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

On 2025-02-28 14:30:44 +0000, Richard Damon said:

On 2/27/25 11:02 PM, olcott wrote:

On 2/27/2025 7:00 PM, Richard Damon wrote:

On 2/27/25 9:46 AM, olcott wrote:

On 2/27/2025 6:45 AM, Richard Damon wrote:

On 2/26/25 11:24 PM, olcott wrote:

On 2/26/2025 9:59 PM, Richard Damon wrote:

On 2/26/25 8:39 PM, olcott wrote:

On 2/26/2025 10:03 AM, joes wrote:

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.
 

 WTF is the truth value of the negation of nonsense?
The Liar Paradox has ALWAYS simply been nonsense.
 

 But we aren't negating "nonsense", we are negating the actual valid truth value out of the Truth Primative.
 You don't seem to understand that the DEFINITION of what a truth primative is requires that True(Nonsense) be false, not "nonsense".
 

   True("lkekngnkerkn") == false
False("lkekngnkerkn") == false
 

 But ~True("lkekngnkerkn") == true.
 

 Yes
 

so if we can define that lkekngnkerkn is ~True(lkekngnkerkn) then we have a problem.
f

 We are not defining gibberish as anything.
Gibberish evaluates as ~True because it is gibberish.

 But you are trying to define LP := !True(LP) as gibberish.
 

 Prolog already knows that it <is> gibberish.

 Because, like you, Prolog can't handle the needed logic.
 

 It has an infinite cycle in the directed graph of its
evaluation sequence.

 But infinite cycles are not prohibited in logic systems that support the properties of the Natural Numbers. The MUST allow them or you can't HAVE the Natural Numbers.
 

 See Page 3 for Prolog
https://www.researchgate.net/ publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence  

 Just shows your stupidity, thinking that all logic is just primitive, and not understanding what the Godel sentence actually is. Your mind seems to have blocked out the actual sentence presented earlier because you know you don't understand it, so you think it must be gibberisn, but it is you mind that is gibberish.
 You didn't give it the ACTUAL Godel sentence, just the simplified interpretation of it. The problem is that the actual Godel sentence can't be expressed in Prolog, as it uses 2nd order logic operations, which Prolog doesn't handle.

There is a (long) sentence of first order logic that can be used as a Gödel
sentence in a first order proof that the first oder Peano arithmetic is
incomplete. Prolog can handle that sentence (e.g., as a list of characters)
if the implementation has sufficiently memory.
--
Mikko