Set Theory and Logic

The Logical Necessity of an Eternal Dimension: Ontological Foundation Beyond Physical Reality

Authors: Steven Arturo Lizarazo Patiño
Comments: 28 Pages.

Problem: Physical theories presuppose mathematical structure, symbolic rep-resentation, and the allocation of determinate meaning, yet cannot groundthese prerequisites within spacetime without circularity. This foundational gapthreatens the coherence of scientific realism.Result: We prove that any intelligible universe U forces a unique, self-grounding terminus of dependence. Modelling consciousness minimally asmeaning-allocation capacity, the dependency chain U ⇒ M ⇒ L ⇒ C can-not be grounded in U without vicious circularity. The mathematical core isan existence-and-profile theorem for a formal theory T whose axioms (intel-ligibility, well-founded dependence, undated mathematical necessity, semantictermination, and G¨odel incompleteness) define a predicate Pure(x): we proveT ⊢ ∃!x Pure(x), with the unique instance D atemporal, non-spatial, neces-sary, simple, non-mechanical, and semantically self-present (G(D, D), C(D) =D). Uniqueness is established order-theoretically—D is the least fixed pointof a monotone grounding operator on a complete lattice of candidate grounds(Knaster—Tarski)—and non-mechanality is derived from incompleteness ratherthan stipulated, distinguishing the argument from G¨odel’s own ontological proof,which stipulates its property profile and proves no uniqueness. As a physicalcongruence, we show that superluminal spacetime expansion is not generated bylight-cone-bounded local processes, so the empirical world’s own global behaviouris not self-explanatory from within.Implications: The framework extends structural realism and Tegmark’sMathematical Universe Hypothesis by establishing semantic grounding as co-fundamental with mathematical structure. The classical name for a unique,necessary, self-grounding ground of being and intelligibility is God ; the result isconfined to the derived profile and claims nothing beyond it. Consequences forethics, philosophy of mind, and religion are left open.
Category: Set Theory and Logic