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

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.

*You just don't understand this at its foundational level*

You make me laugh, sometimes (at you, not with you).

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).

As for your attempts to pretend that unprovable statements are the same
as false statements, Mark Twain got it right when he asked "How many legs
does a dog have if you call a tail a leg?".  To which the answer is
"Four: calling a tail a leg doesn't make it one.".

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

--
Alan Mackenzie (Nuremberg, Germany).