ABSTRACT

Frege came to believe that a language containing vague predicates was essentially defective – that it was philosophically intolerable that predicates should occur for which it was not always determinate whether or not they could truly be ascribed to an object. Expressions of this conception are scattered throughout his writings. When, more seldom, he argues for it, it is on the ground that logical transformations may fail when applied to sentences containing expressions whose range of application has been only partially defined. It is not just a matter of the Law of Excluded Middle. Let F be a predicate defined only among, and universally applying to, individuals which are G. Then anything G is F. But the contrapositive fails: we cannot say that anything not-F is not-G, since the concept of having or lacking F has been fixed only for things which are G. 1