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

On 3/1/25 8:17 PM, olcott wrote:

On 3/1/2025 3:58 PM, Richard Damon wrote:

On 3/1/25 2:58 PM, olcott wrote:

On 3/1/2025 2:45 AM, Mikko wrote:

On 2025-02-28 22:04:31 +0000, olcott said:
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On 2/28/2025 4:04 AM, Mikko wrote:

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

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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.
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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.

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In honour of Gödel this is usually called "incomplete".
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Where "incomplete" has always been an idiom for stupid wrong.
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No, only in your faulty logic.
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Incomplete means that there are some truths that can't be proven in the system.
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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.

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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.

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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.

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Logic doesn't care about truths and truth makers except in the (usually
uninteresting) special cases where truth makers are found in the logic
itself.
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Incompleteness(math) and Undecidability(logic) are
artifacts of defining the term provable(math)
in a way that is inconsistent with provable(common)
{shown to be definitely true by whatever means}.
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Nopw, because shown(common) requires a finite sequence to show to someone, as people can not see all of an infinite sequence
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 If the Goldbach conjecture is true and there is only
an infinite sequence as its truth-maker then this
infinite sequence <is> its proof(common)
{shown to be definitely true by whatever means}.
 

No, an infinite sequence is not a "proof" as you can not SHOW an infinite sequence.
All you are doing is showing that you don't know what the definition of PROOF is.
Do you have an actual reference for your definition, I suspect not, and you are just proving that you are nothing but a pathological liar, where the "shown" actually allows something inexpressible.
Because, until you can actually express in writing or symbology, that infinite sequence, that shows that every step is true, you haven't SHOWN it to be true,
Testing and showing the results of an infinite set of trials, can not be SHOWN in a way that a person can understand.
Note, sometimes, the infinite series can be reduced by a induction or related process, then the proof is finite, but if there is no reduction to the finite, the infinite number of step just isn't a proof,
You are just showing your ignorance of the meaning of the words.