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)

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)

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)

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)

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)

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)

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)

It is common in the cognitive and computational sciences to regard virtual reality (VR) as composed of illusory experiences, given its immersive character. In this paper, we adopt an ecological-enactive perspective on cognition (Sect. 3) to evaluate the nature of VR and one’s engagement with it. Based on a post-cognitivist conception of illusion, we reject the commonly held assumption that virtual reality experiences (VREs) are illusory (Sect. 4). Our positive take on this issue is that VR devices, like other technological (...) devices, can be embodied during use, which is why they can be the source of experiences (Sect. 5). We then propose a new concept to interpret VREs, namely, _allusion_, which means that the subject acts _as if_ the virtual experiences are real (Sect. 6). This kind of engagement has a volitional aspect, which is evident in the onboarding of VR devices and which allows us to distinguish VREs from other experiences. We conclude that, even though we have experiences that afford certain interactions in VR, the strong continuity between cognitive and biological processes is not sustained therein. This characterizes a difference of kind—given the current state of technology—between VREs and fully fledged cognitive states, which nevertheless allows for constrained experimentation in cognitive science. (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)

Topics in Cognitive Science, Volume 14, Issue 2, Page 363-387, April 2022.

This paper argues that the still-emerging paradigm of situated cognition requires a more systematic perspective on media to capture the enculturation of the human mind. By virtue of being media, cultural artifacts present central experiential models of the world for our embodied minds to latch onto. The paper identifies references to external media within embodied, extended, enactive, and predictive approaches to cognition, which remain underdeveloped in terms of the profound impact that media have on our mind. To grasp this impact, (...) I propose an enactive account of media that is based on expansive habits as media-structured, embodied ways of bringing forth meaning and new domains of values. We apply such habits, for instance, when seeing a picture or perceiving a movie. They become established through a process of reciprocal adaptation between media artifacts and organisms and define the range of viable actions within such a media ecology. Within an artifactual habit, we then become attuned to a specific media work that engages us. Both the plurality of habits and the dynamical adjustments within a habit require a more flexible neural architecture than is addressed by classical cognitive neuroscience. To detail how neural and media processes interlock, I will introduce the concept of neuromediality and discuss radical predictive processing accounts that could contribute to the externalization of the mind by treating media themselves as generative models of the world. After a short primer on general media theory, I discuss media examples in three domains: pictures and moving images; digital media; architecture and the built environment. This discussion demonstrates the need for a new cognitive media theory based on enactive artifactual habits—one that will help us gain perspective on the continuous re-mediation of our mind. (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)

In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on (...) two closely related questions: whether it is adequate to speak of a number sense and how philosophers can make sense of the claim by cognitive scientists that numbers are perceptual entities. Moreover, I offer further support to Stevens’s distinction between numerosity and numerousness by showing that they are relational properties that emerge through different relationships between agents and their environments. The final conclusion is that, by adopting Stevens’s distinctions, numbers do not need to be seen as perceptual entities, since the so-called number sense is better described as a sense of numerousness. (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)