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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,sci.math
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Tarski
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Date: Sun, 9 Feb 2025 16:30:34 -0600
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On 2/9/2025 11:04 AM, Richard Damon wrote:
> On 2/9/25 9:31 AM, olcott wrote:
>> On 2/9/2025 1:18 AM, Julio Di Egidio wrote:
>>> On 08/02/2025 16:51, Ross Finlayson wrote:
>>>> On 02/08/2025 07:32 AM, olcott wrote:
>>>
>>>>> (2) Semantics is fully integrated into every expression of
>>>>> language with each unique natural language sense meaning
>>>>> of a word having its own GUID.
>>>
>>> Illusion and the tyranny of delusion, ad nauseam.
>>>
>>>>> And I am finishing the job. I may have only one month left.
>>>>> The cancer treatment that I will have next month has a 5% chance
>>>>> of killing me and a 1% chance of ruining my brain. It also has
>>>>> about a 70% chance of giving me at least two more years of life.
>>>
>>> Food be your medicine, medicine be your food.  Conversely,
>>> good luck with any of that.
>>>
>>>> Instead of just usual model theory and axiomatics
>>>> and "what's true in the logical theory", "what's
>>>> not falsified in the scientific theory", you can
>>>> have a theory where the quantity is truth, and
>>>> then there's a Comenius language of it that only
>>>> truisms are well-formed formulas, then the Liar
>>>> "paradox" is only a prototype of a fallacy,
>>>
>>> Rather, then there is no such thing as a "fallacy", only
>>> flat positivism and Newspeak.  Indeed, Popper already is
>>> yet another bad joke at best, but WTF would you know...
>>>
>>
>> In other words you did not understand what he said thus
>> replied to his words with nonsense gibberish pure rhetoric
>> with no actual basis in reasoning.
>>
>>  >> there's a Comenius language of it that only
>>  >> truisms are well-formed formulas
>>
>> True(L,x) <is> a mathematical mapping from finite string
>> expressions of language through a truthmaker to finite
>> strings expressions providing formalized semantic meanings
>> making the expression true.
>>
>> The prototype of a fallacy that he referred to is the
>> recursive structure of pathological self-reference that
>> never resolves to a truth value.
> 
> And, such a mapping can't exist if the language allows references like:
> 
> x is defined to be !True(L, x)
> 

When we frame it the succinct way that Ross framed it
 >> there's a Comenius language of it that only
 >> truisms are well-formed formulas

Then the above expression is simply rejected as not
a WFF of this Comenius language.

> As such a statement can't be mapped to True or False without also 
> mapping True to False or False to True.
> 
> Note, he shows that such a statement CAN be formed in logic system with 
> certain minimal properties, like being able to express the Natural 
> Numbers and their properties.
> 
> So, I guess you are admitting that to you "logic" can't handle something 
> like mathematics.
> 

The Comenius language expresses the key essence of the most
important aspect of my idea, rejecting expressions that do
not evaluate to Boolean as ill-formed. It only has TRUE
and ill-formed. My system has TRUE, FALSE and ill-formed.

All undecidable propositions fall into the ill-formed category
and logic is otherwise essentially unchanged.

>>
>>> We live in a yellow submarine, just yellower and yellower.
>>>
>>> -Julio
>>>
>>
>>
> 


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