Vagueness by Numbers? No Worries
--------------------------------

Rosanna Keefe (`Vagueness by Numbers' MIND 107 1998 565--79) argues that
theories of vagueness based upon fuzzy logic and set theory rest on a
confusion: once we have assigned a number to an object to represent (for
example) its *height*, there is no distinct purpose left to be served by
assigning a number to the object to represent its *degree of tallness*; she
claims that ``any numbers assigned in an attempt to capture the vagueness of
`tall' do no more than serve as another measure of height.'' In this paper I
defend fuzzy theories of vagueness against Keefe's attack.  I show that the
numbers that we assign to objects to measure (for example) heights serve a
quite distinct purpose from the numbers that fuzzy theories of vagueness assign
to objects to measure degrees of tallness: the two sorts of assignment are both
*formally* and *conceptually* distinct; the fuzzy approach to vagueness is
well-motivated and free of confusion.