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

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.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer