 Consider a literary historiographer who, weary of debate about the identity of the first book, demonstrates that ‘book’ is vague by assembling a slippery slope ranging from early non-books to paradigm books. According to Peirce, the demonstration succeeds only if the spectrum contains some intrinsically doubtful cases. They are what makes ‘book’ vague. Fine’s negative thesis is that this reductionist explanation relies on an impossible explanandum. A booklet can no more be an intrinsically borderline book than it can be intrinsically misshelved. Fine’s positive thesis is that slippery slopes suffice to demonstrate the vagueness of ‘book’. There are borderline books only in the way there are heavy books. In contrast to ‘mass’, ‘heavy’ requires relativization to a gravitational field. ‘Borderline’ requires relativization to a range of cases.