Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...) I argue that although more research is needed, it is at least possible to develop the REC position consistently with the state-of-the-art empirical research on the development of arithmetical cognition. After this, I move the focus to the question whether the radical enactivist account can explain the objectivity of arithmetical knowledge. Against the realist view suggested by Hutto, I argue that objectivity is best explained through analyzing the way universal proto-arithmetical abilities determine the development of arithmetical cognition. (shrink)

One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...) show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge. (shrink)

In recent years, philosophers have developed accounts of cognitive and affective scaffolding to describe the contribution of environmental resources to the realization of mental abilities. However, an integrative account, which captures scaffolding relations in general terms and across domains, is currently lacking. To close this gap, this paper proposes a pattern theory of scaffolding. According to this theory, the functional and causal role of an environmental resource for an individual agent or a group of agents concerning a mental ability in (...) a situational context can be specified by multiple conditions that a scaffold can satisfy. On this view, scaffolds can be described in terms of patterns of relevance-weighted, gradually satisfied scaffolding conditions. The resulting theory will be applied to cases of mathematical cognition to demonstrate its plausibility and feasibility. The pattern theory of scaffolding, it will be shown, has important implications for research on embodied, embedded, extended, and enactive (4E) cognition. (shrink)

Material Engagement Theory, which forms the focus of this special issue, is a relatively new development within cognitive archaeology and anthropology, but one that has important implications for many adjacent fields of research in phenomenology and the cognitive sciences. In How Things Shape the Mind I offered a detail exposition of the major working hypotheses and the vision of mind that it embodies. Here, introducing this special issue, more than just presenting a broad overview of MET, I seek to enrich (...) and extend that vision and discuss its application to the study of mind and matter. I begin by laying out the philosophical roots, theoretical context and intellectual kinship of MET. Then I offer a basic outline of this theoretical framework focusing on the notions of thinging and metaplasticity. In the last part I am using the example of pottery making to illustrate how MET can be used to inform empirical research and how it might complement new research in phenomenology and embodied cognitive science. (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. Furthemore, 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)

Recent work has established a framework for explaining the origin of cognitive novelties—qualitatively distinct cognitive traits—in human beings. This niche construction approach argues that humans engineer epistemic environments in ways that facilitate the ontogenetic and phylogenetic development of such novelties. I here argue that attention to the organized relations between content-carrying informational vehicles, or informational form, is key to a valuable explanatory strategy within this project, what I call structural-causal explanations. Drawing on recent work from Cecilia Heyes, and developing a (...) case study around a novel mathematical capacity, I demonstrate how structural-causal explanations can contribute to the niche construction approach by underwriting the application of explanatory tools and generating new empirical targets. (shrink)

Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of (...) whether devices are used in counting, which ones are used, and how they are used. (shrink)