Refuting Gödel's 1931 Incompleteness Theorem in one sentence (v2)

[peteolcott]

HERE IS THE ONE SENTENCE:
If the notion of True(x) is defined as provable from axioms and
axioms are stipulated to be finite strings having the semantic
property of Boolean true then every expression of language that
not a theorem or an axiom is not true.

HERE IS HOW THAT ONE SENTENCE REFUTES 1931 INCOMPLETENESS:
https://plato.stanford.edu/entries/goedel-incompleteness
The first incompleteness theorem states that in any consistent formal
system F within which a certain amount of arithmetic can be carried
out, there are statements of the language of F which can neither be
proved nor disproved in F. (Raatikainen 2018)

When we formalize the essence of above we get this logic sentence:
∃F ∈ Formal_System ∃G ∈ Closed_WFF(F) (G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G)))

We are assuming consistency without specifying it and we don’t
limit the scope to arithmetic. If the above sentence is false
then Gödel is wrong.

Within the sound deductive inference model the G of this expression:
((F ⊬ G) ∧ (F ⊬ ¬G)) is a closed WFF that is neither true or false,
thus excluding it from membership in the set of logic sentences.

Within the sound deductive inference model the RHS portion of this
expression: G ↔ ((F ⊬ G) ∧ (F ⊬ ¬G)) cannot be evaluated for
material equivalence with G because it is not a logic sentence.

∴ There is no G that is materially equivalent to its own unprovability
and its own irrefutability because this would require it to be materially
equivalent to neither True or False.

HERE IS THE REST OF THIS POST
http://liarparadox.org/index.php/2019/05/15/deductively-sound-formal-proofs-of-mathematical-logic/

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Copyright 2019 Pete Olcott
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