Re: Mathematical incompleteness has always been a misconception --- Tarski

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:

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(2) Semantics is fully integrated into every expression of
language with each unique natural language sense meaning
of a word having its own GUID.

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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.

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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,

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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...
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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.
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 >> there's a Comenius language of it that only
 >> truisms are well-formed formulas
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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.
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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.

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We live in a yellow submarine, just yellower and yellower.
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-Julio
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--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer