 In defense of the contentfulness of these identity claims, one might argue that the term “appearance” and “thing in itself” each has an extension, a set of objects, and the question of identity is perfectly well-formed: do these two sets have a non-empty intersection? If so, at least one appearance is identical to a thing in itself. But this argument begs the question by assuming that the question of whether the set of appearances and the set of thing in themselves has an intersection is itself well-formed; whether this is the case is precisely what is at issue.