The boundaries of many categories, and hence the boundaries between their names, are often vague (Lehrer 1970, Labov 1973). At the same time, the child who is just learning the denotation of a word often makes ‘mistakes’ and may over-extend words to include objects that do not belong to the adult category (e.g. Clark 1973). The present study is concerned with when children learn that boundaries are vague. It was hypothesized that children would first over-extend the use of terms such as cup and define the domain of denotation discretely on the basis of one or two perceptual factors, and only later would they learn that category boundaries are often vague because of the interdependence of physical and functional (i.e. cultural) properties. Children aged 3, 6, 9 and 12 years were asked to name and to sort twenty-five different drinking vessels; then they were asked for definitions of cup and glass and were also asked to choose the best exemplar present of each category. The results showed that children go through three stages. First, they over-extend the term cup. Next, they focus only on certain perceptual properties. Finally, they show growing awareness of functional properties and hence of the vagueness of the boundary between cups and glasses.