The Precondition of Logical‑Consistency for Cosmic Existence: A Screening Hypothesis under Structural‑Realism

This paper proposes and defends a metaphysical hypothesis concerning cosmic existence: logical‑consistency constitutes a necessary condition for any cosmic configuration to achieve ontological admissibility. Unlike existing physical‑cosmological theories which treat physical laws as fundamental premises, this paper argues that a more fundamental layer of "logical screening" precedes physical selection. I first define an abstract logical space L, understood as the set of mathematically describable structures accessible to human rational cognition, while suspending a strong ontological commitment to its independent reality. I argue that a system containing an irresolvable logical contradiction, such as φ ∧ ¬φ, will degenerate into a trivial system under classical logic owing to the principle of explosion, making stable negation operators and state‑distinction impossible. Even if paraconsistent logic is admitted, its inability to establish physical distinguishability prevents it from corresponding to an observable universe. Even when a formal time‑geometry can be defined within a paraconsistent system, such time is physically non‑existent without discrete measurable events. Drawing on model‑theoretic tools, and taking structural‑realism explicitly as its interpretive framework (rather than a neutral premise), I equate the cognisable content of a physical world with its mathematical structure. The mathematical structures and physical laws of candidate systems surviving this logical screening are not intentionally designed, but emerge as inevitable projections constrained by logical consistency. This paper lays out the full reasoning chain of the hypothesis, distinguishes syntactic undecidability from semantic ambiguity to address challenges stemming from Gödel’s theorems, positions itself as an axiomatic supplementation (rather than a replacement) of Tegmark’s Mathematical‑Universe‑Hypothesis, and puts forward empirical predictions subject to falsification grounded in physical‑theory constraints.