Logicality: The Boundary Between Formal Syntax and Logical Authority

Logic must produce logic to be logical. This manuscript introduces the principle of logicality: a system possesses logical authority only when its admissible domain and deductive rules are simultaneously co-determined by the same primitive closure datum and closure reproduces admissibility under its own rules. The central object is the exact pair-valued Logical Closure Datum \(T_B(\Lambda)=(B,\Lambda')\), where \(B\) is the simultaneously co-determined reproduced basis and \(\Lambda'\) is the produced logical state. 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. We then separate two independent modes of metalogical failure: admissibility failure, where a syntactic candidate never enters the logical domain, and reproduction failure, where an admitted candidate fails to close to an admitted produced state over the reproduced basis. The resulting Gödel Non-Transfer Theorem separates formal incompleteness from logical authority, mathematics, and physical closure. Ultimately, this principle establishes a strict boundary for both the formal and physical sciences: anything outside of the Logical Closure Datum is metalogical in nature and does not carry logical authority.