Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas.

Imitation, deliberation, and mindreading are characteristically human sociocognitive skills. Research on imitation and its role in social cognition is flourishing across various disciplines. Imitation is surveyed in this target article under headings of behavior, subpersonal mechanisms, and functions of imitation. A model is then advanced within which many of the developments surveyed can be located and explained. The shared circuits model (SCM) explains how imitation, deliberation, and mindreading can be enabled by subpersonal mechanisms of control, mirroring, and simulation. It is cast at a middle, functional level of description, that is, between the level of neural implementation and the level of conscious perceptions and intentional actions. The SCM connects shared informational dynamics for perception and action with shared informational dynamics for self and other, while also showing how the action/perception, self/other, and actual/possible distinctions can be overlaid on these shared informational dynamics. It avoids the common conception of perception and action as separate and peripheral to central cognition. Rather, it contributes to the situated cognition movement by showing how mechanisms for perceiving action can be built on those for active perception.;>;>The SCM is developed heuristically, in five layers that can be combined in various ways to frame specific ontogenetic or phylogenetic hypotheses. The starting point is dynamic online motor control, whereby an organism is closely attuned to its embedding environment through sensorimotor feedback. Onto this are layered functions of prediction and simulation of feedback, mirroring, simulation of mirroring, monitored inhibition of motor output, and monitored simulation of input. Finally, monitored simulation of input specifying possible actions plus inhibited mirroring of such possible actions can generate information about the possible as opposed to actual instrumental actions of others, and the possible causes and effects of such possible actions, thereby enabling strategic social deliberation. Multiple instances of such shared circuits structures could be linked into a network permitting decomposition and recombination of elements, enabling flexible control, imitative learning, understanding of other agents, and instrumental and strategic deliberation. While more advanced forms of social cognition, which require tracking multiple others and their multiple possible actions, may depend on interpretative theorizing or language, the SCM shows how layered mechanisms of control, mirroring, and simulation can enable distinctively human cognitive capacities for imitation, deliberation, and mindreading.

The development of analogical reasoning has traditionally been understood in terms of theories of adult competence. This approach emphasizes structured representations and structure mapping. In contrast, we argue that by taking a developmental perspective, analogical reasoning can be viewed as the product of a substantially different cognitive ability – relational priming. To illustrate this, we present a computational (here connectionist) account where analogy arises gradually as a by-product of pattern completion in a recurrent network. Initial exposure to a situation primes a relation that can then be applied to a novel situation to make an analogy. Relations are represented as transformations between states. The network exhibits behaviors consistent with a broad range of key phenomena from the developmental literature, lending support to the appropriateness of this approach (using low-level cognitive mechanisms) for investigating a domain that has normally been the preserve of high-level models. Furthermore, we present an additional simulation that integrates the relational priming mechanism with deliberative controlled use of inhibition to demonstrate how the framework can be extended to complex analogical reasoning, such as the data from explicit mapping studies in the literature on adults. This account highlights how taking a developmental perspective constrains the theory construction and cognitive modeling processes in a way that differs substantially from that based purely on adult studies, and illustrates how a putative complex cognitive skill can emerge out of a simple mechanism.

It is widely assumed that human learning and the structure of human languages are intimately related. This relationship is frequently suggested to derive from a language-specific biological endowment, which encodes universal, but communicatively arbitrary, principles of language structure (a Universal Grammar or UG). How might such a UG have evolved? We argue that UG could not have arisen either by biological adaptation or non-adaptationist genetic processes, resulting in a logical problem of language evolution. Specifically, as the processes of language change are much more rapid than processes of genetic change, language constitutes a “moving target” both over time and across different human populations, and, hence, cannot provide a stable environment to which language genes could have adapted. We conclude that a biologically determined UG is not evolutionarily viable. Instead, the original motivation for UG – the mesh between learners and languages – arises because language has been shaped to fit the human brain, rather than vice versa. Following Darwin, we view language itself as a complex and interdependent “organism,” which evolves under selectional pressures from human learning and processing mechanisms. That is, languages themselves are shaped by severe selectional pressure from each generation of language users and learners. This suggests that apparently arbitrary aspects of linguistic structure may result from general learning and processing biases deriving from the structure of thought processes, perceptuo-motor factors, cognitive limitations, and pragmatics.

Autistic-spectrum conditions and psychotic-spectrum conditions (mainly schizophrenia, bipolar disorder, and major depression) represent two major suites of disorders of human cognition, affect, and behavior that involve altered development and function of the social brain. We describe evidence that a large set of phenotypic traits exhibit diametrically opposite phenotypes in autistic-spectrum versus psychotic-spectrum conditions, with a focus on schizophrenia. This suite of traits is inter-correlated, in that autism involves a general pattern of constrained overgrowth, whereas schizophrenia involves undergrowth. These disorders also exhibit diametric patterns for traits related to social brain development, including aspects of gaze, agency, social cognition, local versus global processing, language, and behavior. Social cognition is thus underdeveloped in autistic-spectrum conditions and hyper-developed on the psychotic spectrum.;>We propose and evaluate a novel hypothesis that may help to explain these diametric phenotypes: that the development of these two sets of conditions is mediated in part by alterations of genomic imprinting. Evidence regarding the genetic, physiological, neurological, and psychological underpinnings of psychotic-spectrum conditions supports the hypothesis that the etiologies of these conditions involve biases towards increased relative effects from imprinted genes with maternal expression, which engender a general pattern of undergrowth. By contrast, autistic-spectrum conditions appear to involve increased relative bias towards effects of paternally expressed genes, which mediate overgrowth. This hypothesis provides a simple yet comprehensive theory, grounded in evolutionary biology and genetics, for understanding the causes and phenotypes of autistic-spectrum and psychotic-spectrum conditions.

Over the last quarter century, the dominant tendency in comparative cognitive psychology has been to emphasize the similarities between human and nonhuman minds and to downplay the differences as “one of degree and not of kind” (Darwin 1871). In the present target article, we argue that Darwin was mistaken: the profound biological continuity between human and nonhuman animals masks an equally profound discontinuity between human and nonhuman minds. To wit, there is a significant discontinuity in the degree to which human and nonhuman animals are able to approximate the higher-order, systematic, relational capabilities of a physical symbol system (PSS) (Newell 1980). We show that this symbolic-relational discontinuity pervades nearly every domain of cognition and runs much deeper than even the spectacular scaffolding provided by language or culture alone can explain. We propose a representational-level specification as to where human and nonhuman animals' abilities to approximate a PSS are similar and where they differ. We conclude by suggesting that recent symbolic-connectionist models of cognition shed new light on the mechanisms that underlie the gap between human and nonhuman minds.

Sign languages provide direct evidence for the relation between human languages and the body that engenders them. We discuss the use of the hands to create symbols and the role of the body in sign language verb systems, especially in two quite recently developed sign languages, Israeli Sign Language and Al-Sayyid Bedouin Sign Language.

How can “predictive simulation” – as a conscious phenomenon, related to goal imagery – be interchangeable with mirroring, which is an automatic response that, from a first-person perspective, enters awareness only after the act? The correspondence between perception of another's action and execution of one's similar action may be an example of a general perception-motor interface that maps perception onto behaviour or disposition towards action, without the need for simulation.

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.

Although Penn et al's incisive critique of comparative cognition is welcomed, their heavily computational and representational account of cognition commits them to a purely internalist view of cognitive processes. This perhaps blinds them to a distributed alternative that raises the possibility that the human cognitive revolution occurred outside the head, and not in it.

Autism and schizophrenia are presented as the extremes of disorders affecting the social brain. By viewing human cognition impairment in terms of competence and performance, a variety of social brain disorders can be identified along the autistic-psychotic continuum.

According to the target article authors, initial experience with a circumstance primes a relation that can subsequently be applied to a different circumstance to draw an analogy. While I broadly agree with their claim about the role of relational priming in early analogical reasoning, I put forward a few concerns that may be worthy of further reflection.

Susan Hurley's shared circuits model (SCM) rightly begins in action and progresses through a series of layers; but it fails to reach action understanding because it relies on mirroring as a driving force, draws on heavily criticized theories, and neglects the need for shared experience in our grasp of social understanding.

Penn et al. propose the relational reinterpretation hypothesis as an explanation of the profound discontinuities that they identify between human and nonhuman cognition. This hypothesis is not a genuine replacement for the explanations that they reject, however, because as it stands, it simply redescribes the phenomena it is trying to explain.

Co-morbidity of schizophrenia and autism is low because interpersonal concerns of schizophrenic patients presuppose developmental achievements that are absent in autism. Autism may arise if primary anxiety is not overcome at a key developmental stage by affective synchronisation between infant and caregiver. Schizophrenic patients will have learned to regulate primitive anxiety by affectively attuning to narrow social networks but remain highly vulnerable to exclusion from larger groups.

We agree that much of language evolution is likely to be adaptation of languages to properties of the brain. However, the attempt to rule out the existence of language-specific adaptations a priori is misguided. In particular, the claim that adaptation to “moving targets” cannot occur is false. Instead, the details of gene-culture coevolution in language are an empirical matter.

Though there are holes in the theory of how children move through stages of numerical competence, the current approach offers the most promising avenue for characterizing changes in competence as children confront new mathematical concepts. Like the science of mathematics, children's discovery of number is rooted in intuitions about sets, and not purely in analytic truths.

The target article criticises neural-symbolic systems as inadequate for analogical reasoning and proposes a model of analogy as transformation (i.e., learning). We accept the importance of learning, but we argue that, instead of conflicting, integrated reasoning and learning would model analogy much more adequately. In this new perspective, modern neural-symbolic systems become the natural candidates for modelling analogy.

Although Penn et al. make a good case for the existence of deep cognitive discontinuity between humans and animals, they fail to explain how such a discontinuity could have evolved. It is proposed that until the advent of words, no species had mental representations over which higher-order relations could be computed.

The current consensus among most researchers is that natural number is not built solely upon a foundation of mental magnitudes. On their way to the conclusion that magnitudes do not form any part of that foundation, Rips et al. pass rather quickly by theories suggesting that mental magnitudes might play some role. These theories deserve a closer look.