I am still confused about provability.
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Let a statement P is, sort-of-says like this.
P: ( "X is provable" ∧ "P is provable" )
If ( X is provable ∧ P is provable ) is provable → (P is provable) is provable → P is provable
Hence,
( X is provable V P is provable ) ⊢ "P is provable"
IF (P is provable) is provable → P is provable → (X is provable ∧ P is provable) is provable
"P is provable" ⊢ ( X is provable ∧ P is provable)
Therefore,
( X is provable ∧ P is provable ) :⇔ "P is provable"
So,original statement P is sort-of-says like this
P: "P is provable"
By the Löb's theorem, P is provable.
What the error of this reasoning?