Gettier, Epistemic Closure, and the Necessity of N₁: A TNA Critique of Justified True Belief

This paper analyzes the Gettier problem through the framework of the Theory of Axiomatic Necessity (TNA), demonstrating that the failure of Justified True Belief (JTB) is an epistemological manifestation of Failure of Local Closure. We argue that internally accessible cognitive structures (N₀) are inherently insufficient to guarantee genuine knowledge without a non-derivable external legitimizing infrastructure (N₁). By reinterpreting classical counterexamples, we show that "epistemic luck" is not a superficial design flaw, but structural proof that no sufficiently complex cognitive system can self-generate its own legitimacy or anchor its operational coherence to truth non-accidentally. Under TNA, knowledge is redefined not as an accumulation of justified internal data (), but as an state of structural admissibility licensed by a deeper participation in reality. Ultimately, the Gettier crisis reveals that cognition cannot achieve complete self-closure, positioning the N₁ operator as a permanent, non-smooth infrastructure necessary to rescue epistemology from accidental truth and systemic incoherence.