No one knows whether I am thin. I am not clearly thin; I am not clearly not thin. The word ‘thin’ is too vague to enable an utterance of ‘TW is thin’ to be recognized as true or as false, however accurately my waist is measured and the result compared with vital statistics for the rest of the population. I am a borderline case for ‘thin’. If you bet someone that the next person to enter the room will be thin, and I walk through the door, you will not know whether you are entitled to the winnings. Suppose that an utterance of ‘TW is thin’ is either true or false. Then since we do not know that TW is thin and do not know that TW is not thin, we are ignorant of something. Either ‘TW is thin’ expresses an unknown truth, or ‘TW is not thin’ does. We do not even have an idea how to find out whether TW is thin, given my actual measurements and those of the rest of the population. Arguably, we cannot know in the circumstances that TW is thin or that TW is not thin; in that sense, we are necessarily ignorant of something. Most work on vagueness has taken it for granted that these consequences are absurd. It therefore rejects the original supposition that an utterance of ‘TW is thin’ is either true or false. Borderline cases are held not to involve ignorance, on the grounds that there is no fact of the matter for us to know, hence nothing for us to be ignorant of. On this view, vague utterances in borderline cases are not bivalent.