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

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?

As for your attempts to pretend that unprovable statements are the same
as false statements,

I never said that ~True(L,x) == False(L,x).

Neither did Alan claim that you did.

I have been saying the direct opposite of your claim for
years now. False(L, x) == True(L, ~x)

Then if G is false, ~G must be true, but you want it to also be false.
That's a contradiction.

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.".

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Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.