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.

Christiansen & Chater (C&C) suggest that language is an organism, like us, and that our brains were not selected for Universal Grammar (UG) capacity; rather, languages were selected for learnability with minimal trial-and-error experience by our brains. This explanation is circular: Where did our brain's selective capacity to learn all and only UG-compliant languages come from?

We argue that autism and psychosis spectrum disorders cannot be conceptualized as polar extremes of mentalizing ability. We raise two main objections: (1) the autistic-psychotic continuum, as conceptualized by the authors, excludes defining features of schizophrenia spectrum: negative symptoms, which correlate more strongly with mentalizing impairments; and (2) little evidence exists for a relationship between mentalizing ability and positive symptoms.

I catalog several concepts associated with finite cardinals, and then invoke them to interpret and evaluate several passages in Rips et al.'s target article. Like the literature it discusses, the article seems overly quick to ascribe the possession of certain concepts to children (and of set-theoretic concepts to non-mathematicians).

It is argued that the multilayered model offered by the shared circuits model (SCM) falls short of capturing an essential aspect of social cognition, namely, its distributed nature. The SCM therefore falls short of modeling emergent social cognition and behavior.

Analogy by priming learned transformations of (causally) related objects fails to explain an important class of inference involving abstract source-target relations. This class of analogical inference extends to ad hoc relationships, precluding the possibility of having learned them as object transformations. Rather, objects may be placed into momentarily corresponding, symbolic, source-target relationships just to complete an analogy.

That language is shaped to fit the human brain is close to the Chomskyan position. The target article by Christiansen & Chater (C&C) assumes an entity, “(the) language,” outside individual heads. What is the nature of this entity? Linguistic niche-construction and co-evolution of language and genes are possible, with some of what evolved being language-specific. Recent generative theory postulates much less than the old Universal Grammar (UG).

Data on toddler language acquisition and use support the idea of a cognitive “supermodule” that can resolve contradictory claims about human-animal similarities. Examples of imagination, aesthetic evaluation, theory of mind (ToM), and language learning reveal higher-order, relational, abstract capabilities early on. Although language itself may be a consequence of exercising this supermodule, it enables further cognitive operations on indirect experience to go far beyond animal accomplishments.

The thesis of discontinuity between humans and nonhumans requires evidence from formal reasoning tasks that rules out solutions based on associative strategies. However, insightful problem solving can be often credited through talking to humans, but not to nonhumans. We note the paradox of assuming that reasoning is orthogonal to language and enculturation while employing the criterion of using language to compare what humans and nonhumans know.

People cannot understand intentions behind observed actions by direct simulation, because goal inference is highly context dependent. Context dependency is a major source of computational intractability in traditional information-processing models. An embodied embedded view of cognition may be able to overcome this problem, but then the problem needs recognition and explication within the context of the new, layered cognitive architecture.

The claim that language is shaped by the brain is weakened by lack of clear specification of what necessary and sufficient properties the brain actually imposes. To account for human intellectual superiority, it is proposed that language did require special brain evolution (Deacon 1997), but that what evolved was a merely quantitative change – in representation space – rather than a radically new invention.

Autism and early-onset schizophrenia share common dimensions of social communication deficits. The possible role of common genetic factors has to be seriously considered, such as the serotonin transporter gene that influences the severity of social communication impairments (negative symptoms) and hallucinations (positive symptoms). Autism and the negative syndrome of schizophrenia might be at one extreme of a continuum, and paranoid schizophrenia (positive symptoms) at the other extreme.

Rips et al. appear to discuss, and then dismiss with counterexamples, the brain-based theory of mathematical cognition given in Lakoff and Núñez (2000). Instead, they present another theory of their own that they correctly dismiss. Our theory is based on neural learning. Rips et al. misrepresent our theory as being directly about real-world experience and mappings directly from that experience.

The authors' claim that analogical reasoning is the product of relational priming is compatible with language processing work that emphasizes the role of low-level automatic processes in the alignment of situation models in dialogue. However, their model ignores recent behavioral evidence demonstrating a “lexical boost” effect on relational priming. We discuss implications of these data.

According to Rips et al., numerical cognition develops out of two independent sets of cognitive primitives – one that supports enumeration, and one that supports arithmetic and the concepts of natural numbers. I argue against this proposal because it incorrectly predicts that natural number concepts could develop without prior knowledge of enumeration.

Three related issues are addressed. First, Hurley treats emulation and imitation as a straightforward dichotomy with emulation emerging first. Recent conceptual analyses and “ghost” chimpanzee experiments challenge this. Second, other recent chimpanzee experiments reveal high-fidelity social transmission, questioning whether copying fidelity is the brake on cumulative culture. Finally, other cognitive processes such as pretence need to be integrated.

The real reason for the apparent discontinuity between human and nonhuman minds is that all closely related hominids have become extinct. Nonetheless, I agree with Penn et al. that comparative psychology should aim to establish what cognitive traits humans share with other animals and what traits they do not share, because this could make profound contributions to genetics and neuroscience. There is, however, no consensus yet, and Penn et al.'s conclusion that it all comes down to one trait is premature.

The target article develops a computational connectionist model for analogy-making from a developmental perspective and evaluates this model using simple analogies. Our commentary critically reviews the advantages and limits of this approach, in particular with respect to its expressive power, its capability to generalize across analogous structure and analyze systematicity in analogies.

Neural circuits linking local operations in the cortex and the basal ganglia confer reiterative capacities, expressed in seemingly unrelated human traits such as speech, syntax, adaptive actions to changing circumstances, dancing, and music. Reiteration allows the formation of a potentially unbounded number of sentences from a finite set of syntactic processes, obviating the need for the hypothetical “Narrow Faculty of Language.”

Social cognition is a broad term, incorporating all aspects of social functioning from perceiving emotional stimuli to attributional style and theory of mind. Not distinguishing between these different capacities may confound the interpretation of the data deriving from studies of the relationship between psychiatric disorders and the social brain. The distinction between cognitive and affective components of social cognition is clearly exemplified by the abnormalities observed in psychopathy and Williams syndrome.