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Abstraction and Infinity

Paolo Mancosu

Abstract

The book provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. The notion of abstraction in question is that related to the use of abstraction principles in neo-logicism. The most familiar abstraction principle in this context is Hume’s Principle. Hume’s Principle says that two concepts have the same number if and only if the objects falling under each one of them can be put in one–one correspondence. Chapter 1 shows that abstraction principles were quite widespread in the mathematical practice that preceded Fr ... More

Keywords: Abstraction, Infinity, Neo-logicism, Frege, philosophy of mathematics, Hume’s Principle

Bibliographic Information

Print publication date: 2016 Print ISBN-13: 9780198746829
Published to Oxford Scholarship Online: January 2017 DOI:10.1093/acprof:oso/9780198746829.001.0001

Authors

Affiliations are at time of print publication.

Paolo Mancosu, author
Department of Philosophy, UC Berkeley