Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth

On 2/27/25 9:46 AM, olcott wrote:

On 2/27/2025 6:45 AM, Richard Damon wrote:

On 2/26/25 11:24 PM, olcott wrote:

On 2/26/2025 9:59 PM, Richard Damon wrote:

On 2/26/25 8:39 PM, olcott wrote:

On 2/26/2025 10:03 AM, joes wrote:

Am Wed, 26 Feb 2025 08:34:47 -0600 schrieb olcott:

On 2/26/2025 6:18 AM, joes wrote:

Am Tue, 25 Feb 2025 12:40:04 -0600 schrieb olcott:

On 2/25/2025 12:15 PM, joes wrote:

Am Mon, 24 Feb 2025 20:02:49 -0600 schrieb olcott:

On 2/24/2025 6:12 PM, Richard Damon wrote:

On 2/24/25 6:11 PM, olcott wrote:

On 2/24/2025 6:27 AM, Richard Damon wrote:

On 2/23/25 11:39 PM, olcott wrote:

On 2/23/2025 8:50 PM, Richard Damon wrote:

On 2/23/25 1:08 PM, olcott wrote:

>

Sure I do.
A Systems is semantically sound if every statement that can be
proven is actually true by the systems semantics,

That is very good.
>

in other words, the system doesn't allow the proving of a false
statement.

That is not too bad yet ignores that some expressions might not
have any truth value.

Which has nothing to do with "soundness".

When any system assumes that every expression is true or false and
is capable of encoding expressions that are neither IT IS STUPIDLY
WRONG.

In honour of Gödel this is usually called "incomplete".

Where "incomplete" has always been an idiom for stupid wrong.

Your understanding of logic is incomplete.

Which is to say, stupidly wrong.
>

The screwed up notion of "incomplete" is anchored in the stupid idea
that {true in the system} is not required to be {provable in the
system}.

You are about a century behind on the foundations of mathematics.
>

Any expression of language that can only be verified as true on the
basis of other expressions of language either has a semantic connection
truthmaker to these other expressions or IT IS SIMPLY NOT TRUE.

I.e. its negation is true.
>

>
WTF is the truth value of the negation of nonsense?
The Liar Paradox has ALWAYS simply been nonsense.
>

>
But we aren't negating "nonsense", we are negating the actual valid truth value out of the Truth Primative.
>
You don't seem to understand that the DEFINITION of what a truth primative is requires that True(Nonsense) be false, not "nonsense".
>

>
  True("lkekngnkerkn") == false
False("lkekngnkerkn") == false
>

>
But ~True("lkekngnkerkn") == true.
>

 Yes
 

so if we can define that lkekngnkerkn is ~True(lkekngnkerkn) then we have a problem.
f

 We are not defining gibberish as anything.
Gibberish evaluates as ~True because it is gibberish.

But you are trying to define LP := !True(LP) as gibberish.

 

And this is what Tarski proves can be done if the system can represent the properties of the Natural Numbers, and has a True predicate.
>
"False" as a predicate was never mentioned, and is just your strawman you use to divert attention from the problem with your logic.
>

 False is defined as the negation of the expression is true.
This is how Wittgenstein and I  have always defined this.
Wittgenstein understood these things.

Note, True isn't a "value" it is the predicate.

 X = "lkekngnkerkn"
There is no truth-maker for X or for ~X proving
that X is not a truth-bearer.

But there is a truth-maker for LP defined as ~True(LP), that truth maker is the Truth predicate itself.

 

You are just tooo stupid to understand that you are just a pathological liar.

 Your lack of knowledge of the philosophical foundations
of truth is not even your own stupidity it is your ignorance.

Your lack of understanding of formal logic shows your stupidity.
Tarski is NOT talking in some abstract phiosophical theory, but working inside a precise Formal Thoery where things are solidly defined.

 Truth itself works a certain way. Logic tries to get
away with overriding the way that truth really works.
 

It eeems you don't really know what "truth" is, since you blow it up so often with your lies.
Note the predicate "True" isn't just a statement asking if its parameter is true or not, it is a formal logic predicate, that is DEFINED to always have a truth value. Your failure to understand that just shows your utter stupidity.
Note, your "idol" Wittgenstein was a hold out who tried to deny that some of the foundation that were imagined just were not true. Your emulation of him, just says you have failed to learn from the last century of developments.
So, it seems you have decided to stay on the Titanic, and keep on asking "What Iceberg?" as the ship is sinking.
Sorry, you are just proving your stupidity.