Hume poses a problem for conceiving of identity. It has been confused with Frege's famous puzzle how identity sentences can be both true and informative. But Hume's is a different problem, resolved neither by Frege nor Hume himself. We may think that the problem arises from simple conclusions that we know how to rectify. But it doesn't, and we don't. The problem is this: In order to conceive that something is identical with itself, we have to do so in a way compatible with being ignorant whether it is identical with itself. That means we have to be able to conceive that it is distinct from itself. But that is inconceivable, or at least it is unless there is a way to conceive of the very same thing as both many and one.