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

On 2/28/2025 4:04 AM, Mikko wrote:

On 2025-02-26 01:33:48 +0000, olcott said:
 

On 2/25/2025 5:58 PM, Richard Damon wrote:

On 2/25/25 1:40 PM, olcott wrote:

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:

On 2/22/2025 9:56 PM, Richard Damon wrote:

On 2/22/25 1:42 PM, olcott wrote:

On 2/22/2025 3:25 AM, Mikko wrote:

On 2025-02-22 04:44:35 +0000, olcott said:

On 2/21/2025 7:05 PM, Richard Damon wrote:

On 2/21/25 6:19 PM, olcott wrote:

On 2/20/2025 2:54 AM, Mikko wrote:

On 2025-02-18 03:59:08 +0000, olcott said:

>

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.
>

>
No, only in your faulty logic.
>
Incomplete means that there are some truths that can't be proven in the system.
>

>
That comes from stupidly failing to require {true in the system}
to require {proven in the system}. Fix this one stupid mistake
and all of incompleteness goes away.

 No, that merely means that "true in the system" is incomplete in some
systems (e.g., natural numbers). There are sentences that are true in
practical applications of the system but not in the system itself.
That is not a defect as it does not prevent useful practical aplications.
 

The bottom line here is that expressions that do not have
a truth-maker are always untrue. Logic screws this up by
overriding the common meaning of terms with incompatible
meanings. Provable(common) means has a truth-maker.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer