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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception
Date: Wed, 5 Feb 2025 10:05:16 -0600
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On 2/5/2025 6:08 AM, Richard Damon wrote:
> On 2/4/25 11:30 PM, olcott wrote:
>> On 2/3/2025 6:39 PM, Richard Damon wrote:
>>> On 2/3/25 12:00 PM, olcott wrote:
>>>> 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.
>>>
>>> Which can be a connection of infinite length.
>>>
>>>>
>>>> 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.
>>>
>>> But provable is a statment about the existance of a FINITE sequence 
>>> of connection
>>>
>>
>> That IS NOT what Proof[0] means.
>> Proof[0] means that a connection to a truth-maker exists.
>>
> 
> Show me an actual formal system defined that allows "Proof" to be an 
> infinite connection to the truth-maker. All you are doing ios proving 
> that you are just making up everything you say,
> 

Math is not allowed to change the base meaning of terms.
When-so-ever any expression of formal or natural language X lacks
a connection to its truthmaker X remains untrue.

> I think part of the problem is you just don't understand what a Formal 
> System is, and since Incompleteness is a property of Formal System (not 
> just general philosophy) that is an important part.
> 
> Of course, your big part for not understanding Formal Systens is you 
> don't believe you need to follow the rules, and that is fundamental to 
> Formal Logic, so its concepts are just foreign to you.
> 
> Sorry, you are just proving your total ignorance of what you talk about, 
> and so ignorant that you can't see your ignorance.


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