From God, Not ∅: A Structural Redefinition of Mathematical Foundations from Meaning-Based Axioms

This paper proposes a foundational shift in mathematics by replacing the abstract, syntactic construct of the empty set (∅) with a meaning-saturated structure, denoted as “God.” Defined axiomatically, the God-structure acts as an origin of formal systems via self-referential interpretation, observer embedding, and semantic recursion. We critique the classical set-theoretic paradigm by showing that ∅ relies on non-trivial syntax, violating its claim of true emptiness. Instead, we offer axioms (G1–G3) for a meaning-centric framework and demonstrate how natural numbers can be reconstructed without vacuous primitives. This paradigm connects formal logic with ontological insight, bridging mathematics, philosophy, and information theory.