Karenleigh A. Overmann

Numerosity, Abstraction, and the Emergence of Symbolic Thinking

In this paper we tentatively propose that one of the feral cognitive bases for modern symbolic thinking may be numerosity, that is, the ability to appreciate and understand numbers. We proffer that numerosity appears to be an inherently abstractive process, which is supported by numerous human infant and monkey studies. We also review studies that demonstrate that the neurological substrate for numerosity is primarily the intraparietal sulcus of the parietal lobes, the angular and supramarginal gyri in the inferior parietal lobes, and areas of the prefrontal cortex. We also speculate that the lower level of abstraction involved in numerosity may serve as a basis for higher-level symbolic thinking, such as number and letter symbolism and sequencing. We further speculate that these two levels of abstraction may give rise to highly sophisticated characteristics of modern human language, such as analogizing and metaphorizing.

Beyond Writing: The Development of Literacy in the Ancient Near East

Previous discussions of the origins of writing in the Ancient Near East have not incorporated the neuroscience of literacy, which suggests that when southern Mesopotamians wrote marks on clay in the late fourth millennium, they inadvertently reorganized their neural activity, a factor in manipulating the writing system to reflect language, yielding literacy through a combination of neurofunctional change and increased script fidelity to language. Such a development appears to take place only with a sufficient demand for writing and reading, such as that posed by a state-level bureaucracy; the use of a material with suitable characteristics; and the production of marks that are conventionalized, handwritten, simple and non-numerical. From the perspective of Material Engagement Theory (MET), writing and reading represent the interactivity of bodies, materiality and brains: movements of hands, arms and eyes; clay and the implements used to mark it and form characters; and vision, motor planning, object recognition and language. Literacy is a cognitive change that emerges from and depends upon the nexus of interactivity of the components.

Material Scaffolds in Numbers and Time

The present article develops a framework for interpreting Upper Palaeolithic artefacts from an analysis of material complexity, numeration systems and timekeeping using cultural categorizations, insights on the emergence of number terms in language, and the astronomy practices of 33 contemporary hunter-gatherer societies. Our key findings suggest that astronomy originates in the ability to estimate and infer contextual relations among natural phenomena and transitions from these natural associations to material representations and cognitive technologies that mediate conceptual apprehensions of time as a substance that can be quantified. Given that artefacts may act as scaffolds for explicit concepts of numbers, and numbers scaffold explicit concepts of time, prehistoric artefacts such as the Blombos Cave beads (c. 75,000 bp), Abri Blanchard and Cellier artefacts (c. 28,000 bp), and plaque from Grotte du Tai (c. 14,000 bp) may represent similar scaffolding and conceptual development in numbers and time. It is proposed that the prehistoric societies making these artefacts possessed, in addition to material complexity, the abilities to express quantities in language and to use material externalization and cognitive technologies. Furthermore, the Abri Blanchard artefact is proposed to represent externalized working memory, a very modern interaction between mind and material culture.

The false dichotomy: a refutation of the Neandertal indistinguishability claim.

In the debate about the demise of the Neandertal, several scholars have claimed that humanitys nearest relatives were indistinguishable archaeologically, and thus behaviorally and cognitively, from contemporaneous Homo sapiens. They suggest that to hold otherwise is to characterize Neandertals as inferior to H. sapiens, a false dichotomy that excludes the possibility that the two human types simply differed in ways visible to natural selection, including their cognition. Support of the Neandertal indistinguishability claim requires ignoring the cranial differences between the two human types, which have implications for cognition and behavior. Further, support of the claim requires minimizing asymmetries in the quantity and degree of behavioral differences as attested by the archaeological record. The present paper reviews the evidence for cognitive and archaeological differences between the two human types in support of the excluded middle position.

Numerosity Structures the Expression of Quantity in Lexical Numbers and Grammatical Number

Using data from the World Atlas of Language Structures and other sources, this study analyzed 905 languages for the presence of grammatical number (GN) and lexical numbers (LNs) to investigate what the distribution of these linguistic features might suggest about the relationship between language and numerosity, the perceptual system for quantity. Nearly 7% of the sample had LNs but lacked GN, and GN never occurred without LNs, implying that LNs may develop first and that GN is neither necessary nor sufficient for developing LNs, despite its role in helping children acquire number concepts when present as a feature of language. The geographic-temporal distribution of the two linguistic features additionally supported the idea that LNs may emerge prior to GN. Furthermore, the “one-two-three-many” structure of both LNs and GN, along with the failure of historic artificial intelligence modeling to converge on real-world number system solutions, suggested that numerosity may structure the expression of quantity in both linguistic domains. The role of the hand in numbers (the interaction of numerosity with cognitive processes such as finger gnosia, haptic perception, and neural reactions to tools) implies that LNs may originate in tactile engagement with material structures that may subsequently extend to nontactile domains, such as GN.

Recursion: what is it, who has it, and how did it evolve?

Recursion is a topic of considerable controversy in linguistics, which stems from its varying definitions and its key features, such as its universality, uniqueness to human language, and evolution. Currently, there appear to be at least two common senses of recursion: (1) embeddedness of phrases within other phrases, which entails keeping track of long-distance dependencies among phrases and (2) the specification of the computed output string itself, including meta-recursion, where recursion is both the recipe for an utterance and the overarching process that creates and executes the recipes. There are also at least two evolutionary scenarios for the adaptive value of recursion in human language. The gradualist position posits precursors, such as animal communication and protolanguages, and holds that the selective purpose of recursion was for communication. The saltationist position assumes no gradual development of recursion and posits that it evolved for reasons other than communication. In the latter view, some heritable event associated with a cognitive prerequisite of language, such as Theory of Mind or working memory capacity, allowed recursive utterances. Evolutionary adaptive reasons for recursive thoughts were also proffered, including diplomatic speech, perlocutionary acts, and prospective cognitions. WIREs Cogni Sci 2011 2 547-554 DOI: 10.1002/wcs.131 For further resources related to this article, please visit the WIREs website.

Number Concepts Are Constructed through Material Engagement: A Reply to Sutliff, Read, and Everett

Mathematical ideas—including numbers—are not innate, as Sutliff (2016, in this issue) avers, but culturally constructed concepts (De Freitas and Sinclair 2014; Núñez 2009; Read 2016, in this issue) created through the interactivity of brains, bodies, and materiality (Malafouris 2013). Certainly, the natural numbers (i.e., the numbers used in counting sequences) demonstrate significant cross-cultural commonality, both as concepts and in their overall method of invention. Such commonality is entirely predictable, given that the natural numbers are concepts of cardinality shared by sets of objects (Russell 1910, 1920) realized through human psychological, physiological, and behavioral interactions with the same material world and motivated and conventionalized by similar social requirements and transactions. However, even the natural numbers are not identical across number systems.Within a particular system, theymay change over time, from being equivalences (“that many”) to collections (“two tokens and two tokens are four tokens”) to entities related numerically to similar entities (“two plus two is four”; Gowers 2008). Across number systems, the natural numbers also differ in such matters as what they can be applied to (animate beings are not always included); how they are applied (through numeral classifiers; to single or pairs of objects); who learns and uses them within a society (they can be privileged knowledge); whether they comprise an open (extensible) or closed system; the materiality used to realize, represent, and manipulate them (which informs how they are conceived); and how they are manipulated, their degree of manipulability, and the types of operations they can be used with (discussed below). Nor is the realization of number concepts a function of “the consciousness of self in time” (Sutliff 2016). Brouwer’s introspectionist view of the natural numbers, which he “derived from the old metaphysical view that individual consciousness is the one and only source of knowledge” (Ferreirós 2008:148–149), may suffice to explain numerical origins for those who agree that numbers are innate (though Brouwer’s

Cognitive Archaeology and the Cognitive Sciences

Cognitive archaeology uses cognitive and psychological models to interpret the archaeological record. This chapter outlines several components that may be essential in building effective cognitive archaeological arguments. It also presents a two-stage perspective for the development of modern cognition, primarily based upon the work of Coolidge and Wynn. The first describes the transition from arboreal to terrestrial life in later Homo and the possible cognitive repercussions of terrestrial sleep. The second stage proposes that a genetic event may have enhanced working memory in Homo sapiens (specifically in terms of Baddeley’s multicomponent working memory model). The present chapter also reviews the archaeological and neurological bases for modern thinking, and the latter arguments are primarily grounded in the significance of the morphometric rescaling of the parietal lobes, which appears to have distinguished Homo sapiens from Neandertals.

The Cultural Challenge in Mathematical Cognition

In their recent paper on “Challenges in mathematical cognition”, Alcock and colleagues (Alcock et al. [2016]. Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41) defined a research agenda through 26 specific research questions. An important dimension of mathematical cognition almost completely absent from their discussion is the cultural constitution of mathematical cognition. Spanning work from a broad range of disciplines – including anthropology, archaeology, cognitive science, history of science, linguistics, philosophy, and psychology – we argue that for any research agenda on mathematical cognition the cultural dimension is indispensable, and we propose a set of exemplary research questions related to it.

Thinking Materially: Cognition as Extended and Enacted

Human cognition is extended and enacted. Drawing the boundaries of cognition to include the resources and attributes of the body and materiality allows an examination of how these components interact with the brain as a system, especially over cultural and evolutionary spans of time. Literacy and numeracy provide examples of multigenerational, incremental change in both psychological functioning and material forms. Though we think materiality, its central role in human cognition is often unappreciated, for reasons that include conceptual distribution over multiple material forms, the unconscious transparency of cognitive activity in general, and the different temporalities of metaplastic change in neurons and cultural forms.