic that admits an infinite series of 
> steps as a "proof", as we can not do an infinite series of steps, and a 
> proof is normally about knowledge, and thus needs to be about something 
> that we can actually do.
> 
> We can do a finite series of steps to show that an infinite series of 
> steps exist in another system by the properties of meta-logic, but that 
> is not a "proof" in that other system, only in the meta-system, again 
> something that seems to be beyond your understanding.
> 
> And, you are wrong that "truth" only has a single base meaning, as Truth 
> is established by several different meanings each given a different 
> "class" of Truth.
> 
> I'm sorry, but you are just showing that you don't really understand the 
> terms you are using, and tha that you don't even have enough of a basis 
> to understand that you don't understand the terms.
> 
> You HAVE been shown this, and your repeatedly repeating the same proven 
> false claims just shows that you are totally ignorant of what you talk 
> about, and have no concern about the actual meaning of Truth. This shows 
> that you native tounge is that of your "father", the tounge of lies, 
> which you try your best to sprea.
> 
> Sorry that you are sealing your fate, which you are likely going to see 
> sooner than you want.


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer