This paper examines the logical problem of language acquisition drawing upon an experimental study on children’s knowledge of anaphoric <em>one</em> by Lidz, Waxman and Freedman (2003). The finding was that, upon being presented with the instruction “<em>Look! A yellow bottle. Do you see another one?</em>”, 18-month-old children prefer to look at a yellow bottle rather than to a bottle of a different color. According to Lidz et al. (2003), the results that children cannot interpret <em>one</em> as anaphoric to head nouns. We point out that the experimental findings are not explained under the hypothesis offered by the authors of that study. Secondly, we consider whether, under current assumptions, children’s knowledge of anaphoric <em>one</em> can be inferred from the properties of the final state. Thirdly, we reaffirm the validity of the Poverty of the Stimulus argument, despite the challenge posed by the learning model proposed by Regier and Gahl (2004). Finally, we draw upon recent psycholinguistic work to propose an explanation for the findings documented by Lidz et al. (2003) that is independent from – though consistent with – their knowledge of the constraint on anaphoric <em>one</em>.