Quote Originally Posted by DavidSh View Post
I guess this goes to show that people use words to mean different things. Freshman philosophy will tell you that "knowledge" is "justified true belief", so allows for belief that is actually justified with a proof. There is a wide space between "I believe that Cantor's diagonal argument is valid", based on a careful analysis of the argument, and "I believe in fairies", based on acceptance of folklore.
That might be because in philosophy proving something is a bit more difficult and the concept of knowledge by necessity allows a fluid gradation of proof. In science the typical understanding of knowledge is that is something proven to work whether anyone believes it or not as the universe does not care how we feel about it.

But those are indeed just semantic details.