Metaphor and mathematics

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.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Interdisciplinary Studies

Grantor

University of Saskatchewan

Year dc:date.issued

2014

Author dc:creator

• Postnikoff, Derek

Advisor dc:contributor.advisor

• Hoffman, Sarah

Committee members dc:contributor.committeemember

• Dayton, Eric
• Pfeifer, Karl
• Bremner, Murray
• Glanfield, Florence
• O'Hagan, Emer

• mathematical cognition
• philosophy of mathematics
• philosophy of language
• figurative language
• metametaphor
• mathematics education

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10388/ETD-2014-04-1527

OAI identifier oai:identifier

oai:harvest.usask.ca:10388/ETD-2014-04-1527