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

On 2025-02-11 14:05:25 +0000, olcott said:

On 2/11/2025 3:42 AM, Mikko wrote:

On 2025-02-10 13:21:56 +0000, olcott said:
 

On 2/10/2025 6:41 AM, Richard Damon wrote:

On 2/9/25 11:03 PM, olcott wrote:

On 2/9/2025 6:19 PM, Richard Damon wrote:

On 2/9/25 6:20 PM, olcott wrote:

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.
 

  So, what does True(L, x) say for an x defined as !True(L, x)
 All answers are just wrong.
 

 *The simplest way for you to understand this is*
 On 2/8/2025 9:51 AM, Ross Finlayson wrote:
 > then there's a Comenius language of it that only
 > truisms are well-formed formulas...
 In the Comenius language: x := ~True(L,x)
is rejected as an ill-formed-formula.
Ross really did boil down the essence much more succinctly.
 

 So, what is the answer? What answer does True(L, x) return?
 

When x := ~True(L, x) then the Comenius language parser
returns: Syntax Error.

 Which Comenius language parser you tried?
Can you give an example of what that parser does accept?
 

 There is an inheritance hierarchy tree of knowledge
https://en.wikipedia.org/wiki/Ontology_(information_science)
containing all of the basic facts. Each node on this tree
has its own unique GUID. These facts are formalized natural
language using something like Montague Grammar. This provides all
of the unique sense meanings of every natural language term.
 When a finite string expression of language lacks a connection
though a truthmaker to the semantics meanings that make it
true then it is rejected as untrue.
 x := ~True(L, x) is rejected as untrue where L is the
body of human knowledge.

So the best you can do is to respond verbosely hoping that we
don't notice that you can't answer the question. But we notice.
--
Mikko