Joshua Rasmussen's "How Reason Can Lead to God" Through the Lens of TNA: Necessary Foundation as Admissibility Structure

This paper reinterprets Joshua Rasmussen’s contemporary rationalist argument for a necessary foundation of reality through the formal framework of the Theory of Axiomatic Necessity (TNA). By mapping Rasmussen's contingent entities onto the operational domain ($N_0$) and his proposed foundation onto the admissibility domain ($N_1$) , we reformulate the metaphysical problem of dependency as a structural constraint governed by the theorem of Failure of Local Closure. While Rasmussen derives an ontological conclusion pointing toward a necessary being , TNA remains epistemologically agnostic, demonstrating instead that infinite explanatory regresses merely expose the structural inability of any $N_0$ system to internally derive its own legitimizing rules or existence. Ultimately, this comparative analysis illustrates that the recurring philosophical pursuit of an ultimate foundation is a specialized manifestation of a broader structural boundary inherent to all operational frameworks.