Andrea Bender

The Limits of Counting: Numerical Cognition Between Evolution and Culture

Number words that, in principle, allow all kinds of objects to be counted ad infinitum are one basic requirement for complex numerical cognition. Accordingly, short or object-specific counting sequences in a language are often regarded as earlier steps in the evolution from premathematical conceptions to greater abstraction. We present some instances from Melanesia and Polynesia, whose short or object-specific sequences originated from the same extensive and abstract sequence. Furthermore, the object-specific sequences can be shown to be cognitively advantageous for calculations without notation because they use larger counting units, thereby abbreviating higher numbers, enhancing the counting process, and extending the limits of counting. These results expand our knowledge both regarding numerical cognition and regarding the evolution of numeration systems.

Nature and culture of finger counting: diversity and representational effects of an embodied cognitive tool.

Studies like the one conducted by Domahs et al. (2010, in Cognition) corroborate that finger counting habits affect how numbers are processed, and legitimize the assumption that this effect is culturally modulated. The degree of cultural diversity in finger counting, however, has been grossly underestimated in the field at large, which, in turn, has restricted research questions and designs. In this paper, we demonstrate that fingers as a tool for counting are not only naturally available, but are also-and crucially so-culturally encoded. To substantiate this, we outline the variability in finger counting and illustrate each of its types with instances from the literature. We argue that the different types of finger counting all constitute distinct representational systems, and we use their properties-dimensionality, dimensional representation, base and sub-base values, extendibility and extent, sign count, and regularity-to devise a typology of such systems. This allows us to explore representational effects, that is, the cognitive implications these properties may have, for instance, for the efficiency of information encoding and representation, ease of learning and mastering the system, or memory retrieval and cognitive load. We then highlight the ambivalent consequences arising from structural inconsistencies between finger counting and other modes of number representation like verbal or notational systems, and we discuss how this informs questions on the evolution and development of counting systems. Based on these analyses, we suggest some directions for future research in the field of embodied cognition that would profit substantially from taking into account the cultural diversity in finger counting.

Mapping spatial frames of reference onto time: A review of theoretical accounts and empirical findings

When speaking and reasoning about time, people around the world tend to do so with vocabulary and concepts borrowed from the domain of space. This raises the question of whether the cross-linguistic variability found for spatial representations, and the principles on which these are based, may also carry over to the domain of time. Real progress in addressing this question presupposes a taxonomy for the possible conceptualizations in one domain and its consistent and comprehensive mapping onto the other-a challenge that has been taken up only recently and is far from reaching consensus. This article aims at systematizing the theoretical and empirical advances in this field, with a focus on accounts that deal with frames of reference (FoRs). It reviews eight such accounts by identifying their conceptual ingredients and principles for space-time mapping, and it explores the potential for their integration. To evaluate their feasibility, data from some thirty empirical studies, conducted with speakers of sixteen different languages, are then scrutinized. This includes a critical assessment of the methods employed, a summary of the findings for each language group, and a (re-)analysis of the data in view of the theoretical questions. The discussion relates these findings to research on the mental time line, and explores the psychological reality of temporal FoRs, the degree of cross-domain consistency in FoR adoption, the role of deixis, and the sources and extent of space-time mapping more generally.

Should Anthropology Be Part of Cognitive Science

Anthropology and the other cognitive science (CS) subdisciplines currently maintain a troubled relationship. With a debate in topiCS we aim at exploring the prospects for improving this relationship, and our introduction is intended as a catalyst for this debate. In order to encourage a frank sharing of perspectives, our comments will be deliberately provocative. Several challenges for a successful rapprochement are identified, encompassing the diverging paths that CS and anthropology have taken in the past, the degree of compatibility between (1) CS and (2) anthropology with regard to methodology and (3) research strategies, (4) the importance of anthropology for CS, and (5) the need for disciplinary diversity. Given this set of challenges, a reconciliation seems unlikely to follow on the heels of good intentions alone.

Anthropology in Cognitive Science

This paper reviews the uneven history of the relationship between Anthropology and Cognitive Science over the past 30 years, from its promising beginnings, followed by a period of disaffection, on up to the current context, which may lay the groundwork for reconsidering what Anthropology and (the rest of) Cognitive Science have to offer each other. We think that this history has important lessons to teach and has implications for contemporary efforts to restore Anthropology to its proper place within Cognitive Science. The recent upsurge of interest in the ways that thought may shape and be shaped by action, gesture, cultural experience, and language sets the stage for, but so far has not fully accomplished, the inclusion of Anthropology as an equal partner.

Understanding conditional promises and threats

Conditional promises and threats are speech acts that are used to manipulate other peoples behaviour. Studies on human reasoning typically use propositional logic to analyse what people infer from such inducements. While this approach is sufficient to uncover conceptual features of inducements, it fails to explain them. To overcome this limitation, we propose a multilevel analysis integrating motivational, linguistic, deontic, behavioural, and emotional aspects. Commonalities and differences between conditional promises and threats on various levels were examined in two experiments. The first shows that both types of inducements are understood as being complementary on the linguistic level, but not reversible, due to the specific temporal order of their actions. In addition, it gives a first assessment of emotional reactions. The second experiment investigated the novel question of whether complementary promises and threats, despite semantic differences, both imply an obligation to cooperate on the deontic level. The data corroborate this hypothesis, and they support various appraisal-theoretical assumptions on the elicitation of emotions. They also reveal that content affects not only the attribution of emotions, but also the deontic interpretation.

Temporal Frames of Reference: Conceptual Analysis and Empirical Evidence from German, English, Mandarin Chinese and Tongan

Despite a close correspondence between spatial and temporal cognition, empirical approaches to the two domains have used distinct theoretical conceptions: frames of reference for the former, and moving perspectives and reference-point metaphors for the latter. Our analysis reveals that these conceptions can ‐ and should ‐ be related more closely to each other. Mapping spatial frames of reference (FoRs) onto temporal relations, we obtain a taxonomy that allows us to distinguish more types of referencing than existing conceptions do and that is applicable to linguistic cases not accounted for so far. A cross-cultural experiment with speakers of German, English, Chinese and Tongan provides evidence for the psychological reality of the newly proposed FoRs and establishes culture-specific preferences. We conclude that spatial referencing systems indeed help to organize temporal representations.

The Cultural Constitution of Cognition: Taking the Anthropological Perspective

To what extent is cognition affected by culture? And how might cognitive science profit from an intensified collaboration with anthropology in exploring this issue? In order to answer these questions, we will first give a brief description of different perspectives on cognition, one that prevails in most cognitive sciences – particularly in cognitive psychology – and one in anthropology. Three basic assumptions of cognitive science regarding the separability of content and process, the context-independence of processing, and the culture-independence of processing will then be discussed. We argue that these assumptions need to be questioned and scrutinized cross-culturally. A thorough examination of these issues would profit considerably from collaboration with anthropologists, not only by enabling deeper insight into the cultures under scrutiny, but also by synergistic effects that would allow for a more comprehensive understanding of human cognition.

Numeral Classifiers and Counting Systems in Polynesian and Micronesian Languages: Common Roots and Cultural Adaptations

Polynesian and Micronesian languages inherited a decimal number system from Proto-Oceanic, and individually extended it on one or more dimensions: in length by adding terms for larger numbers, in breadth by specifying numeral classifiers for certain objects (prevailing in Micronesia), and in factor by introducing a larger counting unit (prevailing in Polynesia). Specific counting systems are characterized by a combination of these features: They are based on larger counting units (multiplication function) and apply to certain objects only (object specificity). This paper surveys the distribution of each extension type in Polynesian and Micronesian number systems, characterizes the features that they share, and analyzes the constitutive role that numeral classifiers play for specific counting systems. It is concluded that in most of these languages, number systems are composed according to similar principles, while the divergence in classifiers, objects of reference, and factors chosen results from cultural adaptations, some of which might have been responses to socioeconomic requirements and served purposes of cognitive facilitation.

Explicating Numerical Information: When and How Fingers Support (or Hinder) Number Comprehension and Handling

Numbers are of enormous significance for modern society. They form the basis of currency and economic systems, of measurement and calculation, of engineering and the natural sciences, and, as a matter of course, lie at the heart of mathematics. Therefore, teaching mathematical skills plays an important role in preschool and school education. However, before children are able to perform their first symbolic algorithms such as multi-digit addition and multiplication they must have mastered two representational number systems: a verbal system (e.g., English number words) and a notational system (e.g., Arabic digits). The main competence that children have to acquire with these systems is to represent and handle the numerical information internally (Zhang and Norman, 1995). Using ones fingers for numerical tasks may indicate that parts of the internal processes still require external support and are not mastered adequately, but it would be erroneous to infer that finger strategies are not worthy of support. On the contrary: we argue that ones fingers, applied properly, provide a natural, and readily available toolkit for modeling numerical information and reflecting on numerical concepts (cf. Fuson and Secada, 1986; Carpenter et al., 1999; Wright et al., 2002; Guha, 2006; Andres et al., 2008). This position is exemplified for the acquisition of the verbal number system and for verbal processes involved in counting and calculating. Following Zhang and Normans (1995) representational analysis of notational systems, we analyze which features of the verbal system can be accessed externally, which have to be represented internally, and how this may be supported – or hindered – by finger counting strategies.