The aspect of GEB that has not withstood the test of time is the Gödel part.
[Gödel 1931] seemed to have settled the issue of inferential undecidablity{∃[Ψ:Proposition](⊬Ψ)∧(⊬¬Ψ)} in the positive using the proposition I'mUnprovable, such that I’mUnprovable⇔⊬I’mUnprovable.
However, existence of I’mUnprovable would enable the following cyberattack [cf. Wittgenstein 1937]:
Proof of a contradiction in foundations: First prove
I’mUnprovable using proof by contradictions as follows:
In order to obtain a contradiction, hypothesize
¬I’mUnprovable. Therefore ⊢I’mUnprovable
(using I’mUnprovable⇔⊬I’mUnprovable).
Consequently, ⊢⊢I’mUnprovable using
ByProvabilityOfProofs {⊢∀[Ψ:Proposition<i>](⊢Ψ)⇒⊢⊢Ψ}.
However, ⊢¬I’mUnprovable (using
I’mUnprovable⇔⊬I’mUnprovable), which is the
desired contradiction.
Using proof by contradiction, ⊢I’mUnprovable meaning
⊢⊢I’mUnprovable using ByProvabilityOfProofs. However,
⊢¬I’mUnprovable (using I’mUnprovable⇔⊬I’mUnprovable),
which is a contradiction in foundations.
Strong types prevent construction of I’mUnprovable using the following recursive definition: I’mUnprovable:Proposition<i>≡⊬I’mUnprovable. Note that (⊬I’mUnprovable):Proposition<i+1> because I’mUnprovable is a propositional variable in the right hand side of the definition of I’mUnprovable:Proposition<i>. Consequently, I’mUnprovable:Proposition<i>⇒I’mUnprovable:Proposition<i+1>, which is a contradiction.
The crucial issue with the proofs in [Gödel 1931] is that the Gödel number of a proposition does not capture its order. Because of orders of propositions, the Diagonal Lemma [Gödel 1931] fails to construct the proposition I’mUnprovable.
[Gödel 1931] seemed to have settled the issue of inferential undecidablity{∃[Ψ:Proposition](⊬Ψ)∧(⊬¬Ψ)} in the positive using the proposition I'mUnprovable, such that I’mUnprovable⇔⊬I’mUnprovable.
However, existence of I’mUnprovable would enable the following cyberattack [cf. Wittgenstein 1937]:
Strong types prevent construction of I’mUnprovable using the following recursive definition: I’mUnprovable:Proposition<i>≡⊬I’mUnprovable. Note that (⊬I’mUnprovable):Proposition<i+1> because I’mUnprovable is a propositional variable in the right hand side of the definition of I’mUnprovable:Proposition<i>. Consequently, I’mUnprovable:Proposition<i>⇒I’mUnprovable:Proposition<i+1>, which is a contradiction.The crucial issue with the proofs in [Gödel 1931] is that the Gödel number of a proposition does not capture its order. Because of orders of propositions, the Diagonal Lemma [Gödel 1931] fails to construct the proposition I’mUnprovable.
See the following for more explanation: "Epistemology Cyberattacks" https://papers.ssrn.com/abstract=3603021