When faced with a sentence like, “some of the toys are on the table”, adults, but not preschoolers, compute a scalar implicature, taking the sentence to suggest that not all the toys are on the table. Although this difference is sometimes attributed to children’s difficulties in processing and pragmatic understanding, this paper explores the hypothesis that children fail to compute scalar implicatures because they lack knowledge about relevant lexical alternatives to words like “some”. Four-year-olds were shown pictures in which two objects fit a description and a third object did not, and were asked to judge the truth value of statements that relied on context-independent alternatives (e.g. only some of the toys are on the table) or contextual alternatives (e.g. only the drum and the ball are on the table). Children computed scalar implicatures only in the case of contextual alternatives, and only when the statements were grammatically strengthened, supporting the hypothesis that children’s difficulties with scalar implicature result from a lack of knowledge of the relevant alternatives.