Early quantitative skills cannot be directly extended to provide the richness, precision, and sophistication of the concept of natural number. These skills must interact with top-down mathematical schemas, which can be explained by bodily grounded everyday mechanisms for abstraction and imagination (e.g., conceptual metaphor, blending) that are both biologically plausible and culturally shaped (established beyond the child's mind).

A necessary consequence of the nature of neural transmission systems is that as change in the physical state of a time-varying event takes place, delays produce error between the instantaneous registered state and the external state. Another source of delay is the transmission of internal motor commands to muscles and the inertia of the musculoskeletal system. How does the central nervous system compensate for these pervasive delays? Although it has been argued that delay compensation occurs late in the motor planning stages, even the earliest visual processes, such as phototransduction, contribute significantly to delays. I argue that compensation is not an exclusive property of the motor system, but rather, is a pervasive feature of the central nervous system (CNS) organization. Although the motor planning system may contain a highly flexible compensation mechanism, accounting not just for delays but also variability in delays (e.g., those resulting from variations in luminance contrast, internal body temperature, muscle fatigue, etc.), visual mechanisms also contribute to compensation. Previous suggestions of this notion of “visual prediction” led to a lively debate producing re-examination of previous arguments, new analyses, and review of the experiments presented here. Understanding visual prediction will inform our theories of sensory processes and visual perception, and will impact our notion of visual awareness.

An attractive feature of Neuroconstructivism, Vol. I: How the Brain Constructs Cognition is its emphasis on the active role of the individual in neural and behavioural development and the importance of the interplay with the environment. Certain aspects of development are omitted, however, such as specializations for the distinctive ecologies of infancy and childhood and the scaffolding-like features of behaviour seen during development. It was also a pity that so little credit was given to many scientists who have contributed to just those aspects of development on which the authors focus.

The unified framework for addiction (UFA) formulated by Redish et al. is a tour de force. It uniquely predicts that there should be multiple addiction syndromes and pathways – a diversity that would reflect the complexity of the mammalian brain decision system. Here I explore some of the evolutionary and developmental ramifications of UFA and derive several new avenues for research.

An attention shift from a stationary to a changing object has to occur in feature – rather than physical – space, in order to bind these stimuli into a unitary percept. This time-consuming shift leads to the perception of a changing stimulus further ahead along its trajectory. This attentional framework is able to accommodate the flash-lag effect in its multiple empirical manifestations.

The conceptual building blocks suggested by developmental psychologists may yet play a role in how the human learner arrives at an understanding of natural number. The proposal of Rips et al. faces a challenge, yet to be met, faced by all developmental proposals: to describe the logical space in which learners ever acquire new concepts.

Why has the labeled line versus across-fiber pattern debate of taste coding not been resolved? Erickson suggests that the basic tastes concept has no rational definition to test. Similarly, however, taste neuron types, which are fundamental to the across-fiber pattern concept, have not been formally defined, leaving this concept with no rational definition to test. Consequently, the two concepts are largely indistinguishable.

Though we agree with their argument that language is shaped by domain-general learning processes, Christiansen & Chater (C&C) neglect to detail how the development of these processes shapes language change. We discuss a number of examples that show how developmental processes at multiple levels and timescales are critical to understanding the origin of domain-general mechanisms that shape language evolution.

To successfully interact with a dynamic world, our actions must be guided by a continuously changing anticipated future. Such anticipations must be tuned to the processing delays in the nervous system as well as to the slowness of the body, something that requires constant adaptation of the predictive mechanisms, which in turn require that sensory information be processed at different time-scales.

Language learning is not primarily driven by a motivation to describe invariant features of the world, but rather by a strong force to be a part of the social group, which by definition is not invariant. It is not sufficient for language to be fit for the speaker's perceptual motor system. It must also be fit for social interactions.

How children learn number concepts reflects the conceptual and logical distinction between counting numbers, based on a same-size concept for collections of objects, and natural numbers, constructed as an algebra defined by the Peano axioms for arithmetic. Cross-cultural research illustrates the cultural specificity of counting number systems, and hence the cultural context must be taken into account.

Contrary to the outstanding simplistic view of the taste system, learning studies show a more complex picture. Behavioral data using conditioned taste preference and aversion tasks support the idea that mixtures involve complex interactions between individual taste cues. Evidence from taste conditioned blocking, taste perceptual learning, and taste learned preferences is considered to support such a view. Greater support for research in taste learning and memory is required for a complete understanding of taste recognition.

The ten vulnerabilities discussed in the target article vary in their likelihood of producing temporary preference for addictive activities – which is the phenomenon that puzzles conventional motivational theory. Direct dopaminergic stimulation, but probably not the other vulnerabilities, may contribute to the necessary concavity of addicts' delay discounting curves, as may factors that the senior author analyzes elsewhere. Whatever their origins, these curves can themselves account for temporary preference, sudden craving, and the “automatic” habits discussed here.

Mareschal and his colleagues argue that cognition consists of partial representations emerging from organismic constraints placed on information processing through development. However, any notion of constraints must consider multiple sensory modalities, and their gradual integration across development. Multisensory integration constitutes one important way in which developmental constraints may lead to enriched representations that serve more than immediate behavioural goals.

Neural delays, which are generally defined as visuomotor delays in interceptive actions, must be compensated to enable accurate timing in movement. Visuomotor delays can depend on the kind of task, the use of information, and the skill of the performer. The compensation for such delays does not necessarily require prediction or representation but can be made by an attunement of some parameters in what is called a law of control.

Our target article argued that a genetically specified Universal Grammar (UG), capturing arbitrary properties of languages, is not tenable on evolutionary grounds, and that the close fit between language and language learners arises because language is shaped by the brain, rather than the reverse. Few commentaries defend a genetically specified UG. Some commentators argue that we underestimate the importance of processes of cultural transmission; some propose additional cognitive and brain mechanisms that may constrain language and perhaps differentiate humans from nonhuman primates; and others argue that we overstate or understate the case against co-evolution of language genes. In engaging with these issues, we suggest that a new synthesis concerning the relationship between brains, genes, and language may be emerging.

Redish et al. suggest that their failures-in-decision-making framework for understanding addiction can also contribute to improving our understanding of a variety of psychiatric disorders. In the spirit of reflecting on the significance and scope of their research, I briefly develop the idea that their framework can also contribute to improving our understanding of the pervasive problem of procrastination.

Rips et al.'s critique is misplaced when it faults the induction model for not explaining the acquisition of meta-numerical knowledge: This is something the model was never meant to explain. More importantly, the critique underestimates what children know, and what they have achieved, when they learn the cardinal meanings of the number words “one” through “nine.”

From our deep interest in the neuroconstructivist framework, we would like to comment on two fundamental aspects of Mareschal et al.'s work: the role of neuroconstructivism for clinical work with people suffering from developmental disorders; and the relation between the process of progressive specialization and the increasing abstraction of representations in development.

The physical properties that signify objects differ dramatically, so that the organization of sensory systems must reflect those differences. Although all senses may encode peripheral sensory information using across-fiber firing distributions, an economical coding system for each sense will necessarily differ. An economical code must maximize information about objects, whether they are predators or foods.