The meaning and function of counting are subservient to the arithmetic principles of ordering, addition, and subtraction for positive cardinal values. Beginning language learners can take advantage of their nonverbal knowledge of counting and arithmetic principles to acquire sufficient knowledge of their initial verbal instantiations and move onto a relevant learning path to assimilate input for more advanced, abstract understandings.

Susan Hurley's impressive article about the shared circuit model (SCM) raises two important issues. First, I suggest that the SCM presupposes relational coding rather than translational coding as neural code. Second, the SCM being the basis for self implies that the self may be characterized as format, relational, and embodied and embedded, rather than by specific and isolated higher-order cognitive contents.

Crespi & Badcock (C&B) convincingly argue that autism and schizophrenia are diametric malfunctions of the social brain, but their core imprinting hypothesis is less persuasive. Much of the evidence they cite is unrelated to their hypothesis, is selective, or is overstated; their hypothesis lacks a clearly explained mechanism; and it is unclear how their explanation fits in with known aspects of the disorders.

Analogy-making is an ability with which we can abstract from surface similarities and perceive deep, meaningful similarities between different mental objects and situations. I propose that mental objects are dynamically changing sets of potentially interchangeable connotations. Unfortunately, most models of analogy seem devoid of both semantics and relevance-extraction, postulating analogy as a one-to-one mapping devoid of connotation transfer.

The target article discusses a model of how brain circuits mediate social behaviors such as imitation and mindreading. Hurley suggests potential mechanisms for development of shared circuits. We propose that empirical studies can be designed to differentiate the influence of genetic and learning-based factors on the development of shared circuits. We use the mirror neuron system as a model system.

The “rational bubble” stance espoused in the target article confounds cultural symbolic achievements with individual cognitive competences. With no explicit role for learning, the core rationale for claiming a major functional discontinuity between humans and other species rests on a hybrid formal model LISA (Learning and Inference with Schemas and Analogies) now overtaken by new models of cognitive growth and new empirical studies within an embodied systems stance.

This commentary aims to highlight what exactly is controversial about the traditional Universal Grammar (UG) hypothesis and what is not. There is widespread agreement that we are not born “blank slates,” that language universals exist, that grammar exists, and that adults have domain-specific representations of language. The point of contention is whether we should assume that there exist unlearned syntactic universals that are arbitrary and specific to Language.

It is important to take a developmental approach to the problem of analogy. One limitation of this approach, however, is that it does not deal with the complexity of making analogical inferences. There are a few key principles of analogical inference that are not well captured by the analogical relational priming (ARP) model.

I ask whether it is necessary that principles of number be mentally represented and point to the role of language in determining cultural variation. Some cultures possess extensive counting systems that are finite. I suggest that learning number principles is similar to learning conservation and, as such, might be derived from learning about the empirical properties of objects and other individuals in combinations.

By conceiving of autism and psychosis as diametrically opposite phenotypes of underactive and overactive mentalizing, respectively, Crespi & Badcock (C&B) commit themselves to a continuum view of intercorrelated mentalizing functions. This view fails to acknowledge dissociations between mentalizing functions and that psychotic people show a mixture of both hypo- and hyper-mentalizing.

Analogy employs a neurocognitive working-memory (WM) system to activate and bind relational representations, integrate multiple relations, and suppress distracting information. Analogy experiments exploring these processes have used a variety of methodologies including dual tasks, neuropsychology, and functional neuroimaging, as well as experiments with children and older adults. Collectively, these experiments provide a rich set of results useful in evaluating any model of analogy and its development.

True to its sensorimotor inspiration, Hurley's shared circuits model (SCM) describes goal-states only within a homeostatic mechanism for action control, neglecting to consider other functions of goals – namely, evaluation and motivation. This restriction thwarts Hurley's project of identifying the information resources enabling social cognition. In order to master intentional behavior, deliberation, and action understanding, we need to be more than just “control freaks.”

Rips et al. consider whether representations of individual objects or analog magnitudes are building blocks for the concept natural number. We argue for a third core capacity – the ability to bind representations of individuals into sets. However, even with this addition to the list of starting materials, we agree that a significant acquisition story is needed to capture natural number.

A number of studies suggest that women find artistically creative men attractive, especially in the short-term mating context. Artistic creativity (but not mathematical or technical creativity) is linked to psychosis-proneness. I hypothesise that in preferring artistically creative men, women may be choosing paternal genotypes that make babies that are not excessively somatically demanding on them.

Explaining the transition from nonhuman to human behavior is a major scientific problem. Penn et al. argue for discontinuous evolution; they review many relevant papers but miss some that disagree with their stance. Given the shifting ground on which Penn et al.'s theories are based, and the likelihood of future studies providing additional information on continuities, a more open approach to continuity is warranted.

We propose that some aspects of language – notably intersubjectivity – evolved to fit the brain, whereas other aspects – notably grammar – co-evolved with the brain. Cladistic analysis indicates that common basic structures of both action and grammar arose in phylogeny six million years ago and in ontogeny before age two, with a shared prefrontal neural substrate. In contrast, mirror neurons, found in both humans and monkeys, suggest that the neural basis for intersubjectivity evolved before language. Natural selection acts upon genes controlling the neural substrates of these phenotypic language functions.

We make three points: (1) Overlooked studies of nonhuman communication originally inspired, but no longer support, the blinkered view of mental continuity that Penn et al. critique. (2) Communicative discontinuities between animals and humans might be rooted in social-cognitive discontinuities, reflecting a common lacuna in Penn et al.'s relational reinterpretation mechanism. (3) However, relational reinterpretation need not be a qualitatively new representational process.

The shared circuits model (SCM) relies on well-regarded theories of perception-action, mirror neurons, and forward models, but the functional/informational level of the model limits its ability to explain complex behavior such as true imitation. Data from our lab and others confirm the more general details of the model, accepted by most, but specify the neural mechanisms involved in perception-action processes.

Leech et al.'s analysis adds to an emerging consensus of the role of priming in analogy-making. However, their model cannot scale up to adult-level performance because not all relations can be cast as functions. One-size-fits-all accounts cannot capture the richness of analogy. Proportional analogies and transitive inferences can be made by nonstructural mechanisms. Therefore, these tasks do not generalize to tasks that require structure mapping.

According to the recursive reminding hypothesis, repetition interacts with episodic memory to produce memory representations that encode – and recursively embed – experiences of reminding. These representations provide the rememberer with a basis for differentiating among the first time something happens, the second time it happens, and so on. I argue that such representations could mediate children's understanding of natural number.