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Space, Time, and Stuff$
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Frank Arntzenius

Print publication date: 2012

Print ISBN-13: 9780199696604

Published to Oxford Scholarship Online: May 2012

DOI: 10.1093/acprof:oso/9780199696604.001.0001

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 Calculus as geometry

 Calculus as geometry

Chapter:
(p.213) 8 Calculus as geometry
Source:
Space, Time, and Stuff
Author(s):

Frank Arntzenius

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199696604.003.0008

This chapter argues that calculus, the theory of differentiation and integration that permeates modern science, can be formulated as a purely geometric theory, which does not entail the existence of mathematical objects such as numbers, sets and functions. In particular it is argued that modern differential geometry can be ‘nominalised’, i.e. be formulated in such a way that it does not entail the existence of mathematical entities, by making judicious use of the geometric structure of the fibre bundles spaces which were encountered in chapter 6.

Keywords:   calculus, differential geometry, fibre bundles, nominalism, numbers, sets

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