An evolutionary psychological perspective drawing on sexual selection theory can better explain sex differences in aggression and violence than can social constructionist theories. Moreover, there is accumulating evidence that, in accordance with predictions derived from sexual selection theory, men modulate their willingness to engage in risky and violent confrontations in response to cues to fitness variance and future prospects.

Dream research shows sex differences in dream aggression that fit very well with the findings for waking-life aggressive behaviour. Dream studies are a valuable tool for investigating variables underlying the sex difference in aggression. One might argue that studying dream aggression might be even more promising because aggression in dreams is not socially labelled, as being aggressive in waking life is.

Social roles theorists claim that differences between the sexes are of limited consequence. Such misperceptions lead to misunderstanding the important role of sexual selection in explaining phenotypic differences both between species and within humans. Countering these claims, we explain how sexual dimorphism in humans affect expressions of artistic display and patterns of male and female aggression across the ovulatory cycle.

At the heart of the debate between social role theorists and evolutionary psychologists is whether natural selection has designed the minds of the sexes differently to some interesting extent. In this commentary I describe the standards of evidence for both the positive and negative claims. In my opinion, Archer has met the standard for designed sex differences in intrasexual conflict.

The relation between testosterone levels and aggressive behavior is well established. From an evolutionary viewpoint, testosterone can explain at least part of the sex differences found in aggressive behavior. This explanation, however, is mediated by factors such as prenatal testosterone levels and basal levels of cortisol. Especially regarding sex differences in aggression during adolescence, these mediators have great influence. Based on developmental brain structure research we argue that sex differences in aggression have a pre-pubertal origin and are maintained during adolescence. Evidence of prenatal, adolescent, and adult levels of testosterone in relation to aggression taken together, support Archer's argument for sexual selection as the driver of sex differences in aggression.

As Archer argues, recent developmental data on human physical aggression support the sexual selection hypothesis. However, sex differences are largely due to males on a chronic trajectory of aggression. Maternal characteristics of these males suggest that, in societies with low levels of physical violence, females with a history of behavior problems largely contribute to maintenance of physical aggression sex differences.

Nothing is gained by opposing “sexual selection” and “social roles,” or by proclaiming the supremacy of one over the other. Instead, we should develop a unitary model of gene-culture coevolution, allowing for the complex interaction of both, and varying importance of each, all within our double, species-specific, adaptive, evolutionary track.

My response is organized into three sections. The first revisits the theme of the target article, the explanatory power of sexual selection versus social role theory. The second considers the range and scope of sexual selection, and its application to human sex differences. Two topics are examined in more detail: (1) the paternity uncertainty theory of partner violence; (2) evolution of inter-group aggression. Section 4 covers ultimate and proximal explanations and their integration within an ethological approach. I consider the development of sex differences in aggression, and their causal mechanisms, within this framework.

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex.

The type of processing of numerical dimensions varies greatly and is governed by context. Considering this flexibility in tandem with a fuzzy demarcation line between automatic and intentional processes, it is suggested that testing the effect of notation should not be confined to automatic processing, in particular to passive viewing. Recent behavioral data satisfying the authors' stipulations reveal a considerable, though perhaps not exclusive, core of common abstract processing.

The theory put forward by Cohen Kadosh & Walsh (CK&W) proposing that semantic representations of numerical magnitude in the parietal cortex are format-specific, does not specify how these representations might be constructed over the course of learning and development. The developmental predictions of the non-abstract theory are discussed and the need for a developmental perspective on the abstract versus non-abstract question highlighted.

Like number representation, basic arithmetic seems to be a natural candidate for abstract instantiation in the brain. To investigate this, researchers have examined effects of numeral format on elementary arithmetic (e.g., 4+5 vs. four+five). Different numeral formats often recruit distinct processes for arithmetic, reinforcing the conclusion that number processing is not necessarily abstracted away from numeral format.

The dual-code proposal of number representation put forward by Cohen Kadosh & Walsh (CK&W) accounts for only a fraction of the many modes of numerical abstraction. Contrary to their proposal, robust data from human infants and nonhuman animals indicate that abstract numerical representations are psychologically primitive. Additionally, much of the behavioral and neural data cited to support CK&W's proposal is, in fact, neutral on the issue of numerical abstraction.

In this commentary, I support and augment Cohen Kadosh & Walsh's (CK&W's) argument that numerical representations are not abstract. I briefly review data that support the non-abstract nature of the representation of numbers between zero and one, and I discuss how a failure to test alternative hypotheses has led researchers to erroneously conclude that numerals automatically activate their semantic meaning.

Cohen Kadosh & Walsh (CK&W) neglect the solid empirical evidence for a convergence of notation-specific representations onto a shared representation of numerical magnitude. Subliminal priming reveals cross-notation and cross-modality effects, contrary to CK&W's prediction that automatic activation is modality and notation-specific. Notation effects may, however, emerge in the precision, speed, automaticity, and means by which the central magnitude representation is accessed.

Cohen Kadosh & Walsh (CK&W) present convincing evidence indicating the existence of notation-specific numerical representations in parietal cortex. We suggest that the same conclusions can be drawn for a particular type of numerical representation: the representation of time. Notation-dependent representations need not be limited to number but may also be extended to other magnitude-related contents processed in parietal cortex (Walsh 2003).

We contrapose computational models using representations of numbers in parietal cortical activity patterns (abstract or not) with dynamic models, whereby prefrontal cortex (PFC) orchestrates neural operators. The neural operators under PFC control are activity patterns that mobilize synaptic matrices formed by learning into textured oscillations we observe through the electroencephalogram from the scalp (EEG) and the electrocorticogram from the cortical surface (ECoG). We postulate that specialized operators produce symbolic representations existing only outside of brains.

The goal of the present commentary is to show that past results on automatic numerical processing in different notations are consistent with the idea of an abstract numerical representation. This is done by reviewing the relevant studies and giving alternative explanations to the ones proposed in the target article.

Much evidence cited by Cohen Kadosh & Walsh (CK&W) in support of their notation-specific representation hypothesis is based on tasks requiring automatic number processing. Several of these findings can be alternatively explained by differential expertise in mapping numerical symbols onto semantic magnitude representations. The importance of considering symbol-referent mapping expertise in theories on numerical representations is highlighted.

I challenge two points in Cohen Kadosh & Walsh's (CK & W) argument: First, the definition of abstraction is too restricted; second, the distinction between representations and operations is too clear-cut. For example, taking Jean Piaget's “conservation of number task,” I propose that another way to avoid orthodoxy in the field of numerical cognition is to consider inhibition as an alternative idea of abstraction.