Discussion:
Refuting Incompleteness and Undefinability Version(13) (World class expert coaching)
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peteolcott
2018-11-05 02:11:10 UTC
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A world class expert provided some coaching. They have published very much
in the field of Incompleteness and many related fields.

They changed this:
∀F ∈ Formal_Systems (∃G ∈ F (G ↔ ∃Γ ⊆ F ~(Γ ⊢ G)))

into this:
L(F) means the language of formal system F.
∀F (F ∈ Formal_Systems & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
Q here is Robinson Arithmetic (the theorem fails for some weaker formal systems)

I realized that Q is not needed if the following expression evaluates to False:
∃F ∈ Formal_Systems ∃G ∈ L(F) (G ↔ ~(F ⊢ G))

The following analysis seems to refute Gödel 1931 Incompleteness as long as
the term "satisfiable" is interpreted using the conventional meanings of the
symbols within symbolic logic.

If G was Provable in F this contradicts its assertion: G is not Provable in F
If ~G was Provable in F this contradicts its assertion: G is Provable in F.
Since G is neither Provable nor Refutable in F it forms a Gödel sentence in F.

Because G is not satisfiable in any Formal System F, the Gödel sentence does not exist.

Copyright 2018 Pete Olcott
Franz Gnaedinger
2018-11-05 07:44:02 UTC
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Post by peteolcott
Copyright 2018 Pete Olcott
Peter Olcott knows the absolute and complete and total truth, he is the author
of life and creator of life, he has hundred reasons to believe that he is God,
he creates our future minds in order that we can go on existing, he is both
a human being and God, he is the one Creator of the Universe (claims he made
in sci.lang). Metaphors are a forte of human word language and a precious tool
of the mind. Allgod fought metaphors for years and called them "a crime against
logic." And then, all of a sudden, he changed his opinion, accepted metaphors
and denied that he called them a crime against logic. So he can turn around
his opinion by 180 degrees and still or again be in possession of the absolute
etcetera. What he assumes are not just ordinary notions, prone to error and
mistake and illusion, they are always and forevermore tha sbolute etcetera,
patatee and patata.
Arnaud Fournet
2018-11-05 14:12:24 UTC
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Post by peteolcott
A world class expert provided some coaching. They have published very much
in the field of Incompleteness and many related fields.
∀F ∈ Formal_Systems (∃G ∈ F (G ↔ ∃Γ ⊆ F ~(Γ ⊢ G)))
L(F) means the language of formal system F.
∀F (F ∈ Formal_Systems & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
Q here is Robinson Arithmetic (the theorem fails for some weaker formal systems)
∃F ∈ Formal_Systems ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
The following analysis seems to refute Gödel 1931 Incompleteness as long as
the term "satisfiable" is interpreted using the conventional meanings of the
symbols within symbolic logic.
If G was Provable in F this contradicts its assertion: G is not Provable in F
If ~G was Provable in F this contradicts its assertion: G is Provable in F.
Since G is neither Provable nor Refutable in F it forms a Gödel sentence in F.
Because G is not satisfiable in any Formal System F, the Gödel sentence does not exist.
Copyright 2018 Pete Olcott
ah, a repeated metastasis of Péter la Crotte garbage.
Péter la Crotte is going Altzheimer...

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