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

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:

We are answering the question:
What are the relationships between arbitrary finite strings such
that the semantic property of True(L, x)
(where L and x are finite strings) can always be correctly
determined for every finite string having a truth value that is
entirely verified by its relation to other finite strings.
>

And, if the logic system can support the properties of the Natural
Number system, and a definition of the predicate True, it can be
shown that you can create the equivalent of
>
Let P be defined as Not( True(L, P))
in that system, and thus P is a semantically valid,

>
Not at all. That is the same as saying you know that it is true that
all squares are always round.

Really, then where is the error in his derivation?

You clearly have no idea what "semantically sound" means.
The only correct rebuttal to this is you proving that you do know this
by providing the details of exactly what "semantically sound" means.

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.