Christiansen & Chater's (C&C's) argument rests on an assumption that convergent cultural evolution can produce similar (complex) behaviours in isolated populations. In this commentary, I describe how experiments recently carried out by Caldwell and colleagues can contribute to the understanding of such phenomena.

Hurley's high level of generality suggests that a control-theoretic framework underpins all of the phenomena in question, but this is problematic. In contrast to the action-perception domain, where the control-theoretic framework certainly applies, there is no evidence that this framework equally applies to feelings and emotions, such as pain, touch, and disgust, where mirroring and simulational mindreading are also found.

The philosophy of mathematics may not be helpful to the psychology of number development because they differ in their purposes.

Leech et al.'s model proposes representing relations as primed transformations rather than as structured representations (explicit representations of relations and their roles dynamically bound to fillers). However, this renders the model unable to explain several developmental trends (including relational integration and all changes not attributable to growth in relational knowledge). We suggest looking to an alternative computational model that learns structured representations from examples.

What is the status of the dichotomy proposed and the nosological validity of the contrasting pathologies described in the target article? How plausibly can dysregulated imprinting explain the array of features described, compared with other genetic models? We believe that considering alternative models is more likely to lead in the long term to the correct classification and explanation of the component behaviours.

The conjunctive conception takes imitation to be a combination of observational learning and copying. In the target article, and elsewhere, this conception generates problems in (1) explaining the copying of intransitive actions, (2) elucidating the potential functions of imitation, and (3) recognising when the correspondence problem has been avoided rather than solved. Hurley's careful use of subpersonal and personal levels of explanation shows us how to tackle these and other questions about imitation.

Sound comparative psychology and modern evolutionary and developmental biology emphasize powerful effects of developmental conditions on the expression of genetic endowment. Both demand that evolutionary theorists recognize these effects. Sound comparative psychology also demands experimental procedures that prevent experimenters from shaping the responses of human and nonhuman beings to conform to theoretical expectations.

Evolutionary contingencies select organisms based on what they can do; brains and other evolved structures serve their behavior. Arguments that brains drive language structure get the direction wrong; with functional issues unacknowledged, interactions between central structures and periphery are overlooked. Evidence supports a peripherally driven central organization. If language modules develop like other brain compartments, then environmental consistencies can engender both structural and functional language units (e.g., the different phonemic, semantic, and grammatical structures of different languages).

We agree with Penn et al. that our human cognitive superiority derives from our exceptional relational ability. We far exceed other species in our ability to grasp analogies and to combine relations into higher-order structures (Gentner 2003). However, we argue here that possession of an elaborated symbol system – such as human language – is necessary to make our relational capacity operational.

The shared circuits model (SCM) is a useful explanatory framework that can be applied to interpersonal synchrony by incorporating temporal dynamics. Temporally precise predictive simulations and mirroring enable interpersonal synchrony. When partners' movements are highly synchronous, the self/other distinction can be blurred.

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.

We evaluate whether evidence from conceptual combination supports the relational priming model of analogy. Representing relations implicitly as patterns of activation distributed across the semantic network provides a natural and parsimonious explanation of several key phenomena observed in conceptual combination. Although an additional mechanism for role resolution may be required, relational priming offers a promising approach to analogy.

Recognising that signed languages are true languages adds to the variety of forms that languages can take. Such recognition also allows one to differentiate those aspects of language that depend on the medium (voiced or signed) from those that depend on more cognitive aspects. At least some aspects of language, such as symbolic representation, time markers, and generativity, may derive from the communication of the products of mental time travel, and from the sharing of remembered past and planned future episodes.

In the target article, Crespi & Badcock (C&B) propose a novel hypothesis based on observations that a large set of phenotypic traits exhibit diametrically opposite phenotypes in autism-spectrum versus psychotic-spectrum conditions. They propose that development of these conditions is mediated in part by alterations in “genomic imprinting.” This hypothesis is based on the model of the Prader-Willi and Angelman syndromes. The authors have produced a masterful discussion of the differences between psychosis and autism. Of course, another article could be written on the similarities.

The failure of current bootstrapping accounts to explain the emergence of the concept of natural numbers does not entail that no link exists between intuitive and formal number concepts. The epidemiology of representations allows us to explain similarities between intuitive and formal number concepts without requiring that the latter are directly constructed from the former.

Autism and psychosis manifest private speech disruptions analogous to their diametrical opposition along the autism-psychosis continuum. Autism has naturally suppressed private speech with predictable structural deficits when it does surface; psychosis has overt but ineffectual private speech with similar structural deficits. These private speech oppositions are best understood in the context of the control processes of cognitive-computational architectures.

Universal Grammar (UG) is indeed evolutionarily implausible. But if languages are just “adapted” to a large primate brain, it is hard to see why other primates do not have complex languages. The answer is that humans have evolved a specialized and uniquely human cognitive architecture, whose main function is to compute mappings between arbitrary signals and communicative intentions. This underlies the development of language in the human species.

Relational priming is argued to be a deeply inadequate model of analogy-making because of its intrinsic inability to do analogies where the base and target domains share no common attributes and the mapped relations are different. Leech et al. rely on carefully handcrafted representations to allow their model to make a complex analogy, seemingly unaware of the debate on this issue fifteen years ago. Finally, they incorrectly assume the existence of fixed, context-independent relations between objects.

Depth electrode recordings in the human mesial frontal cortex have revealed individual neurons with mirror properties. A third of these cells have excitatory properties during action execution and inhibitory properties during action observation. These cells – which we call super mirror neurons – provide the neural mechanism that implements the functions of layers 3+4 of the shared circuits model (SCM).

We propose that the missing link from nonhuman to human cognition lies with our ability to form, modify, and re-form dynamic bindings between internal representations of world-states. This capacity goes beyond dynamic feature binding in perception and involves a new conception of working memory. We propose two tests for structured knowledge that might alleviate the impasse in empirical research in nonhuman animal cognition.