This paper presents a formal proof for the validity of General Relativity and Quantum Mechanics based on the ‘Axiom of Finite Information.’ We demonstrate that if the speed of information transfer were infinite, or if space-time were perfectly continuous, the universe would contain states of infinite information density, leading to logical singularities. Furthermore, we prove that because physical laws must be encoded within the universe itself, a ‘Theory of Everything’ is precluded by Godelian incompleteness, ensuring that a universal theory can never exist.