The logical correspondence between computability and determinacy Computable problems can be regarded in philosophy as corresponding to human deductive reasoning ability, that is, starting from axioms and deriving conclusions step by step through deterministic rules. This reasoning process corresponds to the deterministic computational model of the Turing Machine, first systematically proposed by Turing in his 1936 paper "On computable numbers and their applications in decision problems". If the problem can be judged, it is closer to human intuition, induction, and analogy ability, and belongs to the category of "relatively computable". Turing introduced the concept of "Oracle Machine" in his doctoral thesis "Ordinal Logic Systems" in 1938 to study the solvability of problems with a given amount of extra information (i.e. "oracle"). The oracle machine breaks through the limitations of ordinary Turing machines and can handle problems beyond traditional computing frameworks, reflecting the role of intuition and prior knowledge in cognition. Therefore, the difference between computability and decidability is not only a division at the formal logical level, but also reflects the dual structure of deduction and induction in human cognition: the former strictly relies on rules, while the latter allows for "jumping" and "foresight".