Experimental studies indicate that nonhuman animals and infants represent numerosities above three or four approximately and that their mental number line is logarithmic rather than linear. In contrast, human children from most cultures gradually acquire the capacity to denote exact cardinal values. To explain this difference, I take an extended mind perspective, arguing that the distinctly human ability to use external representations as a complement for internal cognitive operations enables us to represent natural numbers. Reviewing neuroscientific, developmental, and anthropological evidence, (...) I argue that the use of external media that represent natural numbers (like number words, body parts, tokens or numerals) influences the functional architecture of the brain, which suggests a two-way traffic between the brain and cultural public representations. (shrink)

Where does the mind stop and the rest of the world begin? The question invites two standard replies. Some accept the demarcations of skin and skull, and say that what is outside the body is outside the mind. Others are impressed by arguments suggesting that the meaning of our words "just ain't in the head", and hold that this externalism about meaning carries over into an externalism about mind. We propose to pursue a third position. We advocate a very different (...) sort of externalism: an _active externalism_, based on the active role of the environment in driving cognitive processes. (shrink)

Hutchins examines a set of phenomena that have fallen between the established disciplines of psychology and anthropology, bringing to light a new set of relationships between culture and cognition.

Regina Fabry has proposed an intriguing marriage of enculturated cognition and predictive processing. I raise some questions for whether this marriage will work and warn against expecting too much from the predictive processing framework. Furthermore I argue that the predictive processes at a sub-personal level cannot be driving the innovations at a social level that lead to enculturated cognitive systems, like those explored in my target paper.

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

To analyze the task of mental arithmetic with external representations in different number systems we model algorithms for addition and multiplication with Arabic and Roman numerals. This demonstrates that Roman numerals are not only informationally equivalent to Arabic ones but also computationally similar—a claim that is widely disputed. An analysis of our models' elementary processing steps reveals intricate tradeoffs between problem representation, algorithm, and interactive resources. Our simulations allow for a more nuanced view of the received wisdom on Roman numerals. (...) While symbolic computation with Roman numerals requires fewer internal resources than with Arabic ones, the large number of needed symbols inflates the number of external processing steps. (shrink)

I argue that examining the explanatory power of the hypothesis of extended cognition (HEC) offers a fruitful approach to the problem of cognitive system demarcation. Although in the discussions on HEC it has become common to refer to considerations of explanatory power as a means for assessing the plausibility of the extended cognition approach, to date no satisfying account of explanatory power has been presented in the literature. I suggest that the currently most prominent theory of explanation in the special (...) sciences, James Woodward’s contrastive-counterfactual theory, and an account of explanatory virtues building on that theory can be used to develop a systematic picture of cognitive system demarcation in the psychological sciences. A major difference between my differential influence (DI) account and most other theories of cognitive extension is the cognitive systems pluralism implied by my approach. By examining the explanatory power of competing traditions in psychological memory research, I conclude that internalist and externalist classificatory strategies are characterized by different profiles of explanatory virtues and should often be considered as complementary rather than competing approaches. This suggests a deflationary interpretation of HEC. (shrink)

Various analytical tools originally developed for theories of mechanistic explanation have recently been imported into the ongoing debate on the hypothesis of extended cognition. One such tool that appears particularly relevant to that debate is Craver’s mutual manipulability account of constitution, most of all because it promises to settle the debate on experimental grounds. This paper investigates whether it is possible to deliver on that promise. We first find that, far from grounding an experimental evaluation of HEC, MM is conceptually (...) incompatible with both internalist and externalist accounts of cognition. Next, we propose a suitable modification of MM, MM*, but it turns out that MM* presupposes rather than produces clarity on the extension of cognition. Moreover, subject to MM* the inference to constitution is radically empirically underdetermined. Finally, we argue that our results can be generalized and conclude that, for principled reasons, it is impossible to experimentally determine whether cognitive processes have extracerebral constituents. Determining the extension of cognition is an inherently pragmatic matter. (shrink)

The domain of numbers provides a paradigmatic case for investigating interactions of culture, language, and cognition: Numerical competencies are considered a core domain of knowledge, and yet the development of specifically human abilities presupposes cultural and linguistic input by way of counting sequences. These sequences constitute systems with distinct structural properties, the cross-linguistic variability of which has implications for number representation and processing. Such representational effects are scrutinized for two types of verbal numeration systems—general and object-specific ones—that were in parallel (...) use in several Oceanic languages. The analysis indicates that the object-specific systems outperform the general systems with respect to counting and mental arithmetic, largely due to their regular and more compact representation. What these findings reveal on cognitive diversity, how the conjectures involved speak to more general issues in cognitive science, and how the approach taken here might help to bridge the gap between anthropology and other cognitive sciences is discussed in the conclusion. (shrink)

This paper examines the justification for the hypothesis of extended cognition. HEC claims that human cognitive processes can, and often do, extend outside our head to include objects in the environment. HEC has been justified by inference to the best explanation. Both advocates and critics of HEC claim that we can infer the truth value of HEC based on whether HEC makes a positive or negative explanatory contribution to cognitive science. I argue that IBE cannot play this epistemic role. A (...) serious rival to HEC exists with a differing truth value, and this invalidates IBEs for both the truth and the falsity of HEC. Explanatory value to cognitive science is not a guide to the truth value of HEC.Keywords: Extended mind; Extended cognition; Embedded cognition; Externalism; Inference to the best explanation; Functionalism. (shrink)

How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the (...) initial segment of the natural numbers on the basis of the Fregean definitions, but do not learn the natural number structure as a whole on the basis of Hume's principle. Therefore, we need to account for some of the consistency of our number concepts with the Dedekind-Peano axioms in other terms. (shrink)

Mangarevan traditionally contained two numeration systems: a general one, which was highly regular, decimal, and extraordinarily extensive; and a specific one, which was restricted to specific objects, based on diverging counting units, and interspersed with binary steps. While most of these characteristics are shared by numeration systems in related languages in Oceania, the binary steps are unique. To account for these characteristics, this article draws on—and tries to integrate—insights from anthropology, archeology, linguistics, psychology, and cognitive science more generally. The analysis (...) of mental arithmetic with these systems reveals that both types of systems entailed cognitive advantages and served important functions in the cultural context of their application. How these findings speak to more general questions revolving around the theoretical models and evolutionary trajectory of numerical cognition will be discussed in the. (shrink)

Our epistemic access to mathematical objects, like numbers, is mediated through our external representations of them, like numerals. Nevertheless, the role of formal notations and, in particular, of the internal structure of these notations has not received much attention in philosophy of mathematics and cognitive science. While systems of number words and of numerals are often treated alike, I argue that they have crucial structural differences, and that one has to understand how the external representation works in order to form (...) an advanced conception of numbers. The relation between external representations and mathematical cognition will be discussed by drawing on experimental results from cognitive science and mathematics education, and I argue for the constitutive role of external representations for the development of an advanced conception of numbers. (shrink)

In their papers for this issue, Sterelny and Sutton provide a dimensional analysis of some of the ways in which mental and cognitive activities take place in the world. I add two further dimensions, a dimension of manipulation and of transformation. I also discuss the explanatory dimensions that we might use to explain these cases.

Expertise is usually thought of as an individual achievement. The expert is a receptacle for knowledge and skills. The knowledge and skills required for expertise are usually thought of as residing...

Five-year-old children categorized as skilled versus unskilled counters were given verbal estimation and number word comprehension tasks with numerosities 20 – 120. Skilled counters showed a linear relation between number words and nonsymbolic numerosities. Unskilled counters showed the same linear relation for smaller numbers to which they could count, but not for larger number words. Further tasks indicated that unskilled counters failed even to correctly order large number words differing by a 2 : 1 ratio, whereas they performed well on (...) this task with smaller numbers, and performed well on a nonsymbolic ordering task with the same numerosities. These findings provide evidence that large, approximate numerosity representations become linked to number words around the time that children learn to count to those words reliably. (shrink)

Only recently the focus in numerical cognition research has considered multi-digit number processing as a relatively new and yet understudied domain in mathematical cognition. In this chapter: we argue that single-digit number processing is not sufficient to understand multi-digit number processing; provide an overview on which representations and effects have been investigated for multi-digit numbers; suggest a conceptual distinction between place-identification, place-value activation, and place-value computation; identify language influences on multi-digit number processing along that conceptual distinction; and argue that for (...) numerical development indices of multi-digit number processing may be more suitable predictors of later arithmetical performance than classical single-digit measure such as the distance effect or non-numerical variables. In the final section, we summarize the important issues in multi-digit number processing, outline future directions and try to encourage readers to contribute to a new, exciting, yet understudied domain of numerical cognition. (shrink)