Abstract
Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A particularly important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. Conceptual metaphor theory, a branch of cognitive linguistics, describes how abstract mathematical concepts are grounded in concrete physical representations. In this paper, we consider the implications of this research for the metaphysics and epistemology of mathematics. In the case of metaphysics, we argue that embodied mathematics is neutral in the sense of being compatible with all existing accounts of what mathematical entities really are. However, embodied mathematics may be able to revive an older position known as psychologism and overcome the difficulties it faces. In the case of epistemology, we argue that the evidence collected in the embodied mathematics literature is inconclusive: It does not show that abstract mathematical thinking is constituted by metaphor; it may simply show that abstract thinking is facilitated by metaphor. Our arguments suggest that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how we come to have knowledge of it.
Highlights
Embodied approaches to cognition emphasize the role of the body, action, and sensory perception in mental processes
In the case of epistemology, we argue that the available empirical evidence collected in the embodied mathematics literature inconclusive: It does not show that abstract thinking is grounded in or constituted by metaphor; it may show that abstract thinking is facilitated by metaphor
We argue that accounts of mathematical thinking do not directly support conclusions about the metaphysical nature of mathematics, insofar as results about embodied mathematical cognition are consistent with all the main positions in the philosophy of mathematics, including Platonism and nominalism
Summary
Reviewed by: Markus Pantsar, University of Helsinki, Finland Paul Henry Thibodeau, Oberlin College, United States. Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. In the case of metaphysics, we argue that embodied mathematics is neutral in the sense of being compatible with all existing accounts of what mathematical entities really are. In the case of epistemology, we argue that the evidence collected in the embodied mathematics literature is inconclusive: It does not show that abstract mathematical thinking is constituted by metaphor; it may show that abstract thinking is facilitated by metaphor. Our arguments suggest that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how we come to have knowledge of it
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