Three experiments tested preschoolers' use of abstract principles to classify and label objects by shape or function. Three- and 4-year-olds were instructed to match objects by shape or function. Four-year-olds readily adopted either rule, but 3-year-olds followed only the shape rule. Without a rule, 4-year-olds tended to match by shape unless object function was shown during matching (Experiment 2). Three-year-olds' ability to use a function rule was tested in several conditions (re-presenting functions; reminders to "use the rule"; repeating rule on every trial). None induced consistent function matching (Experiment 3). Supplemental memory and verbal tasks showed that 3-year-olds have trouble using function as an abstract basis of comparison. Naming data, however, show that preschoolers are learning that object labels are based on function. The results show preschoolers' growing flexibility in adopting abstract generalization rules and growing knowledge of conventions for extending words.