When Maxwell arrives at work in the morning, he always parks in one of two spots: C8 or D8. Half the time he parks in C8, and half the time he parks in D8. Today Maxwell parked in C8. It’s lunchtime at work. Maxwell and his assistant are up in the archives room searching for a particular document. Maxwell says, “I might have left the document in my car.” The assistant asks, “Mr. Maxwell, is your car parked in space C8? It’s not unheard of for cars to be stolen.” Maxwell thinks carefully for a moment and then responds, “No, my car has not been stolen. It is parked in C8.”With that example began John Turri's "Epistemic closure and folk epistemology," where he went on to add that:
The epistemic closure principle says, roughly, that if one knows that P, and one knows that if P then Q, and one infers Q, then one knows Q.Maxwell may have been misapplying logic, when he thought carefully: he recalled that he had parked in C8, rather than D8, and so he thought that his car was in C8 (unless it had, as his assistant noted, been stolen), from which he may have concluded that it was not stolen (unless it was). (But perhaps he took the low chance of his car having been stolen to be reason enough to think that it had not been stolen. And for all we know the archive's windows looked down on C8.)
Most people think that Maxwell knew that his car was parked in C8 (assuming that it had not been stolen), but not that it had not been stolen, which contradicts Epistemic Closure: if Maxwell knows that his car is in C8, and he knows that if his car is in C8 then it has not been stolen, which he seemed to know, because he did seem to infer, from it being in C8, that it had not been stolen, then Closure says that Maxwell did know that his car had not been stolen.
What I find interesting is how logical it seems, to go from Maxwell knowing that his car was in C8 rather than D8 (which I think he did know), to Maxwell knowing that his car was in C8 (which most people think he did know), to Maxwell knowing that his car was still in C8, to Maxwell knowing that his car had not been taken out of C8 (which most people think he did not know). Were that sequence formalized, would we be further from the dark?