Rule Truth: The Nature of Mathematics as Rule-Based Cognition

The ``unreasonable effectiveness'' of mathematics in the natural sciences has historically driven philosophers toward Platonism—the belief that mathematical entities exist in an independent, absolute realm. Energy-Efficiency Theory (EET), strictly enforcing the ontological boundaries of Core Rules v4. 2, dismantles this metaphysical assumption. Through Postulate 1 (Energy Monism), we establish that mathematics is not an ontological reality but an epistemic proxy. It is a highly specialized cognitive strategy that compresses real-space regularities into a closed, rule-based symbolic system to minimize the thermodynamic cost of inference (Ėₑ₄ₒ₏). Consequently, mathematical truth is Rule Truth, not Absolute Truth. We apply the v4. 2 interface rules to resolve the paradox of mathematical validity: while mathematical axioms originate as energetic abstractions from real space (Natural Causality), the validity of mathematical theorems is guaranteed entirely by internal symbolic consistency (Rule Causality). By explicitly enforcing Prohibited Moves 5 and 7, this paper prevents the category errors that conflate the origin of rules with their guarantor. Mathematics is the most powerful Pseudo-Truth ever forged by algorithmic submersion, but it remains a map, not the territory. Keywords: Rule Truth; Mathematics; Rule-Based Cognition; Energy-Efficiency Theory; Platonism; Formalism; Wigner's Unreasonable Effectiveness; Gödel's Incompleteness