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      Metaphor and mathematics

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      POSTNIKOFF-DISSERTATION.pdf (1.278Mb)
      Date
      2014-06-12
      Author
      Postnikoff, Derek
      Type
      Thesis
      Degree Level
      Doctoral
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      Abstract
      Traditionally, mathematics and metaphor have been thought of as disparate: the former rigorous, objective, universal, eternal, and fundamental; the latter imprecise, derivative, nearly - if not patently - false, and therefore of merely aesthetic value, at best. A growing amount of contemporary scholarship argues that both of these characterizations are flawed. This dissertation shows that there are important connexions between mathematics and metaphor that benefit our understanding of both. A historically structured overview of traditional theories of metaphor reveals it to be a notion that is complicated, controversial, and inadequately understood; this motivates a non-traditional approach. Paradigmatically shifting the locus of metaphor from the linguistic to the conceptual - as George Lakoff, Mark Johnson, and many other contemporary metaphor scholars do - overcomes problems plaguing traditional theories and promisingly advances our understanding of both metaphor and of concepts. It is argued that conceptual metaphor plays a key role in explaining how mathematics is grounded, and simultaneously provides a mechanism for reconciling and integrating the strengths of traditional theories of mathematics usually understood as mutually incompatible. Conversely, it is shown that metaphor can be usefully and consistently understood in terms of mathematics. However, instead of developing a rigorous mathematical model of metaphor, the unorthodox approach of applying mathematical concepts metaphorically is defended.
      Degree
      Doctor of Philosophy (Ph.D.)
      Department
      Interdisciplinary Studies
      Program
      Interdisciplinary Studies
      Supervisor
      Hoffman, Sarah
      Committee
      Dayton, Eric; Pfeifer, Karl; Bremner, Murray; Glanfield, Florence; O'Hagan, Emer
      Copyright Date
      April 2014
      URI
      http://hdl.handle.net/10388/ETD-2014-04-1527
      Subject
      mathematical cognition
      philosophy of mathematics
      philosophy of language
      figurative language
      metametaphor
      mathematics education
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