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In good company? On Hume’s Principle and the assignment of numbers to infinite concepts

Paolo Mancosu

in Abstraction and Infinity

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198746829
eISBN:
9780191809095
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198746829.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics, History of Philosophy

In this chapter Mancosu generalizes some worries, raised by Richard Heck, emerging from the theory of numerosities (discussed in Chapter 3) to a line of thought resulting in what he calls a ‘good ... More


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

Paolo Mancosu

in Abstraction and Infinity

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198746829
eISBN:
9780191809095
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198746829.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics, History of Philosophy

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 ... More


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