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

On 2/26/25 9:34 AM, olcott wrote:

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.
>

 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}.
 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.
 When math creates the idiomatic meaning of "provable" that
diverges from its common meaning math diverges from what
actual true really is.
 

No, what is "screwed up" is the idea that something can't be true until we know it, which is a consequence of your attempted definition, as has can we know if something is provable unless we have the proof, at which point we have the knowledge.
Maths definition does not diverge from the "common" meaning, as we can show something that needs an infinite number of steps.
Your problem is you just don't have an understanding of what that means, because the only logic you seem to understand is inherently finite, and thus doesn't get to that level.
Simple question for you to think on.
If you have a statement about a property of a computation done on EVERY natural number, and it turns out that it will actually work for every natural number, but we have no method to actually PROVE that fact with a finite proof, is that statement true or not?
We can not prove it, as we haven't found a method to generalize the computation to show it works for every number, no inductive proof, or anything like that.
So, does the lack of a proof, and even the fact that it can not be prove, make the statement non-true? (It can't be false, since that would require proving its opposite, but since the initial premise was that it works for every number, there is not instance that shows it to be false).
If we just thought it couldn't be proven, but someone finally figures out some method to prove it, does that mean its truth value CHANGED?
Do you see that you concept makes "Truth" a relative concept, not an absolute one?
Your problem is you just can't imagine the ability for something to be true but unknown, or even unknowable. That is YOUR problem, not a problem with logic.
All you are doing is proving that you just don't understand what truth actually is,