Thanks for the clarification.

Seems like the surprise quiz paradox isn’t unique in illustrating the flaws of formal logic from your perspective. So ideally one would bracket those in thinking about the SQP. Perhaps the paradox isn’t so paradoxical for independent reasons.

On the kk situation, I’m thinking maybe the student doesn’t know on day 4 that he knew on day 1. I feel totally fine resisting the inference that his knowledge has to survive the change in circumstances. Why shouldn’t it be similarly unlikely that his knowledge of knowledge survives? As the student thinks about things at the end of day 4, the argument has given little assurance that he’ll know that he knew. He should think on day 4, “huh, maybe I never knew.”

One way to think of this is that the student knows that he knows in general. If he knows p at t then he knows that he knows p at t. That’s probably an assumption the student needs. And his kk knowledge is no more guaranteed to survive the changing circumstances than his knowledge.