Quick Thought

Amber brought up an interesting question in the course of a discussion regarding Tim Burton and the MOMA exhibit. Tim Burton, apparently, did not believe he was worthy of a feature at the MOMA as he does not consider himself an artist. An animator and director yes, but not a traditional visual artist.
How is the label of artist applied? If the person in question denies it, are they still an artist? In video art the name John Cage inevitably comes up, but he was not an artist. He was a musician, not a visual artist. Nam June Paik and Pipilotti Rist also are practicing musicians. The answer for them could be made simpler: they are artists when they are creating visual artwork and musicians when they compose music. But the question remains where the line is drawn.
Is it even important that there isn't consensus?
It's certainly not a new question, but one that I felt was relevant.