The nature of presupposition projection from the scope of quantificational expressions, particularly negative ones, continues to be both theoretically and empirically controversial. We experimentally investigate the interpretation of sentences like None of the bears won the race, which could in principle be associated with three projection options, giving rise to: an existential reading, on which at least one of the bears participated and none won; a universal reading, on which all of the bears participated and none won; and a presuppositionless reading on which none of the bears both participated and won. We used a covered box task to investigate English-speaking adults’ and children’s interpretations of such sentences. The results from the adult participants provide empirical evidence for all three readings; the results from the child participants, however, reveal no evidence for the existential reading. We discuss our results in light of competing theoretical accounts, focusing on options for reconciling the theories with the experimental data from both adults and children.