Paolo Mancosu, Abstraction and Infinity. Oxford University Press, 2016

Georg Schiemer

doi:10.1007/978-3-030-40947-0_19

Titel

Paolo Mancosu, Abstraction and Infinity. Oxford University Press, 2016

Autor*in

Georg Schiemer

Institut für Philosophie, Fakultät für Philosophie und Bildungswissenschaft, Universität Wien

Abstract

Paolo Mancosu‘s recent book investigates two central concepts in the foundations of mathematics, namely abstraction and infinity. The main focus of the book concerns so-called abstraction principles or definitions by abstraction. Roughly put, an abstraction principle is a biconditional statement of the form: For all a, b in D: F(a) = F(b) if and only if a ~ b, where F presents a function or an abstraction operator and sim an equivalence relation between objects in a given set D. As is well known, such definitions became prominent in Frege’s work, in particular in his Grundlagen der Arithmetik §64 of 1884, and play a crucial role in current debates on neologicism, in particular on the logic and epistemological status of Hume’s Principle (and related principles). The central claim developed in the book is that the discussion of such abstraction principles did not originate with Frege’s work, but that there is rich and multifaceted mathematical prehistory of uses of “definitions by abstraction” in different mathematical fields. The first part of Mancosu’s book gives the first systematic study of abstraction principles in mathematical practice before Frege.

Stichwort

Philosophy

Objekt-Typ

book part

Sprache

Englisch [eng]

Persistent identifier

phaidra.univie.ac.at/o:1246921

DOI

10.1007/978-3-030-40947-0_19

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