Recursive Definition and Existential Nullity: A Semantic Refutation of Nihilism Beyond ZFC Constraints

This paper examines the logical validity of the existential nihilist proposition P , commonly expressed as "Life has no meaning." Responding to critiques regarding the subjective scope of consciousness and the gradient nature of "meaning," we refine the definitions of the existential set L and the valuation function M. We demonstrate that whether L is defined as a universal set or a subjective stream of consciousness, and whether M is binary or fuzzy, the proposition P constitutes a self-referential paradox isomorphic to the Liar Paradox. Specifically, under fuzzy logic systems, the valuation function converges to an undecidable mid- point (0.5), mathematically refuting the nihilist claim of Absolute Null (0). Finally, we distinguish our logical dissolution of the problem from the existentialist solutions of Camus and Sartre, proposing that the valid cognitive act is not definition but rigorous phenomenological description.