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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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The logical and philosophical reflection on definitions by abstraction: From Frege to the Peano school and Russell

The logical and philosophical reflection on definitions by abstraction: From Frege to the Peano school and Russell

Chapter:
(p.60) 2 The logical and philosophical reflection on definitions by abstraction: From Frege to the Peano school and Russell
Source:
Abstraction and Infinity
Author(s):

Paolo Mancosu

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198746829.003.0003

The second chapter is divided into two parts, the first of which analyzes Frege’s discussion of abstraction principles in section 64 of the Grundlagen der Arithmetik. In his investigations on Frege, Mancosu provides for the first time a contextual analysis of this pivotal section of the Grundlagen by rooting Frege’s concerns in the geometrical tradition originating with Hermann Grassmann and in the tradition of attempts aimed at proving the parallel postulate by making the notion of ‘direction’. The second part of Chapter 2 gives an extended analysis of the Peano school (Peano, Burali-Forti and Padoa, among others) and Russell and shows how in their considerations on abstraction principles they foreshadowed many of the philosophical and foundational concerns that have been at the center of attention in the neo-logicist discussion.

Keywords:   Frege, definition by abstraction, geometry, directions, theory of parallels, Peano, Russell, neo-logicism

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