Abstraction and Infinity (Hardback)
  • Abstraction and Infinity (Hardback)
zoom

Abstraction and Infinity (Hardback)

(author)
£49.99
Hardback 240 Pages / Published: 15/12/2016
  • We can order this

Usually dispatched within 1 week

  • This item has been added to your basket
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.

Publisher: Oxford University Press
ISBN: 9780198746829
Number of pages: 240
Weight: 494 g
Dimensions: 234 x 166 x 18 mm


MEDIA REVIEWS
Paolo Mancosu's Abstraction and Infinity expertly straddles the history and philosophy of mathematics. ... Mancosu's work is well written and has been well received by those involved with neo-logicism. But it also offers readers not engaged in such debates an opportunity to reflect on the fact that of two intuitively true principles for comparing finite collections (one-to-one correspondence and part-whole inclusion), the historic choice of equinumerosity by Cantor for investigating infinite collections was and is not as cut-and-dried as some believe. And, of course, the book provides a valuable scholarly account of the history of definition by abstraction, the use of equivalence relations, and notions of infinity. * Calvin Jongsma, Mathematical Association of America Reviews *
This is a very rich and rewarding book. It provides not merely a much-needed, detailed account of the history of so called definitions by abstraction or abstraction principles, but also advances the current philosophical debate about the foundational status of such principles. These themes are presented in a beautifully clear prose which makes this book, quite simply, a joy to read - not something that is easily accomplished by a book in the history and philosophy of mathematics ... I highly recommend Mancosu's book to philosophers and mathematicians interested in the philosophy or the history of mathematics and logic. ... Mancosu not only proves to be one of the great detectives of the history of mathematical practice, but shows us how an historical approach to mathematical practice can, and in this case, does successfully move forward our current debates in the philosophy of mathematics. * Notre Dame Philosophical Reviews *

You may also be interested in...

Happy
Added to basket
£8.99
Paperback
A Little History of Philosophy
Added to basket
£9.99   £7.99
Paperback
Utopia for Realists
Added to basket
£8.99   £7.99
Paperback
The Myth of Sisyphus
Added to basket
Meditations
Added to basket
£10.00
Hardback
Ikigai
Added to basket
£12.99   £9.99
Hardback
Meditations
Added to basket
£7.99   £5.99
Paperback
The Tipping Point
Added to basket
£9.99   £7.99
Paperback
On the Shortness of Life
Added to basket
£4.99
Paperback
Enlightenment Now
Added to basket
£12.99
Paperback
Skin in the Game
Added to basket
Thus Spoke Zarathustra
Added to basket
£9.99   £7.99
Paperback
I Am Dynamite!
Added to basket
£25.00
Hardback
Wabi Sabi
Added to basket
£12.99
Hardback
The Road Less Travelled
Added to basket

Reviews

Please sign in to write a review

Your review has been submitted successfully.