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Abstraction and Infinity$
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Paolo Mancosu

Print publication date: 2016

Print ISBN-13: 9780198746829

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198746829.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 29 October 2020

The mathematical practice of definitions by abstraction from Euclid to Frege (and beyond)

The mathematical practice of definitions by abstraction from Euclid to Frege (and beyond)

Chapter:
(p.12) 1 The mathematical practice of definitions by abstraction from Euclid to Frege (and beyond)
Source:
Abstraction and Infinity
Author(s):

Paolo Mancosu

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198746829.003.0002

The first chapter is devoted to showing that, contrary to what Frege intimates in the Grundlagender Arithmetik, abstraction principles were quite widespread in the mathematical practice that preceded Frege’s discussion of them. Mancosu cites extensively from nineteenth century sources in number theory, geometry, algebra, vector theory, set theory and foundations of the number systems, in order to show the widespread use of abstraction principles in the mathematical practice of the time and to articulate the foundational problems such principles gave rise to.

Keywords:   Abstraction principles, Frege, mathematical practice, foundations of mathematics

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