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

On 2/9/2025 5:05 PM, Richard Damon wrote:

On 2/9/25 5:30 PM, olcott wrote:

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

 And if True(L, x) isn't "well formed" then True fails to meet the requirements of a predicate,

Not at all. True(L,x) is no longer baffled by semantically
incorrect expressions and rejects them as IFF ill-formed-formula.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer