Complexity Isn't Enough: The Carlo Principle and the New Standard for Scientific Legitimacy

Abstract

This paper introduces the Carlo Principle, a structural criterion for scientific completeness based on bidirectional explanation. Modern scientific theories often excel at translating simple observations into complex formal structures, yet fail to translate those structures back into simple, intelligible consequences. This asymmetry reveals a foundational flaw: a theory that can explain upward but not downward is incomplete. Using three independent mathematical frameworks — category theory, information theory, and model theory — the paper demonstrates that completeness requires invertibility, lossless information flow, and semantic grounding. The Carlo Principle is formalised as a bidirectional mapping between conceptual simplicity and formal complexity, expressed through the condition G(F(s))=s. Relativity is presented as the canonical example of a complete theory, showing how simple observations become Minkowski geometry and how that geometry returns simple, testable predictions. The paper introduces the Completeness Criterion, a practical diagnostic tool for evaluating scientific theories, and explores its implications for physics, mathematics, philosophy of science, pedagogy, and future theory‑building. This work establishes bidirectional completeness as a new standard for scientific legitimacy and integrates the Carlo Principle into the broader Carlo Field canon. v2 in pdf Keywords & Subjects: The Carlo Principle; bidirectional completeness; scientific theory structure; invertibility; category theory; information theory; model theory; conceptual grounding; semantic interpretability; lossless mappings; explanatory symmetry; Minkowski spacetime; relativity foundations; theory evaluation; epistemology; philosophy of science; mathematical formalism; conceptual reduction; falsifiability; pedagogy of scientific theories; structural criteria for legitimacy; complexity justification; upward and downward mappings; scientific methodology; theoretical physics foundations; Carlo Field canon. Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com