There is a very large number of quantifiers in English, so many that it seems impossible that the only information that they convey is about amounts. Building on the earlier work of Moxey and Sanford (1987), we report three experiments showing that positive and negative quantifiers focus on different subsets of the logical possibilities that quantifiers allow semantically. Experiments 1 and 2 feature a continuation task with quantifiers that span a full range of denotations (from near 0% to near 100%) and show that the effect is not restricted to quantifiers denoting small amounts. This enables a distinction to be made between generalization and complement set focus proper. The focus effects extend to comprehension, as shown by a self-paced reading study (Experiment 3). It is noted that the focus effects obtained are compatible with findings from earlier work by Just and Carpenter (1971), which used a verification paradigm, and in fact these effects constitute a direct test of inferences Just and Carpenter made about mechanisms of encoding negative quantifiers. A related but different explanation is put forward to explain the present data. The experiments show a quantifier function beyond the simple denotation of amount.