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On 11/13/2024 10:33 AM, joes wrote:Not until your create your logic system like Z & F did to make ZFC.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:>>The details are unimportant. Gödel's theorem is correct. Your ideasI have addressed your point perfectly well. Gödel's theorem isYOU FAIL TO SHOW THE DETAILS OF HOW THIS DOES NOT GET RID OF
correct,
therefore you are wrong. What part of that don't you understand?
INCOMPLETENESS.
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 youWhen the definition of Incompleteness:
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).
>
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.
Is: "What time is it?" false?Neither did Alan claim that you did.As for your attempts to pretend that unprovable statements are the sameI never said that ~True(L,x) == False(L,x).
as false statements,
>I have been saying the direct opposite of your claim forThen if G is false, ~G must be true,
years now. False(L, x) == True(L, ~x)
Is: "What time is it?" true?
If neither true nor false then not a truth bearer.
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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