Formalizing Absence: Ontological Framework Between Zero, ∅, and Symbolic Non-being Toward a Symbolic Metaphysics of Absence and Unrepresentability

This paper examines the ontological and symbolic dimensions of absence and nothingness through a multi-layered analysis spanning classical philosophy, existentialism, and contemporary metaphysics. It distinguishes between three conceptual modalities: the absence within being, the metaphysical zero as a formal placeholder, and the unrepresentable ∅ as a limit-concept. Drawing from ancient sources such as Parmenides and Democritus, and extending through Heidegger, Sartre, and modern symbolic logic, the study proposes an ontological model wherein ∅ is not a void but a pre-representational fold—neither being nor non-being. The paper further engages with thermodynamic entropy and mathematical nullity to support its thesis that symbolic nothingness functions as a condition of potentiality rather than negation. The aim is to bridge metaphysical abstraction with formal semantics, suggesting a new philosophical grammar for understanding absence beyond binary opposition. Implications for the philosophy of language, cosmology, and negative theology are briefly discussed. Final construction offers not a closure, but a topology. Each symbol—1, 0, ∅—represents not a quantity, but a horizon. What follows is not a definition, but a diagram of metaphysical tension.