In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities, there is widespread skepticism about the possibility of giving non-representational accounts of cognitive capacities such as memory, imagination or abstract thought. In this paper, I (...) will critically examine the view that there are fundamental limitations to non-representational explanations of cognition. Rather than challenging these arguments on general grounds, I will examine a set of human cognitive capacities that are generally thought to fall outside the scope of non-representational accounts, i.e. numerical cognition. After criticizing standard representational accounts of numerical cognition for their lack of explanatory power, I will argue that a non-representational approach that is inspired by radical enactivism offers the best hope for developing a genuine naturalistic explanatory account for these cognitive capacities. (shrink)

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)

In this paper I study the development of arithmetical cognition with the focus on metaphorical thinking. In an approach developing on Lakoff and Núñez, I propose one particular conceptual metaphor, the Process → Object Metaphor, as a key element in understanding the development of mathematical thinking.

Cognitive innovation has shaped and transformed our cognitive capacities throughout history. Until recently, cognitive innovation has not received much attention by empirical and conceptual research in the cognitive sciences. This paper is a first attempt to help close this gap. It will be argued that cognitive innovation is best understood in connection with cumulative cultural evolution and enculturation. Cumulative cultural evolution plays a vital role for the inter-generational transmission of the products of cognitive innovation. Furthermore, there are at least two (...) important functions of enculturation for cognitive innovation. First, enculturation is responsible for the ontogenetic acquisition of cognitive practices governing the interaction with innovative products. Second, successful processes of enculturation provide opportunities for subsequent innovative processes. The trans-generational trajectory of calculation from mathematical symbol systems to the first digital computers will serve as a paradigm example of the delicate interplay of cognitive innovation, cumulative cultural evolution, and enculturation. (shrink)

This paper aims to clarify Merleau-Ponty’s contribution to an embodied-enactive account of mathematical cognition. I first identify the main points of interest in the current discussions of embodied higher cognition and explain how they relate to Merleau-Ponty and his sources, in particular Husserl’s late works. Subsequently, I explain these convergences in greater detail by more specifically discussing the domains of geometry and algebra and by clarifying the role of gestalt psychology in Merleau-Ponty’s account. Beyond that, I explain how, for Merleau-Ponty, (...) mathematical cognition requires not only the presence and actual manipulation of some concrete perceptible symbols but, more strongly, how it is fundamentally linked to the structural transformation of the concrete configurations of symbolic systems to which these symbols appertain. Furthermore, I fill a gap in the literature by explaining Merleau-Ponty’s claim that these structural transformations are operated through motor intentionality. This makes it possible, in turn, to contrast Merleau-Ponty’s approach to ontologically idealistic and realistic views on mathematical objects. On Merleau-Ponty’s account, mathematical objects are relational entities, that is, gestalts that necessarily imply situated cognizers to whom they afford a specific type of engagement in the world and on whom they depend in their eventual structural transformations. I argue that, by attributing a strongly constitutive role to phenomenal configurations and their motor transformation in mathematical thinking, Merleau-Ponty contributes to clarifying the worldly, historical, and socio-cultural aspects of mathematical truths without compromising what we perceive as their universality, certainty, and necessity. (shrink)

In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created (...) yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize, or on the ability to approximate quantities, or both, (...) fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. (shrink)

Rational agency is of central interest to philosophy, with evolutionary accounts of the cognitive underpinnings of rational agency being much debated. Yet one building block—our ability to argue—is less studied, except Mercier and Sperber’s argumentative theory :57–74, https://doi.org/10.1017/s0140525x10000968, 2011, in The enigma of reason. Harvard University Press, Cambridge, 2017). I discuss their account and argue that it faces a lacuna: It cannot explain the origin of argumentation as a series of small steps that reveal how hominins with baseline abilities of (...) the trait in question could turn into full-blown owners of it. This paper then provides a first sketch of the desired evolutionary trajectory. I argue that reasoning coevolves with the ability to coordinate behavior. After that, I establish a model based on niche construction theory. This model yields a story with following claims. First, argumentation came into being during the Oldowan period as a tool for justifying information ‘out of sight’. Second, argumentation enabled hominins to solve collective action problems with collaborators out of sight, which stabilized argumentative practices eventually. Archeological findings are discussed to substantiate both claims. I conclude with outlining changes resultant from my model for the concept of rational agency. (shrink)

Following Marr’s famous three-level distinction between explanations in cognitive science, it is often accepted that focus on modeling cognitive tasks should be on the computational level rather than the algorithmic level. When it comes to mathematical problem solving, this approach suggests that the complexity of the task of solving a problem can be characterized by the computational complexity of that problem. In this paper, I argue that human cognizers use heuristic and didactic tools and thus engage in cognitive processes that (...) make their problem solving algorithms computationally suboptimal, in contrast with the optimal algorithms studied in the computational approach. Therefore, in order to accurately model the human cognitive tasks involved in mathematical problem solving, we need to expand our methodology to also include aspects relevant to the algorithmic level. This allows us to study algorithms that are cognitively optimal for human problem solvers. Since problem solving methods are not universal, I propose that they should be studied in the framework of enculturation, which can explain the expected cultural variance in the humanly optimal algorithms. While mathematical problem solving is used as the case study, the considerations in this paper concern modeling of cognitive tasks in general. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...) computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

Arithmetical cognition is the result of enculturation. On a personal level of analysis, enculturation is a process of structured cultural learning that leads to the acquisition of evolutionarily recent, socio-culturally shaped arithmetical practices. On a sub-personal level, enculturation is realized by learning driven plasticity and learning driven bodily adaptability, which leads to the emergence of new neural circuitry and bodily action patterns. While learning driven plasticity in the case of arithmetical practices is not consistent with modularist theories of mental architecture, (...) it can be enriched by the theory of neural reuse. According to neural reuse, cerebral regions are reused to contribute to multiple neural circuits in functionally constrained ways throughout ontogeny. By hypothesis, learning driven plasticity is complemented by learning driven bodily adaptability, which suggests that there is an interesting functional relationship between finger gnosis, finger counting, and arithmetical practices. The emerging perspective on enculturated arithmetical cognition will be complemented by considerations on associated developmental and acquired disorders, namely developmental dyscalculia and acquired acalculia. The upshot is that we need to take the cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturation into account in order to arrive at a better understanding of the phylogenetic and ontogenetic conditions of arithmetical cognition. (shrink)

In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the use of (...) lettered diagrams; and the creation of linguistic formulae. Together, these artifacts formed the professional language of geometry. In this respect, the case of Greek geometry clearly shows that explanations of geometric reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice. Cognitive artifacts in Greek geometry constrained the repertoire of admissible inferential operations, which made these proofs inter-subjectively testable and compelling. By focusing on the cognitive operations on artifacts, we also stress that mental mechanisms that contribute to these operations are still poorly understood, in contrast to those mechanisms which drive symbolic logical inference. (shrink)

Mathematical cognition has become an interesting case study for wider theories of cognition. Menary :1–20, 2015) argues that arithmetical cognition not only shows that internalist theories of cognition are wrong, but that it also shows that the Hypothesis of Extended Cognition is right. I examine this argument in more detail, to see if arithmetical cognition can support such conclusions. Specifically, I look at how the use of numerals extends our arithmetical abilities from quantity-related innate systems to systems that can deal (...) with exact numbers of arbitrary size. I then argue that the system underlying our grasp of small numbers is an unhelpful case study for Menary; it doesn’t support an argument for externalism over internalism. The system for large numbers, on the other hand, clearly displays important interactions between public numeral systems and our cognitive processes. I argue that the large number system supports an argument against internalist theories of arithmetical cognition, but that one cannot conclude that the Hypothesis of Extended Cognition is correct. In other words, the large number case doesn’t decide between the Hypothesis of Extended Cognition and the Hypothesis of EMbedded Cognition. (shrink)

We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...) to highlight a potential danger of intellectual enculturation. (shrink)

Many of our cognitive capacities are the result of enculturation. Enculturation is the temporally extended transformative acquisition of cognitive practices in the cognitive niche. Cognitive practices are embodied and normatively constrained ways to interact with epistemic resources in the cognitive niche in order to complete a cognitive task. The emerging predictive processing perspective offers new functional principles and conceptual tools to account for the cerebral and extra-cerebral bodily components that give rise to cognitive practices. According to this emerging perspective, many (...) cases of perception, action, and cognition are realized by the on-going minimization of prediction error. Predictive processing provides us with a mechanistic perspective that helps investigate the functional details of the acquisition of cognitive practices. The argument of this paper is that research on enculturation and recent work on predictive processing are complementary. The main reason is that predictive processing operates at a sub-personal level and on a physiological time scale of explanation only. A complete account of enculturated cognition needs to take additional levels and temporal scales of explanation into account. This complementarity assumption leads to a new framework—enculturated predictive processing—that operates on multiple levels and temporal scales for the explanation of the enculturated predictive acquisition of cognitive practices. Enculturated predictive processing is committed to explanatory pluralism. That is, it subscribes to the idea that we need multiple perspectives and explanatory strategies to account for the complexity of enculturation. The upshot is that predictive processing needs to be complemented by additional considerations and conceptual tools to realize its full explanatory potential. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

Drawing on a range of literature, I introduce two new concepts for understanding and exploring distributed cognition: resilience engineering and degeneracy. By re-examining Ed Hutchins’ ethnographic study of the navigation team I show how a focus on the developmental acquisition of cognitive practices can draw out several crucial insights that have been overlooked. Firstly, that the way in which agents learn and acquire cognitive practices enables a form of resilience engineering: the process by which the system is able to overcome (...) and adapt to errors and the vagaries of nature. Secondly, that the best way to engineer a resilient system is through promoting degeneracy – how differing structures produce the same function – at the level of cognitive practices. These two features show that focusing on cognitive practices and developmental trajectories is important for both greater explanatory leverage; and is also useful in regard to the practicalities of designing real-world cognitive systems. (shrink)

Vehicle externalism maintains that the vehicles of our mental representations can be located outside of the head, that is, they need not be instantiated by neurons located inside the brain of the cogniser. But some disagree, insisting that ‘non-derived’, or ‘original’, content is the mark of the cognitive and that only biologically instantiated representational vehicles can have non-derived content, while the contents of all extra-neural representational vehicles are derived and thus lie outside the scope of the cognitive. In this paper (...) we develop one aspect of Menary’s vehicle externalist theory of cognitive integration—the process of enculturation—to respond to this longstanding objection. We offer examples of how expert mathematicians introduce new symbols to represent new mathematical possibilities that are not yet understood, and we argue that these new symbols have genuine non-derived content, that is, content that is not dependent on an act of interpretation by a cognitive agent and that does not derive from conventional associations, as many linguistic representations do. (shrink)

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)

Mathematical cognition is widely regarded as the epitome of the kind of cognition that systematically eludes enactivist treatment. It is the parade example of abstract, disembodied cognition if ever there was one. As it is such an important test case, this paper focuses squarely on what Gallagher has to say about mathematical cognition in Enactivist Interventions. Gallagher explores a number of possible theories that he holds could provide useful fodder for developing an adequate enactivist account of mathematical cognition. Yet if (...) the analyses of this paper prove sound, then some of the central approaches he considers are simply not fit for such service. That said, in the final analysis, if crucial additions and subtractions are made, there is a real chance of fashioning a promising enactivist account of mathematical cognition. (shrink)

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least, scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his (...) ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts. (shrink)

Predictive Processing accounts of Cognition, PPC, promise to forge productive alliances that will unite approaches that are otherwise at odds. Can it? This paper argues that it can’t—or at least not so long as it sticks with the cognitivist rendering that Clark and others favor. In making this case the argument of this paper unfolds as follows: Sect. 1 describes the basics of PPC—its attachment to the idea that we perceive the world by guessing the world. It then details the (...) reasons why so many find cognitivist interpretations to be inevitable. Section 2 examines how prominent proponents of cognitivist PPC have proposed dealing with a fundamental problem that troubles their accounts—the question of how the brain is able to get into the great guessing game in the first place. It is argued that on close inspection Clark’s solution, which he calls bootstrap heaven is—once we take a realistic look at the situation of the brain—in fact bootstrap hell. Section 3 argues that it is possible to avoid dwelling in bootstrap hell if one adopts a radically enactive take on PPC. A brief sketch of what this might look like is provided. (shrink)

Explaining humans as rational creatures—capable of deductive reasoning—remains challenging for evolutionary naturalism. Schechter 437–464, 2011, 2013) proposes to link the evolution of this kind of reasoning with the ability to plan. His proposal, however, does neither include any elaborated theory on how logical abilities came into being within the hominin lineage nor is it sufficiently supported by empirical evidence. I present such a theory in broad outline and substantiate it with archeological findings. It is argued that the cognitive makeup of (...) any animal is constituted by being embedded in a certain way of life. Changing ways of life thus foster appearances of new cognitive abilities. Finally, a new way of life of coordinated group behavior emerged within the hominins: anticipatory group planning involved in activities like making sophisticated spears for hunting. This gave rise to human logical cognition. It turned hominins into domain-general reasoner and adherents of intersubjective norms for reasoning. However, as I argue, it did not—and most likely could not—give rise to reason by deductive logic. More likely, deductive reasoning entered our world only a few thousand years ago: exclusively as a cultural artifact. (shrink)

Research in evolutionary biology and philosophy of biology and cognition strongly suggests that human organisms modify their environment through active processes of niche construction. Recently, proponents of the free-energy principle and variational active inference have argued that their approach can deepen our understanding of the reciprocal causal relationship between organisms and their niche on various scales. This paper examines the feasibility and scope of variational formalisations and conceptualisations of the organism-niche nexus with a particular focus on the extended active inference (...) account. I will draw a conceptual distinction between selective niche construction, developmental niche construction, and organism-niche coordination dynamics and argue that these notions capture different causal patterns, each of which with a distinct scope. Against this background, I will analyse and discuss the extended active inference account and its strategy to integrate variational active inference with work on extended cognition. The proponents of extended active inference assume that their account can provide an explanation of selective niche construction, developmental niche construction, and organism-niche coordination dynamics. However, my key claim will be that this account has the potential to elucidate the workings of organism-niche coordination dynamics, but does not adequately capture the causal patterns of selective niche construction and developmental niche construction. (shrink)

In this paper, we argue that several recent ‘wide’ perspectives on cognition (embodied, embedded, extended, enactive, and distributed) are only partially relevant to the study of cognition. While these wide accounts override traditional methodological individualism, the study of cognition has already progressed beyond these proposed perspectives towards building integrated explanations of the mechanisms involved, including not only internal submechanisms but also interactions with others, groups, cognitive artifacts, and their environment. The claim is substantiated with reference to recent developments in the (...) study of “mindreading” and debates on emotions. We claim that the current practice in cognitive (neuro)science has undergone, in effect, a silent mechanistic revolution, and has turned from initial binary oppositions and abstract proposals towards the integration of wide perspectives with the rest of the cognitive (neuro)sciences. (shrink)

Mathematicians’ use of external representations, such as symbols and diagrams, constitutes an important focal point in current philosophical attempts to understand mathematical practice. In this paper, we add to this understanding by presenting and analyzing how research mathematicians use and interact with external representations. The empirical basis of the article consists of a qualitative interview study we conducted with active research mathematicians. In our analysis of the empirical material, we primarily used the empirically based frameworks provided by distributed cognition and (...) cognitive semantics as well as the broader theory of cognitive integration as an analytical lens. We conclude that research mathematicians engage in generative feedback loops with material representations, that they use representations to facilitate the use of experiences of handling the physical world as a resource in mathematical work, and that their use of representations is socially sanctioned and enabled. These results verify the validity of the cognitive frameworks used as the basis for our analysis, but also show the need for augmentation and revision. Especially, we conclude that the social and cultural context cannot be excluded from cognitive analysis of mathematicians’ use of external representations. Rather, representations are socially sanctioned and enabled in an enculturation process. (shrink)

Menary OpenMIND, MIND Group, Frankfurt am Main, 2015) has argued that the development of our capacities for mathematical cognition can be explained in terms of enculturation. Our ancient systems for perceptually estimating numerical quantities are augmented and transformed by interacting with a culturally-enriched environment that provides scaffolds for the acquisition of cognitive practices, leading to the development of a discrete number system for representing number precisely. Numerals and the practices associated with numeral systems play a significant role in this process. (...) However, the details of the relationship between the ancient number system and the discrete number system remain unclear. This lack of clarity is exacerbated by the problem of symbolic estrangement and the fact that unique features of how numeral systems represent require our ancient number system to play a dual role. These issues highlight that Dehaene’s From monkey brain to human brain, MIT Press, Cambridge, pp 133–157, 2005) neuronal recycling hypothesis may be insufficient to explain the neural mechanisms underlying the process of enculturation. In order to explain mathematical enculturation, and enculturation more generally, it may be necessary to adopt Anderson’s :245–266, 2010; After phrenology: neural reuse and the interactive brain, MIT Press, Cambridge, 2014) theory of neural reuse. (shrink)

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least, scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his (...) ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts. (shrink)

This paper shows how a radical approach to enactivism provides a way of clarifying and unifying different varieties of enactivism and enactivist-friendly approaches so as to provide a genuine alternative to classical cognitivism. Section 1 reminds readers of the broad church character of the enactivism framework. Section 2 explicates how radical enactivism is best understood not as a kind of enactivism per se but as a programme for radicalizing and consolidating the many different enactivist offerings. The main work of radical (...) enactivism is to RECtify, existing varieties of enactivism and other cognate approaches so as to strengthen and unify them into a single collective that can rival classical ways of thinking about mind and cognition. Section 3 shows how even seemingly non-enactivist explanatory offerings—such as predictive processing accounts of cognition—might be RECtified and brought within the enactivist explanatory fold. Section 4 reveals why, once RECtified, enactivist offerings, broadly conceived, qualify as genuine and revolutionary alternatives to classical ways of understanding cognition. (shrink)

In a recent paper, Jakob Hohwy argues that the emerging predictive processing perspective on cognition requires us to explain cognitive functioning in purely internalistic and neurocentric terms. The purpose of the present paper is to challenge the view that PP entails a wholesale rejection of positions that are interested in the embodied, embedded, extended, or enactive dimensions of cognitive processes. I will argue that Hohwy’s argument from analogy, which forces an evidentiary boundary into the picture, lacks the argumentative resources to (...) make a convincing case for the conceptual necessity to interpret PP in solely internalistic terms. For this reason, I will reconsider the postulation and explanatory role of the evidentiary boundary. I will arrive at an account of prediction error minimization and its foundation on the free energy principle that is fully consistent with approaches to cognition that emphasize the embodied and interactive properties of cognitive processes. This gives rise to the suggestion that explanatory pluralism about the application of PP is to be preferred over Hohwy’s explanatory monism that follows from his internalistic and neurocentric view of predictive cognitive systems. (shrink)