Even for aduelts, quantifiers such as "all", "some", "every" seem to involve difficult mapping between logic and grammar. A sentence like "every boy ate every food" requires a little concentration before the meaning comes through. One might think that there is no natural mapping of such sophisticated aspectes of cognition onto grammatical structure. Current linguistic theory, however, reveals that syntax puts sharp limits on how quantification works. The study of quantifiers might reveal how cognition connects to grammar and how they are intertwined int he process of acquisition. We will try to present the acquisition problem in a manner slightly abstracted from the technical details of linguistic theory.