Rips et al. claim that the principles underlying the structure of natural numbers cannot be inferred from interactions with the physical world. However, in their target article they failed to consider an important source of interaction: finger counting. Here, we show that finger counting satisfies all the conditions required for allowing the concept of numbers to emerge from sensorimotor experience through a bottom-up process.

With his massive redeployment hypothesis (MRH), Anderson claims that novel cognitive functions are likely to rely on pre-existing circuits already possessing suitable resources. Here, we put forward recent findings from studies in numerical cognition in order to show that the role of sensorimotor experience in the ontogenetical development of a new function has been largely underestimated in Anderson's proposal.

Cohen Kadosh & Walsh (CK&W) argue that recent findings challenge the hypothesis of abstract numerical representations. Here we show that because, like many other authors in the field, they rely on inaccurate definitions of abstract and non-abstract representations, CK&W fail to provide compelling evidence against the abstract view.