I. Kant: Setting Boundaries

Kant’s “Copernican Revolution” revealed the boundaries of human reason. He used “glasses” as a metaphor:

• Phenomenal world = Cognizable
• Thing-in-itself = Incognizable

Reason constructs the experiential world through categories and intuition, but cannot directly grasp the thing-in-itself. The Critique of Judgment further explains the “bridging method” between phenomena and the thing-in-itself, but this is not intuitive cognition, rather a possibility of connection.‍

II. Hegel: Breaking Boundaries‍

Hegel was dissatisfied with Kant’s “boundary theory.” He proposed dialectics:

• Contradiction drives the development of reason
• Negation of negation = Transfinite iteration
• Reason continuously polishes the glasses through “sublation” (Aufhebung).

Hegel’s conclusion is: the Absolute Spirit can ultimately make the glasses 100% transparent, and the thing-in-itself fully manifest. In other words, he believed reason would eventually break through the limits set by Kant.‍

III. Gödel and Turing: The End and Transcendence of Formalization‍

Gödel and Turing transformed philosophical problems into mathematical logic and computation theory.

• Core correspondences: Formal system = Kant’s phenomenal world
• Completeness = Thing-in-itself
• Consistency = Non-contradiction
• Computability = Cognizable

Key results: Gödel’s incompleteness theorem: Any sufficiently powerful and consistent system must be incomplete → Kant’s “glasses” become formalized into a theorem.

• Turing machine: Strict formalization, finite computability → Corresponds to Kant’s phenomenal world.
• Oracle machine: A decision-making bridge beyond the system → Corresponds to Kant’s Critique of Judgment.
• Ordinal logic system: Transfinite iterative boundary expansion → Corresponds to Hegel’s dialectical logic.‍

IV. A Unified Picture‍

• Kant: Setting boundaries
• Hegel: Approaching boundaries
• Gödel/Turing: Proving that boundaries cannot be eliminated, but allowing infinite approximation, while introducing an external oracle perspective
  

The logical chain can be understood as follows:

• Kant — Setting the boundary
• Hegel — Attempting to break the boundary
• Gödel/Turing — Proving the boundary’s real existence, but expansion paths and external oracles remain possible
  

V. Conclusion

This chain of thought shows:

• Kant = The boundary setter
• Hegel = The dialectical expander
• Gödel/Turing = The formal proof-givers
  

From philosophy → to logic → and then to computation, human reason always unfolds between finitude and infinite approximation.