cam a22 7 4500 551354933 CHVBK 20201114033111.0 m d cr |n |||||||| 160620t20162016enk sb 001 0 eng d 2016945125 978-0-19-874682-9 (hbk.) 0-19-874682-2 (SERSOL)ssj0001799787 (WaSeSS)ssj0001799787 YDXCP eng YDXCP BTCTA OCLCQ CDX YDX ERASA OCLCF DLC WaSeSS QA9 .M2945 2016 510.1 23 Mancosu Paolo author Abstraction and infinity [Elektronische Daten] Paolo Mancosu 1st ed. Oxford Oxford University Press c2016 1 online resource (viii, 222 p.) Includes bibliographical references and index. Lizenzbedingungen können den Zugang einschränken. License restrictions may limit access. Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating 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. This principle is at the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism.-- Mathematics Philosophy Infinite Infinite (OCoLC)fst00972421 fast Mathematics Philosophy (OCoLC)fst01012213 fast http://dx.doi.org/10.1093/acprof:oso/9780198746829.001.0001 Uni Basel: Volltext https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780198746829.001.0001/acprof-9780198746829 Uni Bern: Volltext BK020053 XK020053 XK020000 Oxford Scholarship Online Philosophy Collection 2016-2017 E-Books von 360MarcUpdates Oxford Scholarship Online IDSBB A145 A145 145VT NELA1451802 IDSBB B405 B405 405VT NELB4052004 IDSBB 100 1- Mancosu Paolo author IDSBB 856 40 http://dx.doi.org/10.1093/acprof:oso/9780198746829.001.0001 Uni Basel: Volltext IDSBB 856 40 https://oxford.universitypressscholarship.com/view/10.1093/acprof:oso/9780198746829.001.0001/acprof-9780198746829 Uni Bern: Volltext SWISSBIB 490606024