Causality as Meta-Logic: A Completeness Proof for EET Epistemology

Every knowledge system presupposes a meta-logic: a fundamental way of moving from premises to conclusions. Throughout history, philosophers have proposed various candidates—deduction, induction, analogy, dialectics, intuition, insight, aesthetic judgment, and mystical revelation. Energy-Efficiency Theory (EET) makes a radical claim: all valid cognitive judgments can be reduced to exactly two types of causality—Natural Causality and Rule Causality. There is no third way. This document provides a rigorous completeness proof for this claim. We first precisely define Natural Causality (cognition validated by real-space energy exchange) and Rule Causality (cognition validated by internal symbolic consistency), as established in Dual Causality. We then systematically reduce every proposed ``third'' meta-logic to one of these two forms, or to a submerged, mixed, or degenerate variant thereof. Crucially, we ground this reduction in physical necessity. Drawing on the Algorithmic Submersion Protocol, we show that any finite-energy computational system must converge to binary search architecture. Binary search is precisely the atomic operation of causal reasoning: ``Does A lead to B? '' Therefore, causality is not an arbitrary human cognitive style; it is the thermodynamically mandated structure of any physically realized intelligence. We further apply Postulate 3 (Barrier Asymmetry: Eb^melt Eb^form) to explain the ``illusion of logical necessity. '' Because the topological barrier to melting down our hardwired causal constraints is astronomically high, we subjectively experience causality as an unbreakable universal law rather than an energy-saving heuristic. This proof establishes the epistemological foundation for the Six Forms of Truth, the Energy-Efficiency Spectrum, and all EET applications. It demonstrates that dual causality is complete, necessary, and sufficient for all valid cognition.: Meta-logic; Causality; Natural Causality; Rule Causality; Completeness Proof; Algorithmic Submersion; Binary Search; Epistemology; Energy-Efficiency Theory