From God, Not ∅: A Structural Redefinition of Mathematical Foundations from Meaning-Based Axioms
Year: 2025
Type: article
Abstract: 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.
Author: 上田, 高之
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6967904612
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