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

On 2024-11-13 23:01:50 +0000, olcott said:

On 11/13/2024 4:45 AM, Mikko wrote:

On 2024-11-12 23:17:20 +0000, olcott said:
 

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))

 That's correct (although T is usually used instead of L).
Per this definition the first order group theory and the first order
Peano arithmetic are incomplete.

 Every language that can by any means express self-contradiction
incorrectly shows that its formal system is incomplete.

That "incorrectly shows" is non-sense. A language does not show,
incorrectly or otherwise. A proof shows but not incorrectly. But
for a proof you need a theory, i.e. more than just a language.
That a theory can't prove something is usually not provable in the
theory itself but usually needs be proven in another theory, one
that can be interpreted as a metatheory.
--
Mikko