Tarski Undefinability Theorem Succinct Refutation
Posted: Sat Mar 07, 2020 7:04 pm
Modal Logic
◊P ↔ ¬□¬P // Possibly(P) ↔ ¬Necessarily(¬P)
□P ↔ ¬◊¬P // Necessarily(P) ↔ ¬Possibly(¬P)
∀P (P ∈ Analytical_Knowledge(P) ↔ □P)
A universal truth predicate that refutes the Tarski Undefinability Theorem can be easily derived simply as membership in the set of Analytical_Knowledge.
∀P (□P ≡ Sound_Deductive_Proof(P) ≡ Theorem(P))
Assumes Haskell Curry definition of axiom (see linked paper).
Copyright 2020 Pete Olcott
https://www.researchgate.net/publicatio ... bout_Godel
◊P ↔ ¬□¬P // Possibly(P) ↔ ¬Necessarily(¬P)
□P ↔ ¬◊¬P // Necessarily(P) ↔ ¬Possibly(¬P)
∀P (P ∈ Analytical_Knowledge(P) ↔ □P)
A universal truth predicate that refutes the Tarski Undefinability Theorem can be easily derived simply as membership in the set of Analytical_Knowledge.
∀P (□P ≡ Sound_Deductive_Proof(P) ≡ Theorem(P))
Assumes Haskell Curry definition of axiom (see linked paper).
Copyright 2020 Pete Olcott
https://www.researchgate.net/publicatio ... bout_Godel