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

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.