Re: The philosophy of logic reformulates existing ideas on a new basis --- infallibly correct

On 2024-11-14 01:09:18 +0000, Richard Damon said:

On 11/13/24 11:50 AM, olcott wrote:

On 11/13/2024 10:33 AM, joes wrote:

Am Wed, 13 Nov 2024 09:11:13 -0600 schrieb olcott:

On 11/13/2024 5:57 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/10/2024 2:36 PM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 11/10/2024 1:04 PM, Alan Mackenzie wrote:

 

I have addressed your point perfectly well.  Gödel's theorem is
correct,
therefore you are wrong.  What part of that don't you understand?

YOU FAIL TO SHOW THE DETAILS OF HOW THIS DOES NOT GET RID OF
INCOMPLETENESS.

The details are unimportant.  Gödel's theorem is correct.  Your ideas
contradict that theorem.  Therefore your ideas are incorrect.  Again,
the precise details are unimportant, and you wouldn't understand them
anyway.  Your ideas are as coherent as 2 + 2 = 5.

 

Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) When the above
foundational definition ceases to exist then Gödel's proof cannot
prove incompleteness.

 

What on Earth do you mean by a definition "ceasing to exist"?  Do you
mean you shut your eyes and pretend you can't see it?
Incompleteness exists as a concept, whether you like it or not.
Gödel's theorem is proven, whether you like it or not (evidently the
latter).
 

When the definition of Incompleteness:
Incomplete(L) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
    becomes
¬TruthBearer(L,x) ≡  ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Then meeting the criteria for incompleteness means something else
entirely and incompleteness can no longer be proven.

 

What does incompleteness mean then?
 

 Incompleteness ceases to exist the same way that Russell's
Paradox ceases to exist in ZFC.

 Not until your create your logic system like Z & F did to make ZFC.

It wouldn't be that simple. Zermelo and Fraenkel accepted ordinary logic
but Olcott wants to reject that so he would need to start with building
a new logical foundation.
--
Mikko