Author : Kit Fine
Release : 2002-08-01
Genre : Philosophy
Kind : eBook
Book Rating : 264/5 ( reviews)

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Book Synopsis The Limits of Abstraction by : Kit Fine

Download or read book The Limits of Abstraction written by Kit Fine. This book was released on 2002-08-01. Available in PDF, EPUB and Kindle. Book excerpt: What is abstraction? To what extent can it account for the existence and identity of abstract objects? And to what extent can it be used as a foundation for mathematics? Kit Fine provides rigorous and systematic answers to these questions along the lines proposed by Frege, in a book concerned both with the technical development of the subject and with its philosophical underpinnings. Fine proposes an account of what it is for a principle of abstraction to be acceptable, and these acceptable principles are exactly characterized. A formal theory of abstraction is developed and shown to be capable of providing a foundation for both arithmetic and analysis. Fine argues that the usual attempts to see principles of abstraction as forms of stipulative definition have been largely unsuccessful but that there may be other, more promising ways of vindicating the various forms of contextual definition. The Limits of Abstraction breaks new ground both technically and philosophically, and is essential reading for all those working on the philosophy of mathematics.