Metaphors for Mathematics from Pasch to Hilbert

How mathematicians conceive of the nature of mathematics is reflected in the metaphors they use to talk about it. In this paper I investigate a change in the use of metaphors in the late nineteenth and early twentieth centuries. In particular, I argue that the metaphor of mathematics as a tree was u...

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Bibliographic Details
Published in:Philosophia mathematica 2016-10, Vol.24 (3), p.308-329
Main Author: Schlimm, Dirk
Format: Article
Language:English
Subjects:
Mathematicians
Metaphor
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Summary:How mathematicians conceive of the nature of mathematics is reflected in the metaphors they use to talk about it. In this paper I investigate a change in the use of metaphors in the late nineteenth and early twentieth centuries. In particular, I argue that the metaphor of mathematics as a tree was used systematically by Pasch and some of his contemporaries, while that of mathematics as a building was deliberately chosen by Hilbert to reflect a different view of mathematics. By taking these metaphors seriously we attain a new vantage point for understanding historical changes in conceptions of mathematics.
ISSN:0031-8019
1744-6406
DOI:10.1093/philmat/nkv039