Predicates such as 'tall' or 'to know Latin', that intuitively denote permanent properties, are called ''individual level predicates''. Many peculiar properties of this class of predicates have been noted in the literature. One such property is that we cannot say '?John is sometimes tall'. Here is a way to account for this property: this sentence sounds odd because it triggers the scalar implicature that the alternative 'John is always tall' is false, which cannot be, given that tallness is a permanent property. This idea faces two challenges. The first challenge is to make sense of the weird nature of this scalar implicature: it must be surprisingly robust, so that it cannot be overridden; furthermore, it must be blind to the common knowledge that tallness is a permanent property, since this piece of common knowledge makes the two alternatives equivalent. The second challenge is to find a way to extend this idea to other more complicated properties of individual level predicates, such as: restrictions on the interpretation of their bare plural subjects, noted in Carlson (1977), Milsark (1977) and Fox (1995); restrictions on German word order, noted in Diesing (1992); restrictions on Q-adverbs, noted in Kratzer (1995); etcetera. In this talk, I will try to defend the idea of an implicature-based theory of individual level predicates by facing these two challenges.