I used to think the following was a nice little analytic truth.

• If immediately prior to _t_, _S_ does not know that _p_, and at _t_ she does know that _p_, then at _t_, _S_ learns that _p_.

But now I’m convinced there are counterexamples to it. Here are four putative counterexamples, some of which might be convincing.

A few months ago, Alice learned that the President McKinley was assassinated. Soon after, she forgot this. Just now, she was reminded that President McKinley was assassinated. So she now knows that President McKinley was assassinated, and just before now she didn’t. But she didn’t just learn that President McKinley was assassinated, she was reminded of it.

Bob starts our story in Fake Barn Country. He is looking straight at a genuine barn on a distant hill, and forms the belief that there is a barn on that hill. Since he’s in fake barn country, he doesn’t know there is a barn on the hill. At _t_, while Bob is still looking at the one genuine barn, all the fake barns are instantly destroyed by a visiting spaceship, from a race which doesn’t put up with nonsense like fake barns. After the barns are destroyed, Bob’s belief that there is a barn on that hill is knowledge. So at _t_ he comes to know, for the first time, that there is a barn on that hill. But he doesn’t learn that there is a barn on that hill at _t_; if he ever learned that, it was when he first laid eyes on the barn.

Carol is trapped in Gilbert Harman’s dead dictator story. She has read the one newspaper that correctly (and sensitively) reported that the dictator has died. She hasn’t seen the copious other reports that the dictator is alive, but the existence of those reports defeats her putative knowledge that the dictator is alive. At _t_, all the other news sources change their tune, and acknowledge the dictator has died. So at _t_, Carol comes to know for the first time that the dictator has died. But she doesn’t learn this at _t_; if she ever learns it, it is when she reads the one true newspaper.

Ted starts our story believing (truly, at least in the world of the story) that Bertrand Russell was the last analytic philosopher to win the “Nobel Prize in literature”:http://nobelprize.org/nobel_prizes/literature/laureates/. The next day, the 2011 Nobel Prize in literature is announced. A trustworthy and reliable friend of Ted’s tells him that Fred has won the Nobel Prize in literature. Ted believes this, and since Fred is an analytic philosopher, Ted reasonably infers that, as of 2011 at least, Bertrand Russell was not the last analytic philosopher to win the Nobel Prize in literature. This conclusion is true, but not because Fred won. In fact, Ed, who is also an analytic philosopher, won the 2011 Nobel Prize in literature. At _t_, Ted is told that it is Ed, not Fred, who won the prize. Since Ted knows that Ed is also an analytic philosopher, this doesn’t change his belief that Bertrand Russell was not the last analytic philosopher to win the Nobel Prize in literature. But it does change that belief from a mere justified true belief into knowledge. But arguably it is not at _t_ that Ted learns that Bertrand Russell was not the last analytic philosopher to win the Nobel Prize in literature, since just like in the last two cases, Ted’s evidence for this conclusion does not improve.