Philosophical analysis explores why zero must exist in formal systems, highlighting structural consequences.
Why does zero exist? Mathematics declares it by axiom, never explaining why the axiom is necessary. Philosophy approaches the question but cannot close it. This paper argues that zero's necessity is a structural consequence of Axiom II of Meta-Originary Ontology (Structural Incompleteness): any persistent formal system must contain a symbol representing its own boundary. Zero is not the symbol of nothing — it is the symbol of a system acknowledging what it cannot contain. This reading unifies the mathematical history of zero, the philosophical problem of non-being, and structural ontology into a single coherent account.
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Chen et al. (2026) studied this question.
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