A different objection, following Eliezer’s PS, is that:
Between me and a red box, there is a wall with a hole. I see the red box through the hole, and therefore know that the box is red. I reason, however, that I might have instead chosen to sit somewhere else, and I would not have been able to see the red box through the hole, and would not believe that the box is red.
Or more formally: If I know P, then I know (P or Q) for all Q, but:
Between me and a red box, there is a wall with a hole. I see the red box through the hole, and therefore know that the box is red. I reason, however, that I might have instead chosen to sit somewhere else, and I would not have been able to see the red box through the hole, and would not believe that the box is red.
This is a more realistic, and hence better, version of the counterexample that I gave in my ETA to this comment.
A different objection, following Eliezer’s PS, is that:
Between me and a red box, there is a wall with a hole. I see the red box through the hole, and therefore know that the box is red. I reason, however, that I might have instead chosen to sit somewhere else, and I would not have been able to see the red box through the hole, and would not believe that the box is red.
Or more formally: If I know P, then I know (P or Q) for all Q, but:
P ⇒ Believes (P)
does not imply
(P v Q) ⇒ Believes (P v Q)
This is a more realistic, and hence better, version of the counterexample that I gave in my ETA to this comment.