Metaphor and mathematics

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Date
2014-06-12Author
Postnikoff, Derek
Type
ThesisDegree Level
DoctoralMetadata
Show full item recordAbstract
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 StudiesProgram
Interdisciplinary StudiesSupervisor
Hoffman, SarahCommittee
Dayton, Eric; Pfeifer, Karl; Bremner, Murray; Glanfield, Florence; O'Hagan, EmerCopyright Date
April 2014Subject
mathematical cognition
philosophy of mathematics
philosophy of language
figurative language
metametaphor
mathematics education