This paper aims to provide a rigorous systematic proof, from the perspective of meta-logic and mathematical foundations, for the proposition that "the foundation of truth and science lies in the unity of causality and consistency." By formalizing the notions of theoretical systems, truth, causality, and consistency, we demonstrate the logical necessity of each as a condition for scientific theories, and subsequently prove that their unity is a necessary and sufficient condition for the existence of truth. Utilizing cutting-edge tools from model theory, category theory, proof theory, recursion theory, and mathematical physics, we construct a multi-layered rigorous proof. In particular, we demonstrate the irrefutability of this proposition within the realm of reason—any rational attempt to deny it falls into self-refutation. The conclusion shows that the unity of causality and consistency is not an empirical generalization or cultural construct, but an a priori structure of rational thought and scientific practice, the first law of existence itself.
Jianbing zhu (Tue,) studied this question.