It is of deep interest to both linguists and psychologists alike to account for how young children acquire an understanding of number words. In their commentaries, Barner and Butterworth both point out that an important question highlighted by the work of Syrett, Musolino, and Gelman, and one that remains highly controversial, is where number meanings originate. In doing so, both Barner and Butterworth presented excellent examples of two different types of learning accounts. Barner favors a pragmatic bootstrapping account in which cues provided by language may signal to children that number words denote properties of sets. Butterworth favors an account that is situated within a number-specific domain. He suggests that a separate nonverbal natural number arithmetic domain guides verbal learning and is skeptical about the view that number word meanings can be bootstrapped from language. These commentaries have led Syrett, Musolino, and Gelman to view their account as a multidimensional one, appealing to aspects of both proposals. Children must learn the arithmetic-relevant meanings of numerical terms and symbols. They also need to learn about the cardinality-denoting properties of number words as these commentaries and a long line of developmental literature on number word meaning remind us. But this discussion also highlights the fact that knowledge of exact cardinality only scratches the surface of the many meaningful uses of number words. Beneath the surface lies a system that must be flexible enough to take language users beyond exact cardinality, but also constrained enough to generate only those logically possible options that are allowed by the grammar. A new challenge for researchers investigating number word acquisition will be to try to understand how knowledge of cardinality and the conceptual representations of number word meaning interact with abstract linguistic representations to allow children to arrive at the correct interpretations of sentences containing numerically quantified expressions.