Sieghard Beller

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.

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.

The logic of content effects in propositional reasoning: The case of conditional reasoning with a point of view

In order to resolve the controversial discussion regarding content effects in deductive reasoning, we propose distinguishing between two inferential sources—an arguments form, and additional relations people associate with the arguments content—and analysing their interplay. Both sources are equally necessary in order to understand the role content plays in deductive reasoning. People make valid deductions from the content relations (content competence), but in thematic reasoning tasks, these deductions lead to the intriguing phenomenon known as content effects. Focusing on the interplay of both sources of inferences, the dual source distinction enables a novel class of predictions to be made, namely the correct mastery of the logical connectors (form competence) in tasks that require the individual to think about an arguments form in relation to its content. To illustrate the dual source approach and its implications, the selection task paradigm of conditional reasoning with a point of view is used in combination with two content domains: conditional promises with cheating and non-cheating perspectives and technical systems with causal perspectives. Experimental findings corroborate all three phenomena: content competence, content effects, and form competence. The dual source distinction is discussed with regard to current theories of reasoning.

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.

Deontic norms, deontic reasoning, and deontic conditionals

Deontic reasoning is thinking about whether actions are forbidden or allowed, obligatory or not obligatory. It is proposed that social norms, imposing constraints on individual actions, constitute the fundamental concept for the system of these four deontic modalities, and that people reason from such norms flexibly according to deontic core principles. Two experiments are presented, one on deontic conditional reasoning, the other on “pure” deontic reasoning. Both experiments demonstrate peoples high deontic competence and confirm the proposed representational and inferential principles. Experiment 1 additionally shows small effects of the conditional formulations. These findings support the dual source approach (Beller & Spada, 2003) that distinguishes between domain-specific and domain-general inferences. Implications for other theories of deontic reasoning are discussed.

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.

Conditional reasoning in context: a dual-source model of probabilistic inference.

A dual-source model of probabilistic conditional inference is proposed. According to the model, inferences are based on 2 sources of evidence: logical form and prior knowledge. Logical form is a decontextualized source of evidence, whereas prior knowledge is activated by the contents of the conditional rule. In Experiments 1 to 3, manipulations of perceived sufficiency and necessity mapped on the parameters quantifying prior knowledge. Emphasizing rule validity increased the weight given to form-based evidence relative to knowledge-based evidence (Experiment 1). Manipulating rule form (only-if vs. if-then) had a focused effect on the parameters quantifying form-based evidence (Experiment 3). The model also provides a parsimonious description of data from the so-called negations paradigm and adequately accounts for polarity bias in that paradigm (Experiment 4). Relationships to alternative conceptualizations of conditional inference are discussed.