For nearly a century, Gödel's incompleteness theorems have been interpreted as an absolute boundary on the completeness of logic, mathematics, and physical theory. Here we show that this interpretation rests on a category error: the conflation of unconstrained formal syntax with logical authority. We introduce the principle of logicality: a system possesses logical authority only when its admissible domain and deductive rules are co-determined by the same primitive closure datum. Using the exact pair-valued Logical Closure Datum T_B(Λ) = (B, Λ′), where B is the co-determined reproduced basis, we prove the Logical Co-Determination and No Metalogical Promotion theorems, showing that systems beginning with independently stipulated domains and rules cannot internally derive their own logical authority. Because Gödelian self-reference originates in unconstrained syntactic production, its witness fails to earn admission and reproduction over a co-determined basis. Consequently, Gödel's incompleteness argument is not a limit on logic, mathematics, or physics; it is a syntactic artifact of a system that has failed the logicality test. The issue does not end with Gödel: what remains outside admitted existence, logic, mathematics, and physics is metalogical production without logical authority.