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Mathematics is a struggle for many. To make it more accessible, behavioral and educational scientists are redesigning how it is taught. To a similar end, a few rogue mathematicians and computer scientists are doing something more radical: they are redesigning mathematics itself, improving its ergonomic features. Charles Peirce, an important contributor to ordinary symbolic logic, also introduced a rigorous but non-symbolic, graphical alternative to it that is easier to picture. In the spirit of this iconic logic, George Spencer-Brown founded iconic (...) |
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A popular trend in the sciences of the mind is to understand cognition as embodied, embedded, enactive, ecological, and so on. While some of the work under the label of “embodied cognition” takes for granted key commitments of traditional cognitive science, other projects coincide in treating embodiment as the starting point for an entirely different way of investigating all of cognition. Focusing on the latter, this paper discusses how embodied cognitive science can be made more reflexive and more sensitive to (...) |
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According to Enactivism, cognition should be understood in terms of a dynamic interaction between an acting organism and its environment. Further, this view holds that organisms do not passively receive information from this environment, they rather selectively create this environment by engaging in interaction with the world. Radical Enactivism adds that basic cognition does so without entertaining representations and hence that representations are not an essential constituent of cognition. Some proponents think that getting rid of representations amounts to a revolutionary (...) |
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Embodied approaches to cognition conceive of mental life as emerging from the ongoing relationship between neural and extra-neural resources. The latter include, first and foremost, our entire body, but also the activity patterns enacted within a contingent milieu, cultural norms, social factors, and the features of the environment that can be used to enhance our cognitive capacities (e.g., tools, devices, etc.). Recent work in music education and sport psychology has applied general principles of embodiment to a number of social contexts (...) |
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Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based learning—particularly how actions generate new internal structures that support problem-solving—are not understood. We develop a model of the way manipulations generate internal traces embedding actions, and how these action-traces recombine during problem-solving. This model (...) |
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It is a well-established fact in representationalist cognitive science that concrete concepts influence human perception. In radical, anti-representationalist cognitive science, however, the case is far from clear. One reason for this is that proponents of Radical Enactivism yet have to clarify whether perceptual activity involving concepts is bound to rely on mental content or if it instantiates basic, contentfree cognition. The purpose of this paper is to show that concept-involving perception instantiates REC-style basic cognition. The paper begins by considering ‘cognitive (...) |
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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 (...) |
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