Do we know whether we know something?
I have come across this idea a few times now that knowing does not imply knowing that you know. However, I am having troubled understanding how this could be true given the criteria of knowledge my philosophy professor has laid out. Namely, that it is a) true b) believed c) is justified. In my mind believing something necessarily entails being aware of that belief, or a belief is just a conscious opinion (my philosophy professor has not said this). Given these criteria it seems that knowing implies that it is true and one believes it and has evidence for it. Therefore it is true that you know it, and it also true that you believe that you know it, by necessity. So the only possible difference is whether it is justified that you know it. It seems to me that this is true, as the evidence that you know something seems to be equivalent the evidence for that original something. I'm sure I'm missing something but it would be helpful if I could pinpoint what exactly it is.