Rips et al. argue that the construction of math schemas roughly similar to the Dedekind/Peano axioms may be necessary for arriving at arithmetical skills. However, they neglect the neo-Fregean alternative axiomatization of arithmetic, based on Hume's principle. Frege arithmetic is arguably a more plausible start for a top-down approach in the psychological study of mathematical cognition than Peano arithmetic.

One of the fundamental questions raised by Ruchkin, Grafman, Cameron, and Berndt's (Ruchkin et al.'s) interpretation of no distinct specialized neural networks for short-term storage buffers and long-term memory systems, is that of the link between perception and memory processes. In this framework, we take the opportunity in this commentary to discuss a specific working memory task involving percept formation, temporary retention, auditory imagery, and the attention-based maintenance of information, that is, the verbal transformation effect.

Savage et al. argue for musicality as having evolved for the overarching purpose of social bonding. By way of contrast, we highlight contemporary predictive processing models of human cognitive functioning in which the production and enjoyment of music follows directly from the principle of prediction error minimization.

The two target articles agree that processes of cultural evolution generate richness and diversity in music, but neither address this question in a focused way. We sketch one way to proceed – and hence suggest how the target articles differ not only in empirical claims, but also in their tacit, prior assumptions about the relationship between cognition and culture.

Fitouchi et al. illustrate the cognitive and evolutionary foundations of puritanical morality, while leave the emotional foundation unclear. We complement their theory by proposing moral emotions (e.g., guilt and shame) as characteristic emotions underlying puritanical morality. Our proposition is based on the findings that these moral emotions emerge after violations of puritanical norms and promote self-control and cooperation.

Byrne (2005) assumes that counterfactual thinking requires a comparison of facts with an imagined alternative. In our view, however, this assumption is unnecessarily restrictive. We argue that individuals do not necessarily engage in counterfactual simulations exclusively to evaluate factual reality. Instead, comparative evaluation is often suspended in favor of experiencing the counterfactual simulation as if it were real.

Grossmann presents an exciting and interesting theory on the function of fearfulness. In this commentary it is argued that fearfulness may be a byproduct of a larger executive functioning network and these early regulatory skills considered more broadly may be key building blocks for later cooperative behaviors.

From a statistician's viewpoint, the concepts discussed by Chow relating to “statistical” significance bear little resemblance to the concept developed in statistics. Whether or not “statistical significance” has a place in psychological research is a decision for psychologists, not statisticians, to make, but the decision should be based on a less flawed version of what is being considered.

The driving force in the evolution of language and the human mind was the advantage gained in courtship by efficient communicators. Ontogeny recapitulating phylogeny may offer an alternative to Donald's picture of the relative origins of language and mimesis. Very recent evidence is pertinent to dating the origin of language.

In his article, Grossmann argues that, in the context of human cooperative caregiving, heightened fearfulness in children and human sensitivity to fear in others are adaptive traits. I offer and briefly defend a rival hypothesis: Heightened fearfulness among infants and young children is a maladaptive trait that did not get deselected in the process of evolution because human sensitivity to fear in others mitigates its disadvantageous effects to a sufficient extent.

Motor processes cannot be modeled by a single (unified) model. Instead, a number of models at different levels of description are needed. The concepts of control and control variable only make sense at the functional level. A clear distinction must be made between external models and internal models. General Systems Theory provides the framework for a proper treatment of these issues.

Pickering & Garrod's (P&G's) mechanistic account of dialogue assumes that linguistic alignment between interlocutors takes place automatically, without using cognitive resources. However, even the most basic processes of speech perception depend on resource use. The lack of invariant mapping between input patterns and interpretations in dialogue, as in speech perception, may require controlled, rather than automatic, processing.

Richerson et al. argue that relatively large cultural FST values provide evidence for group structure and therefore scope for group selection. However, recent research on spatial patterns of cultural variation demonstrates that, as in the genetic case, apparent group structure can be a consequence of geographic clines, not group barriers. Such a pattern limits the scope for cultural group selection.

Recent advanced statistical analysis of complex spikes has revealed that their instantaneous firing rate within a time bin of a few milliseconds carries information if many trials are averaged, as happens in motor learning. The firing rate encodes sensory error signals in the inverse-dynamics motor-command coordinates, and these are exactly the same coordinates as for simple spikes. This strongly supports the most critical assumption of the feedback-error-learning model and argues against several hypotheses about the functions of the complex spikes. [HOUK et al.; SIMPSON et al.; SMITH; THACH]

Shepard claims that color constancy needs linear basis-function spectra, and infers the illuminant before removing its dependency. However, of the models of color constancy that have exact (and reasonable) spectral regimes, some do not need linear basis-function expansions of reflectance and illuminant spectra, some do not solve for the illuminant, and some estimate only partial object-reflectance information for single or multiple objects. [Shepard]

The conclusions reached by Leibovich et al. urge the field to regroup and consider new ways of conceptualizing quantitative development. We suggest three potential directions for new research that follow from the authors' extensive review, as well as building on the common ground we can take from decades of research in this area.