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On 3/3/2025 9:08 AM, Mikko wrote:And those systems containing those unknowable truths are by definition incomplete.On 2025-03-01 19:58:21 +0000, olcott said:If True(X) means has a truth-maker and Provable(X)
>On 3/1/2025 2:45 AM, Mikko wrote:>On 2025-02-28 22:04:31 +0000, olcott said:>
>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:When any system assumes that every expression is true or false and isWhich has nothing to do with "soundness".Sure I do.That is very good.
A Systems is semantically sound if every statement that can be proven
is actually true by the systems semantics,
>in other words, the system doesn't allow the proving of a falseThat is not too bad yet ignores that some expressions might not have
statement.
any truth value.
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.
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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.
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.
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.
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}.
No such inconsistency is shown.
>
means shown to have a truth-maker then the only
difference between Provable(X) and True(X) are unknown
truths. Some of these may be unknowable truths requiring
an infinite set of finite proofs.
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