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[deleted] t1_j26zhc1 wrote

Reply to comment by Capital_Net_6438 in /r/philosophy Open Discussion Thread | December 26, 2022 by BernardJOrtcutt

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Capital_Net_6438 t1_j28qpoi wrote

As a fan of logic, rejecting logic isn’t an option for me.

Suppose we don’t assume anything about anyone’s knowledge on day 1. And suppose, as is usually the case, that we’re considering proving a surprise quiz is impossible. Then it surely does not follow that a surprise quiz can’t happen on day 5.

The argument is supposed to go that at the end of day 4, the student knows there’ll be a quiz on day 5. But he has no idea really. We didn’t build him having knowledge into the setup at day 1 and therefore he won’t magically have knowledge at day 4. The assertion that he does have knowledge at that point is totally unsupported.

So of course if we don’t assume anything about the student’s knowledge in the setup there could be a surprise quiz on day 5. Day 5 comes; a quiz happens; and the ignorant student says - “wow, I didn’t see that coming.”

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[deleted] t1_j28uzg2 wrote

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Capital_Net_6438 t1_j2994dl wrote

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.

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