To support the claim that the approximate number system represents rational numbers, Clarke and Beck argue that number perception is abstract and characterized by a second-order character. However, converging evidence from visual illusions and psychophysics suggests that perceived number is not abstract, but rather, is perceptually interdependent with other magnitudes. Moreover, number, as a concept, is second-order, but number, as a percept, is not.
The proposal of Rips et al. is motivated by discontinuity and input claims. The discontinuity claim is that no continuity exists between early (nonverbal) numerical representations and natural number. The input claim is that particular experiences (e.g., cardinality-related talk and object-based activities) do not aid in natural number construction. We discuss reasons to doubt both claims in their strongest forms.