Chapter

 Calculus as geometry

Frank Arntzenius

in Space, Time, and Stuff

Published in print January 2012 | ISBN: 9780199696604
Published online May 2012 | e-ISBN: 9780191738333 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199696604.003.0008
 Calculus as geometry

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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

Chapter.  34598 words.  Illustrated.

Subjects: Metaphysics

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