But the question “Can I prove that induction/Occam’s Razor works?” is different from both “Does it work?” and “Why does it work?”, and we can easily find ourselves in the world where the first question ends up with an irreducible NO and the second one ends up with YES (as you said yourself, |- P and |- []P are different).
But the question “Can I prove that induction/Occam’s Razor works?” is different from both “Does it work?” and “Why does it work?”, and we can easily find ourselves in the world where the first question ends up with an irreducible NO and the second one ends up with YES (as you said yourself, |- P and |- []P are different).