The Fundamental Impossibility Theorems Underlying the Three Laws of Response: A Contradiction-Based Justification of Stability in Natural Systems

This paper establishes three fundamental impossibility theorems that justify the necessity of the Three Laws of Response—boundedness, monotonic improvement, and negative feedback—as universal constraints on the long-term behavior of any stable system. Using reductio ad absurdum, we demonstrate that violating any of these laws leads to contradictions with core principles of thermodynamics, information theory, or control theory. Together, these laws define a non-unique but strictly bounded set of admissible response functions, denoted by $\mathcal{S}$. This set serves as a universal stability manifold across diverse domains, from biology and artificial intelligence to economics and physical cosmology. Our framework offers a constraint-defined grammar for response dynamics, guiding both the classification of real systems and the design of sustainable engineered systems. We conclude by discussing open questions about nonlinearity, statistical degeneration, and the possibility that the universe itself evolves within the response set $\mathcal{S}$.