Personally, I consider it metaphysical because it says something about provability (since, deep down, proofs and programs are the same thing). Truth beyond proo

Personally, I consider it metaphysical because it says something about provability (since, deep down, proofs and programs are the same thing). Truth beyond proof (or at least beyond what's feasible to prove) is bizarre and mysterious. Metaphysics (and physics) is concerned with uncovering the fundamental truths of the universe. Computational complexity indicates this may be unachievable.