The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical (...) ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation. (shrink)

The complementary properties and functions of cognitive artifacts and other external resources are integrated into the human cognitive system to varying degrees. The goal of this paper is to develop some of the tools to conceptualize this complementary integration between agents and artifacts. It does so by proposing a multidimensional framework, including the dimensions of information flow, reliability, durability, trust, procedural transparency, informational transparency, individualization, and transformation. The proposed dimensions are all matters of degree and jointly they constitute a multidimensional (...) space in which situated cognitive systems can be located and have certain dimensional configurations. These dimensions provide a new perspective on the conditions for cognitive extension. They are, however, not meant to provide a set of necessary and sufficient conditions, but to provide a toolbox for investigating the degree and nature of the integration of agent and artifact into “new systemic wholes”. The higher a situated system scores on the proposed dimensions, the more functional integration occurs, and the more tightly coupled the system is. (shrink)

The present research study focuses on how the language of instruction has an impact on the mathematical thinking development as a consequence of using a language of instruction different from the students’ mother tongue. In CLIL (Content and Language Integrated Learning) academic content and a foreign language are leant at the same time, a methodology that is widely used in the schools in the present times. It is, therefore, our main aim to study if the language of instruction in second (...) language immersion programs influences the development of the first formal mathematical concepts. More specifically, if the learning of mathematical concepts in the early ages develops in a similar way if it is taught in the students’ mother tongue and is not influenced by the language used for teaching. Or else, if it can influence the development of the first skills only in the students’ general performance or in certain areas. The results of both the analysis of variance and multiple regression confirm how influencing the language of instruction is when mathematical thinking is developed teaching formal contents in a non-coincidence language. The second language is affecting the resolution of daily life problems, being more competent those students in 1st grades whose language of instruction matched with their mother tongue. (shrink)

This paper explains why Clark’s Extended Mind thesis is not capable of sufficiently grasping how and in what sense external objects and technical artifacts can become part of our human cognition. According to the author, this is because a pivotal distinction between inside and outside is preserved in the Extended Mind theorist’s account of the relation between the human organism and the world of external objects and artifacts, a distinction which they proclaim to have overcome. Inspired by Charles S. Peirce’s (...) philosophy of mind, in particular, the author tries to find a way out of this ‘inside–outside’ fallacy. External objects, artifacts or processes should, according to him, not be conceived as inanimate and unintelligent matter utilised by a separately living, inner mental sphere that has set certain pre-established goals for itself. Mind has rather an artifactual character. It is not extended by an inner biological cognitive core but rather unfolds itself through objects and artifacts. Mind as such is, especially in our modern technological culture, shaped by virtue of and through technical artifacts. Recognizing this artifactual dimension of mind will, the author concludes, enable a more critical analysis of contemporary claims that ascribe certain original and irreducible features to thinking. (shrink)

The aim of this paper is to show that scientific thought experiments and works of science fiction are highly suitable tools for facilitating and increasing understanding of science. After comparing one of Einstein’s most famous thought experiments with the science fiction novel “The Forever War”, I shall argue that both proceed similarly in making some of the more outlandish consequences of special relativity theory intelligible. However, as I will also point out, understanding in thought experiments and understanding in science fiction (...) differ in one important respect: While the former aim at what I shall call “physical understanding”, science fiction novels typically have “existential understanding” as their target. (shrink)

Could neuroimaging evidence help us to assess the degree of a person’s responsibility for a crime which we know that they committed? This essay defends an affirmative answer to this question. A range of standard objections to this high-tech approach to assessing people’s responsibility is considered and then set aside, but I also bring to light and then reject a novel objection—an objection which is only encountered when functional (rather than structural) neuroimaging is used to assess people’s responsibility.

The idea that there is a “Number Sense” (Dehaene, 1997) or “Core Knowledge” of number ensconced in a modular processing system (Carey, 2009) has gained popularity as the study of numerical cognition has matured. However, these claims are generally made with little, if any, detailed examination of which modular properties are instantiated in numerical processing. In this article, I aim to rectify this situation by detailing the modular properties on display in numerical cognitive processing. In the process, I review literature (...) from across the cognitive sciences and describe how the evidence reported in these works supports the hypothesis that numerical cognitive processing is modular. I outline the properties that would suffice for deeming a certain processing system a modular processing system. Subsequently, I use behavioral, neuropsychological, philosophical, and anthropological evidence to show that the number module is domain specific, informationally encapsulated, neurally localizable, subject to specific pathological breakdowns, mandatory, fast, and inaccessible at the person level; in other words, I use the evidence to demonstrate that some of our numerical capacity is housed in modular casing. (shrink)

Recent research has suggested that the Pirahã, an Amazonian tribe with a number-less language, are able to match quantities > 3 if the matching task does not require recall or spatial transposition. This finding contravenes previous work among the Pirahã. In this study, we re-tested the Pirahãs’ performance in the crucial one-to-one matching task utilized in the two previous studies on their numerical cognition, as well as in control tasks requiring recall and mental transposition. We also conducted a novel quantity (...) recognition task. Speakers were unable to consistently match quantities > 3, even when no recall or transposition was involved. We provide a plausible motivation for the disparate results previously obtained among the Pirahã. Our findings are consistent with the suggestion that the exact recognition of quantities > 3 requires number terminology. (shrink)

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, (...) and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future. (shrink)

Embedded and embodied approaches to cognition urge that (1) complicated internal representations may be avoided by letting features of the environment drive behavior, and (2) environmental structures can play an enabling role in cognition, allowing prior cognitive processes to solve novel tasks. Such approaches are thus in a natural position to oppose the ‘thesis of linguistic structuring’: The claim that the ability to use language results in a wholesale recapitulation of linguistic structure in onboard mental representation. Prominent examples of researchers (...) adopting this critical stance include Andy Clark, Michael Wheeler, and Mark Rowlands. But is such opposition warranted? Since each of these authors advocate accounts of mental representation that are broadly connectionist, I survey research on formal language computation in artificial neural networks, and argue that results indicate a strong form of the linguistic structuring thesis is true: Internal representational systems recapitulate significant linguistic structure, even on a connectionist account of mental representation. I conclude by sketching how my conclusion can nonetheless be viewed as consistent with and complimentary to an embedded/embodied account of the role of linguistic structure in cognition. (shrink)

Biological sciences have strived to adopt the conceptual framework of physics and have become increasingly quantitatively oriented, aiming to refute the assertion that biology appears unquantifiable, unpredictable, and messy. But despite all effort, biology is characterized by a paucity of quantitative statements with universal applications. Nonetheless, many biological disciplines—most notably molecular biology—have experienced an ascendancy over the last 50 years. The underlying core concepts and ideas permeate and inform many neighboring disciplines. This surprising success is probably not so much attributable (...) to mathematical and statistical approaches in molecular biology, but rather to the preponderance of qualitative approaches, especially visualization. Visualizations can be afforded by quantitative research, but usually they rely on both, quantitative and qualitative research. I claim the following three features to be responsible for the unceasing zeal for using visualizations: visual representations facilitate reasoning, images can be cognitively processed in a “fast” manner, and abstractions of visual representations prompt conceptual advances. In summary, visualizations have largely contributed to the success of molecular biology by conveying its concepts to other disciplines, and at the same time, eclipsing mere quantitative approaches. However, visualizations also bear the risk of misinterpretation when traversing neighboring disciplines and even more so when pervading nonscientific domains. (shrink)

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

One of the most important questions in the young field of numerical cognition studies is how humans bridge the gap between the quantity-related content produced by our evolutionarily ancient brains and the precise numerical content associated with numeration systems like Indo-Arabic numerals. This gap problem is the main focus of this paper. The aim here is to evaluate the extent to which cultural factors can help explain how we come to think about numbers beyond the subitizing range. To do this, (...) I summarize Clark’s notion of a difference maker in explaining complex causation that criss-crosses between mind and world and apply it to Menary’s Open MIND. MIND Group, Frankfurt, 2015a) discussion of mathematical cognition as a case of enculturation. I argue that while Menary’s views on enculturation can help explain what makes the difference between numerate and anumerate cultures, it cannot help specify what makes the difference between numerate and anumerate individuals. I argue that features of enculturation do not provide an account of innovation capable of explaining how individuals manage to improve and modify the practices of their cultural niche. This is because Menary’s construal of the role of enculturation in the development of mathematical cognition focuses mostly on the inheritance and transmission of practices, not on their origins, which involve individual-level understanding, rather than population-level practices and pressures. The upshot is that culture provides the necessary background conditions against which individuals can innovate. This role is crucial in the development of numerical abilities—crucial, but explanatorily limited. (shrink)

In this paper we explore the interpretation of quantity expressions in Yudja, an indigenous language spoken in the Amazonian basin, showing that while the language allows reference to exact cardinalities, it does not generally allow reference to exact measure values. It does, however, allow non-exact comparison along continuous dimensions. We use this data to argue that the grammar of exact measurement is distinct from a grammar allowing the expression of exact cardinalities, and that the grammar of counting and the grammar (...) of measurement may use numerals with different, though related interpretations. As Yudja shows, the language of measurement is not automatically acquired along with the knowledge of exact numeral expressions. We show that the ‘gap’ between prelinguistic intuitions about quantity in terms of numerosity and counting, which is bridged by the learning of language expressing exact cardinality, is paralleled by a similar gap between prelinguistic intuitions about quantity on a continuous dimension and measuring: this gap too must be bridged by language which expresses exact measure values. Our results suggest that the enculturation process by which we develop skills to perform abstract operations in the domain of measurement is (1) language dependent and (2) distinct from the process by which we learn to perform abstract calculations in the cardinal domain. (shrink)

This paper explores several paths a distinctive third wave of extended cognition might take. In so doing, I address a couple of shortcomings of first- and second-wave extended cognition associated with a tendency to conceive of the properties of internal and external processes as fixed and non-interchangeable. First, in the domain of cognitive transformation, I argue that a problematic tendency of the complementarity model is that it presupposes that socio-cultural resources augment but do not significantly transform the brain’s representational capacities (...) during diachronic development. In this paper I show that there is available a much more dynamical explanation—one taking the processes of the brain’s enculturation into patterned practices as transforming the brain’s representational capacities. Second, in the domain of cognitive assembly, I argue that another problematic tendency is an individualistic notion of cognitive agency, since it overlooks the active contribution of socio-cultural practices in the assembly process of extended cognitive systems. In contrast to an individualistic notion of cognitive agency, I explore the idea that it is possible to decentralize cognitive agency to include socio-cultural practices. (shrink)

While cognitive scientists increase their tentative incursions in the social domains traditionally reserved for social scientists, most sociologists and anthropologists keep decrying those attempts as reductionist or, at least, irrelevant. In this paper, we argue that collaboration between social and cognitive sciences is necessary to understand the impact of the social environment on the shaping of our mind. More specifically, we dwell on the cognitive strategies and early-developing deontic expectations, termed naïve sociology, which enable well-adapted individuals to constitute, maintain and (...) understand basic social relationships. In order to specify the way in which the demanding character of typical social relationships can be recognized in situ, we introduce the concept of “deontic affordances”. Finally, we shed light on the continuum that might relate a primitive naïve sociology, dedicated to the processing of invariant properties of the social life and a mature naïve sociology, necessary for dealing with the variable properties of cultural forms of life. (shrink)

We examine the question of which aspects of language are uniquely human and uniquely linguistic in light of recent suggestions by Hauser, Chomsky, and Fitch that the only such aspect is syntactic recursion, the rest of language being either specific to humans but not to language (e.g. words and concepts) or not specific to humans (e.g. speech perception). We find the hypothesis problematic. It ignores the many aspects of grammar that are not recursive, such as phonology, morphology, case, agreement, and (...) many properties of words. It is inconsistent with the anatomy and neural control of the human vocal tract. And it is weakened by experiments suggesting that speech perception cannot be reduced to primate audition, that word learning cannot be reduced to fact learning, and that at least one gene involved in speech and language was evolutionarily selected in the human lineage but is not specific to recursion. The recursion-only claim, we suggest, is motivated by Chomsky’s recent approach to syntax, the Minimalist Program, which de-emphasizes the same aspects of language. The approach, however, is sufficiently problematic that it cannot be used to support claims about evolution. We contest related arguments that language is not an adaptation, namely that it is “perfect,” non-redundant, unusable in any partial form, and badly designed for.. (shrink)

Ever wonder if it is possible to construct a numeric scale for environmental variables, like one does for the temperature? This paper is an attempt to construct one. There are two main parts: section “Statistical Analysis of Variations” presents a general statistical strategy for environmental factor selection. Section “Nonlinear Analytical Geometric Model of Variations” develops an analytical geometric representation of system variations in response to environmental changes. The model is used to quantify the effects of environmental interactions. The paper treats (...) only one-dimensional case, however, the derivation of the case of multiple independent factors follows immediately. The general method developed in this paper may prove applicable to many different fields, such as extensions beyond classical physics, economics, and other sciences. Section “Conclusion” provides an illustration of applications, examples and implications of the results. (shrink)

Adult number representations can belong to either of two types. One is discrete, language-specific, and culturally-derived; the other is analog and language-independent. Quantitative evidence is presented to demonstrate that analog number representations are adult-like in young children. Five- to 7-year-olds accurately estimated rapidly presented groups of 5--11 items. Groups were presented in random order and random arrangements controlling for overall area. Children's data were qualitatively, and to some degree quantitatively, similar to adult data with one exception: the ratio of the (...) standard deviation of estimates to mean estimates decreased with age. (shrink)

Cognitive neuroscience aims to improve our understanding of aspects of human learning and performance by combining data acquired with the new brain imaging technologies with data acquired in cognitive psychology paradigms. Both neuroscience and psychology use the philosophical assumptions underpinning the natural sciences, namely the scientific method, whereby hypotheses are proposed and tested using quantitative approaches. The relevance of 'brain science' for the classroom has proved controversial with some educators, perhaps because of distrust of the applicability of so-called 'medical models' (...) to education. Nevertheless, the brain is the main organ of learning, and so a deeper understanding of the brain would appear highly relevant to education. Modern science is revealing the crucial role of biology in every aspect of human experience and performance. This does not mean that biology determines outcomes. Rather, there is a complex interplay between biology and environments. Improved knowledge about how the brain learns should assist educators in creating optimal learning environments. Neuroscience can also identify 'biomarkers' of educational risk, and provide new methodologies to test the effects of educational interventions. (shrink)

Although deductive reasoning is a closed system, one's beliefs about the world can influence validity judgements. To understand the associated functional neuroanatomy of this belief-bias we studied 14 volunteers using event-related fMRI, as they performed reasoning tasks under neutral, facilitatory and inhibitory belief conditions. We found evidence for the engagement of a left temporal lobe system during belief-based reasoning and a bilateral parietal lobe system during belief-neutral reasoning. Activation of right lateral prefrontal cortex was evident when subjects inhibited a prepotent (...) response associated with belief-bias and correctly completed a logical task, a finding consistent with its putative role in cognitive monitoring. By contrast, when logical reasoning was overcome by belief-bias, there was engagement of ventral medial prefrontal cortex, a region implicated in affective processing. This latter involvement suggests that belief-bias effects in reasoning may be mediated through an influence of emotional processes on reasoning. (shrink)

Recently, there has been a great deal of interest in the idea that natural language enhances and extends our cognitive capabilities. Supporters of embodied cognition have been particularly interested in the way in which language may provide a solution to the problem of abstract concepts. Toward this end, some have emphasized the way in which language may act as form of cognitive scaffolding and others have emphasized the potential importance of language-based distributional information. This essay defends a version of the (...) cognitive enhancement thesis that integrates and builds on both of these proposals. I argue that the embodied representations associated with language processing serve as a supplementary medium for conceptual processing. The acquisition of a natural language provides a means of extending our cognitive reach by giving us access to an internalized combinatorial symbol system that augments and supports the context-sensitive embodied representational systems that exist independently of language. (shrink)

In the past decades, recent paradigm shifts in ethology, psychology, and the social sciences have given rise to various new disciplines like cognitive ethology and evolutionary psychology. These disciplines use concepts and theories of evolutionary biology to understand and explain the design, function and origin of the brain. I shall argue that there are several good reasons why this approach could also apply to human mathematical abilities. I will review evidence from various disciplines (cognitive ethology, cognitive psychology, cognitive archaeology and (...) neuropsychology) that suggests that the human capacity for mathematics is a category-specific domain of knowledge, hard-wired in the brain, which can be explained as the result of natural selection. (shrink)

Recent work in cognitive science highlights the importance of exem- plar-based know-how in supporting human expertise. Influenced by this model, certain accounts of moral knowledge now stress exemplar- based, non-sentential know-how at the expense of rule-and-principle based accounts. I shall argue, however, that moral thought and reason cannot be understood by reference to either of these roles alone. Moral cognition – like other forms of ‘advanced’ cognition – depends crucially on the subtle interplay and interaction of multiple factors and forces (...) and especially (or so I argue) between the use of linguistic tools and formulations and more biologically basic forms of thought and reason. (shrink)