Abstract
This paper considers two mysteries having to do with vagueness. The first pertains to existence. An argument is presented for the following conclusion: there are possible cases in which âThere exists something that is Fâ is of indeterminate truth-value and with respect to which it is not assertable that there are borderline-cases of being F. It is contended that we have no conception of vagueness that makes this result intelligible. The second mystery has to do with ordinary vague predicates, such as âtallâ. An argument is presented for the conclusion that although there are people who are tall to degree 1 âdefinitely tall, tall without qualificationâ, no greatest lower bound can be assigned to the set of numbers n such that a man who is n centimeters tall is tall to degree 1. But, since this set is bounded from below, this result seems to contradict a well-known property of the real numbers.