The Limits of Abstraction
By (author) Kit Fine
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Limits of Abstraction by Kit Fine
Book DescriptionWhat 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.
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Book DetailsISBN: 9780199246182
(224mm x 145mm x 18mm)
Imprint: Clarendon Press
Publisher: Oxford University Press
Publish Date: 1-Aug-2002
Country of Publication: United Kingdom
Books By Author Kit Fine
Semantic Relationism, Paperback (July 2009)
Kit Fine argues for a fundamentally new approach to the study of representation in language and thought. His key idea is that there may be representational relationships between expressions or elements of thought that are not grounded in the intrinsic representational features of the expressions or elements themselves.
Limits of Abstraction, Paperback (May 2008)
Kit Fine develops a Fregean theory of abstraction, and suggests that it may yield a new philosophical foundation for mathematics, one that can account for both our reference to various mathematical objects and our knowledge of various mathematical truths. The Limits of Abstraction breaks new ground both technically and philosophically.
Modality and Tense, Paperback (July 2005)» View all books by Kit Fine
Drawing together a series of essays on possibility, necessity, and tense, this book covers areas, such as: the possible-worlds analysis of counterfactuals; the compatibility of special relativity with presentism; and the nature of first-personal experience. It also argues for the existence of distinctive forms of natural and normative necessity.
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Author Biography - Kit Fine
Kit Fine is Professor of Philosophy at New York University.
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