Yes... when I first saw this paradox, the author of the article I was reading (maybe Martin Gardner?) pointed out that 'uninteresting' is itself not well-defined.
I think the uninteresting number one can be described without worrying about 'interestingness'. It works out as the same as saying something like the set of numbers that are not the smallest number in any set in some arbitrary collection of sets including this one.
It's the 'including this one' part that is causing the trouble, not which other sets are included in the arbitrary collection.
