Metaphor and the Philosophical Implications of Embodied Mathematics

Bodo Winter, Jeff Yoshimi

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1 Citation (Scopus)
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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.
Original languageEnglish
Article number569487
Pages (from-to)569487
JournalFrontiers in Psychology
Publication statusPublished - 2 Nov 2020


  • cognitive linguistics
  • conceptual metaphor
  • embodied cognition
  • embodied mathematics
  • mathematical cognition
  • numerical cognition
  • philosophy of mathematics

ASJC Scopus subject areas

  • Psychology(all)


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