Discrete Distinguishability as the Ontological Basis of Logic

This paper proposes a discrete foundation of logic based on distinguishability and order. It challenges the standard view that logical systems are grounded in truth values and instead takes acts of distinction as the primary logical units. We introduce the axiom of discrete distinguishability, according to which only discretely distinguishable states are ontologically admissible. On this basis, logical operations are derived from relations between distinctions rather than taken as primitive. Classical and non-classical logics are reconstructed as specific organizations of distinction structures. The framework replaces truth-based semantics with realizability-based semantics, where satisfaction is defined in terms of compatible and composable distinctions. Continuous domains are interpreted as limit constructions over discrete systems rather than as ontological primitives. The resulting theory provides a unified and minimal foundation for logic, integrating syntax, semantics, model theory, and computation within a single structure grounded in distinguishability.